CN104200269A - Real-time fault diagnosis method based on online learning minimum embedding dimension network - Google Patents

Abstract

The invention provides a real-time fault diagnosis method based on an online learning minimum embedding dimension network. The method includes determining a minimum embedding dimension number of a time sequence based on a neural network; performing normalized processing on network input samples, and reconstructing network input and output sample values according to the time sequence; training a learning network online, and adjusting the network structure dynamically; performing anti-normalized calculation on the output results of the learning network, figuring out the difference between the output value and an actual observation value, comparing the difference with a set detection threshold, and achieving the purpose of fault diagnosis. The method has the advantages that a node increasing rule and a simplification rule are added in the network online learning process, the activation of the neurons is judged according to the maximum output of a hidden layer in the process of increasing, a slide window is added in the simplification process, the error simplification is avoided, the network online adjustment is only performed on the neurons with large response, the network calculation quantity is reduced, and the instantaneity of fault diagnosis is improved.

Description

A kind of based on the minimum real-time fault diagnosis method that embeds dimension network of on-line study

Technical field

The present invention relates to fault diagnosis field, be specifically related to a kind of based on the minimum real-time fault diagnosis method that embeds dimension network of on-line study.

Background technology

Along with the further raising that security of system is required, people wish to work as when system breaks down can provide fault detect and isolation information automatically, and system degradation trend is judged, to avoid fault further expand and propagate.Like this, just can there is time enough to take reliable measure to prevent that fault from occurring, and avoids unnecessary loss.

Fault diagnosis is the gordian technique that strengthens system reliability, and the real-time that improves fault diagnosis is the key factor of this technology.Existing fault diagnosis technology can be divided into two classes: first kind method is mainly based on seasonal effect in time series method, according to the variation tendency of system past and present status, the further state of development of estimating system, see with actual detected value calculated difference the threshold value that whether reaches fault, thereby judgement removes system, whether break down; Equations of The Second Kind method is the method based on qualitative analysis, according to the Qualitative Knowledge of system, carries out analysis ratiocination, thereby realizes fault diagnosis.

Time Series Method is regarded data as a sequence of arranging by chronological order, and sets up matching seasonal effect in time series mathematical model by the correlativity between adjacent data.At present, conventional Time Series Method mainly contains two kinds: a kind of is parameter model, first supposes that temporal data model meets some requirements, then through the estimation of model parameter is obtained to corresponding output valve.If the model of supposing and realistic model are variant, it is poor that diagnosis performance can become, and this method is to carry out fitting data sequence with linear model, and therefore it is not suitable for nonlinear system in essence.Another kind is non-parametric model method, and it does not need the accurate mathematical model of system, and application is comparatively extensive.

In various non-parametric model methods, neural net method, owing to not needing to set up in advance the mathematical model of reflection system physics law, therefore has extremely strong non-linear mapping capability, and it is used widely in fault diagnosis.At present, comprise that the multiple neural network structures such as BP network, RBF network, recurrent neural networks have all obtained application in time series analysis.But, utilize neural network must pass through the process of off-line training and cannot realize online training time series modeling, therefore network lacks the ability of study to the variation of sequence, and the measured deviation of sequence, uncertain disturbance etc. all can cause network generalization to decline.MRAN (Minimal Resource Allocating Network) learning algorithm has added the condition of simplifying, those are removed the smaller node of network output contribution, but ought not satisfy condition, need to adjust selected all hidden layers center and weights, until meet certain error requirements.When selected hidden node is many, this adjustment process calculated amount is larger, more consuming time.Especially each state of failure system is in the early stage constantly variation of fault, and the diagnostic network of off-line training is also difficult to meet the requirement of real-time.

Summary of the invention

While the object of the invention is to reduce system, become the calculated amount of status fault diagnostic method, improve real-time and the accuracy of fault diagnosis.

According to technical scheme provided by the invention, described a kind of real-time fault diagnosis method based on the minimum embedding dimension of on-line study network comprises the steps:

1) first step: determine the minimum dimension that embeds of time series based on neural network.Nonlinear Time Series x (t) | x (t) ∈ R ¹, t=0,1...L, it in T predicted value is constantly:

Y(T+1)＝f(X(T)) (1)

Wherein, X (T)=[x (T), x (T-1) ... x (T-p)], L ∈ Z ⁺, represent whole length of time series, p ∈ Z ⁺, representing the embedding dimension, Y (T+1) is T predicted value constantly.Based on neural network, to time series modeling, can obtain:

$\hat{x}(T+1)=\hat{f}(x\left(T\right),x(T-1),...,x(T-p))---\left(2\right)$

Target is to make approach as far as possible x (T+1).

According to embedding dimension theorem, neighbour's data are at the p dimension reconstruction attractor 2 near points of giving an example, still very near in p+1 dimension reconstruction attractor, otherwise are exactly pseudo-neighbour.The minimum dimension time series that embeds requires not have pseudo-neighbour's data.By judgement a (i, p), whether surpass set-point and judge whether these data are pseudo-adjacent

$a(i,p)=\frac{|x_{i+p}-x_{n(i,p)+p}|}{\left|\right|y_i\left(p\right)-y_{n(i,p)}\left(p\right)\left|\right|}---\left(3\right)$

For avoiding the impact of a (i, p) initial value and signal skew, definition:

$E\left(p\right)=\frac{1}{N-p}\underset{i=1}{\overset{N-p}{\mathrm{\Σ}}}a(i,p)---\left(4\right)$

E (p) represents the mean value of all a (i, p), and the E here (p) only relies on and embeds dimension p.When dimension changes from p to p+1, definition:

E ₁(p)＝E(p+1)/E(p) (5)

If work as p>p ₀time, E ₁(p) just no longer change p ₀+ 1 is exactly the embedding dimension of required time series network.

2) second step: network input sample is normalized, and according to time series reconstructed network input and output sample value.For Nonlinear Time Series value x (1), x (2) ..., x (m), utilizes formula

$x^{\′}\left(i\right)=\frac{x\left(i\right)-x_{\min }}{x_{\max }-x_{\min }},(i=\mathrm{1,2}\·\·\·m)---\left(6\right)$

By data normalization, x wherein _max, x _minthe maximal value and the minimum value that represent whole time series data.

According to the minimum dimension p that embeds of definite network, by the time series x'(1 after normalization), x'(2) ... x'(m) be reconstructed, form the input and output sample pair of neural network, by x'(1), x'(2) ... x'(m) be divided into k group, every group has p+1, front p value inputted the input of node, a rear expectation value as learning network output node as learning network.

3) the 3rd step: online training study network, dynamically adjust network structure.Select the output of RBF network calculations

$f\left(X_i\right)=w_0+\underset{k=1}{\overset{k=K}{\mathrm{\Σ}}}{w}_k{\mathrm{\φ}}_k\left(X_i\right)---\left(7\right)$

X wherein _i=[x ₁... x _n] ∈ R ⁿfor network input, f (X _i) ∈ R is the output of corresponding network, w _kthe output that is k hidden node connects weights, w ₀for output offset constant, be the action function of hidden node, radial basis function is elected Gaussian type as:

${\mathrm{\φ}}_k\left(X_i\right)=\exp (-\frac{1}{{\mathrm{\σ}}_k^2}{\left|\right|X_i-u_k\left|\right|}^2)---\left(8\right)$

U _k∈ R ⁿfor existing data center, σ _kexpansion constant for this RBF function.

When on-line study neural network starts, without Hidden unit, network dynamically determines whether in learning process need to be by input X _iincrease to Hidden unit, increase criterion is:

|e _i|＝Y _i-f(X _i)>e _min (9)

${\mathrm{\&beta;}}_{\max }=\underset{k}{\mathrm{Max}}\left({\mathrm{\&phi;}}_k\right)<e_{\mathrm{tn}}---\left(10\right)$

If network output f is (X _i) and desired value Y _ibetween error enough large, according to formula (9), to add hidden neuron, e _minrepresentative expectation approximation accuracy.Input X for formula (10) _ieffect lower network neuron output φ _krepresent k neuronic activity.

The initial e of algorithm _tn=ξ _max, e _tnby exponential law, successively decrease, the hidden node parameter newly increasing by criterion is:

w _k+1＝e _n

u _k+1＝X _n (11)

σ _k+1＝ν‖X _n-u _nr‖

Wherein ν is iteration factor, u _nrbe and input sample X _nnearest central point.

If sample (X _i, Y _i) do not meet and increase neuronic criterion condition, just need to utilize gradient descent method to center u _k, expansion constant σ _k, weight w _kadjust.The real-time of adjusting for improving network, N neuron parameter of Zhi Dui center and sample close together adjusted:

$\begin{array}{c}{\mathrm{\&Delta;u}}_k=-\frac{\&PartialD;E}{{\&PartialD;u}_k}=-\frac{\&PartialD;E}{\&PartialD;f\left(X_i\right)}\frac{\&PartialD;f\left(X_i\right)}{\&PartialD;{\mathrm{\&phi;}}_k}\frac{\&PartialD;{\mathrm{\&phi;}}_k}{\&PartialD;u_k}\\ =(Y_i-f\left(X_i\right))w_k\left[2(X_i-u_k)\exp (-\frac{1}{{\mathrm{\&sigma;}}_k^2}{\left|\right|X_i-u_k\left|\right|}^2)\frac{1}{{\mathrm{\&sigma;}}_k^2}\right]\end{array}---\left(12\right)$

u _k＝u _k+ηΔu _k (13)

$\begin{array}{c}{\mathrm{\&Delta;\&sigma;}}_k=-\frac{\&PartialD;E}{{\&PartialD;\mathrm{\&sigma;}}_k}=-\frac{\&PartialD;E}{\&PartialD;f\left(X_i\right)}\frac{\&PartialD;f\left(X_i\right)}{\&PartialD;{\mathrm{\&phi;}}_k}\frac{\&PartialD;{\mathrm{\&phi;}}_k}{\&PartialD;{\mathrm{\&sigma;}}_k}\\ =(Y_i-f\left(X_i\right))w_k\left[2{\left|\right|X_i-u_k\left|\right|}^2\exp (-\frac{1}{{\mathrm{\&sigma;}}_k^2}{\left|\right|X_i-u_k\left|\right|}^2)\frac{1}{{\mathrm{\&sigma;}}_k^3}\right]\end{array}---\left(14\right)$

σ _k＝σ _k+ηΔσ _k (15)

${\mathrm{\&Delta;w}}_k=-\frac{\&PartialD;E}{{\&PartialD;w}_k}=-\frac{\&PartialD;E}{\&PartialD;f\left(X_i\right)}\frac{\&PartialD;f\left(X_i\right)}{\&PartialD;w_k}=(Y_i-f\left(X_i\right)){\mathrm{\&phi;}}_k---\left(16\right)$

w _k＝w _k+ηΔw _k (17)

Wherein η is learning rate, k=1 ..., N,

For simplifying as far as possible network structure, improve on-line study speed, the relatively little hidden node of neural network output contribution is removed from learning network, principle is that this removing will not affect the performance of overall network.Calculate each sample to (X _i, Y _i) output of hidden node

${\mathrm{\&sigma;}}_k^i=w_k\exp (-\frac{1}{{\mathrm{\&sigma;}}_k^2}{\left|\right|X_i-u_k\left|\right|}^2)---\left(18\right)$

Obtain maximum hidden node output and be standardized as:

${\mathrm{\&lambda;}}_k^i=\left|\frac{o^i}{o_{\max }}\right|(k=1,\&CenterDot;\&CenterDot;\&CenterDot;K)---\left(19\right)$

If met remove k hidden node.

4) the 4th step: the output of renormalization network, and relatively realize fault diagnosis according to threshold value.The Output rusults of learning network is carried out to renormalization computing

$\hat{f}\left(X_i\right)=x_{\min }+(x_{\max }-x_{\min })f\left(X_i\right)---\left(20\right)$

The input sample new to each, utilize the Time Series Method of on-line study network of the present invention, dynamically adjust network hidden node number, after position and weights, obtain learning network output, ask for the difference between output valve and actual observed value, then by this difference, compare with the detection threshold of setting, realize the object of fault diagnosis.

The invention has the beneficial effects as follows:

1) described a kind of based on the minimum real-time fault diagnosis method that embeds dimension network of on-line study, in network design process, combining node increases criterion and contributes the relatively little criterion of simplifying based on network is exported, in increase process, utilize the neuronic activity of maximum output judgement of hidden layer, simplify in process and added moving window, avoided simplifying by mistake.

2) described a kind of based on the minimum real-time fault diagnosis method that embeds dimension network of on-line study, the online adjustment process of network is only carried out compared with large neuron output response ratio, has greatly reduced network calculations amount, has improved the real-time of fault diagnosis.

3) described a kind of based on the minimum real-time fault diagnosis method that embeds dimension network of on-line study, network dimensionality does not need to provide a large amount of subjective parameters, has improved accuracy, asks in process restricted little to the number of needed sample.

Accompanying drawing explanation

Fig. 1 is on-line study neural network real-time fault diagnosis algorithm flow chart

Embodiment

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described further.

As shown in Figure 1, when on-line fault diagnosis method of the present invention is carried out fault judgement to real application systems, its on-line learning algorithm is obviously better than batch processing learning algorithm.At every turn, when processing new data, do not need again to train, improved real-time and diagnostic accuracy, and on-line study limits without any priori the number of training sample, the requirement of realistic application.

Choose the tank reactor of continuous stirring as the invention process case, utilize and set forth fault diagnosis algorithm of the present invention.Tank reactor model description is:

$\frac{d{C}_A}{\mathrm{dt}}=\frac{q}{V}(C_{\mathrm{Af}}-C_A)-k_0\exp (-\frac{E}{\mathrm{RT}})C_A---\left(21\right)$

$\frac{\mathrm{dT}}{\mathrm{dt}}=\frac{q}{V}(T_f-T)+\frac{-\mathrm{\&Delta;H}}{\mathrm{\&rho;}{C}_P}{k}_0\exp (-\frac{E}{\mathrm{RT}})C_A+\frac{\mathrm{UA}}{\mathrm{V\&rho;}{C}_P}(T_c-T)---\left(22\right)$

In above-mentioned model, q is time-varying parameter, the method that adopts parameter and state joint to estimate, and using q as extended mode, state variable is defined as x=[x ₁, x ₂, x ₃]=[C _a, T, q] ^t, controlled quentity controlled variable u=T _c, output variable y=[y ₁, y ₂] ^t=[C _a, T] ^t, the object of reactor control law is to carry out the tracking of concentration set point.Adopt Euler's discrete method that discretize is carried out in formula (21), (22), and be x according to original state ₁(0)=0.2 mol/L, x ₂(0)=400 open, x ₃(0)=100 liters/min, sampling time interval dt=0.2 divides and in computing machine, represents tank reactor model.

When tank reactor system is from k=100, charging flow velocity q index curve declines:

$q\left(k\right)=q\left(100\right)+1-\exp \left(\frac{k-100}{80}\right)---\left(23\right)$

Hope can be by reaction density C _athe Neural Network Online learning algorithm designing by the present invention with temperature of reaction T calculates, and compares with system concentration, temperature under normal circumstances, if its difference surpasses certain threshold value, thinks that system breaks down.

First according to definite method of minimum embedding dimension, determine respectively temperature of reaction T and reaction density C _aminimum embed dimension, in computing machine, according to formula (21), (22), construct successively reaction density C _atime series with temperature of reaction T.

To reaction density C _atime series solve, calculate E _con(p), can obtain E _con(1)=2.0932, E _con(2)=1.0705, E _con(3)=1.0514, E _con(4)=1.0469.Due to | E _con(3)-E _con(4) |=0.0045<0.005, so corresponding embedding dimension p=4; The embedding dimension of trying to achieve equally temperature of reaction T is also 4.

Secondly, according to the minimum of trying to achieve, embed dimension, reconstruct temperature of reaction T and reaction density C _atime series, when the input data of on-line study network are x'(1), x'(2),, x'(p), x'(2), x'(3) ..., x'(p+1) and x'(k), x'(k+1),, in the time of x'(k+p-1), the desired output of map network is x'(p+1), x'(p+2) and x'(k+p), and then obtain the real-time training sample pair of neural network.

Utilize fixed training sample to the on-line learning algorithm proposing with the present invention respectively to temperature of reaction T and reaction density C _atrain, obtain network center, the parameters such as weights, computational grid output f (X _i), X wherein _i=(x'(i), x'(i+1) ..., x'(i+p-1)).When on-line learning algorithm is initial, e _tn=ξ _max, e _tnby exponential law, successively decrease, e _tn=max{ ξ _maxγ ⁿ, ζ _min, 0< γ <1 is constant, with the flatness that guarantees that network approaches, wherein ξ _maxand ζ _minit is the initial parameter of selecting.For the condition of simplifying in further limiting network on-line study process, avoid simplifying fault, affect the accuracy of network output, in the process of simplifying, add moving window, work as m continuous sample standard deviation establishment just carried out to network and simplify, wherein M is selectable data window length.

Finally to network output renormalization, computing obtains: and then ask for the learning network calculating output valve of temperature and concentration and the difference between actual observed value, and ask for the difference between output valve and actual observed value, then by this difference, compare with the detection threshold of setting, realize the object of fault diagnosis.

Above-described embodiment is only for example of the present invention is clearly described, and be not the restriction to embodiments of the present invention, for those of ordinary skill in the field, can also make other changes in different forms on the basis of the above description.

Claims (1)

1. based on the minimum real-time fault diagnosis method that embeds dimension network of on-line study, its feature comprises: determine the minimum dimension that embeds of time series based on neural network; Network input sample is normalized, and according to time series reconstructed network input and output sample value; Online training study network, dynamically adjusts network structure; The Output rusults of learning network is carried out to renormalization computing, ask for the difference between output valve and actual observed value, then by this difference, compare with the detection threshold of setting, realize the object of fault diagnosis.

1) first step: determine the minimum dimension that embeds of time series based on neural network.Nonlinear Time Series x (t) | x (t) ∈ R ¹, t=0,1...L, it in T predicted value is constantly:

Y(T+1)＝f(X(T)) (1)

Wherein, X (T)=[x (T), x (T-1) ... x (T-p)], L ∈ Z ⁺, represent whole length of time series, p ∈ Z ⁺, representing the embedding dimension, Y (T+1) is T predicted value constantly.Based on neural network, to time series modeling, can obtain:

$\hat{x}(T+1)=\hat{f}(x\left(T\right),x(T-1),...,x(T-p))---\left(2\right)$

Target is to make approach as far as possible x (T+1).

According to embedding dimension theorem, neighbour's data are at the p dimension reconstruction attractor 2 near points of giving an example, still very near in p+1 dimension reconstruction attractor, otherwise are exactly pseudo-neighbour.The minimum dimension time series that embeds requires not have pseudo-neighbour's data.By judgement a (i, p), whether surpass set-point and judge whether these data are pseudo-adjacent

$a(i,p)=\frac{|x_{i+p}-x_{n(i,p)+p}|}{\left|\right|y_i\left(p\right)-y_{n(i,p)}\left(p\right)\left|\right|}---\left(3\right)$

For avoiding the impact of a (i, p) initial value and signal skew, definition:

$E\left(p\right)=\frac{1}{N-p}\underset{i=1}{\overset{N-p}{\mathrm{\&Sigma;}}}a(i,p)---\left(4\right)$

E (p) represents the mean value of all a (i, p), and the E here (p) only relies on and embeds dimension p.When dimension changes from p to p+1, definition:

E ₁(p)＝E(p+1)/E(p) (5)

If work as p>p ₀time, E ₁(p) just no longer change p ₀+ 1 is exactly the embedding dimension of required time series network.

2) second step: network input sample is normalized, and according to time series reconstructed network input and output sample value.For Nonlinear Time Series value x (1), x (2) ..., x (m), utilizes formula

$x^{\&prime;}\left(i\right)=\frac{x\left(i\right)-x_{\min }}{x_{\max }-x_{\min }},(i=\mathrm{1,2}\&CenterDot;\&CenterDot;\&CenterDot;m)---\left(6\right)$ By data normalization, x wherein _max, x _minthe maximal value and the minimum value that represent whole time series data.

According to the minimum dimension p that embeds of definite network, by the time series x'(1 after normalization), x'(2) ... x'(m) be reconstructed, form the input and output sample pair of neural network, by x'(1), x'(2) ... x'(m) be divided into k group, every group has p+1, front p value inputted the input of node, a rear expectation value as learning network output node as learning network.

3) the 3rd step: online training study network, dynamically adjust network structure.Select the output of RBF network calculations

$f\left(X_i\right)=w_0+\underset{k=1}{\overset{k=K}{\mathrm{\&Sigma;}}}{w}_k{\mathrm{\&phi;}}_k\left(X_i\right)---\left(7\right)$

X wherein _i=[x ₁... x _n] ∈ R ⁿfor network input, f (X _i) ∈ R is the output of corresponding network, w _kthe output that is k hidden node connects weights, w ₀for output offset constant, be the action function of hidden node, radial basis function is elected Gaussian type as:

${\mathrm{\&phi;}}_k\left(X_i\right)=\exp (-\frac{1}{{\mathrm{\&sigma;}}_k^2}{\left|\right|X_i-u_k\left|\right|}^2)---\left(8\right)$

U _k∈ R ⁿfor existing data center, σ _kexpansion constant for this RBF function.

When on-line study neural network starts, without Hidden unit, network dynamically determines whether input Xi to be increased to Hidden unit in learning process, increases criterion and is:

|e _i|＝|Y _i-f(X _i)|>e _min (9)

${\mathrm{\&beta;}}_{\max }=\underset{k}{\mathrm{Max}}\left({\mathrm{\&phi;}}_k\right)<e_{\mathrm{tn}}---\left(10\right)$

If network output f is (X _i) and desired value Y _ibetween error enough large, according to formula (9), to add hidden neuron, e _minrepresentative expectation approximation accuracy.Input X for formula (10) _ieffect lower network neuron output φ _krepresent k neuronic activity.

The initial e of algorithm _tn=ξ _max, e _tnby exponential law, successively decrease, the hidden node parameter newly increasing by criterion is:

w _k+1＝e _n

u _k+1＝X _n (11)

σ _k+1＝ν‖X _n-u _nr‖

Wherein ν is iteration factor, u _nrbe and input sample X _nnearest central point.

If sample (X _i, Y _i) do not meet and increase neuronic criterion condition, just need to utilize gradient descent method to center u _k, expansion constant σ _k, weight w _kadjust.The real-time of adjusting for improving network, N neuron parameter of Zhi Dui center and sample close together adjusted:

$\begin{array}{c}{\mathrm{\&Delta;u}}_k=-\frac{\&PartialD;E}{{\&PartialD;u}_k}=-\frac{\&PartialD;E}{\&PartialD;f\left(X_i\right)}\frac{\&PartialD;f\left(X_i\right)}{\&PartialD;{\mathrm{\&phi;}}_k}\frac{\&PartialD;{\mathrm{\&phi;}}_k}{\&PartialD;u_k}\\ =(Y_i-f\left(X_i\right))w_k\left[2(X_i-u_k)\exp (-\frac{1}{{\mathrm{\&sigma;}}_k^2}{\left|\right|X_i-u_k\left|\right|}^2)\frac{1}{{\mathrm{\&sigma;}}_k^2}\right]\end{array}---\left(12\right)$

u _k＝u _k+ηΔu _k (13)

$\begin{array}{c}{\mathrm{\&Delta;\&sigma;}}_k=-\frac{\&PartialD;E}{{\&PartialD;\mathrm{\&sigma;}}_k}=-\frac{\&PartialD;E}{\&PartialD;f\left(X_i\right)}\frac{\&PartialD;f\left(X_i\right)}{\&PartialD;{\mathrm{\&phi;}}_k}\frac{\&PartialD;{\mathrm{\&phi;}}_k}{\&PartialD;{\mathrm{\&sigma;}}_k}\\ =(Y_i-f\left(X_i\right))w_k\left[2{\left|\right|X_i-u_k\left|\right|}^2\exp (-\frac{1}{{\mathrm{\&sigma;}}_k^2}{\left|\right|X_i-u_k\left|\right|}^2)\frac{1}{{\mathrm{\&sigma;}}_k^3}\right]\end{array}---\left(14\right)$

σ _k＝σ _k+ηΔσ _k (15)

${\mathrm{\&Delta;w}}_k=-\frac{\&PartialD;E}{{\&PartialD;w}_k}=-\frac{\&PartialD;E}{\&PartialD;f\left(X_i\right)}\frac{\&PartialD;f\left(X_i\right)}{\&PartialD;w_k}=(Y_i-f\left(X_i\right)){\mathrm{\&phi;}}_k---\left(16\right)$

w _k＝w _k+ηΔw _k (17)

Wherein η is learning rate, k=1 ..., N,

For simplifying as far as possible network structure, improve on-line study speed, the relatively little hidden node of neural network output contribution is removed from learning network, principle is that this removing will not affect the performance of overall network.Calculate each sample to (X _i, Y _i) output of hidden node

${\mathrm{\&sigma;}}_k^i=w_k\exp (-\frac{1}{{\mathrm{\&sigma;}}_k^2}{\left|\right|X_i-u_k\left|\right|}^2)---\left(18\right)$

Obtain maximum hidden node output and be standardized as:

${\mathrm{\&lambda;}}_k^i=\left|\frac{o^i}{o_{\max }}\right|(k=1,\&CenterDot;\&CenterDot;\&CenterDot;K)---\left(19\right)$

If met remove k hidden node.

4) the 4th step: the output of renormalization network, and relatively realize fault diagnosis according to threshold value.The Output rusults of learning network is carried out to renormalization computing

$\hat{f}\left(X_i\right)=x_{\min }+(x_{\max }-x_{\min })f\left(X_i\right)---\left(20\right)$

The input sample new to each, utilize the Time Series Method of on-line study network of the present invention, dynamically adjust network hidden node number, after position and weights, obtain learning network output, ask for the difference between output valve and actual observed value, then by this difference, compare with the detection threshold of setting, realize the object of fault diagnosis.