CN104537417A - Fault diagnosis method for optimizing feedforward neural network observer on basis of convex combination algorithm - Google Patents

Abstract

The invention discloses a fault diagnosis method for optimizing a single-hidden-layer feedforward neural network on the basis of a convex combination algorithm. The method is used for intelligent fault diagnosis. According to the method, the single-hidden-layer feedforward neural network is optimized by means of the convex combination algorithm, and a weight is updated through iteration to adjust information of a hidden layer. Meanwhile, a new error function is introduced to evaluate error performance. The function is used for solving optimization parameters by decoupling the weight, and parameter calculation speed is increased. Meanwhile, a state observer of the neural network is built and used for observing a nonlinear system abstracted from engineering, system output prediction of the next step is carried out by means of the output value of the state observer, and accordingly system fault diagnosis and detection can be achieved.

Description

The method for diagnosing faults of feedforward neural network observer is optimized based on Frank-Wolfe algorithm

Technical field

The present invention relates to the method for diagnosing faults of neural network, specifically relate to a kind of method for diagnosing faults optimizing feedforward neural network viewer based on Frank-Wolfe algorithm, it belongs to mode identification technology.

Background technology

The development of fault diagnosis technology mainly experienced by the three phases such as Artificial Diagnosis, modern diagnosis and intelligent diagnostics.Be developed so far, method for diagnosing faults can be divided into the method based on analytic model, the method based on signal transacting and Knowledge based engineering method etc.Along with the development of science and technology, systems grow is complicated, simple dependence can not meet the reliability requirement of equipment based on the conventional fault diagnosis method of mathematical model, therefore Intelligent Fault Diagnosis Technique more and more obtains the great attention in each field, especially in control field, as the control annual meeting of the U.S., the control of IEEE and decision making meeting, International Federation of Automatic Control (IFAC) etc., all Intelligent Fault Diagnosis Technique is classified as important discussion special topic.Because it is more suitable for the development of modern science and technology, the Theories and methods in contemporary front line science also must penetrate in Intelligent Fault Diagnosis Technique, as neural network theory and particle filter etc.In recent years, all kinds of intelligent failure diagnosis method is obtained for and develops fast, such as, based on diagnostic techniquess such as neural network, neural network Adaptive Observer and support vector machine.Wherein neural network realizes Nonlinear Mapping relation complicated between fault and sign by study for the connection weight expressing fault diagnosis knowledge.

Owing to having some following advantage, in recent years, intelligent failure diagnosis method is subject to the favor of Fault diagnosis expert and scholar day by day.

(1) mathematical models of object is not needed.

(2) knowledge and experience of diagnostician can be effectively utilized, collect numerous expertise to the random diagnosing malfunction occurred.

(3) there is the inferential capability as diagnostician, automatically realize the mapping from failure symptom to failure cause.

(4) there is certain associative ability and antijamming capability, possess study mechanism, diagnostic knowledge can be obtained from the diagnosis example in past.

(5) to diagnostic result, there is interpretability.

Expert system, neural network, fuzzy theory, rough set theory, Data-Fusion theory, wavelet theory, fault tree and they each other with the main manifestations method that the fusion of they and out of Memory treatment technology is artificial intelligence means, in diagnostic field, they are paid attention to more and more widely.

(1) expert system diagnosis methods: primarily of part compositions such as knowledge base, database, inference machine, interpreter, failure symptom acquisition and man-machine interactions.Mainly on the basis of expert knowledge library, database, carry out fault diagnosis by the knowledge in inference machine comprehensive utilization knowledge base according to certain inference method.Expert system has had practical application in fields such as Aero-Space, chemical industry, nuclear industry, and brings huge social and economic benefits.

(2) Neural Network Diagnosis Method: because neural network has very strong non-linear mapping capability, can relation exactly between the failure symptom of Simulation of Complex equipment and failure cause, and there is parallel processing capability, self-learning capability and memory capability, because being successfully applied to fault diagnosis field.Fault diagnosis based on neural network has been applied to multiple field such as industry, national defence.

(3) fuzzy diagnosis method: fault diagnosis carrys out judgment device state by the relation between research fault and sign.Due to the complicacy of practical factor, be difficult between fault and sign represent by accurate mathematical model, simply can not represent with " having " and "None", and require to the possibility of generation of being out of order, abort situation and degree.Problems fuzzy logic can solve preferably.Fuzzy logic diagnostic method can overcome the difficulty brought due to the uncertainty of process itself, inexactness and noise etc., and calculating is simple, application is convenient, thus process complication system large dead time, time become and non-linear in, demonstrate its superiority.The application of fuzzy logic in fault diagnosis is combined with additive method, mostly as fuzzy neural network, fuzzy expert system etc.

(4) rough set diagnostic method: rough set theory is the method for thought based on indistinguishability and knowledge expression simplification, keeping under the prerequisite that classification capacity is constant, by Reduction of Knowledge, from data, inference logic rule is as the model of knowledge system.It has been given a definition ambiguity and probabilistic concept in the meaning of classification.Utilize rough set theory to carry out Fault Tree Diagnosis Decision table to system and carry out yojan process, the redundancy of the various fault signature inherence of interpre(ta)tive system, for system fault diagnosis provides new effective way.

(5) diagnosing information fusion fault method: information fusion technology utilizes multi-source information, to obtain the informix treatment technology of more objective, the more essential understanding to same thing or target.It refers to means collections such as utilizing multisensor and integrated various information source, multimedia and multi-format information, the information such as such as electric signal, temperature, image, electromagnetic radiation, thus generate complete, accurate, timely and effective integrated information, then carry out fault diagnosis according to certain judgment rule.Information fusion technology is widely used at present in military field.At present, data fusion method for diagnosing faults mainly contains Bayes reasoning, D-S evidential reasoning and neural Network Data Fusion etc.

In recent years, although intelligent trouble diagnosis algorithm progress is fast, a lot of intelligent method is suggested, and still there are some problems:

(1) knowledge base is huge.Current Intelligent Fault Diagnose Systems adopts production rule to represent the experimental knowledge of expert mostly, in order to the target making diagnostic system reach efficient, practical, a large amount of expertises must be needed to form huge knowledge base.The diagnostic system of main equipment, corresponding knowledge base is huger, and this gives the arrangement of knowledge base, calling of knowledge rule brings adverse effect.

(2) dark, shallow knowledge binding ability is poor.In concrete intelligent diagnosis system, when the ultimate principle and expertise that realize certain field combine, ability is poor.Some depth knowledge are good not in compatibility, are difficult to realize unification in same knowledge base.

(3) system update ability.The ability that system shows in automatic acquisition knowledge is also poor, although add the function of some Machine self-learning, is difficult to be in operation discovery and creating knowledge.Although neural network can alleviate this contradiction, require a large amount of training samples and be difficult to obtain, and along with the upgrading of diagnosis object, whole neural network theory wants re-training.

(4) fault sample is difficult to obtain.Along with the raising of automatization level and the develop rapidly of computing machine, for most of equipment, a large amount of normal data of reflection equipment running status easily obtain, and the acquisition of fault data is more difficult.

Summary of the invention

The object of the present invention is to provide a kind of method for diagnosing faults optimizing feedforward neural network observer based on Frank-Wolfe algorithm, to solve the problem such as calculation of complex in feedforward neural network method for diagnosing faults, the method is by obtaining required weights to the decoupling zero of network parameter and iteration, the calculating of derivative is not introduced in process, thus enormously simplify the calculating of network, improve counting yield, providing new method for providing detection efficiency and degree of accuracy.

For achieving the above object, the method for diagnosing faults optimizing feedforward neural network observer based on Frank-Wolfe algorithm provided by the invention, key step is as follows:

1) sample input and the sample of, choosing sample system export;

2), the sample of sample system input input feedforward neural network observer is obtained estimating to export;

3), obtain estimating that exporting residual error is according to estimation output and actual output:

$e_y\left(t\right)=y\left(t\right)-\hat{y}\left(t\right)$

In formula, y (t) represents that sample exports, represent and estimate to export;

If estimation of error function is

In formula, U is weighting diagonal matrix; Its fault detect rule is:

Wherein, T is the threshold value of fault detect.

Described feedforward neural network observer is that its optimizing process is as follows based on Frank-Wolfe algorithm optimization neural network observer:

1) the single hidden layer feedforward neural network of structure, is formed;

(1) input value and the input value of n fault of nonlinear system sample, is obtained; Hidden layer neuron number h is selected according to input value output valve;

(2), initialization cluster centre and weight matrix select the initial cluster center that h value is different;

(3), calculate the distance of n sample input value and initial cluster center, its formula is:

||x _i-c _j||＝(x _i-c _j) ^T(x _i-c _j)，i＝1,2,...,n,j＝1,2,...,h

(4), utilize fuzzy C-means clustering determination cluster centre, complete single hidden layer feedforward neural network;

2) Frank-Wolfe algorithm optimization list hidden layer feedforward neural network, is adopted;

(1), defining error function E is:

In formula, V ⁺for the pseudoinverse of weight matrix V, W=[w _ij] _{p × n}for input layer is to the weight matrix of hidden layer, d _irepresent desired output, h _ifor the basis function of single hidden layer feedforward neural network;

In order to find suitable V ^{+ *}, W ^*make E (V ^{+ *}, W ^*)=0, asks error function to the partial derivative of weight matrix

$\frac{\∂E}{\∂V^{+}}=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}(V^{+}{d}_i-h_i)d_i^T$

Order $\∂E/\∂V^{+}=0,$ Can obtain

V ^+*＝HD ^T(DD ^T) ^-1

In formula, H=[h ₁, h ₂..., h _n] _{p × n}, D=[d ₁, d ₂..., d _n] _{m × n};

(2) for sample input and desired output (x _i, d _i) and arbitrary initial cluster centre and weight matrix x is input vector matrix, then

Definition

$Z_k=V_k^{+}D$

In formula, k is iterations;

Then

$Z_0=V_0^{+}D$

If Z ₀=H ₀, then error is 0;

Otherwise, repeat step 2 by after following formula adjustment weight matrix);

$V_{k+1}^{+}=[\mathrm{\α}{H}_k+(1-\mathrm{\α})Z_k]D^{+}$

In formula, 0 < α, β < 1.

The described fuzzy C-mean algorithm FCM cluster determination cluster centre that utilizes is: n vector x _i(i=1,2 ..., n) be divided into c ambiguity group, ask the cluster centre often organized, make the cost function of non-similarity index reach minimum; FCM fuzzy division, makes each data-oriented point value determine that it belongs to the degree of each group in the degree of membership that [0,1] is interval; Its detailed process is as follows:

(1) data normalization, normalizes to sample data [0,1];

(2) with the random number initialization Subject Matrix U of value between [0,1];

(3) cluster centre c is calculated _j, j=1 ..., h;

(4) given price value function.If it is less than certain threshold values determined, or its relative last time cost function value knots modification be less than certain threshold values, then algorithm stops;

(5) calculate new U matrix, return step (2).

The present invention compared with prior art advantage is:

The present invention adopts the feedforward neural network fault detection method of Frank-Wolfe algorithm optimization to detect fault of nonlinear system, by obtaining required weights to the decoupling zero of network parameter and iteration, the calculating of derivative is not introduced in process, thus enormously simplify the calculating of network, improve counting yield.And this observer has higher susceptibility to Nonlinear Dynamic nervous system fault, even if multivariate input does not increase too many complicacy yet, so be easy to expand in multi-input multi-output system, be conducive to real-time online application.

Accompanying drawing explanation

Fig. 1 is Fuzzy C-Means Cluster Algorithm process flow diagram;

Fig. 2 is Frank-Wolfe algorithm optimized network process flow diagram;

Fig. 3 is that Frank-Wolfe algorithm optimizes feedforward neural network observer model.

Embodiment

For checking the present invention is based on the superiority that Frank-Wolfe algorithm optimizes feedforward neural network fault detection method, below in conjunction with example, the present invention is described in further detail.

The detection method optimizing feedforward neural network based on Frank-Wolfe algorithm is applied in fault of nonlinear system diagnoois and test by the present invention, verifies fault diagnosis of the present invention and detectability by state observation.

1) obtain fault of nonlinear system sample data, data can obtain according to nonlinear state equation, select suitable hidden layer neuron number h, build single hidden layer feedforward neural network according to input and output.

2) initialization cluster centre and weight matrix select the initial cluster center that h different, and make k=1.The method of initial cluster center is a lot, as random selecting from sample input, or h sample input before selecting, but different value need be got in this h primary data center.Here cluster centre is obtained by random selecting.

3) distance of the input of all samples and cluster centre is calculated

||x _i-c _j||＝(x _i-c _j) ^T(x _i-c _j)，i＝1,2,...,n,j＝1,2,...,h

4) fuzzy C-mean algorithm (FCM) cluster determination cluster centre is utilized.

FCM is n vector x _i(i=1,2 ..., n) be divided into h ambiguity group, and ask the cluster centre often organized, make the cost function of non-similarity index reach minimum.FCM fuzzy division, makes each data-oriented point value determine that it belongs to the degree of each group in the degree of membership that [0,1] is interval.Adapt with introducing fuzzy division, Subject Matrix U has allowed the element of value between [0,1].But, add that normalization specifies, the degree of membership of a data set and always equal 1:

$\underset{j=1}{\overset{h}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}=1,\&ForAll;i=1,...,n$

So, the cost function (or objective function) of FCM is:

$J(U,c_1,...,c_h)=\underset{j=1}{\overset{h}{\mathrm{\&Sigma;}}}{J}_j=\underset{j=1}{\overset{h}{\mathrm{\&Sigma;}}}\underset{i}{\overset{n}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}^m{d}_{\mathrm{ij}}^2$

Here u _ijbetween 0 ~ 1; c _jfor the cluster centre of ambiguity group j, d _ij=|| c _j-x _i|| be the Euclidean distance between a jth cluster centre and i-th data point; And m ∈ [1 ,+∞) be a weighted index.

Be constructed as follows new objective function, can try to achieve and make J (U, c ₁..., c _h) reach the necessary condition of minimum value:

$\stackrel{\&OverBar;}{J}(U,c_1,...,c_h,{\mathrm{\&lambda;}}_1,...,{\mathrm{\&lambda;}}_n)=J(U,c_1,...,c_h)+{\mathrm{\&Sigma;}}_{i=1}^n{\mathrm{\&lambda;}}_i(\underset{j=1}{\overset{h}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}-1)=\underset{j=1}{\overset{h}{\mathrm{\&Sigma;}}}\underset{i}{\overset{n}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}^m{d}_{\mathrm{ij}}^2+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i(\underset{j=1}{\overset{h}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}-1)$

Here λ _i, i=1 to n is the Lagrange multiplier of n constraint formula.To the differentiate of all input parameters, make J (U, c ₁..., c _h) reach minimum necessary condition and be:

$c_j=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}^m{x}_i}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}^m}$

$u_{\mathrm{ij}}=\frac{1}{\underset{k=1}{\overset{h}{\mathrm{\&Sigma;}}}{\left(\frac{d_{\mathrm{ij}}}{d_{\mathrm{ik}}}\right)}^{2/(m-1)}}$

By above-mentioned two necessary conditions, Fuzzy C-Means Cluster Algorithm is a simple iterative process.When batch processing mode runs, FCM the following step determination cluster centre c _jwith Subject Matrix U:

(1) with the random number initialization Subject Matrix U of value between [0,1];

(2) h cluster centre c is calculated _j, j=1 ..., h;

(3) given price value function.If it is less than certain threshold values determined, or its relative last time cost function value knots modification be less than certain threshold values, then algorithm stops;

(4) new U matrix is calculated; Return step (2).

Above-mentioned algorithm also can first initialization cluster centre, and then performs iterative process.

5) weights are carried out decoupling zero, try to achieve weights

V ^+*＝HD ^T(DD ^T) ^-1

In formula, H=[h ₁, h ₂..., h _n] _{p × n}, D=[d ₁, d ₂..., d _n] _{m × n}

6) Frank-Wolfe algorithm optimization

For given input and desired output (x _i, d _i) and arbitrary initial weight matrix x is input vector matrix, then

Order $Z_k=V_k^{+}D,$ Then

$Z_0=V_0^{+}D$

If Z ₀=H ₀, then error is 0.Otherwise, make error function minimum by following formula adjustment weight matrix.

$V_{k+1}^{+}=[\mathrm{\&alpha;}{H}_k+(1-\mathrm{\&alpha;})Z_k]D^{+}$

In formula, 0 < α, β < 1.

By above-mentioned iteration, just can obtain suitable weight matrix, α, β are less, and speed of convergence is faster.

Be used in fault-detecting-observer by the network trained, utilize the output valve of this network state observer, the system of carrying out next step exports forecast, thus the fault detect of just feasible system.

From above-mentioned steps, by obtaining required weights to the decoupling zero of network parameter and iteration, not introducing the calculating of derivative in process, thus enormously simplify the calculating of network, improve counting yield.And this observer has higher susceptibility to Nonlinear Dynamic nervous system fault, even if multivariate input does not increase too many complicacy yet, so be easy to expand in multi-input multi-output system, be conducive to real-time online application.

Claims (3)

1. optimize the method for diagnosing faults of feedforward neural network observer based on Frank-Wolfe algorithm, it carries out on the basis of sample system Mathematical Models, it is characterized in that: its process is as follows:

1) sample input and the sample of, choosing sample system export;

2), the sample of sample system input input feedforward neural network observer is obtained estimating to export;

3), obtain estimating that exporting residual error is according to estimation output and actual output:

$e_y\left(t\right)=y\left(t\right)-\hat{y}\left(t\right)$

In formula, y (t) represents that sample exports, represent and estimate to export;

If estimation of error function is

$\mathrm{\&gamma;}\left(t\right)=e_y^T\left(t\right)U{e}_y\left(t\right)$

In formula, U is weighting diagonal matrix; Its fault detect rule is:

Wherein, T is the threshold value of fault detect.

2. the method for diagnosing faults optimizing feedforward neural network based on Frank-Wolfe algorithm according to claim 1, is characterized in that: described feedforward neural network observer is that its optimizing process is as follows based on Frank-Wolfe algorithm optimization neural network observer:

1) the single hidden layer feedforward neural network of structure, is formed;

(1) input and output of n fault of nonlinear system sample, are obtained; Hidden layer neuron number h is selected according to input value output valve;

(2), initialization cluster centre and weight matrix (V ₀ ⁺, W ₀), from system failure sample, select the different sample of h value to be initial cluster center;

(3), calculate the distance of the input of n sample and initial cluster center, its formula is:

||x _i-c _j||＝(x _i-c _j) ^T(x _i-c _j)，i＝1,2,...,n,j＝1,2,...,h；

In formula: x _irepresent sample input, c _jrepresent initial cluster center;

(4), utilize fuzzy C-means clustering determination cluster centre, complete single hidden layer feedforward neural network;

2) Frank-Wolfe algorithm optimization list hidden layer feedforward neural network, is adopted;

(1), defining error function E is:

In formula, V ⁺for the pseudoinverse of weight matrix V, W=[w _ij] _{p × n}for input layer is to the weight matrix of hidden layer, d _irepresent desired output, h _ifor the basis function of single hidden layer feedforward neural network;

In order to find suitable V ^{+ *}, W ^*make E (V ^{+ *}, W ^*)=0, asks error function to the partial derivative of weight matrix

$\frac{\&PartialD;E}{{\&PartialD;V}^{+}}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(V^{+}{d}_i-h_i)d_i^T$

Order $\&PartialD;E/{\&PartialD;V}^{+}=0,$ Can obtain

V ^+*＝HD ^T(DD ^T) ^-1

In formula, H=[h ₁, h ₂..., h _n] _{p × n}, D=[d ₁, d ₂..., d _n] _{m × n};

(2) for sample input and desired output (x _i, d _i) and arbitrary initial cluster centre and weight matrix (V ₀ ⁺, W ₀), X is input vector matrix, then

Definition

Z _k＝V _k ⁺D

In formula, k is iterations;

Then

Z ₀＝V ₀ ⁺D

If Z ₀=H ₀, then error is 0;

Otherwise, repeat step 2 by after following formula adjustment weight matrix);

$V_{k+1}^{+}=[{\mathrm{\&alpha;H}}_k+(1-\mathrm{\&alpha;})Z_k]D^{+}$

In formula, 0 < α, β < 1.

3. the method for diagnosing faults optimizing feedforward neural network based on Frank-Wolfe algorithm according to claim 1, is characterized in that: the described fuzzy C-mean algorithm FCM cluster determination cluster centre that utilizes is: n vector x _i(i=1,2 ..., n) be divided into c ambiguity group, ask the cluster centre often organized, make the cost function of non-similarity index reach minimum; FCM fuzzy division, makes each data-oriented point value determine that it belongs to the degree of each group in the degree of membership that [0,1] is interval; Its detailed process is as follows:

(1) data normalization, normalizes to sample data [0,1];

(2) with the random number initialization Subject Matrix U of value between [0,1];

(3) cluster centre c is calculated _j, j=1 ..., h;

(4) given price value function.If it is less than certain threshold values determined, or its relative last time cost function value knots modification be less than certain threshold values, then algorithm stops;

(5) calculate new U matrix, return step (2).