CN108845546B - Dynamic process monitoring method based on BP neural network autoregressive model - Google Patents

Dynamic process monitoring method based on BP neural network autoregressive model Download PDF

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CN108845546B
CN108845546B CN201810658889.0A CN201810658889A CN108845546B CN 108845546 B CN108845546 B CN 108845546B CN 201810658889 A CN201810658889 A CN 201810658889A CN 108845546 B CN108845546 B CN 108845546B
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宋励嘉
童楚东
俞海珍
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Abstract

The invention discloses a dynamic process monitoring method based on a BP neural network autoregressive model, aiming at establishing a nonlinear autoregressive model by utilizing the BP neural network and implementing dynamic process monitoring on the basis. The method mainly comprises the steps of firstly identifying an autocorrelation model of the sampled data of the monitored object by using a BP neural network, and secondly monitoring the process by using the error filtered by the BP neural network autoregressive model. The method has the main advantages that firstly, a nonlinear autoregressive model is established by utilizing the nonlinear fitting capacity of the BP neural network so as to achieve the purpose of eliminating the nonlinear autocorrelation characteristics in the measured variables; secondly, the method not only utilizes the capability that the error has the abnormal change condition capable of reflecting the nonlinear autocorrelation characteristic, but also provides convenience for establishing a subsequent fault detection model because the error data has no autocorrelation any more. It can be said that the method of the invention is more suitable for dynamic process monitoring.

Description

Dynamic process monitoring method based on BP neural network autoregressive model
Technical Field
The invention relates to a data-driven process monitoring method, in particular to a dynamic process monitoring method based on a BP neural network autoregressive model.
Background
Modern process industrial processes are usually in a continuous and efficient production state, and the expectations for the reliability and effectiveness of process monitoring systems are increasing to ensure the operational requirements of product quality stability, production safety, running state stability, and the like. Under industrial big data stream, the technical means of utilizing a mechanism model to implement process monitoring is increasingly not suitable for the monitoring requirements of modern process industrial processes. Furthermore, the degree of utilization of industrial big data represents a high level of industrial management. Therefore, data-driven process monitoring methodology technology is gaining favor in this large context. Due to the development of advanced instrument technology, sampling time intervals are greatly shortened, and time sequence autocorrelation among sampling data is a problem which needs to be considered in a data-driven process monitoring method, because abnormal changes of the time sequence autocorrelation can also reflect that a monitored process object enters an abnormal working condition. The most classical Dynamic process monitoring method is a Dynamic Principal Component Analysis (DPCA) method based on an amplification matrix, and the basic idea is to introduce a delay measurement value into each training sample data to form an amplification matrix, so that the amplification matrix can simultaneously consider the cross-correlation between the sample data time sequence autocorrelation and the variables.
In addition, researchers have proposed using an Auto-Regression Model (ARM) to mine the sequence autocorrelation between sampled data, and the parameters of the ARM can be generally estimated by a partial least squares algorithm. The ARM has the advantages that sequence autocorrelation does not exist in the output error of the ARM model, and the change condition of the error can reflect the abnormal change condition of the autocorrelation of the original sampling data sequence, so that the ARM model achieves two purposes. From this point of view, the core of the idea of implementing dynamic process monitoring with ARM is how to filter out the time-series autocorrelation characteristics of the original sampled data.
However, considering the complexity of the scale of modern industrial processes, it is no longer appropriate to describe the autocorrelation between sampled data using linear ARM, and it should be described using non-linear ARM. As a classical nonlinear modeling algorithm, the neural network technology is widely researched and applied, and the figure can be found in the fields of pattern recognition, nonlinear system identification, market analysis and the like. Among them, the Back Propagation (BP) learning algorithm is the most common feedforward neural network learning algorithm, and the corresponding neural network model is generally called as a BP neural network model. It is worth mentioning that the neural network model needs to give input and output data when training. The training data of process monitoring is usually a model for establishing single classification, and generally, sampling data cannot be simply classified into input data and output data, because abnormal change of any measurement variable is an appearance of fault. This is why in the field of data-driven process monitoring, few process monitoring methods using neural networks have emerged.
Disclosure of Invention
The invention aims to solve the main technical problems that: how to establish a nonlinear autoregressive model by using a BP neural network and implement dynamic process monitoring on the basis of the nonlinear autoregressive model. Specifically, the method mainly comprises the steps of firstly identifying an autocorrelation model of the sampled data of the monitored object by using a BP neural network, and secondly carrying out process monitoring by using errors filtered by an autoregressive model of the BP neural network.
The technical scheme adopted by the invention for solving the technical problems is as follows: a dynamic process monitoring method based on a BP neural network autoregressive model comprises the following steps:
(1) collecting samples in normal operation state in production process, and forming training data set X e R according to sampling timen ×mLet matrix X be [ X ]1，x1，…，xn]TLast n-d sample data x in (1)d+1，xd+2，…，xnThe output matrix Y ═ x constituting the autoregressive modeld+1，xd+2，…，xn]TThe input matrix Z of the autoregressive model is constructed as follows:
Figure GSB0000186528820000021
wherein n is the number of training samples, m is the number of measurement variables of the monitored object, R is the real number set, Rn×mThe real number matrix of N × m dimension is shown, d is the number of delay measurement data, N-d, and the upper label T shows the transpose of the matrix or vector.
(2) Respectively carrying out normalization processing on each column vector in the input matrix Z and the output matrix Y according to the following formula, namely:
x＝(x-xmin)/(xmax-xmin) (2)
in the above formula, x represents any column vector in matrix Z or matrix Y, and xmaxAnd xminRepresenting the maximum and minimum values of the vector x, respectively.
(3) Constructing a three-layer BP neural network: the number of nodes of the input layer is dm, the number of nodes of the output layer is m, the number of nodes of the hidden layer is suggested to be set to be 2dm, the activation function of the hidden layer is an S-shaped function, and the activation function of the output layer is a linear function.
The linear and sigmoidal activation functions used in the method of the invention are shown below:
g(u)＝u (3)
Figure GSB0000186528820000022
in the above formula, u represents a function argument, g (u) is a linear activation function, and f (u) is an S-type activation function.
(4) Sending the normalized input Z and output Y to a BP neural network for training operation to obtain the weight coefficient of each neuron node after optimization of the BP neural network, wherein the specific implementation process is as follows:
the method includes the steps of firstly, randomly initializing weight coefficients of each neuron node of a neural network.
And calculating output values of the hidden layer and the output layer.
Calculating the error under the condition of the current weight coefficient by using the actual output value of the neural network model and the output value of the output layer, and judging that the error precision requirements are met according to the errors? If so, finishing the optimization of the neural network model; if not, go to step (iv).
(iv) determine whether the maximum number of iterations has been reached? If yes, ending the optimization of the neural network model; if not, the weight coefficients of the neuron nodes of the hidden layer and the output layer are adjusted according to the error, and then the step II is returned.
(5) Output error to BP neural network model
Figure GSB0000186528820000031
Each column in the array is normalized to obtain a new data matrix with a mean value of 0 and a standard deviation of 1
Figure GSB00001865288200000312
(6) Establishing a fault detection model based on a principal component analysis algorithm, and reserving a model parameter set theta ═ P, Lambda, Dlim，QlimTherein of
Figure GSB0000186528820000032
Outputting a data matrix for an output layer of the neural network model, P being a projective transformation matrix, and Λ being a covariance of principal componentsMatrix, DlimAnd QlimThe specific implementation processes are as follows:
calculating
Figure GSB0000186528820000033
Covariance matrix of
Figure GSB0000186528820000034
Solving all the characteristic values gamma of C1≥γ2≥…≥γmCorresponding feature vector p1，p2…，pm；
Setting the number k of the reserved principal components as the minimum value meeting the following conditions, and forming a load matrix P (P) by the corresponding k eigenvectors1，p2…，pk]；
Figure GSB0000186528820000035
Fourthly, calculating the upper control limit D of the monitoring statistical indexes D and Q according to the formula shown in the specificationlimAnd Dlim：
Figure GSB0000186528820000036
Figure GSB0000186528820000037
In the above formula, F (alpha, k, N-d-k) represents the value of F distribution with k degree of freedom and N-d-k under the confidence degree alpha (generally 99 percent),
Figure GSB0000186528820000038
Represents a degree of freedom of h-2 a2The value of the chi-square distribution of/v under the confidence coefficient alpha, the weighting coefficient g ═ v/(2a), a and v respectively represent the estimated mean value and the estimated variance of the Q monitoring index.
The steps (1) to (6) are offline modeling stages of the method of the present invention, and the steps (7) to (11) shown below are online dynamic process monitoring implementation processes of the method of the present invention.
(7) Collecting data samples x at the latest sampling instantt∈Rm×1And finding out the delay measurement data x thereoft-1，xt-2，…，xt-dForming an input vector z ═ x of the autoregressive modelt-1 T，xt-2 T，…，xt-d T]Where the subscript t denotes the current latest sampling instant.
(8) For input ring z and xtThe same normalization processing as in step (2) is performed.
(9) Inputting the vector z into the BP neural network obtained by training in the step (4), thereby obtaining the output of the output layer of the neural network
Figure GSB0000186528820000039
(10) For error
Figure GSB00001865288200000310
Performing the same normalization process as in step (5) to obtain data vectors
Figure GSB00001865288200000311
(11) Calling the parameter set reserved in the step (6) to implement online fault detection, wherein the specific implementation process comprises the following steps:
calculating specific values of monitoring statistical indexes D and Q according to the following formula:
Figure GSB0000186528820000041
Figure GSB0000186528820000042
② according to the concrete numerical values of D and Q and corresponding control upper limit DlimAnd QlimAnd (3) deciding whether the fault occurs or not, namely judging whether the condition is met: d is less than or equal to DlimAnd Q is less than or equal to Qlim(ii) a If so, the current sample is sampled under normal working conditions, and the step (7) is returned to continue to monitor the next new sample data; if not, the current sampling data comes from the fault working condition.
Compared with the traditional method, the method has the advantages that:
firstly, the method utilizes the nonlinear fitting capability of a BP neural network to establish a nonlinear autoregressive model so as to achieve the purpose of eliminating nonlinear autocorrelation characteristics in measured variables; secondly, the method takes the error as the monitored object, not only utilizes the capability of the error to reflect the abnormal change condition of the nonlinear autocorrelation characteristic, but also provides convenience for the establishment of a subsequent process monitoring model based on the PCA algorithm because the autocorrelation on the time sequence of the error data does not occur any more. It can be said that the method of the present invention is more suitable for dynamic process modeling and monitoring.
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FIG. 1 is a flow chart of an embodiment of the method of the present invention.
Fig. 2 is a schematic diagram of the specific implementation steps of the BP neural network.
FIG. 3 is a diagram illustrating autocorrelation feature culling in error.
FIG. 4 is a comparison graph of the monitoring details of TE process material C inlet temperature faults.
Detailed Description
The method of the present invention is described in detail below with reference to the accompanying drawings and specific embodiments.
As shown in FIG. 1, the invention discloses a dynamic process monitoring method based on a BP neural network autoregressive model. The following description of a specific embodiment of the method of the present invention is given in conjunction with an example of a specific industrial process.
Before describing the specific implementation case, the basic principle of the BP neural network is briefly described. Let BP neural network input mode be alpha ═ alpha1，α2，…，αdm]The output of the hidden layer is beta ═ beta1，β2，…，β2dm]The output of the output layer is [ gamma ] - [ gamma ]1，γ2，…，γm]Nerve of the diseaseThe actual output value of the network is y ═ y1，y2，…，ym]. According to the BP neural network principle, the hidden layer output beta can be obtained as follows:
Figure GSB0000186528820000043
in the above formula, betajOutput, w, representing the jth neuron of the hidden layer0j＝θ、x0In the present embodiment, θ is 0.
Similarly, the output γ of the kth neuron of the output layerkThe calculation method is as follows:
Figure GSB0000186528820000044
then, the error under the current weight coefficient condition is:
Figure GSB0000186528820000045
the idea of adjusting the weight coefficients by the BP neural network is to iteratively adjust according to the method shown in equation (7) with the fastest error reduction. Therefore, a step length η can be set, and η units are adjusted in the negative gradient direction each time, that is, the adjustment amount of the weight value each time is:
Figure GSB0000186528820000051
the adjustment sequence of the BP neural network is as follows:
firstly, adjust the weight from hidden layer to output layer, set vkFor the input of the kth neuron of the output layer, there are:
Figure GSB0000186528820000052
Figure GSB0000186528820000053
then, the formula for iteratively adjusting the weights from the hidden layer to the output layer is:
wjk＝wjk-η(yk-γk)g′(vk)βj(11)
similarly, the iterative formula of weight adjustment from the input layer to the hidden layer can be inferred as follows:
Figure GSB0000186528820000054
in the above formula, ukIs the input to the k-th neuron of the hidden layer.
And (3) carrying out iterative adjustment according to the formulas, wherein the error is gradually reduced until the set precision or the maximum iteration number is achieved, and the specific implementation steps of the BP neural network are shown in FIG. 2.
The application object is from the U.S. Tennessee-Ismann (TE) chemical process experiment, and the prototype is a practical process flow of an Ismann chemical production workshop. At present, the TE process has been widely used as a standard experimental platform for fault detection research due to the complexity of the process. The entire TE process includes 22 measured variables, 12 manipulated variables, and 19 constituent measured variables. The TE process object may simulate a variety of different fault types, such as material inlet temperature step changes, cooling water fault changes, and so forth. To monitor the process, 33 process variables were selected as shown in table 1. Due to the short sampling interval time, the TE process sampling data inevitably has sequence autocorrelation. Moreover, due to the complex characteristics of the TE process, the non-linear characteristics between the sampled data are significant, and therefore non-linear modeling should be implemented. The following describes the detailed implementation steps of the present invention in conjunction with the TE process.
Table 1: the TE process monitors variables.
Figure GSB0000186528820000055
Figure GSB0000186528820000061
Firstly, establishing a dynamic process monitoring model by using 960 sampling data under the normal working condition of the TE process, and comprising the following steps of:
step (1): collecting samples in normal operation state in production process, and forming training data set X e R according to sampling time960×33Let matrix X be [ X ]1，x1，…，xn]TThe last n-d in (1) 958 sample data x3，x4，…，x960Forming regression model output matrix Y ═ x3，x4，…，x960]The input matrix Z of the regression model is as follows:
Figure GSB0000186528820000062
step (2): and respectively carrying out normalization processing on each column vector in the input matrix Z and the output matrix Y.
And (3): and constructing a three-layer BP neural network.
And (4): and sending the normalized input Z and output Y to a BP neural network for training operation to obtain the weight coefficient of each neuron node after the BP neural network is optimized.
And (5): output error to BP neural network model
Figure GSB0000186528820000063
Each column in the array is normalized to obtain a new data matrix with a mean value of 0 and a standard deviation of 1
Figure GSB0000186528820000064
And (6): establishing a fault detection model based on a principal component analysis algorithm, and reserving a model parameter set theta ═ P, Lambda, Dlim，Qlim}。
To verify that the error no longer contains nonlinear autocorrelation characteristics, the error matrix is modified
Figure GSB0000186528820000065
A schematic diagram of the autocorrelation corresponding to the first 18 vectors is shown in fig. 3. It can be seen from fig. 3 that the autocorrelation features of the original training data have been removed, and no autocorrelation exists in the error.
Secondly, collecting a test data set under the condition that the inlet temperature of the TE process material C is in fault change, and implementing online process monitoring. It is worth noting that the first 160 sample data of the test data set were collected from normal conditions, and fault conditions were introduced from 161 moments.
And (7): collecting data samples x at the latest sampling instantt∈R33×1And finding out the delay measurement data x thereoft-1，xt-2To form the input vector z of the autoregressive model.
And (8): for input vectors z and xtThe same normalization processing as in step (2) is performed.
And (9): inputting the vector z into the BP neural network obtained by training in the step (4), thereby obtaining the output of the output layer of the neural network
Figure GSB0000186528820000071
Step (10): for error
Figure GSB0000186528820000072
Performing the same normalization process as in step (5) to obtain data vectors
Figure GSB0000186528820000073
Step (11): and (4) calling the parameter set reserved in the step (6) to carry out online fault detection.
Finally, the details of the process monitoring of the change in the temperature of the inlet for material C by the method of the present invention are shown in FIG. 4. As can be seen from fig. 4, the method of the present invention can continuously trigger the fault alarm after the fault occurs.
The above embodiments are merely illustrative of specific implementations of the present invention and are not intended to limit the present invention. Any modification of the present invention within the spirit of the present invention and the scope of the claims will fall within the scope of the present invention.

Claims (3)

1. A dynamic process monitoring method based on a BP neural network autoregressive model is characterized by comprising the following steps:
the implementation of the offline modeling phase is as follows:
step (1): collecting samples in normal operation state in production process, and forming training data set X e R according to sampling timen ×mChanging X to [ X ]1，x1，…，xn]TLast n-d sample data x in (1)d+1，xd+2，…，xnThe output matrix Y ═ x constituting the autoregressive modeld+1，xd+2，…，xn]TThe input matrix Z of the autoregressive model is constructed as follows:
Figure FSB0000189230860000011
wherein n is the number of training samples, m is the number of measurement variables of the monitored object, R is the real number set, Rn×mA real number matrix representing N multiplied by m dimension, d is the number of delay measurement data, N is N-d, and an upper label T represents the transposition of the matrix or the vector;
step (2): respectively carrying out normalization processing on each column vector in the input matrix Z and the output matrix Y according to the formula shown in the specification
x＝(x-xmin)/(xmax-xmin) (2)
In the above formula, x represents any column vector in the input matrix Z or the output matrix Y, and xmaxAnd xminRespectively representing the maximum value and the minimum value of the column vector x;
and (3): constructing a three-layer BP neural network: the number of nodes of the input layer is dm, the number of nodes of the output layer is equal to the number of measurement variables of the monitored object, the number of nodes of the hidden layer is set to be 2dm, the activation function of the hidden layer is an S-shaped function, and the activation function of the output layer is a linear function, which are respectively shown as follows:
g(u)＝u (3)
Figure FSB0000189230860000012
in the above formula, u represents a function argument, g (u) is a linear activation function, and f (u) is an S-type activation function;
and (4): sending the normalized input matrix Z and the normalized output matrix Y to a BP neural network for training operation to obtain the weight coefficient of each neuron node after the BP neural network is optimized;
and (5): output error to BP neural network model
Figure FSB0000189230860000013
Each column in the array is normalized to obtain a new data matrix with a mean value of 0 and a standard deviation of 1
Figure FSB0000189230860000014
Wherein
Figure FSB0000189230860000015
Outputting a data matrix for an output layer of the neural network model;
and (6): establishing a fault detection model based on a principal component analysis algorithm, and reserving a model parameter set theta ═ P, Lambda, Dlim，QlimP is a projective transformation matrix, Λ is a covariance matrix of principal components, DlimAnd QlimRespectively monitoring the upper control limits of the statistical indexes D and Q;
the implementation flow of online process monitoring is as follows:
and (7): collecting data samples x at the latest sampling instantt∈Rm×1And measuring data x of d previous time instantst-1，xt-2，…，xt-dInput vector z ═ x constituting autoregressive modelt-1 T，xt-2 T，…，xt-d T]Wherein the subscript t denotes the current latest sampling time;
and (8): for input vectors z and xtCarrying out the same normalization processing as in the step (2);
and (9): inputting the vector z into the BP neural network obtained by training in the step (4), thereby obtaining the output of the output layer of the neural network
Figure FSB0000189230860000021
Step (10): for error
Figure FSB0000189230860000022
Performing the same normalization process as in step (5) to obtain data vectors
Figure FSB0000189230860000023
Step (11): calling the parameter set reserved in the step (6) to implement online fault detection, wherein the specific implementation process comprises the following steps:
calculating specific values of monitoring statistical indexes D and Q according to the following formula:
Figure FSB0000189230860000024
② according to the concrete numerical values of D and Q and corresponding control upper limit DlimAnd QlimAnd (3) deciding whether the fault occurs or not, namely judging whether the condition is met: d is less than or equal to DlimAnd Q is less than or equal to Qlim(ii) a If so, the current sample is sampled under normal working conditions, and the step (7) is returned to continue to monitor the next new sample data; if not, the current sampling data comes from the fault working condition.
2. The dynamic process monitoring method based on the BP neural network autoregressive model as claimed in claim 1, wherein the specific implementation process of training the BP neural network in the step (4) is as follows:
randomly initializing weight coefficients of each neuron node of a neural network;
calculating output values of the hidden layer and the output layer;
calculating the error under the condition of the current weight coefficient by the actual output value of the neural network model and the output value of the output layer, and judging whether the error meets the error precision requirement according to the error; if so, finishing the optimization of the neural network model; if not, turning to the fourth step;
judging whether the maximum iteration times is reached; if yes, ending the optimization of the neural network model; if not, the weight coefficients of the neuron nodes of the hidden layer and the output layer are adjusted according to the error, and then the step II is returned.
3. The dynamic process monitoring method based on the BP neural network autoregressive model as claimed in claim 1, wherein the specific implementation process of establishing the fault detection model in the step (6) is as follows:
calculating
Figure FSB0000189230860000025
Covariance matrix of
Figure FSB0000189230860000026
Solving all the characteristic values gamma of C1≥γ2≥…≥γmCorresponding feature vector p1，p2…，pm；
Setting the number k of the reserved principal components as the minimum value meeting the following conditions, and forming a load matrix P (P) by the corresponding k eigenvectors1，p2…，pk]；
Figure FSB0000189230860000027
Fourthly, calculating the upper control limit D of the monitoring statistical indexes D and Q according to the formula shown in the specificationlimAnd Qlim：
Figure FSB0000189230860000031
Figure FSB0000189230860000032
In the above formula, F (α, k, N-d-k) represents a value of F distribution having a degree of freedom of k and N-d-k with a confidence of 99%,
Figure FSB0000189230860000033
Represents a degree of freedom of h-2 a2The value of the chi-square distribution of/v under the confidence coefficient alpha, the weighting coefficient g ═ v/(2a), a and v respectively represent the estimated mean value and the estimated variance of the Q monitoring index.
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