CN104090228B - Analog circuit fuzzy group identification method - Google Patents

Abstract

The invention discloses an analog circuit fuzzy group identification method. The general characteristic of the fault voltage of an analog circuit element is derived through a theory, wherein the characteristic is that a real part and an imaginary part meet an equation of a circle. According to the characteristic, the fuzzy group identification method is provided. The method includes the steps that fault-free simulation is conducted on each fault source firstly, so that a fault-free voltage value of each measuring point is obtained; simulation is conducted under two fault conditions, so that two fault voltage values are obtained; according to the three voltage values, an equation set of the circle is solved, so that circle characteristic parameters are obtained; the circle characteristic parameters corresponding to the fault sources are compared and the fault sources with the three same parameters are classified into a fuzzy group. According to the method, a transmission function is not needed, an achieving method is simple, a fuzzy group identification result is not related to a testing method, and the accuracy is the same as that of a transmission function and symbol analysis method.

Description

A Method for Recognition of Fuzzy Groups in Analog Circuits

technical field

The invention belongs to the technical field of fault diagnosis of analog circuits, and more specifically relates to a method for identifying fuzzy groups of analog circuits.

Background technique

A fuzzy group is defined as a set of components for which there is no unique solution to the test equations for the analog circuit under test. In layman's terms, this group of components can produce the same output. Determining the fuzzy group information of analog circuits is the primary task of analog circuit testability design and fault diagnosis. Fuzzy group information is determined by the characteristics of the analog circuit under test and has nothing to do with the test method. At present, there are mainly two methods for fuzzy group identification. One is to determine the information of the fuzzy group by performing QR decomposition on the test equation group (transfer function of different measuring points). This type of method is affected by the QR decomposition error, and its accuracy drops sharply as the circuit scale increases. Another method is to symbolize the test equations, which avoids the QR decomposition error. The basic idea is to establish the transfer function equations on all measuring points first.

The equations in the transfer function equation system for an analog circuit can be expressed as:

Among them, p=[p ₁ ,p ₂ ,…,p _R ] ^T represents the potential fault source parameter vector, the superscript T represents the transposition, k represents the number of equations, that is, the number of measuring points, l represents the serial number of the measuring point, and s represents the complex Frequency, m represents the maximum order, n _l represents the number of items in the numerator; b _j (p) and b _m (p) represent coefficients of the equation and are polynomials of p.

For each equation in equation group (1), the derivatives of each fault source parameter p _r ∈ p are calculated. The matrix B shown in formula (2) is obtained.

The testability index of the circuit under test is equal to the rank of matrix B, and it is independent of the complex frequency s. The testability matrix B can be expressed in the following form.

in and B _j , (j=1,2,...,m-1), are the coefficients of the fault diagnosis equation calculated in formula (1). The Jacobian matrix of the system is equivalent to matrix B, and if the rank of B is equal to the number of unknown parameters, the value of the component can be uniquely determined. If testability, that is, the rank of the matrix B is less than the number of unknown parameters R, not all faults can be distinguished, and the rank of the matrix reflects the fuzzy group information.

The calculation of the symbolic analysis method is much easier than the transfer function, but the coefficient of the complex frequency s in the denominator of the test equation must be equal to 1, and it still cannot get rid of the dependence on the transfer function.

Contents of the invention

The purpose of the present invention is to overcome the deficiencies of the prior art and provide a method for identifying fuzzy groups in analog circuits. The method does not need a transfer function, and the circle equation of each element in the analog circuit can be obtained through the measured point voltage obtained through simulation. By comparing the circle The characteristic parameters of the equation can identify the fuzzy group.

In order to realize the purpose of the above invention, the present invention theoretically deduces the voltage of the components in the tested analog circuit, and draws a conclusion: for each fault source, under any fault source parameter, the real part and imaginary part of the voltage generated at the same measuring point All of them satisfy the same circle equation. By comparing the characteristic parameters of the circle equation corresponding to each fault source, it can be judged whether the fault source can be distinguished. Propose analog circuit fuzzy group identification method of the present invention according to this conclusion, specifically comprise the following steps:

S1: Carry out no-fault simulation on the analog circuit to obtain the no-fault voltage of the measuring point t j represents the imaginary unit;

S2: let d=1;

S3: Change the parameter x _d of the dth fault source element to x _d1 and x _d2 for simulation respectively, and obtain the fault voltage at the measuring point t, which are recorded as

S4: if but Let the circle characteristic parameters wd=1, v _d =-K _d , r _d =0, otherwise solve the following equations to obtain the circle characteristic parameters w _d , v _d , r _d :

S5: judge whether d= _NF , _NF represents the number of fault sources, if yes, enter step S6, otherwise make d=d+1, return to step S3;

S6: Compare the circle characteristic parameters corresponding to each fault source, and classify the fault sources with the same three parameters into a fuzzy group.

The fuzzy group identification method for analog circuits of the present invention derives the general characteristics of the fault voltage of analog circuit components theoretically: the real part and the imaginary part satisfy the circle equation, and a fuzzy group identification method is proposed according to the characteristics: The fault-free voltage value of the measuring point is obtained by simulation, and then two fault voltage values are obtained by simulation under two fault conditions, and the circle equations are solved according to the three voltage values to obtain the circle characteristic parameters, and the circle characteristic parameters corresponding to each fault source are compared , classify the fault sources with the same three parameters into a fuzzy group. The invention does not need a transfer function, its realization method is simple, and the recognition result of the fuzzy group has nothing to do with the test method, and the accuracy is the same as that of the transfer function and the symbol analysis method.

Description of drawings

Fig. 1 is an analog circuit diagram;

Fig. 2 is the equivalent circuit diagram of the analog circuit shown in Fig. 1;

Fig. 3 is a schematic diagram of the voltage source function of the analog circuit shown in Fig. 1;

Fig. 4 is a schematic diagram of fault source action of the analog circuit shown in Fig. 1;

Fig. 5 is the specific implementation flow chart of analog circuit fuzzy group identification method of the present invention;

Fig. 6 is a schematic diagram of an analog circuit in an embodiment;

Figure 7 is the characteristic circle corresponding to each fault source drawn according to the characteristic parameters of the circle equation in Table 1.

detailed description

Specific embodiments of the present invention will be described below in conjunction with the accompanying drawings, so that those skilled in the art can better understand the present invention. It should be noted that in the following description, when detailed descriptions of known functions and designs may dilute the main content of the present invention, these descriptions will be omitted here.

In order to better illustrate the technical contents and invention points of the present invention, the theoretical derivation process of the present invention will be described first.

Figure 1 is an analog circuit diagram. As shown in Figure 1, the analog circuit N consists of an independent voltage source excitation. Indicates the voltage phasor obtained at the selected measuring point, and x is a passive component. According to the substitution theorem, x can be replaced by an independent voltage source with the same voltage as its terminals, resulting in an equivalent circuit. FIG. 2 is an equivalent circuit diagram of the analog circuit shown in FIG. 1 . According to Thevenin's theorem, there are:

in, is the open-circuit voltage phasor of ports a and b in Figure 2; Z ₀ is the Thevenin impedance value between a and b, and Z _x is the impedance value of element x. According to Thevenin's theorem, The values of Z 0 and Z ₀ are independent of Z _x , and are determined only by the fault-free component parameters and the network structure. Figure 2 with Figure 1 are equal. In Figure 2, the analog circuit N consists of with Motivate together. According to the principle of superposition, the voltage in Figure 2 equal with The algebraic sum of the output voltages when acting alone. FIG. 3 is a schematic diagram of the voltage source function of the analog circuit shown in FIG. 1 . FIG. 4 is a schematic diagram of fault source action of the analog circuit shown in FIG. 1 . As shown in Figures 3 and 4, the voltage source and source of failure When acting alone, the output voltage is used respectively with According to the principle of superposition, there are:

Among them, H′(jω) and H″(jω) are the transfer functions from the power supply port and the port where the component x is located to the output port, respectively, and have nothing to do with the parameter value of the component x. Substituting formula (4) into formula (5), eliminating After simplification, the functional relationship between the output voltage and the fault source impedance value Zx _is as follows:

From the above formula, the relationship between the Thevenin equivalent impedance Z ₀ and Z _x can be obtained as follows:

Without loss of generality, each phasor is represented by Cartesian coordinates:

where j is the imaginary unit. because H'(jω), Both H″(jω) and Z ₀ are independent of Z _x , so R ₀ , X ₀ , α and β are also independent of Z _x . Substituting (8) into (7) yields:

Assuming that element x is a resistor, record Z _x = R _x , according to formula (9), the real and imaginary parts on both sides are equal, and we get:

Combine the two equations in (10) to eliminate R _x , and get the following formula:

Eliminate the denominator in (11), it is not difficult to deduce:

because The Thevenin equivalent voltage is assumed to be The output voltage produced by the power supply is The real and imaginary parts of the output voltage of the fault circuit can be expressed as follows:

Substituting formula (13) into formula (12), the following formula is obtained:

Formula (14) can be expressed as:

(U _or -w) ² +(U _oj -v) ² ＝r ² (15)

in,

Equation (15) expresses the circle equation with center (w, v) and radius r on U _or -U _oj plane. Since R ₀ , X ₀ , α and β are independent of the value of x, w and v are also independent of the element x. That is, regardless of the value of the parameter x, the formula (15) is always true, that is, for each fault source, the real part and imaginary part of the voltage generated at the same measuring point under any fault source parameters satisfy the same circle equation . Therefore, the circle equation (15) is a fault model that can be applied to both soft faults and hard faults. And has nothing to do with the test method. The above conclusions are obtained assuming that the fault source (element x) is resistance. If the fault source is capacitance or inductance, the same conclusion can be derived. When the circuit under test has no faults, the output voltage is In fact, the imaginary part is expressed as with Since equation (15) is independent of the parameters of the element x, so with must satisfy this formula, that is, the characteristic trajectories of all fault sources pass through the point

According to the above analysis, for the same measuring point of the analog circuit under test, under different component fault conditions, that is, under different fault source conditions, the real part and imaginary part of the voltage measured at the measuring point correspond to a circle equation respectively. Then by comparing the characteristic parameters of the circle equation corresponding to each fault source, it can be judged whether the fault source can be distinguished, that is, if one or more of the three characteristic parameters of the circle equation obtained under the conditions of two fault sources are different, then the two Fault sources belong to different fuzzy groups, if the three characteristic parameters are exactly the same, they belong to the same fuzzy group.

According to the conclusion obtained from the above theoretical derivation, the fault source of the analog circuit can be identified by the fuzzy group. However, in actual situations, it is difficult to obtain the display expression of the circular equation (15), so the present invention proposes to obtain the characteristic parameters of the circular equation through analog circuit simulation. As we all know, two points determine a straight line, and three points determine a circle (equation). Therefore, it is only necessary to simulate the component parameters of three different fault sources to calculate the three characteristic parameters of the corresponding circle equation. If the three fault voltages obtained by simulation are on a straight line, then the corresponding fault characteristics can be expressed as a straight line with a certain slope, otherwise it can be determined by formula (15).

FIG. 5 is a flow chart of a specific embodiment of the method for identifying analog circuit fuzzy groups in the present invention. As shown in Figure 5, the analog circuit fuzzy group identification method of the present invention comprises the following steps:

S501: No fault simulation:

Carry out no-fault simulation on the analog circuit to obtain the no-fault voltage of the measuring point t

S502: Let d=1.

S503: fault source fault simulation:

Change the component parameter x _d of the dth fault source to x _d1 and x _d2 to simulate respectively, and obtain the fault voltage at the measuring point t, which are recorded as The parameters x _d1 and x _d2 are set according to the actual situation, generally set x _d1 < x _d , x _d2 > x _d .

S504: Calculate the circle feature parameters:

if but Let the circle characteristic parameters w _d =1, v _d =-K _d , r _d =0, otherwise solve the following equations to obtain the circle characteristic parameters w _d , v _d , r _d :

S505: Determine whether d= _NF , where _NF represents the number of fault sources, if yes, go to step S506, otherwise let d=d+1, go back to step S503.

S506: Comparing the circle characteristic parameters corresponding to each fault source, and classifying the fault sources with the same three parameters into a fuzzy group. That is, elements with different parameters are distinguishable. Components with the same parameters are indistinguishable under the current measuring point.

Example

In order to illustrate the implementation process and effects of the present invention, an actual circuit is taken as an example for simulation verification. Fig. 6 is a schematic diagram of an analog circuit in the embodiment. As shown in FIG. 6 , the analog circuit in this embodiment is a band-pass filter circuit, and the measuring point t is the node between the element R1 and the elements R2 and C1. Firstly, the fault-free simulation of the circuit is carried out, and the fault-free voltage of the measuring point t is obtained as Two fault simulations are performed for each fault source in turn. Then, according to the no-fault voltage and fault voltage, the characteristic parameters of the circle equation corresponding to each fault source are obtained. Taking the first fault source resistance R1 as an example, its normal resistance value is 20kΩ. In the fault simulation of this embodiment, the resistance values of the two fault simulations are respectively set to 10kΩ and 40kΩ, and the fault voltages measured at the measuring point t are respectively for Since the three points are not on a straight line, namely:

Therefore, the voltage obtained from the simulation is substituted into formula (16) to calculate the characteristic parameters of the circle equation of the resistor R1.

Table 1 is the fault simulation output voltage and model parameter table of each fault source of the analog circuit in the embodiment.

Table 1

Figure 7 is the characteristic circle corresponding to each fault source drawn according to the characteristic parameters of the circle equation in Table 1. As shown in Figure 7, the characteristic circles corresponding to all fault sources pass through the fault-free voltage There are 6 different circles in Figure 7, indicating that the 7 fault sources in this embodiment are divided into 6 fuzzy groups, in which resistor R4 and resistor R5 have the same characteristic circle and belong to a fuzzy group, and other components belong to a fuzzy group Fuzzy group. Table 2 is the fuzzy group information of this embodiment.

fuzzy group fault source Circle feature parameters (w, v, r) 1 R1 (0.5000,0.1768),0.5304 2 R2 (0.4281,0.0791),0.4353 3 R3 (0.2952,-0.4046),0.1902 4 R4,R5 (-0.4296,-1.0800),1.1627 5 C1 (0.3574,-0.1687),0.2209 6 C2 (0.4096,-0.1079),0.2549

Table 2

According to the transfer function and symbolic analysis method, the fuzzy group identification is carried out on the analog circuit in this embodiment, and the result is consistent with the result shown in Table 2. It can be seen that the accuracy of the method of the present invention is the same as that of the transfer function and the symbolic analysis method, but the advantage of the present invention is that no transfer function is needed, its implementation method is simple, and the fuzzy group identification result is independent of the test method.

Although the illustrative specific embodiments of the present invention have been described above, so that those skilled in the art can understand the present invention, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, As long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are included in the protection list.

Claims (2)

1. A fuzzy group identification method for an analog circuit is characterized by comprising the following steps:

s1: carrying out fault-free simulation on the analog circuit to obtain fault-free voltage of the measuring point t

S2: let d be 1;

s3: the parameter x of the d-th failure source element_dChange to x_d1And x_d2Respectively simulating to obtain the measuring point tFault voltages, respectively

S4: if it is notThenLet the circle characteristic parameter w_d＝1、v_d＝-K_d、r_dIf not, solving the following equation system to obtain the circular characteristic parameter w_d、v_d、r_d：

$\left\{\begin{array}{c}{(U_{or}-w_d)}^2+{(U_{oj}-v_d)}^2={r_d}^2\\ {(U_{1r}-w_d)}^2+{(U_{1j}-v_d)}^2={r_d}^2\\ {(U_{2r}-w_d)}^2+{(U_{2j}-v_d)}^2={r_d}^2\end{array}\right.$

S5: judging whether d is equal to N_F，N_FIndicating the number of fault sources, if yes, entering step S6, otherwise, making d equal to d +1, and returning to step S3;

s6: and comparing the circle characteristic parameters corresponding to each fault source, and classifying the three fault sources with the same parameters into a fuzzy group.

2. The analog circuit ambiguity group identification method of claim 1, wherein the parameter x_d1＜x_d，x_d2＞x_d。