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WO2007085829A1 - Method of measuring with a group of sensors using statistics - Google Patents

Method of measuring with a group of sensors using statistics Download PDF

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Publication number
WO2007085829A1
WO2007085829A1 PCT/GB2007/000245 GB2007000245W WO2007085829A1 WO 2007085829 A1 WO2007085829 A1 WO 2007085829A1 GB 2007000245 W GB2007000245 W GB 2007000245W WO 2007085829 A1 WO2007085829 A1 WO 2007085829A1
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WIPO (PCT)
Prior art keywords
sensing
switches
sensors
msgs
noise
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PCT/GB2007/000245
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French (fr)
Inventor
Michael Charles Leslie Ward
Kiyohisa Nishiyama
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The University Of Birmingham
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Publication of WO2007085829A1 publication Critical patent/WO2007085829A1/en

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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01DMEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
    • G01D3/00Indicating or recording apparatus with provision for the special purposes referred to in the subgroups
    • G01D3/08Indicating or recording apparatus with provision for the special purposes referred to in the subgroups with provision for safeguarding the apparatus, e.g. against abnormal operation, against breakdown
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01DMEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
    • G01D1/00Measuring arrangements giving results other than momentary value of variable, of general application
    • G01D1/14Measuring arrangements giving results other than momentary value of variable, of general application giving a distribution function of a value, i.e. number of times the value comes within specified ranges of amplitude

Definitions

  • This invention relates to a method of sensing.
  • it concerns a sensing method utilizing statistical analysis of a group or plurality of individual sensing elements.
  • the method may be applied to a variety of sensor applications and devices, and may be particularly useful for electronic sensors.
  • a further application of the invention employs Micro System Technology (MST) in the form of a Micro Switch Group Sensor (MSGS) that applies the above sensing method.
  • MST Micro System Technology
  • MSGS Micro Switch Group Sensor
  • thermal noise also known as Johnson-Nyquist noise
  • Johnson-Nyquist noise is an inherent property and can never be completely eliminated. It is caused by fluctuations in the electric current inside an electrical conductor, which happens even without an applied voltage, due to the random thermal motion of the charge carriers (i.e. electrons).
  • Micro Electro-Mechanical System MEMS
  • MST Micro Electro-Mechanical System
  • Microsensors such as accelerometers and gyroscopes have been produced that include integrated signal processing electronics and are just a few hundreds of microns in size.
  • an object of the present invention to provide for a new method of sensing that exploits the fundamental properties of both macroscopic and microscopic devices. That is to use the hitherto undesirable properties of non-linear behaviour and noise to improve the resolution of the device.
  • micro engineered devices it is also desirable to take advantage of the ability to produce many tiny mechanical structures on a single device.
  • a major problem with nano or micro scale devices is that they are more likely to be affected by thermal noise than their macroscopic equivalent, due to having a small mass to surface area ratio.
  • thermal noise is a result of small movements in the particles constituting the tiny devices due to statistical fluctuations in their bombardment by surrounding molecules in the atmosphere, known as Brownian motion.
  • Another source of noise affecting the performance of MEMS devices is due to the inherent randomness in their structure as a result of the imperfect nature of fabrication technology.
  • the device will not be able to perform its sensing function at all. As such, it may relay values that do not correspond to the sensed conditions. These spurious values may provoke unnecessary and perhaps harmful action if the system or operator is not aware that the device has failed.
  • a method of sensing comprising the steps of providing a plurality of sensors, monitoring the state of said sensors, and determining the quantification of the measurand by the probability that a particular state of said sensors would occur for a specific value of the measurand.
  • This method has the advantage that failure of a single sensor, or a relatively small number of sensors, will not prevent an appropriate value of the measurand from being determined. In addition, the random properties or nature of each sensor will be exploited, rather than limiting the resolution of the system.
  • stochastic distribution is associated with the state of the sensors.
  • the stochastic distribution may be a result of stochastic noise in the sensors and/or the sensed environment.
  • stochastic noise may result from thermal noise, such as Johnson-Nyquist noise or Brownian motion, and/or inherent randomness in the physical structure of the sensors.
  • thermal noise such as Johnson-Nyquist noise or Brownian motion
  • any physical quantity within the range of the distribution may be capable of being detected.
  • the sensors provided are micro switches. It is preferable that the number of switches turned on is dependant on the quantification of the measurand being sensed and its stochastic distribution.
  • the switches may be breakable micro machined cantilever beams.
  • the stochastic distribution associated with the fracture strength of each beam may used to determine the effective force acting on the sensors as a group.
  • the error range associated with the force required to break a specific number of beams is relatively small when the number of beams is large, and relatively large when the number of beams is small.
  • the error range associated with the force required to break a beam is relatively small when a relatively long beam is used, and relatively large when a relatively short beam is used.
  • switches with a relatively large statistical variance in their conversion from one state to another are used to measure physical quantity over a wide range of values. It is also preferable that switches with a relatively small statistical variance in their conversion from one state to another are used to measure physical quantity over a narrow range of values.
  • a device comprising a plurality of sensors is capable of sensing by a method according to the present invention.
  • the method of sensing according to the present invention provides for a true digital sensor. This is because each individual sensor can be thought of as either 'on' or 'off according to its physical state. The cumulative number of sensors 'on' (or .'off') at any instant determines the value of the measurand, taking into account the associated stochastic distribution in the system. Thus, the usual analogue-to-digital conversions (or vice versa) can be avoided.
  • Figure 1 is a graphic representation of an ideal switch transfer function
  • Figure 2 is a graphic representation of a stochastic probability distribution
  • Figure 3 is a graphic representation of a probability transfer function
  • Figure 4 is a graphic representation of the cumulative distribution of fracturing
  • Figure 5 is a schematic view of a test specimen
  • Figure 6 is a schematic view of a test set-up for the test specimen of Figure 5;
  • Figure 7 is a graphic representation of experimental data and calculated fracturing probability
  • Figure 8 is a table of probability functions for each state of the MS GS;
  • Figure 9 is a graphic representation of the probability distributions for each state of the MSGS;
  • Figure 10 is a graphic representation of a probability distribution
  • Figure 11 is a graphic representation of the mean force values and errors for each state of the MSGS
  • Figure 12 is a compilation of graphic representations similar to that of Figure 11 for MSGS devices with 10, 100 and 1000 beams for each of four different lengths of beams;
  • Figure 13 is a block diagram of an electric circuit for a MSGS with three switches
  • Figure 14 is the circuit diagram for the MSGS of Figure 13;
  • Figure 15 illustrates the noise signals generated by each noise generator in the MSGS of Figure 13;
  • Figure 16 shows the mean values of the noise signals shown in Figure 15;
  • Figure 17 shows the standard deviation of the noise signals shown in Figure 15
  • Figure 18 shows the probability density and cumulative distribution curves for each of the noise generators in the MSGS of Figure 13;
  • Figure 19 shows the comparator signals for each of the noise generators in the MSGS of Figure 13, for an input voltage of 15OmV;
  • Figure 20 shows the comparator signals for each of the noise generators in the MSGS of Figure 13, for an input voltage of OmV;
  • Figure 21 shows the comparator signals for each of the noise generators in the MSGS of Figure 13, for an input voltage of -15OmV;
  • Figure 22 shows the number of data points high and low for each comparator of the MSGS of Figure 13, for an input voltage of OmV;
  • Figure 23 shows the number of data points high and low for each comparator of the MSGS of Figure 13, for an input voltage of 25mV;
  • Figure 24 shows the average number of data points high and low for each comparator of the MSGS of Figure 13;
  • Figure 25 shows the output signals of the summing amplifier of the MSGS of Figure 13, for the input voltages -75mV, -25mV, 25mV, 5OmV, 75mV and 15OmV;
  • Figure 26 shows the number of comparators high in the MSGS of Figure 13, with respect to each input voltage
  • Figure 27 shows the probability curves for each comparator, in the MSGS of Figure 13, becoming high
  • Figure 28 is a table of the probability distribution functions for each possible situation in the MSGS of Figure 13;
  • Figure 29 shows the plots of the probabilities calculated from the functions in the table of Figure 28;
  • Figure 30 shows the likely voltage ranges for each possible situation to occur in the MSGS of Figure 13
  • Figure 31 shows the probabilities calculated from the experimental results for the MSGS of Figure 13, along with the theoretical curves of Figure 29;
  • Figure 32 shows the standard normal distribution curve and the cumulative distribution curve
  • Figure 33 shows a graphic representation of a probability distribution
  • Figure 34 shows the calculated mean values and error ranges for MSGS devices with 10, 100 and 1000 switches
  • Figure 35 shows the standard deviation, or fluctuation, of the output signal for MSGS devices with 10, 100 and 1000 switches
  • Figure 36 shows a circuit diagram for a MSGS with up to 20 switches
  • Figure 37 shows some examples of the output signals obtained for MSGS devices with 5, 10 and 20 switches
  • Figure 38 shows the distribution of the average voltage and standard deviation for each noise signal
  • Figure 39 shows a graph of input voltage against normalized value z
  • Figure 40 shows the mean value of the output signals for each of the MSGS devices with 5, 10 and 20 switches, along with the theoretical curve for the 20 switch device;
  • Figure 41 shows the standard deviation of the output signals for each of the MSGS devices with 5, 10 and 20 switches, along with the theoretical curves;
  • Figure 42 shows the mean values and standard deviation of the output signals calculated for a 20 switch device but based on the results from the 5 and 10 switch devices, along with the results obtained for the 20 switch device;
  • Figure 43 shows the calculated output signals for a 100 and 1000 switch MSGS device, based on the results from the 20 switch device;
  • Figure 44 shows the standard deviation of the results from Figure 43, along with the theoretical curves
  • Figure 45 compares the ranges of the input voltage predicted by the mean number of switches turned on, with the actual input voltages, for each MSGS.
  • a new sensor concept is described whereby the quantification of the measurand is determined by the probability that a particular state of a group of sensors would occur for a specific value of the measurand.
  • the value being sensed may be obtained in the following way.
  • the probability of some amount of physical quantity producing each possible state of the group of sensors is calculated, taking into account the stochastic noise in the system. Thus, the following probabilities are calculated: all sensors are off, 1 sensor is on, 2 sensors are on, and 3 sensors are on, etc, until all sensors are on.
  • the anticipated mean physical quantity that would result in each of the above states is then calculated.
  • An error associated with this value may also be calculated from the probability distribution. Thus, for any given state of the sensors, the mean value of the physical quantity being measured and the likely error in this value can be determined.
  • This technique provides for a new sensor method employing a group of sensors as opposed to a single sensor. It utilizes the inherent randomness or noise within the sensor group to determine the measurement of the physical quantity being sensed. Thus, conventional sensor thinking has been turned around to exploit the fundamental nature of sensing devices.
  • This new method of sensing provides for a sensor " device with several attractive features. As the sensor device consists of a group of individual sensors, even if one of the sensors fails, the device will still be able to operate as a sensor, albeit with reduced resolution. This characteristic is known as gentle failure and has obvious advantages over a single sensor system. Another benefit of a sensor according to the present invention is that high sensitivity and good resolution can be achieved by employing a large number of sensors. The cumulative effect of such a large sensor group can combat the conventional limitations caused by stochastic noise in the system.
  • the present sensing method provides for a sensor that can be described as a true digital sensor, avoiding the usual digital-to-analogue conversions, as the physical quantity being measured is translated into the number of individual sensors activated.
  • a sensor that exercises the method described above.
  • This sensor is composed of a group of micro switches and has been termed a Micro Switch Group Sensor (MSGS).
  • MSGS Micro Switch Group Sensor
  • the concept of the MSGS is transducing a physical quantity to the number of switches turned on in the device. This is fundamentally different to the conventional sensing concept of transducing a physical quantity to an electrical quantity, such as a voltage, in a stand-alone sensor.
  • a large group or array of micro switches in a MSGS allows for reduced errors in measurement by making them work together as an ensemble. This may be likened to attempting to characterise a gas by pressure as opposed to trying to define the state of each molecule.
  • a MSGS can be considered a sensor array that exploits noise by applying the above method of sensing. It does this by utilizing the thermal noise or randomness in the system to produce a stochastic distribution across the array.
  • the number of sensors (or switches) turned on in the device depends on the cumulative distribution of the array due to the noise in the system. This makes it possible to measure any physical quantity in the range of the distribution.
  • the method according to the present invention enables large arrays of micro switches, subjected to thermal noise, to sense a wide range of physical parameters.
  • a MSGS can also be considered a sensing system that is capable of measuring a physical quantity from the statistical state of a great number of micro switches.
  • an MSGS is a sensor whereby the quantification of the measurand is determined by the statistical state of the micro switch array.
  • a switch which can be turned on by a physical quantity, has a transfer function as illustrated in Figure 1.
  • thermal noise is known to act stochastically as illustrated in Figure 2. Consequently, a switch will have a stochastic distribution associated with a particular physical quantity, about its conversion between 'on' and 'off' .
  • the transfer function of Figure 1 more realistically as the probability transfer function of Figure 3.
  • a device according to the present invention comprising a plurality of such switches, has been designed to exploit this distribution in an improved sensing system. It has thereby become possible to make a sensor capable of exploiting stochastic noise.
  • This MSGS is composed of an array of breakable micro machined cantilever beams that can be used to assess the force presented to the device, for example, during the manufacturing process.
  • the beams were composed of single crystalline silicon, which is a brittle material.
  • Such brittle materials have a stochastic distribution, known as a Weibull distribution, associated with their fracture strengths.
  • the force required to break each beam has a random variation about a mean value.
  • Each cantilever beam can therefore be considered a micro switch that can be turned on (or broken) by some force.
  • the force acting on the array is determinable by observing the number of fractured beams (or levers) and exploiting the stochastic distribution in the system.
  • brittle materials are only capable of elastic deflection while ductile materials can be deformed plastically. Fracturing forces are sensitive to flaws both on the surface and inside the material. The fracturing forces associated with brittle materials tend to scatter around a mean fracturing force when compared to ductile materials. As such, the fracturing stresses of brittle materials need to be assessed by a statistical method.
  • Weibull analysis is a well-known statistical method used for determining the fracturing stress of brittle materials. It is based on the assumption that failure at the most critical flaw will lead to total failure of the device. According to the Weibull method, the probability of fracturing at an arbitrary stress, Pf( ⁇ ), can be determined by Equation (1) below, where ⁇ is stress, ⁇ 0 is a normalizing factor and m is the Weibull modulus.
  • Equation (1) can also be written in the form of Equation (2) below, where g is a value determined by the form of specimen and applied force.
  • Equation (2) can then be rewritten as Equation (3) below.
  • Equation (3) Taking the natural logarithm of Equation (3) twice leads to the linear expression in Equation (4) below.
  • the Weibull modulus, m, and value, g can be obtained by the slope and intercept of the line, respectively.
  • plotting the fracturing stress obtained by experiment can provide the values of Weibull modulus, m, and the value, g, using the least square method to fit a straight line through the results.
  • Equation (2) allows the probability of fracturing Pf to be expressed as a function of the applied force, x, as shown in Equation (6) below.
  • Equation (6) Substituting the values obtained from Equation (4) for the Weibull modulus, m, and value, g, into Equation (6), allows the cumulative distribution diagram of fracturing to be plotted, as shown in Figure 4.
  • test specimens in the example presented were fabricated by micro- machining technology. Each test specimen was designed to comprise four different lengths of cantilever beams, as illustrated in Figure 5. Thus, the test specimens were designed such that the distribution of fracturing forces for each length of beam could be compared. Photolithography and Deep Reactive Ion Etching techniques were used to create the cantilevers from a single crystal silicon wafer with a thickness of 0.3mm.
  • the fracturing force for each cantilever beam was measured using the experimental set-up illustrated in Figure 6.
  • a universal tester was used to apply a force to each beam via a pin.
  • a specimen holder was designed to hold each device on a high resolution set of scales such that the cantilevers were held in suspension and exposed to the pin.
  • Both the universal tester and the scales were computer controlled.
  • the data from the scale was recorded at a sample rate of 10 per second and was transferred directly to the computer.
  • the velocity of the pin was set to move at lmm per minute vertically downwards towards the beams.
  • Fracturing forces were calculated for cantilevers of length 4mm, 6mm, 8mm and 10mm, with the force applied at 3.5mm, 5.5mm, 7.5mm and 8.5mm, respectively from the fixed end of each cantilever beam.
  • Equation (7) The cumulative distribution of fracturing forces, Pf(F), was calculated using Equation (7) below and the individual fracturing forces obtained through the experiments described above.
  • n is the sample number and k is the number of samples broken by a particular force.
  • the Applicants considered a device with five 4mm long single crystalline silicon cantilevers.
  • the number of levers broken (r) by any given force must be between 0 and 5. Therefore, there are six possible situations that can be expected.
  • the probability of each situation occurring for a given force can be calculated using binomial theory.
  • Equation (8) the number of combinations producing each possible situation can be calculated, where n is the sample number and is any integer greater than 1 and r is the number of levers broken and is any integer between 0 and n.
  • Equation (10) the probability of surviving P s (x) is given in Equation (10) below.
  • Equation (12) the mean values of the forces causing each situation may be calculated from Equation (12) below.
  • Equation (13) ⁇ p r (x)xdx (12)
  • p r (x) is the ratio between Pr(x) and the area inside the distribution curve as illustrated in Figure 10.
  • pr(x) can be calculated from Equation (13) below.
  • Pnr(x) is the probability of r in n switches being turned on
  • Pon(x) is the probability of those switches being turned on at a certain amount of physical quantity, x. It should be noted that Equation (15) must always be true.
  • Equation (16) the anticipated mean physical quantity x resulting in each situation can be obtained from Equation (16) below.
  • Equation (16) pnr(x) is the ratio of Pnr(x) and the area inside the curve as shown in Figure 10. It can be calculated from Equation (17) below.
  • the method can be applied to a MSGS where the probability of fracturing of silicon cantilever beams is used to determine the force acting on the system.
  • an electric circuit consisting of an input voltage supply, three noise generators, three comparators and a summing amplifier, was built to simulate a MSGS employing the present sensing method.
  • a block diagram of the circuit is shown in Figure 13 and a circuit diagram is shown in Figure 14.
  • the breakdown of zener diodes was used to generate the noise and high pass filters were used to remove any direct currents.
  • Operational amplifiers were employed to amplify the noise signals and the input voltage was controlled by a potentiometer.
  • the input voltage is the physical quantity being measured and each noise generator and associated comparator behaves as a switch affected by noise. Thus, if the comparator is high, the switch is on and if it is low, the switch is off.
  • each noise generator is compared with an arbitrary input voltage. This results in a signal from each comparator (or switch) that is either high or low. These signals are then summed together by the summing amplifier so that the number of comparators high can be determined from the output voltage. Consequently this circuit can be considered a MSGS comprised of three switches.
  • the experimental procedure involved the circuit of Figure 14 being connected to a personal computer through a digital oscilloscope so that the voltages could be recorded in the computer.
  • the noise signal generated by each of the noise generators was gathered.
  • the signals from the summing amplifier and from each of the three comparators were obtained for input voltages of -15OmV, -10OmV, -75mV, -5OmV, -25mV, OmV, 25mV, 5OmV, 75mV, 10OmV and 15OmV.
  • the data was measured for a duration of 1 second.
  • the data gathered in each 1 -second interval resulted in 752 data points.
  • the experiment was repeated 3 separate times.
  • the noise signals generated by each noise generator 1 , 2 and 3 are shown in Figure 15.
  • the probability density and cumulative distribution curves for each noise generator are shown in Figure 18.
  • the plots are hysterisis diagrams created using all of the gathered data. The curves are derived from Equations (18) and (19) below, which represent the Gaussian distribution function.
  • f(x) and g(x) are the probability density and cumulative distribution, respectively, at the voltage x, where ⁇ is the standard deviation and m is the mean value of the voltage.
  • is the standard deviation
  • m is the mean value of the voltage.
  • the response of the comparators 1, 2 and 3 are plotted over time for the input voltages 15OmV, OmV and -15OmV, respectively, in Figures 19, 20 and 21. From these figures, we can deduce that -144mV can be regarded as low and 139mV can be regarded as high for all comparators. It is clear that the comparator becomes low when the input voltage is low and high when the input voltage is high. In this experiment, values larger than -2.5mV, which is the centre value between -144mV and 139mV, are regarded as high.
  • the output signals from the summing amplifier are shown in Figure 25 for the input voltages -75mV, -25mV, 25mV, 5OmV, 75mV, and 15OmV.
  • the y-axis has been plotted as the number of comparators high. It can be seen that when the input voltage is low, very few comparators are high, and the greater the voltage becomes, the comparators tend to become high more often until all of them are high.
  • this device has four stable situations which are 0 comparators are high, 1 comparator is high, 2 comparators are high and 3 comparators are high. Therefore, from this data, the number of comparators high at each moment can be obtained.
  • the probability function of each switch was obtained from the data from each comparator.
  • the probability of each comparator being high P(x) , at each voltage x was calculated and is shown in Figure 27.
  • the probability was calculated by counting the number of points for which the comparator was high and dividing it by the total number of measured points, as per Equation (20) below.
  • N M ⁇ is the number of points for which the comparator was high and N 7 . is the total number of measured points for each input voltage, 2256.
  • the results of this calculation are plotted in Figure 31 along with the probability curves obtained using the probability function of the comparators or switches, also shown in Figure 29.
  • output of the summing amplifier and the probability curves of the comparator states are in good agreement. This confirms that the MSGS is operating as predicted from the performance of the switches. Hence, it is possible to deduce that a device that has many more switches will also work as predicted.
  • the Applicants built a larger MSGS by electric circuit in order to test the applicability and function of the MSGS theory and method, depending on the number of switches employed in the device. They also considered the theory of the MSGS in relation to the standard normal distribution. This example was chosen in order to facilitate the application of the theory to any measurements with stochastic properties.
  • the cumulative distribution curves relating to the properties of the switches were plotted from the gathered data and the effect on the output signal due to the number of the switches forming the MSGS was evaluated both theoretically and experimentally.
  • the output signals of an MSGS with much larger numbers of switches was predicted by adding the output signals of repeated measurements and comparing these with the theoretical values.
  • the validity of the measurements by the MSGS was evaluated by comparing the predicted input voltage ranges with the actual input voltages.
  • Equation (25) When some amount of physical quantity z is added to this noise, the distribution is expressed as Equation (25).
  • Equation (26) The value of z and z' can always be transferred into the dimension of observed physical quantity by Equation (26).
  • x' is the observed values of noise
  • is the mean value of noise
  • is the standard deviation of noise
  • x is the physical quantity observed.
  • Equation (27) the cumulative distribution function, which is the probability of the switches turned on at z, can be obtained by Equation (27). This relates to the shaded area in the curve of the standard normal . distribution as shown in graph (a) of Figure 32.
  • Equation (28) the probability of the state that n of N switches are turned on, P Nn (z) , can be calculated from Equation (28) below.
  • N C n is the sign of combination calculated from Equation (29) below.
  • Equation (30) must always be true.
  • Equation (31) The anticipated mean physical quantity z for each situation to occur can be calculated from Equation (31).
  • z m [ p Nn (z')z'dz' • (31)
  • Equation (31) p Nn (z) is the ratio between P Nn ⁇ z) and the area inside the curve, which is given by Equation (32) below, and is illustrated in Figure 33.
  • the fluctuation of the number of switches can be expressed as n(z, t,N) , which is a function of z, time, t, and the number of switches composing the MSGS, N.
  • the output signal M(z,t,N) can then be calculated from Equation (34) below. (34)
  • Equation (35) it is possible to calculate the standard deviation of the output signal of the MSGS, ⁇ M ⁇ >N) , by Equation (35) below.
  • n mean (z) is the mean value of the number of switches turned on at a physical quantity z as per Equation (36) below.
  • the device developed for this experiment consisted of an array of noise generators and comparators, with essentially the same function as micro or sub-micron switches affected by noise and inherent randomness.
  • the circuit diagram for this experiment is illustrated in Figure 36 and includes 20 individual noise generators and comparators.
  • an operation amplifier amplifies the noise signal from each zener diode.
  • the direct current is removed by capacitors placed before the noise generators and operation amplifiers.
  • the noise signals are compared with input voltages by the comparators, which are recognized as switches.
  • the output voltage of the summing amplifier determines the number of comparators high or low. Disconnecting the lines coming from the comparators to the summing amplifier can change the number of switches composing the MSGS.
  • tests were performed for a MSGS with 5, 10 and 20 switches.
  • n( ⁇ ,t,N) is the observed fluctuation of the number of switches turned on
  • V oul (x,t,N) is the output signal of the MSGS
  • V allon is the voltage when all the switches are on
  • V a[!off is the voltage when all the switches are off.
  • the values for V alhn and V alloff were obtained from the output voltages for the input voltages 8V and -8V respectively.
  • the performance of the group of switches can be obtained by referring to the output of the MSGS with 20 switches.
  • the mean value of the output ⁇ signal for each possible situation M mean (x,N) can be calculated by Equation (38) below.
  • T is the time interval of the measurement.
  • the sensing method of the present invention could be applied to any system featuring stochastic noise. Moreover, the present sensing method can utilise any statistical properties of a sensing device. Consequently, a wide variety of sensor devices and systems may be developed using the method of the present invention.
  • the present sensing method permits individual sensors to be designed and fabricated to a lower degree of accuracy since it is the number of individual sensors being used that determines the overall accuracy of the device.
  • the present invention provides for an improved method of sensing a physical quantity. Importantly, it enables a MSGS to be utilized as an analogue-to- digital converter, or a true digital sensor, whereby the number of switches turned on relates to the physical quantity being measured.
  • the output is purely digital in nature (i.e. the number of switches turned on) enables the information to be processed directly through a digital circuit, upon a relevant computer clock tick. This may prove revolutionary in the communication of data between computers and sensors.
  • An important advantage with a sensing device according to the present invention is gentle failure. That is, failure of one, or a small number of sensors in the device does not prevent the device from measuring an appropriate value of the physical quantity being sensed.
  • Micro-Switch Group Sensors will be of particular benefit in applications where human life may be at risk. Accordingly, the MSGS may be of particular use in motor vehicles, aircraft, trains and even medical applications.
  • the described method can be applied to produce sensors with extremely high resolution. As such, scientific researchers in the fields of chemistry, physics and medicine would benefit from this kind of sensor.
  • the method of sensing can be applied to sensing applications in a wide variety of fields and industries, not limited to those specifically mentioned.
  • the sensing method of the present invention may be particularly useful in the nuclear industry.
  • a device employing the sensing method of the present invention may take any appropriate form and may comprise mechanical, electronic, chemical or biological features.

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Abstract

A method of sensing comprises the steps of providing a plurality of sensors, monitoring the state of the sensors, and determining the quantification of the measurand by the probability that a particular state of the sensors would occur for a specific value of the measurand. In a particular embodiment, a Micro Switch Group Sensor (MSGS) employs the above method by using the stochastic distribution associated with the fracture strength of each switch to determine the effective force acting on the MSGS.

Description

METHOD OF MEASURING WITH A GROUP OF SENSORS USING STATISTICS
Technical Field
This invention relates to a method of sensing. In particular, it concerns a sensing method utilizing statistical analysis of a group or plurality of individual sensing elements. The method may be applied to a variety of sensor applications and devices, and may be particularly useful for electronic sensors. A further application of the invention employs Micro System Technology (MST) in the form of a Micro Switch Group Sensor (MSGS) that applies the above sensing method.
Background
A traditional sensing system employs a single sensor that is designed to be both linear and devoid of any noise. In the case of electronic sensors, thermal noise (also known as Johnson-Nyquist noise) is an inherent property and can never be completely eliminated. It is caused by fluctuations in the electric current inside an electrical conductor, which happens even without an applied voltage, due to the random thermal motion of the charge carriers (i.e. electrons).
With the advent of Micro System Technology it is possible to fabricate a great number of tiny devices of millimetre, micrometer and even nanometer dimensions. Consequently, it is possible to fabricate thousands of tiny devices on a single silicon chip. These Micro Electro-Mechanical System (MEMS) devices offer huge advantages over conventional macroscopic devices produced by traditional manufacturing technologies, due their compact nature and attendant economies of scale in production. In particular, MST is having a huge impact on the design and development of sensor technology as tiny sensors can be produced which are sensitive and provide a high response. Microsensors such as accelerometers and gyroscopes have been produced that include integrated signal processing electronics and are just a few hundreds of microns in size. Although this is a remarkable achievement, the nature of the sensing element and mode of operation has changed little when compared to its macroscopic origin. Thus, traditionally, microscopic sensing systems have also been developed to comprise a single sensor that is designed to be both linear and devoid of noise.
It is, however, an object of the present invention to provide for a new method of sensing that exploits the fundamental properties of both macroscopic and microscopic devices. That is to use the hitherto undesirable properties of non-linear behaviour and noise to improve the resolution of the device.
In the case of micro engineered devices it is also desirable to take advantage of the ability to produce many tiny mechanical structures on a single device. However, a major problem with nano or micro scale devices is that they are more likely to be affected by thermal noise than their macroscopic equivalent, due to having a small mass to surface area ratio. In this case, such thermal noise is a result of small movements in the particles constituting the tiny devices due to statistical fluctuations in their bombardment by surrounding molecules in the atmosphere, known as Brownian motion. Another source of noise affecting the performance of MEMS devices is due to the inherent randomness in their structure as a result of the imperfect nature of fabrication technology.
All sources of noise pose a particular problem in sensing applications as the noise may be detected in place of or in addition to the parameter being sensed, and therefore will interfere with the sensed results and may prevent a true value from being determined. This will ultimately limit the sensitivity or resolution of the device.
Moreover, if only a single sensor, microsensor or nanosensor is employed and it fails, the device will not be able to perform its sensing function at all. As such, it may relay values that do not correspond to the sensed conditions. These spurious values may provoke unnecessary and perhaps harmful action if the system or operator is not aware that the device has failed.
In addition, existing so-called digital sensors often still require analogue-to- digital conversion (or vice versa) in order to communicate or display the values sensed. This conversion not only involves additional components and processing steps, but may also introduce errors or uncertainty in the measured values.
It is thus a further object of the present invention to provide an improved sensing method, which alleviates the aforementioned problems.
Disclosure of Invention
In accordance with the present invention there is provided a method of sensing comprising the steps of providing a plurality of sensors, monitoring the state of said sensors, and determining the quantification of the measurand by the probability that a particular state of said sensors would occur for a specific value of the measurand.
This method has the advantage that failure of a single sensor, or a relatively small number of sensors, will not prevent an appropriate value of the measurand from being determined. In addition, the random properties or nature of each sensor will be exploited, rather than limiting the resolution of the system.
It is desirable that a stochastic distribution is associated with the state of the sensors. The stochastic distribution may be a result of stochastic noise in the sensors and/or the sensed environment. Thus, stochastic noise may result from thermal noise, such as Johnson-Nyquist noise or Brownian motion, and/or inherent randomness in the physical structure of the sensors. Desirably, any physical quantity within the range of the distribution may be capable of being detected.
In a particular embodiment, the sensors provided are micro switches. It is preferable that the number of switches turned on is dependant on the quantification of the measurand being sensed and its stochastic distribution. The switches may be breakable micro machined cantilever beams. In this case, the stochastic distribution associated with the fracture strength of each beam may used to determine the effective force acting on the sensors as a group. Conveniently, the error range associated with the force required to break a specific number of beams is relatively small when the number of beams is large, and relatively large when the number of beams is small. Desirably, the error range associated with the force required to break a beam is relatively small when a relatively long beam is used, and relatively large when a relatively short beam is used. It is preferable that switches with a relatively large statistical variance in their conversion from one state to another are used to measure physical quantity over a wide range of values. It is also preferable that switches with a relatively small statistical variance in their conversion from one state to another are used to measure physical quantity over a narrow range of values.
In another embodiment, a device comprising a plurality of sensors is capable of sensing by a method according to the present invention.
In addition to the above-mentioned advantages, the method of sensing according to the present invention provides for a true digital sensor. This is because each individual sensor can be thought of as either 'on' or 'off according to its physical state. The cumulative number of sensors 'on' (or .'off') at any instant determines the value of the measurand, taking into account the associated stochastic distribution in the system. Thus, the usual analogue-to-digital conversions (or vice versa) can be avoided.
Brief Description of the Drawings
Particular embodiments of the invention are illustrated in the accompanying drawings wherein: -
Figure 1 is a graphic representation of an ideal switch transfer function;
Figure 2 is a graphic representation of a stochastic probability distribution; Figure 3 is a graphic representation of a probability transfer function; Figure 4 is a graphic representation of the cumulative distribution of fracturing;
Figure 5 is a schematic view of a test specimen; Figure 6 is a schematic view of a test set-up for the test specimen of Figure 5;
Figure 7 is a graphic representation of experimental data and calculated fracturing probability;
Figure 8 is a table of probability functions for each state of the MS GS; Figure 9 is a graphic representation of the probability distributions for each state of the MSGS;
Figure 10 is a graphic representation of a probability distribution; Figure 11 is a graphic representation of the mean force values and errors for each state of the MSGS;
Figure 12 is a compilation of graphic representations similar to that of Figure 11 for MSGS devices with 10, 100 and 1000 beams for each of four different lengths of beams;
Figure 13 is a block diagram of an electric circuit for a MSGS with three switches;
Figure 14 is the circuit diagram for the MSGS of Figure 13; Figure 15 illustrates the noise signals generated by each noise generator in the MSGS of Figure 13;
Figure 16 shows the mean values of the noise signals shown in Figure 15;
Figure 17 shows the standard deviation of the noise signals shown in Figure 15; Figure 18 shows the probability density and cumulative distribution curves for each of the noise generators in the MSGS of Figure 13;
Figure 19 shows the comparator signals for each of the noise generators in the MSGS of Figure 13, for an input voltage of 15OmV;
Figure 20 shows the comparator signals for each of the noise generators in the MSGS of Figure 13, for an input voltage of OmV;
Figure 21 shows the comparator signals for each of the noise generators in the MSGS of Figure 13, for an input voltage of -15OmV;
Figure 22 shows the number of data points high and low for each comparator of the MSGS of Figure 13, for an input voltage of OmV;
Figure 23 shows the number of data points high and low for each comparator of the MSGS of Figure 13, for an input voltage of 25mV;
Figure 24 shows the average number of data points high and low for each comparator of the MSGS of Figure 13;
Figure 25 shows the output signals of the summing amplifier of the MSGS of Figure 13, for the input voltages -75mV, -25mV, 25mV, 5OmV, 75mV and 15OmV;
Figure 26 shows the number of comparators high in the MSGS of Figure 13, with respect to each input voltage;
Figure 27 shows the probability curves for each comparator, in the MSGS of Figure 13, becoming high;
Figure 28 is a table of the probability distribution functions for each possible situation in the MSGS of Figure 13;
Figure 29 shows the plots of the probabilities calculated from the functions in the table of Figure 28;
Figure 30 shows the likely voltage ranges for each possible situation to occur in the MSGS of Figure 13; Figure 31 shows the probabilities calculated from the experimental results for the MSGS of Figure 13, along with the theoretical curves of Figure 29;
Figure 32 shows the standard normal distribution curve and the cumulative distribution curve;
Figure 33 shows a graphic representation of a probability distribution;
Figure 34 shows the calculated mean values and error ranges for MSGS devices with 10, 100 and 1000 switches;
Figure 35 shows the standard deviation, or fluctuation, of the output signal for MSGS devices with 10, 100 and 1000 switches;
Figure 36 shows a circuit diagram for a MSGS with up to 20 switches;
Figure 37 shows some examples of the output signals obtained for MSGS devices with 5, 10 and 20 switches;
Figure 38 shows the distribution of the average voltage and standard deviation for each noise signal;
Figure 39 shows a graph of input voltage against normalized value z;
Figure 40 shows the mean value of the output signals for each of the MSGS devices with 5, 10 and 20 switches, along with the theoretical curve for the 20 switch device;
Figure 41 shows the standard deviation of the output signals for each of the MSGS devices with 5, 10 and 20 switches, along with the theoretical curves;
Figure 42 shows the mean values and standard deviation of the output signals calculated for a 20 switch device but based on the results from the 5 and 10 switch devices, along with the results obtained for the 20 switch device; Figure 43 shows the calculated output signals for a 100 and 1000 switch MSGS device, based on the results from the 20 switch device;
Figure 44 shows the standard deviation of the results from Figure 43, along with the theoretical curves;
Figure 45 compares the ranges of the input voltage predicted by the mean number of switches turned on, with the actual input voltages, for each MSGS.
Detailed Description of the Invention
A new sensor concept is described whereby the quantification of the measurand is determined by the probability that a particular state of a group of sensors would occur for a specific value of the measurand.
In the case where each individual sensor can be in one of two states, i.e. 'on' or 'off , the value being sensed may be obtained in the following way. The probability of some amount of physical quantity producing each possible state of the group of sensors is calculated, taking into account the stochastic noise in the system. Thus, the following probabilities are calculated: all sensors are off, 1 sensor is on, 2 sensors are on, and 3 sensors are on, etc, until all sensors are on. The anticipated mean physical quantity that would result in each of the above states is then calculated. An error associated with this value may also be calculated from the probability distribution. Thus, for any given state of the sensors, the mean value of the physical quantity being measured and the likely error in this value can be determined.
This technique provides for a new sensor method employing a group of sensors as opposed to a single sensor. It utilizes the inherent randomness or noise within the sensor group to determine the measurement of the physical quantity being sensed. Thus, conventional sensor thinking has been turned around to exploit the fundamental nature of sensing devices.
This new method of sensing provides for a sensor " device with several attractive features. As the sensor device consists of a group of individual sensors, even if one of the sensors fails, the device will still be able to operate as a sensor, albeit with reduced resolution. This characteristic is known as gentle failure and has obvious advantages over a single sensor system. Another benefit of a sensor according to the present invention is that high sensitivity and good resolution can be achieved by employing a large number of sensors. The cumulative effect of such a large sensor group can combat the conventional limitations caused by stochastic noise in the system. In addition, the present sensing method provides for a sensor that can be described as a true digital sensor, avoiding the usual digital-to-analogue conversions, as the physical quantity being measured is translated into the number of individual sensors activated.
In a particular embodiment of the invention there is provided a sensor that exercises the method described above. This sensor is composed of a group of micro switches and has been termed a Micro Switch Group Sensor (MSGS). The concept of the MSGS is transducing a physical quantity to the number of switches turned on in the device. This is fundamentally different to the conventional sensing concept of transducing a physical quantity to an electrical quantity, such as a voltage, in a stand-alone sensor. A large group or array of micro switches in a MSGS allows for reduced errors in measurement by making them work together as an ensemble. This may be likened to attempting to characterise a gas by pressure as opposed to trying to define the state of each molecule.
A MSGS can be considered a sensor array that exploits noise by applying the above method of sensing. It does this by utilizing the thermal noise or randomness in the system to produce a stochastic distribution across the array. The number of sensors (or switches) turned on in the device, depends on the cumulative distribution of the array due to the noise in the system. This makes it possible to measure any physical quantity in the range of the distribution. Thus, the method according to the present invention enables large arrays of micro switches, subjected to thermal noise, to sense a wide range of physical parameters.
A MSGS can also be considered a sensing system that is capable of measuring a physical quantity from the statistical state of a great number of micro switches. In other words, an MSGS is a sensor whereby the quantification of the measurand is determined by the statistical state of the micro switch array.
Ideally, a switch, which can be turned on by a physical quantity, has a transfer function as illustrated in Figure 1. However, in the real world, particularly when very tiny dimensions are concerned, such switches will be affected by thermal noise. Thermal noise is known to act stochastically as illustrated in Figure 2. Consequently, a switch will have a stochastic distribution associated with a particular physical quantity, about its conversion between 'on' and 'off' . Thus, we can represent the transfer function of Figure 1 more realistically as the probability transfer function of Figure 3. A device according to the present invention, comprising a plurality of such switches, has been designed to exploit this distribution in an improved sensing system. It has thereby become possible to make a sensor capable of exploiting stochastic noise.
A particular MSGS is described herein. This MSGS is composed of an array of breakable micro machined cantilever beams that can be used to assess the force presented to the device, for example, during the manufacturing process.
In the example presented, the beams were composed of single crystalline silicon, which is a brittle material. Such brittle materials have a stochastic distribution, known as a Weibull distribution, associated with their fracture strengths. Thus, the force required to break each beam has a random variation about a mean value. Each cantilever beam can therefore be considered a micro switch that can be turned on (or broken) by some force.
In accordance with the sensing method described, it will be demonstrated that the force acting on the array is determinable by observing the number of fractured beams (or levers) and exploiting the stochastic distribution in the system.
It should be noted that brittle materials are only capable of elastic deflection while ductile materials can be deformed plastically. Fracturing forces are sensitive to flaws both on the surface and inside the material. The fracturing forces associated with brittle materials tend to scatter around a mean fracturing force when compared to ductile materials. As such, the fracturing stresses of brittle materials need to be assessed by a statistical method. Weibull analysis is a well-known statistical method used for determining the fracturing stress of brittle materials. It is based on the assumption that failure at the most critical flaw will lead to total failure of the device. According to the Weibull method, the probability of fracturing at an arbitrary stress, Pf(σ), can be determined by Equation (1) below, where σ is stress, σ0 is a normalizing factor and m is the Weibull modulus.
Figure imgf000014_0001
Equation (1) can also be written in the form of Equation (2) below, where g is a value determined by the form of specimen and applied force.
Pf(σ) = l-exV(- σmg) (2)
Equation (2) can then be rewritten as Equation (3) below.
~^- = ^(σmg) (3)
Taking the natural logarithm of Equation (3) twice leads to the linear expression in Equation (4) below.
Figure imgf000014_0002
Thus, the Weibull modulus, m, and value, g, can be obtained by the slope and intercept of the line, respectively. As such, plotting the fracturing stress obtained by experiment can provide the values of Weibull modulus, m, and the value, g, using the least square method to fit a straight line through the results.
The stress on a rectangular cross-section beam, associated with an applied force, x, can be calculated from Equation (5) below, where L, b, and h represent the length, breadth and height of the beam respectively. 6xL σ = - (5) bh2
Combining Equations (2) and (5) allows the probability of fracturing Pf to be expressed as a function of the applied force, x, as shown in Equation (6) below.
Figure imgf000015_0001
Substituting the values obtained from Equation (4) for the Weibull modulus, m, and value, g, into Equation (6), allows the cumulative distribution diagram of fracturing to be plotted, as shown in Figure 4.
The test specimens in the example presented, were fabricated by micro- machining technology. Each test specimen was designed to comprise four different lengths of cantilever beams, as illustrated in Figure 5. Thus, the test specimens were designed such that the distribution of fracturing forces for each length of beam could be compared. Photolithography and Deep Reactive Ion Etching techniques were used to create the cantilevers from a single crystal silicon wafer with a thickness of 0.3mm.
The fracturing force for each cantilever beam was measured using the experimental set-up illustrated in Figure 6. As such a universal tester was used to apply a force to each beam via a pin. A specimen holder was designed to hold each device on a high resolution set of scales such that the cantilevers were held in suspension and exposed to the pin. Both the universal tester and the scales were computer controlled. The data from the scale was recorded at a sample rate of 10 per second and was transferred directly to the computer. The velocity of the pin was set to move at lmm per minute vertically downwards towards the beams. Fracturing forces were calculated for cantilevers of length 4mm, 6mm, 8mm and 10mm, with the force applied at 3.5mm, 5.5mm, 7.5mm and 8.5mm, respectively from the fixed end of each cantilever beam.
The cumulative distribution of fracturing forces, Pf(F), was calculated using Equation (7) below and the individual fracturing forces obtained through the experiments described above. In this equation, n is the sample number and k is the number of samples broken by a particular force.
^)=4? (7)
The cumulative distribution of results thus obtained, is plotted in Figure 7. Applying Equation (4) to the results, allows the Weibull modulus, m, and value, g, for each length of lever to be obtained. Thus, the theoretical probability of fracturing for any given amount of force can be calculated according to Equation (6) and this is also plotted in Figure 7. As can be seen, there is good correlation between the experimental results and theoretical curves.
As a further example, the Applicants considered a device with five 4mm long single crystalline silicon cantilevers. Thus, the number of levers broken (r) by any given force must be between 0 and 5. Therefore, there are six possible situations that can be expected. The probability of each situation occurring for a given force can be calculated using binomial theory. Thus, in accordance with Equation (8) below, the number of combinations producing each possible situation can be calculated, where n is the sample number and is any integer greater than 1 and r is the number of levers broken and is any integer between 0 and n.
r\\n-r)\
Thus, as an example, if 2 levers are broken, the number of combinations producing this situation is,
C2= , 5! . = 10 (9)
2 2!(5-2)
Furthermore, if the cumulative distribution of fracturing of 4mm levers is P(x) then the probability of surviving Ps(x) is given in Equation (10) below.
P1(X) = I -P(X) (10)
So, the probability of 2 levers being broken for a particular force x is,
P2(x)=5 C2XP(X)2 x(l-P(χ))3 (11)
Similarly, the probability of each possible situation can be calculated and the resulting equations are shown in the table of Figure 8. The probability curve for each of these six situations is plotted in Figure 9 as a function of applied force. Thus, in this example, the situation that '0 levers are broken' can occur with a force of ON to IN, while the situation '4 levers are broken' can occur with a force of 0.5N to 2.5N.
In addition, the mean values of the forces causing each situation may be calculated from Equation (12) below.
x = \pr (x)xdx (12) In this equation, pr(x) is the ratio between Pr(x) and the area inside the distribution curve as illustrated in Figure 10. Thus, pr(x) can be calculated from Equation (13) below.
Figure imgf000018_0001
As can be seen from Figure 9, the situation 'all levers are broken' merely sets a unit range upon the applied force. This essentially limits the range over which the technique is useful.
The mean force values calculated from Equation 12 are plotted in Figure 11 along with the related errors from the spread of the distributions around the mean values. Note, the situation 'all levers are broken' is omitted from Figure 11 for the reason given above. Thus, when some force is applied to the device, it is possible to refer to Figure 11 to determine the range of applied force by counting the number of levers that are broken.
An investigation was carried out to establish the performance characteristics of a MSGS, according to the present invention, as a function of the number of individual switches (levers). The results of this investigation are shown in Figure 12 for MSGS devices with 10, 100 and 1000 levers for each of four different lengths of lever.
As can be seen from Figure 12, the error range tends to become smaller as the number of levers is increased. The error range also tends to become smaller as the length of the levers is increased. This difference results from the nature of the distribution of fracturing forces on different sized levers. Thus, as shown in Figure 7, shorter levers tend to fracture in a wide range of force in accordance with the Weibull distribution. Consequently, switches with a large variance in their conversion state should be employed for measurements over a wide range of physical quantity, while switches with a small variance in their conversion state should be employed for fine measurements over a narrow range of physical quantity.
From the above examples, it is possible to generalise the sensing method of the present invention as follows. A general MSGS with 'n' number of switches will have a quantity 'r' of them turned on by some amount of physical quantity with a stochastic distribution. The probability of each situation, such as r levers are broken by any force, x, can be defined by Equation (14) below.
PΛΦ,CrxPon(xγ x{l-Pm(x)}"~r (14)
Thus; Pnr(x) is the probability of r in n switches being turned on, while Pon(x) is the probability of those switches being turned on at a certain amount of physical quantity, x. It should be noted that Equation (15) must always be true.
Figure imgf000019_0001
As before, the anticipated mean physical quantity x resulting in each situation can be obtained from Equation (16) below.
Figure imgf000019_0002
In Equation (16), pnr(x) is the ratio of Pnr(x) and the area inside the curve as shown in Figure 10. It can be calculated from Equation (17) below.
PΛ*) *- - (17) Thus, a new micro sensor system has been described. The method of sensing being dependent on a number of switches that can be turned on by a certain amount of physical quantity having a stochastic distribution.
As an example, it has been shown that the method can be applied to a MSGS where the probability of fracturing of silicon cantilever beams is used to determine the force acting on the system.
The vast majority of sensors generate electronic output signals and thus are affected by thermal (Johnson-Nyquist) noise. Consequently, an alternative application of the present sensing method has been devised in order to address the presence of thermal noise in measurements. Unlike the force sensor described above, which exploits the Weibull distribution of fracturing, an electronic sensor is subject to thermal noise, which displays the more common Gaussian distribution. Thus, the Applicants devised the following experiment to confirm that the present sensing method could equally be applied to sensors suffering from electric Gaussian noise.
Thus, an electric circuit, consisting of an input voltage supply, three noise generators, three comparators and a summing amplifier, was built to simulate a MSGS employing the present sensing method. A block diagram of the circuit is shown in Figure 13 and a circuit diagram is shown in Figure 14. The breakdown of zener diodes was used to generate the noise and high pass filters were used to remove any direct currents. Operational amplifiers were employed to amplify the noise signals and the input voltage was controlled by a potentiometer. In this example, the input voltage is the physical quantity being measured and each noise generator and associated comparator behaves as a switch affected by noise. Thus, if the comparator is high, the switch is on and if it is low, the switch is off. During the experiment, the voltage of the noise signal generated by each noise generator is compared with an arbitrary input voltage. This results in a signal from each comparator (or switch) that is either high or low. These signals are then summed together by the summing amplifier so that the number of comparators high can be determined from the output voltage. Consequently this circuit can be considered a MSGS comprised of three switches.
The experimental procedure involved the circuit of Figure 14 being connected to a personal computer through a digital oscilloscope so that the voltages could be recorded in the computer. At first, the noise signal generated by each of the noise generators was gathered. Subsequently, the signals from the summing amplifier and from each of the three comparators were obtained for input voltages of -15OmV, -10OmV, -75mV, -5OmV, -25mV, OmV, 25mV, 5OmV, 75mV, 10OmV and 15OmV. For each input voltage, the data was measured for a duration of 1 second. The data gathered in each 1 -second interval resulted in 752 data points. The experiment was repeated 3 separate times.
The noise signals generated by each noise generator 1 , 2 and 3 are shown in Figure 15. The mean values of the voltage and the standard deviation of each, plus their average values over the three experiments, are shown in Figures 16 and 17, respectively. It can be seen that for the same noise generator, similar values were obtained over each of the three experiments. The probability density and cumulative distribution curves for each noise generator are shown in Figure 18. The plots are hysterisis diagrams created using all of the gathered data. The curves are derived from Equations (18) and (19) below, which represent the Gaussian distribution function.
/(x) =— L=^-m)2 /2σ2 (18) σV2;r
Figure imgf000022_0001
Here, f(x) and g(x) are the probability density and cumulative distribution, respectively, at the voltage x, where σ is the standard deviation and m is the mean value of the voltage. As can be seen, the curves calculated from the average and standard deviations agree well with the plots of hysterisis. Hence, it is clear that the noise sources have the same characteristics.
As examples, the response of the comparators 1, 2 and 3 are plotted over time for the input voltages 15OmV, OmV and -15OmV, respectively, in Figures 19, 20 and 21. From these figures, we can deduce that -144mV can be regarded as low and 139mV can be regarded as high for all comparators. It is clear that the comparator becomes low when the input voltage is low and high when the input voltage is high. In this experiment, values larger than -2.5mV, which is the centre value between -144mV and 139mV, are regarded as high.
Following this analysis, it was possible to count the number of data points that were high and low for each input voltage. In Figures 22 and 23, the results are shown for each comparator at the input voltages OmV and 25mV, respectively. From these figures, it can be seen that the ratio between the numbers of points high and the numbers of points low are very similar for each comparator. Consequently, the average values for each comparator were calculated in order to obtain more accurate statistic values. The average number of high and low points for each comparator is shown in Figure 24 for each input voltage. Thus, it can be seen that the comparators have a common tendency that the higher the input voltage, the more likely they will become high.
The output signals from the summing amplifier are shown in Figure 25 for the input voltages -75mV, -25mV, 25mV, 5OmV, 75mV, and 15OmV. In these graphs, the y-axis has been plotted as the number of comparators high. It can be seen that when the input voltage is low, very few comparators are high, and the greater the voltage becomes, the comparators tend to become high more often until all of them are high. In addition, it is possible to recognise that this device has four stable situations which are 0 comparators are high, 1 comparator is high, 2 comparators are high and 3 comparators are high. Therefore, from this data, the number of comparators high at each moment can be obtained. In Figure 26 the number of comparators high with respect to each input voltage is shown. This figure was plotted using all of the gathered data points so that more representative values can be obtained. The number of comparators high was rounded to whole integers so that all the values could be represented as 0, 1, 2 or 3. Thus, there are four distinct situations that may occur.
The probability function of each switch was obtained from the data from each comparator. The probability of each comparator being high P(x) , at each voltage x , was calculated and is shown in Figure 27. The probability was calculated by counting the number of points for which the comparator was high and dividing it by the total number of measured points, as per Equation (20) below.
/>(*) = ^- (20)
Here, NM≠ is the number of points for which the comparator was high and N7. is the total number of measured points for each input voltage, 2256. These curves can therefore be defined as the probability function of the switches in this MSGS.
From the probability function of each comparator, it is possible to calculate the probability that each possible situation will occur in this device. In this example, there are 4 possible situations. These are no comparators are high, 1 comparator is high, 2 comparators are high and 3 comparators are high. Expressing the probability of the comparators 1 , 2 and 3 being high at some amount of input voltage x , shown in Figure 27, as P^x) , p2(x) and p3(x) , respectively, the probability of each situation, PMgh{x) (for n=0, 1 , 2, or 3) can be calculated by the functions shown in the table of Figure 28. The results of these calculations are plotted in Figure 29.
Calculating the mean voltage value for each situation using Equations (21) and (22) below, and defining the range of the voltage where each situation can occur, it is possible to plot Figure 30 which illustrates the performance of this MSGS. x
Figure imgf000024_0001
(X)xdx (21) ÷nhigh W
Pnhigh W ~ ' (22)
£^wώ
According to Figure 30, when 0 of the comparators are high, the input voltage is less than 5OmV and when 1 comparator is high, the input voltage is between -5OmV and 75mV.
From Figure 26 it is possible to confirm that the situation 0 comparators are high is only really likely to occur below approximately 5OmV of input voltage and the situation that 1 comparator is high is only likely between about -5OmV and 75mV. The ranges of the other possible situations also agree well with the results in Figure 30. Therefore, it has been shown that it is possible to deduce the range of the input voltage by counting the number of comparators that are high.
It is possible to plot the probability distribution of each situation, pnhigh (x) , at each input voltage, x , from the signal of the summing amplifier by counting the number of points for each situation as per Equation (23) below.
Figure imgf000025_0001
Here, Nn is the numbers of points where n (=0, 1 , 2, 3) of comparators are high and N1. is the number of total measured points for each input voltage, which is 2256. The results of this calculation are plotted in Figure 31 along with the probability curves obtained using the probability function of the comparators or switches, also shown in Figure 29. Thus, from Figure 31 , it can be seen that output of the summing amplifier and the probability curves of the comparator states are in good agreement. This confirms that the MSGS is operating as predicted from the performance of the switches. Hence, it is possible to deduce that a device that has many more switches will also work as predicted.
In a further experiment, the Applicants built a larger MSGS by electric circuit in order to test the applicability and function of the MSGS theory and method, depending on the number of switches employed in the device. They also considered the theory of the MSGS in relation to the standard normal distribution. This example was chosen in order to facilitate the application of the theory to any measurements with stochastic properties. The cumulative distribution curves relating to the properties of the switches were plotted from the gathered data and the effect on the output signal due to the number of the switches forming the MSGS was evaluated both theoretically and experimentally. The output signals of an MSGS with much larger numbers of switches was predicted by adding the output signals of repeated measurements and comparing these with the theoretical values. Finally, the validity of the measurements by the MSGS was evaluated by comparing the predicted input voltage ranges with the actual input voltages.
For this experiment, the method of MSGS was considered in relation to devices with 10, 100, and 1000 switches, respectively. A working assumption was that the switches displayed a standard normal distribution function, where the mean value is 0 and the standard deviation is 1. This approach allows for the method to be applied to any MSGS with stochastic properties. Noise has stochastic distribution, which is known as Gaussian distribution. It can be associated with the standard normal distribution by Equation (24) below.
Figure imgf000027_0001
When some amount of physical quantity z is added to this noise, the distribution is expressed as Equation (25).
G(z'-z) = —L exp(- {z'-zf 11) (25)
The value of z and z' can always be transferred into the dimension of observed physical quantity by Equation (26). Here, x' is the observed values of noise, μ is the mean value of noise, σ is the standard deviation of noise and x is the physical quantity observed.
Z'-Z = *'"*" ^ (26) σ
If a switch is turned on when G(z'-z) exceeds ZΛ, which can be regarded as threshold, the cumulative distribution function, which is the probability of the switches turned on at z, can be obtained by Equation (27). This relates to the shaded area in the curve of the standard normal . distribution as shown in graph (a) of Figure 32.
P(z) = [ G(z'~z)dz' (27)
Taking z as the horizontal axis and assuming the value of z± is zero, the curve of Equation (27) can be drawn as shown in graph (b) of Figure 32.
It should be noticed that the curve is the same as the cumulative distribution function of standard normal distribution. From equation (27), the probability of the state that n of N switches are turned on, PNn (z) , can be calculated from Equation (28) below.
PNn {z)=NCn xP{z)" x {l-P{z)}N- (28)
Here, N Cn is the sign of combination calculated from Equation (29) below.
Ni
C - (29) n\(N-n)\
It should be noted that Equation (30) must always be true.
∑^(*) = 1 (30)
The anticipated mean physical quantity z for each situation to occur can be calculated from Equation (31). zm = [ pNn(z')z'dz' • (31)
In Equation (31) above, pNn(z) is the ratio between PNn{z) and the area inside the curve, which is given by Equation (32) below, and is illustrated in Figure 33.
Figure imgf000028_0001
The calculated mean values and each of the error ranges, for devices with 10, 100 and 1000 switches are shown in Figure 34. In this figure, the ratio of the number of switches turned on (n) to the total number of the switches in the device (N) is taken as the horizontal axis. Error ranges for the physical quantity resulting in each possible state were obtained from the standard deviation of each state, using Equation (33) below.
σNn =\ &z-z)2pNn{z)dz (33) According to the statistical method decribed above, 95.44 percent of all possible states are contained in the range of z - 2σNn ≤ z ≤ z + 2σNn . The plots of the maximum and minimum number of switches in Figure 34 are the results for one less than the total number of switches turned on and one more that the least possible number of switches turned on, respectively. Thus, referring to Figure 34, it is possible to obtain the range of physical quantity which is being applied to the array of switches, by counting the number of switches turned on.
Also in Figure 34, it can be observed that the error ranges decrease as the number of switches increase and the error range becomes larger when the number of the switches turned on approaches the minimum and maximum number.
From Figure 34 it is also possible to predict that when a uniform physical quantity is applied to the sensor for a while, the number of switches turned on will change, or fluctuate, arbitrarily in some range. This phenomenon . must be taken into particular consideration when the errors in conversion of the switches are caused by electric noise.
The fluctuation of the number of switches can be expressed as n(z, t,N) , which is a function of z, time, t, and the number of switches composing the MSGS, N. The output signal M(z,t,N) can then be calculated from Equation (34) below. (34)
Figure imgf000029_0001
Here, it is possible to calculate the standard deviation of the output signal of the MSGS, σMω>N) , by Equation (35) below.
Figure imgf000030_0001
Here, nmean(z) is the mean value of the number of switches turned on at a physical quantity z as per Equation (36) below.
Figure imgf000030_0002
The results of the fluctuation calculations for a MSGS with 10, 100 and 1000 switches, respectively, are shown in Figure. 35. Thus, it can be seen that increasing the number of switches employed in the MSGS can reduce the likely fluctuation of the output signal. It is also evident that the standard deviation, σM(zAN) , becomes largest at the center of the measurement range as this is where the largest number of possible situations can occur. Around the maximum and minimum of the measurement range, it can be seen that the standard deviation of the output signal of the MSGS becomes smaller.
Following the above theory of the MSGS, in which some of the performances of the output signals were predicted, the following experimental work was carried out with the aim of observing the output signal of a MSGS, in order to evaluate the performance by comparing the obtained data and the theory.
As with the previous experiment, the device developed for this experiment consisted of an array of noise generators and comparators, with essentially the same function as micro or sub-micron switches affected by noise and inherent randomness. The circuit diagram for this experiment is illustrated in Figure 36 and includes 20 individual noise generators and comparators. As before, an operation amplifier amplifies the noise signal from each zener diode. The direct current is removed by capacitors placed before the noise generators and operation amplifiers. The noise signals are compared with input voltages by the comparators, which are recognized as switches. The output voltage of the summing amplifier determines the number of comparators high or low. Disconnecting the lines coming from the comparators to the summing amplifier can change the number of switches composing the MSGS. In this experiment, tests were performed for a MSGS with 5, 10 and 20 switches.
For input voltages of -8V, -7V, -6V, -5V, -4V, -3V, -2V, -1.5V, -IV, -0.5V, OV, O.5V, IV, 1.5V, 2V, 3V, 4V, 5V, 6V, 7V, 8V, the output signals were gathered as data through a digital oscilloscope and personal computer. The obtained output voltages were then converted into the output signal of the MSGS by Equation (37) below.
M(x,,N) = ^M^ ^ ^^^ -^ W (37) N Vallon(N) -VaIhff (N)
Here, n(χ,t,N) is the observed fluctuation of the number of switches turned on, Voul (x,t,N) is the output signal of the MSGS, Vallon is the voltage when all the switches are on, and Va[!off is the voltage when all the switches are off. The values for Valhn and Valloff were obtained from the output voltages for the input voltages 8V and -8V respectively.
Some examples of the output signals obtained for each of the 5, 10, and 20 switch MSGS devices are shown in Figure 37. From these graphs, it is clear that the greater the number of switches in the device, the smaller the fluctuation of the output signal becomes.
The distribution of the average voltage and the standard deviations of each noise signal are shown in Figure 38. As can be seen, the average voltage and the standard deviation of each noise signal varies depending on the noise generator concerned. In MSGS, these errors can be taken into consideration by obtaining the performance of the group of switches as a whole, and not each individual switch. It can be assumed that the probability of switching is mainly controlled by the noise itself, rather than the randomness of the mean voltage.
The performance of the group of switches can be obtained by referring to the output of the MSGS with 20 switches. The mean value of the output signal for each possible situation Mmean(x,N) can be calculated by Equation (38) below. Here, T is the time interval of the measurement.
^ me∞.Λ(^ ' = W"- j(vj>Jy) =i T *f w(3C N>WA (38)
In fact, this mean value relates to the probability of a particular number of switches of the MSGS being turned on at input voltage x, in the population, which in this case, is the 20 switches composing the MSGS. It is possible to associate x with z using Equation (39) below and finding the same value in the cumulative distribution function as the value mentioned in Equation (38). x = σz + μ (39)
Hence, it is possible to find the mean value and standard deviation of the conversion of the switches in the group by the minimum square theorem, as shown in Figure 39. The standard deviation and the mean value of the conversion of the switches are shown in the approached curve of these plots. To obtain these values, the output signals of -2, -1.5, -1, -0.5, 0, 0.5, 1 , 1.5, and 2V were used.
Substituting the above values for the standard deviation and the mean value into Equations (25) and (26) above, the approached curve of the cumulative distribution function of the group of 20 switches can be obtained. This curve is shown in Figure 40 along with the mean values of the output signals obtained for each of the 5, 10, and 20 switch MSGS's. From this graph, it can be seen that these plots are all very close to the approached curve.
The standard deviation of the output signals are shown in Figure 41 along with the curves calculated by Equations (34) and (35). Here, the standard deviations of the output signals, σM{X}ltN) , are calculated from Equation (40) below.
σ M(x,t,N) (40)
Figure imgf000033_0001
From theses results, it is possible to deduce a general agreement between the theoretical curves and the experimental results. Thus, the predicted performance of the electric circuit has good agreement with the data obtained by the experiment.
From the above-mentioned experimental work, the output signals of MSGS's comprising 5 switches, 10 switches and 20 switches were obtained. It is possible to predict the output signals of a MSGS composed of a larger number of switches by adding up the output signals from the above MSGS's and regarding them as the output of an MSGS with a correspondingly larger number of switches. The output signals obtained by adding m output samples from a MSGS with N number of switches, Mmml(z,t,N) , is expressed in
Equation (41) below.
1 m Mm011l(zAN) = ~∑nr(z,t,N) (41)
In order to confirm this theory, the output signals of the MSGS with 20 switches were compared with the output signals of the MSGS with 5 switches, for which the signals were added 4 times, and the output signals of the MSGS with 10 switches, for which the signals were added twice. The data gathered for this experiment was taken for input voltages from -2V to 2 V by the interval of 0.5V. Figure 42 shows the results of these calculations. It can be seen that the average values are almost the same as the values for each MSGS device, as plotted in Figure 40, and there is good agreement between the values of standard deviation.
In light of the above, the Applicants proposed to predict the output signal of a MSGS with 100 and 1000 switches, respectively, by adding 5 and 50 of the output samples of the MSGS with 20 switches. The results of these calculations are shown in Figure 43. Thus, it can be seen that the fluctuation of the output signal becomes much smaller in MSGS devices with larger numbers of switches. In Figure 44, the standard deviation of these signals and me curves obtained by Equation (35) are compared. Thus, it is possible to say that the experimental results agree well with the theoretical curves.
In this experiment, the output signals of a MSGS with 5, 10 and 20 switches were obtained and the output signals of a MSGS with 100 and 1000 switches were predicted using the output of the MSGS with 20 switches. In Figure 45, the ranges of the input voltage predicted by the mean number of switches turned on are compared with the actual input voltages, for each MSGS comprising a different number of switches. AU of the results for the 5, 10, 20 and 100 switch MSGS 's are performing in the predicted ranges by the cumulative distribution curve. However, there is a gap between the predicted input voltage and the actual input voltage for the input voltage of 2V in the results for the 1000 switch MSGS, shown in graph (e) of Figure 45. This disagreement is considered to be due to the cumulative distribution curve not being precise enough to predict the range of the 1000 switch device. . Notwithstanding this point, it can be seen that the measurements are largely in agreement with the theory of the MSGS.
During this experiment, the standard normal distribution and normal distribution associated with the application of the MSGS method was used to develop the theory of the MSGS. In addition, some of the properties of a MSGS were predicted by the theory. In experimental work, the output signal of the MSGS with 20 switches was successfully observed and compared with the theoretically predicted values. That data was then extracted to predict the output signal of a MSGS with 100 and 1000 switches. The performance of MSGS's with 5, 10, 20 and 100 switches are in good agreement with the theory. Therefore, it can be said that the validity of the present sensing method has been successfully shown.
From the above, it is clear that it is possible to apply the present method of sensing to exploit the stochastic distribution of any sensing system. It has also been shown that it is possible to dramatically increase the reliability of sensor devices by making individual sensors (or switches) work together to utilize the noise associated with such devices.
It should be noted that the sensing method of the present invention could be applied to any system featuring stochastic noise. Moreover, the present sensing method can utilise any statistical properties of a sensing device. Consequently, a wide variety of sensor devices and systems may be developed using the method of the present invention.
In addition, the present sensing method permits individual sensors to be designed and fabricated to a lower degree of accuracy since it is the number of individual sensors being used that determines the overall accuracy of the device.
The present invention provides for an improved method of sensing a physical quantity. Importantly, it enables a MSGS to be utilized as an analogue-to- digital converter, or a true digital sensor, whereby the number of switches turned on relates to the physical quantity being measured. Thus, the fact that the output is purely digital in nature (i.e. the number of switches turned on) enables the information to be processed directly through a digital circuit, upon a relevant computer clock tick. This may prove revolutionary in the communication of data between computers and sensors.
An important advantage with a sensing device according to the present invention is gentle failure. That is, failure of one, or a small number of sensors in the device does not prevent the device from measuring an appropriate value of the physical quantity being sensed. Thus, Micro-Switch Group Sensors will be of particular benefit in applications where human life may be at risk. Accordingly, the MSGS may be of particular use in motor vehicles, aircraft, trains and even medical applications.
In addition, the described method can be applied to produce sensors with extremely high resolution. As such, scientific researchers in the fields of chemistry, physics and medicine would benefit from this kind of sensor.
As a result of the advantages outlined above, it can be appreciated that the method of sensing, according to the present invention, can be applied to sensing applications in a wide variety of fields and industries, not limited to those specifically mentioned. As an example only, the sensing method of the present invention may be particularly useful in the nuclear industry.
A device employing the sensing method of the present invention may take any appropriate form and may comprise mechanical, electronic, chemical or biological features.

Claims

Claims
1. A method of sensing comprising the steps of: providing a plurality of sensors; monitoring the state of said sensors; and determining the quantification of a measurand by the probability that a particular state of said sensors would occur for a specific value of the measurand.
2. A method of sensing as claimed in claim 1 wherein a stochastic distribution is associated with the state of said sensors.
3. A method of sensing as claimed in claim 2 wherein said stochastic distribution is a result of stochastic noise in the sensors and/or sensed environment.
4. A method of sensing as claimed in claim 2 wherein any physical quantity within the range of said distribution is capable of being detected.
5. A method of sensing as claimed in claim 3 wherein said stochastic noise results from thermal noise and/or inherent randomness in the physical structure of said sensors.
6. A method of sensing as claimed in claim 1 wherein said sensors are micro switches.
7. A method of sensing as claimed in claim 6 wherein the number of said switches turned on is dependant on the quantification of the measurand being sensed and its stochastic distribution.
8. A method of sensing as claimed in claim 6 wherein said switches are breakable micro machined cantilever beams.
9. A method of sensing as claimed in claim 8 wherein the stochastic distribution associated with the fracture strength of each beam is used to determine the effective force acting on said sensors.
10. A method of sensing as claimed in claim 9 wherein the error range associated with the force required to break a specific number of beams is relatively small when the number of beams is large, and relatively large when the number of beams is small.
11. A method of sensing as claimed in claim 9 wherein the error range associated with the force required to break a beam is relatively small when a relatively long beam is used, and relatively large when a relatively short beam is used.
12. A method of sensing as claimed in claim 6 wherein switches with a relatively large statistical variance in their conversion from one state to another are used to measure physical quantity over a wide range of values.
13. A method of sensing as claimed in claim 6 wherein switches with a relatively small statistical variance in their conversion from one state to another are used to measure physical quantity over a narrow range of values.
14. A device comprising a plurality of sensors wherein said device is capable of sensing by the method claimed in any of the previous claims.
15. A method of sensing substantially as hereinbefore described with reference to and as shown in the accompanying drawings.
16. A device substantially as hereinbefore described with reference to and as shown in the accompanying drawings.
PCT/GB2007/000245 2006-01-26 2007-01-25 Method of measuring with a group of sensors using statistics WO2007085829A1 (en)

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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE1958497A1 (en) * 1969-02-14 1970-08-27 Rft Messelektronik Dresden Veb Circuit arrangement for the statistical evaluation of measured values and measuring functions
DE19525217A1 (en) * 1995-07-11 1997-01-16 Teves Gmbh Alfred Acquisition and evaluation of safety-critical measurands
US20040102918A1 (en) * 2002-11-27 2004-05-27 Stana James M. Method and apparatus for recording changes associated with acceleration of a structure
US6757641B1 (en) * 2002-06-28 2004-06-29 The United States Of America As Represented By The Administrator Of The National Aeronautics And Space Administration Multi sensor transducer and weight factor

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE1958497A1 (en) * 1969-02-14 1970-08-27 Rft Messelektronik Dresden Veb Circuit arrangement for the statistical evaluation of measured values and measuring functions
DE19525217A1 (en) * 1995-07-11 1997-01-16 Teves Gmbh Alfred Acquisition and evaluation of safety-critical measurands
US6757641B1 (en) * 2002-06-28 2004-06-29 The United States Of America As Represented By The Administrator Of The National Aeronautics And Space Administration Multi sensor transducer and weight factor
US20040102918A1 (en) * 2002-11-27 2004-05-27 Stana James M. Method and apparatus for recording changes associated with acceleration of a structure

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