CN1793897A - Non destructive detection method of anchor rod ultimate bearing capacity - Google Patents

Abstract

The invention discloses a non-destructive detection method for the ultimate bearing capacity of a bolt, which is characterized in that: it adopts structural dynamic measurement technology to obtain information, adopts intelligent signal analysis technology to process the obtained information, and then passes the trained neural network The intelligent identification system is used to predict the detection method of the ultimate bearing capacity of the bolt. The invention has the remarkable characteristics of simple operation, low cost, no damage to the anchor rod, large monitoring area, fast detection speed and high detection accuracy. monitor.

Description

A kind of lossless detection method of anchor rod ultimate bearing capacity

Technical field

The present invention relates to a kind of lossless detection method of anchor rod ultimate bearing capacity.

Background technology

Anchor rod anchored engineering is a key areas of current Geotechnical Engineering, anchor system is because of being in for a long time in the abominable geologic media, easily weathers, the influence of disaster and quality problems occur, in case have an accident, to jeopardize the people's lives and property safety and cause great economic loss.China has used a large amount of anchor poles since the sixties in 20th century in all kinds of engineering designs, used many anchor cables after the seventies, has used soil nailing the nineties more.Its sum will be in hundreds of millions.The advance of these anchor poles, anchor cable, soil nailing, reliability, economy are unquestionable, still,, how long have on earth their serviceable life as in the countless engineerings of permanent supporting? if, will become hidden dangers in project in case lost efficacy, make that engineering ruins in a single day.Therefore, follow the characteristics of anchor rod anchored structural system, develop a kind of not only easy economy, rapid reliable but also harmless anchor pole bearing capacity test method, help to carry out timely monitor and forecast for anchor system, for the reliable means that provide are provided for quality control on construction and Engineering Reliability, to avoiding accident to take place, guarantee the people life property safety, have earth shaking society, economic implications.

Carry out long-term or the short-term monitoring for the anchor pole loads change, can be undertaken by pre-buried various types of dynamometers (by machinery, hydraulic pressure, vibration, principle making such as electric and photoelastic), but these pre-buried dynamometers are because of being subjected to the interference of electromagnetic field big, sensitivity will reduce greatly under the environment moist, that the temperature difference is big, influence its measuring accuracy.For the not anchor pole detection of pre-buried dynamometer, engineering circle mainly adopts the method for on-the-spot drawing experiment to measure anchor pole dead load---displacement curve at present, determines the ultimate bearing capacity of anchor pole, and this method was both directly perceived, reliable again beyond doubt.But tensile load is to convert by the piston area of lifting jack and pressure fuel pump, just can't estimate as for locking back anchor force size and the variation in long-time running, in addition, measure complete load---displacement curve, not only time-consuming length, it is expensive big that (common bolt drawing at present detects and need take out 5% sample and do destructive the detection, every expense is on average up to 500 yuan, China only in mine tunnel engineering the annual consumption of anchor pole just reach more than the 1700km, press 3 meters calculating of anchor pole average headway, total anchor pole consumption is 56.1 ten thousand, calculates by sampling observation rate 5%, the worker need inspect 2.81 ten thousand by random samples, by 500 yuan of calculating of every anchor pole, only inspect one by random samples, the annual need costed more than 1,402 ten thousand yuan, calculate 3 hours detection times by average every anchor pole, need 8.415 ten thousand hours consuming time; Present national examination criteria-sampling observation rate only 5% because of detection faces is little, also is difficult to represent the actual conditions of anchor pole in the whole anchor system.

In a word, detection method for anchor rod system also rests on more traditional method at present, can't adapt to the large-scale engineering requirements on Construction, so the Study on Technology of anchor rod ultimate bearing capacity Non-Destructive Testing is one of key technology of engineering constructions such as traffic, municipal administration always.

Summary of the invention

The object of the present invention is to provide a kind of easy and simple to handle, cost is low, do not damage the detection method of the anchor rod ultimate bearing capacity of anchor pole.

The object of the present invention is achieved like this: it is characterized in that: it is to adopt the structure dynamic testing technology to obtain information, adopt the intelligent signal analytical technology that the information of obtaining is handled, predict the detection method of anchor rod ultimate bearing capacity then by the neural network intelligent identifying system that has trained.

Said method comprises following steps:

(1), the stress wave generator excites and produces the top that acoustic signals acts on anchor pole to be detected;

(2), ultrasonic sensor obtains the moving survey of the sound wave pulse signal that returns through the anchor pole bottom reflection, and sends this signal to signal receiving device;

(3), signal receiving device passes the signal to microprocessor and carries out wavelet packet analysis and extract the energy feature vector;

(4), handle the neural network intelligent identifying system that the energy feature vector input obtain trained and predict, to obtain the ultimate bearing capacity value of anchor pole.

Above-mentioned neural network intelligent identifying system is BP (Back Propagation) network system, and its training step is as follows:

(1), foundation has input layer L _A, hidden layer L _B, output layer L _CThe neural network of layer structure;

(2), provide by input layer L _ATo hidden layer L _B, hidden layer L _BTo output layer L _CCorresponding neuronic initial weight w ₁, w ₂With initial threshold b ₁, b ₂

(3) given input vector p and desired output t;

(4) calculate hidden layer L _BThe neuronic activation value of layer:

a ₁＝f(∑w ₁·p+b ₁)

Calculate output layer L _CNeuronic activation value:

a ₂＝f(∑w ₂·a ₁+b ₂)

(5) calculate output layer L _CThe error function and the gradient thereof of neuron output:

$E=\frac{1}{2}{\mathrm{\Σe}}^2=\frac{1}{2}\mathrm{\Σ}{(t-a_2)}^2$

$\frac{\∂E}{{\∂w}_2}=-{\mathrm{\δ}}_2\·a_1,\frac{\∂E}{{\∂b}_2}=-{\mathrm{\δ}}_2$

δ ₂＝(t-a ₂)·a ₂·(1-a ₂)

(6) whether error in judgement function E satisfies | and E|＜ε, ε are the maximum error that requires, 10 ^-5＜ε＜10 ^-3, if, then:

(7), judge that whether all E satisfy | E|＜ε, ε are the maximum error that requires, 10 ^-5＜ε＜10 ^-3, if then finish;

(8) if step (6), (7) for not, then:

Calculate output layer L _CAnti-pass is to hidden layer L _BThe error function gradient:

$\frac{\∂E}{{\∂w}_1}=-{\mathrm{\δ}}_1\·p,\frac{\∂E}{{\∂b}_1}=-{\mathrm{\δ}}_1$

δ ₁＝δ ₂·w ₂·a ₁·(1-a ₁)

(9) revise hidden layer L _BTo output layer L _CWeights:

$\left.\begin{array}{c}{\mathrm{\Δw}}_2=\mathrm{\α}\·{\mathrm{\δ}}_2\·a_1\\ w_2=w_2+{\mathrm{\Δw}}_2\end{array}\right\}$

In the formula, α is a learning rate, value between 0～1;

Revise output layer L _CThe neuron threshold value:

$\left.\begin{array}{c}{\mathrm{\Δb}}_2=\mathrm{\α}\·{\mathrm{\δ}}_2\\ b_2=b_2+{\mathrm{\Δb}}_2\end{array}\right\}$

Revise input layer L _ATo hidden layer L _BWeights:

$\left.\begin{array}{c}{\mathrm{\Δw}}_1=\mathrm{\β}\·{\mathrm{\δ}}_1\·p\\ w_1=w_1+{\mathrm{\Δw}}_1\end{array}\right\}$

In the formula, β is a learning rate, value between 0～1;

Revise hidden layer L _BThe neuron threshold value:

$\left.\begin{array}{c}{\mathrm{\Δb}}_1=\mathrm{\β}\·{\mathrm{\δ}}_1\\ b_1=b_1+{\mathrm{\Δb}}_1\end{array}\right\}$

Turned to for (4) step.

Wavelet packet analysis of the present invention is an existing mature technology.

The present invention provides a kind of new detection method for the Non-Destructive Testing of anchor pole bearing capacity, overcome the test of existing national standard (GB50086-2001, GB50007-2002) resistance to plucking and only taken a sample 5% and 10%, lack the problem of representative difference because of sample size is few, can make monitoring area reach 100%; That the present invention has is easy and simple to handle, cost is low, do not damage anchor pole, monitoring area big (can reach 100%), detection speed fast (average 5 minutes clock times), distinguishing feature that accuracy of detection is high, not only can apply to the engineering of hot work in progress, and the engineering that can finish to constructing carries out long-term position monitor, and this is that the taseometer used always detects with method for detecting drawing and hardly matches; The anchor rod ultimate bearing capacity that the present invention can be widely used in the engineerings such as natural slope, road slope, building slope, foundation, crag improvement, landslide control, country rock engineering, Tunnel Engineering, pattern foundation pit supporting structure, science of bridge building, mine detects.

Description of drawings

Fig. 1 is the detection system structure composition frame chart of the embodiment of the invention;

Fig. 2 is adopted the neural metwork training block diagram by the embodiment of the invention;

Fig. 3 is the neural network diagram that the embodiment of the invention adopted;

Fig. 4 is the error curve diagram of the anchor rod ultimate bearing capacity of the embodiment of the invention.

Embodiment

Referring to Fig. 1, a kind of lossless detection method of anchor rod ultimate bearing capacity, it is characterized in that: it is to adopt the structure dynamic testing technology to obtain information, adopt the intelligent signal analytical technology that the information of obtaining is handled, discern the detection method of anchor rod ultimate bearing capacity then by the neural network intelligent identifying system that has trained.

This method specifically comprises following steps:

(1), the stress wave generator excites and produces the top that acoustic signals acts on anchor pole to be detected;

(2), ultrasonic sensor obtains the wow flutter that returns through the anchor pole bottom reflection and surveys signal, and sends this signal to signal receiving device;

(3), signal receiving device passes the signal to microprocessor and carries out wavelet packet analysis and extract the energy feature vector;

(4), handle the neural network intelligent identifying system that the energy feature vector input obtain trained and predict, to obtain the ultimate bearing capacity value of anchor pole.

Referring to Fig. 2, above-mentioned neural network intelligent identifying system is BP (Back Propagation) network system, and its training step is as follows:

(1), foundation has input layer L _A, hidden layer L _B, output layer L _CThe neural network of three-decker;

(2), provide by input layer L _ATo hidden layer L _B, hidden layer L _BTo output layer L _CCorresponding neuronic initial weight w ₁, w ₂With initial threshold b ₁, b ₂

(3) given input vector p and desired output t;

(4) calculate hidden layer L _BThe neuronic activation value of layer:

a ₁＝f(∑w ₁·p+b ₁)

Calculate output layer L _CNeuronic activation value:

a ₂＝f(∑w ₂·a ₁+b ₂)

(5) calculate output layer L _CThe error function and the gradient thereof of neuron output:

$E=\frac{1}{2}{\mathrm{\Σe}}^2=\frac{1}{2}\mathrm{\Σ}{(t-a_2)}^2$

$\frac{\∂E}{{\∂w}_2}=-{\mathrm{\δ}}_2\·a_1,\frac{\∂E}{{\∂b}_2}=-{\mathrm{\δ}}_2$

δ ₂＝(t-a ₂)·a ₂·(1-a ₂)

(6) whether error in judgement function E satisfies | and E|＜ε, ε are the maximum error that requires, 10 ^-5＜ε＜10 ^-3, if, then:

(7), judge that whether all E satisfy | E|＜ε, ε are the maximum error that requires, 10 ^-5＜ε＜10 ^-3, if then finish;

(8) if step (6), (7) for not, then:

Calculate output layer L _CAnti-pass is to hidden layer L _BThe error function gradient:

$\frac{\∂E}{{\∂w}_1}=-{\mathrm{\δ}}_1\·p,\frac{\∂E}{{\∂b}_1}=-{\mathrm{\δ}}_1$

δ ₁＝δ ₂·w ₂·a ₁·(1-a ₁)

(9) revise hidden layer L _BTo output layer L _CWeights:

$\left.\begin{array}{c}{\mathrm{\Δw}}_2=\mathrm{\α}\·{\mathrm{\δ}}_2\·a_1\\ w_1=w_2+{\mathrm{\Δw}}_2\end{array}\right\}$

In the formula, α is a learning rate, value between 0～1;

Revise output layer L _CThe neuron threshold value:

$\left.\begin{array}{c}{\mathrm{\Δb}}_2=\mathrm{\α}\·{\mathrm{\δ}}_2\\ b_2=b_2+{\mathrm{\Δb}}_2\end{array}\right\}$

Revise input layer L _ATo hidden layer L _BWeights:

$\left.\begin{array}{c}{\mathrm{\Δw}}_1=\mathrm{\β}\·{\mathrm{\δ}}_1\·p\\ w_1=w_1+{\mathrm{\Δw}}_1\end{array}\right\}$

In the formula, β is a learning rate, value between 0～1;

Revise hidden layer L _BThe neuron threshold value:

$\left.\begin{array}{c}{\mathrm{\Δb}}_1=\mathrm{\β}\·{\mathrm{\δ}}_1\\ b_1=b_1+{\mathrm{\Δb}}_1\end{array}\right\}$

Turned to for (4) step.

Referring to Fig. 3, this Figure illustrates a BP network with a hidden layer, among the figure, p is an input vector, and R is the input number, and Q is input vector (sample), w ₁, b ₁And w ₂, b ₂Be respectively the 1st layer, the 2nd layer neuronic weights and threshold value, S ₁, S ₂Be respectively the 1st layer, the 2nd layer neuron number, a ₁And a ₂Be output vector, in this example, R=5, Q=5, S ₁=3, S ₂=1.

In the data substitution BP network with sample set, adopt the Levenberg-Marquardt optimized Algorithm, after training, network L _ALayer is to L _BWeights between each neuron of layer are as shown in table 1:

Table 1 L _ALayer is to L _BWeights between the layer neuron

L BL A	1	2	3	4	5
						1 2 3	0.3384 0.0024 1.6091	-0.007 -0.0167 0.2149	-0.0038 0.0017 0.0119	0.0101 0.015 -0.0036	0.002 0.007 -0.0191

L _BLayer is to L _CWeights between the layer neuron are: 14.255,13.902,17.128.L _BThe neuronic threshold value of layer is respectively :-0.2355,7.8415 ,-3.8519.L _CThe neuronic threshold value of layer is 13.932.During training, error criterion is 0.02, and the hands-on step number is 234.

Just have association function through the BP network after the training, can predict that concrete steps are as follows to the Engineering anchor rod ultimate bearing capacity: input needs the moving parameter of surveying of the small strain of predictive engine anchor pole; Calculate L _BEach neuronal activation value of layer; Calculate L _CThe neuronic activation value of layer.

For example have the input vector of an anchor pole to be [1.8,50,301,3400,202], the calculating of network is output as 25.16, and with the results of dead load contrast, relative error is 1.8%.

As can be seen from Figure 4: the selection of neural network prediction ability and training sample set has substantial connection, and sample set is bigger, and the parameter coverage is wideer, and then prediction effect better.

Claims (3)

1. A non-destructive testing method for the ultimate bearing capacity of a bolt, characterized in that: it adopts structural dynamic measurement technology to obtain information, adopts intelligent signal analysis technology to process the information obtained, and then intelligently recognizes through the trained neural network A detection method for predicting the ultimate bearing capacity of a bolt in a systematic manner. 2. The non-destructive testing method for the ultimate bearing capacity of a bolt according to claim 1, characterized in that: the method comprises the following steps: (1) The stress wave generator is excited to generate an acoustic wave signal that acts on the top of the bolt to be detected; (2) The ultrasonic sensor obtains the acoustic pulse dynamic measurement signal reflected by the bottom of the bolt, and transmits the signal to the signal receiving device; (3), the signal receiving device transmits the signal to the microprocessor for wavelet packet analysis to extract the energy feature vector; (4) The processed energy eigenvectors are input into the trained neural network intelligent recognition system for prediction, so as to obtain the ultimate bearing capacity value of the bolt. 3. The non-destructive testing method of the ultimate bearing capacity of a bolt as claimed in claim 1 or 2, characterized in that: said neural network intelligent identification system is a BP (Back Propagation) network system, and its training steps are as follows: (1), establish a neural network with a three-layer structure of input layer L _A , hidden layer L _B , and output layer L _C ; (2), giving the initial weights w ₁ , w ₂ and initial thresholds b 1 , _{b 2} of the corresponding neurons from the input layer L _A to the hidden layer L _B , from the hidden layer L _B to the output layer L _C ; (3) given input vector p and expected output t; (4) Calculate the activation value of neurons in the hidden layer L _B layer: a ₁ ＝f(∑w ₁ ·p+b ₁ ) Calculate the activation values of the output layer _LC neurons: a ₂ ＝f(∑w ₂ ·a ₁ +b ₂ ) (5) Calculate the error function and its gradient of output layer _LC neuron output: $\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$ $\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; E.</span>}}{<span\; class="notranslate">\; \&PartialD;</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; E.</span>}}{<span\; class="notranslate">\; \&PartialD;</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}$ δ ₂ =(ta ₂ )·a ₂ ·(1-a ₂ ) (6) Determine whether the error function E satisfies |E|<ε, ε is the maximum error required, 10 ^-5 <ε<10 ^-3 , if yes, then: (7) Determine whether all Es meet |E|<ε, ε is the maximum error required, 10 ^-5 <ε<10 ^-3 , if yes, end; (8), if steps (6), (7) are no, then: Calculate the gradient of the error function from the output layer L _C back to the hidden layer L _B : $\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; E.</span>}}{<span\; class="notranslate">\; \&PartialD;</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; ,</span>\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; E.</span>}}{<span\; class="notranslate">\; \&PartialD;</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}$ δ ₁ = δ ₂ ·w ₂ ·a ₁ ·(1-a ₁ ) (9) Modify the weights from the hidden layer L _B to the output layer L _C : $\left.\begin{array}{c}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right\}$ In the formula, α is the learning rate, which takes a value between 0 and 1; Correct the output layer _LC neuron threshold: $\left.\begin{array}{c}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right\}$ Correct the weights from the input layer L _A to the hidden layer L _B : $\left.\begin{array}{c}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; p</span>}\\ {\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\end{array}\right\}$ In the formula, β is the learning rate, which takes a value between 0 and 1; Modify the hidden layer L _B neuron threshold: $\left.\begin{array}{c}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\end{array}\right\}$ Turn to step (4).

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