CN111679648A - Multivariate closed-loop control loop performance evaluation method based on Gaussian process regression - Google Patents
Multivariate closed-loop control loop performance evaluation method based on Gaussian process regression Download PDFInfo
- Publication number
- CN111679648A CN111679648A CN202010441944.8A CN202010441944A CN111679648A CN 111679648 A CN111679648 A CN 111679648A CN 202010441944 A CN202010441944 A CN 202010441944A CN 111679648 A CN111679648 A CN 111679648A
- Authority
- CN
- China
- Prior art keywords
- loop
- evaluation
- closed
- performance
- output
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Images
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B23/00—Testing or monitoring of control systems or parts thereof
- G05B23/02—Electric testing or monitoring
- G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
- G05B23/0259—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterized by the response to fault detection
- G05B23/0283—Predictive maintenance, e.g. involving the monitoring of a system and, based on the monitoring results, taking decisions on the maintenance schedule of the monitored system; Estimating remaining useful life [RUL]
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- Automation & Control Theory (AREA)
- Feedback Control In General (AREA)
Abstract
The invention relates to a multivariate closed-loop control loop performance evaluation method based on Gaussian process regression, which comprises the following steps: s1, selecting multivariable closed-loop output data to be evaluated; s2, standardizing data; s3, calibrating the data matrix in the step S2
Dividing evaluation segments; and S4, performing autoregressive modeling on the evaluation fragment data matrix X, constructing training input, training output and test input of the model, and determining model parameters by using a least square method. The invention has the beneficial effects that: the method does not need process prior knowledge, utilizes the thought of data driving, can excavate the performance related information contained in the process data on line, carries out performance evaluation on the multivariable closed-loop control system, gives out the evaluation result and the operation suggestion of the comprehensive loop according to the change trend of the performance index, is convenient for a field engineer to directly carry out operation and maintenance on the performance degradation loop through the evaluation result, and can quickly eliminate the loopAnd the automatic evaluation of a closed-loop system is realized due to the road fault, and the safe and efficient operation of the process is ensured.
Description
Technical Field
The invention relates to the field of control performance evaluation of industrial systems, in particular to a multivariate closed-loop control loop performance evaluation method based on Gaussian process regression.
Background
With the rapid development of automation theory and technology, the design and operation scale and complexity of modern industrial systems are gradually increased. The process industry uses primarily PID controllers to maintain important process variables at desired set points. The concept of PID control was introduced in industrial production processes in the 1930 to 1950 s, initially in the case of small-scale processes each with several pneumatic circuits, and now hundreds or even thousands of PID control circuits have been implemented digitally on a large scale. The industry needs an automatic control performance evaluation strategy to evaluate the performance of the control loop according to the business strategy "cannot be evaluated and cannot be managed". The importance of control performance evaluation is that despite the prevalence of PID controllers, subsequent studies have found that the performance of the control loop is not as satisfactory. Most studies have found that "poor performing" control loops are more than desired. Therefore, control performance evaluation is an important asset management technique that maintains efficient operating performance of automated systems in a production plant. In an industrial environment, failure and poor performance of process control loops are common, resulting in reduced machine operability, increased costs, and ultimately impaired production quality and profitability during the entire industrial operation. It is therefore important to evaluate, identify and correct control system faults in a timely manner, which can automatically provide plant personnel with information to determine whether the controlled variables in the process meet specified performance goals and response characteristics, and to assess the performance of the control system. A key requirement for evaluating the control loop is that data from conventional operation and closed loop control should be used. The control performance of the control system is evaluated in real time through the process operation data, the control abnormity can be detected in advance, the loop can be diagnosed and maintained in time, the maintenance cost can be greatly reduced, the maintenance pertinence is increased, the efficient operation of the loop is ensured, the reason causing the performance degradation is corrected in time before the occurrence of serious accidents, and the potential safety hazard in production is reduced. With the rapid development of sensing technology and digital storage technology, it is becoming easier to obtain and store production operation data in industrial fields, and process data contains a large amount of information related to control performance, and control performance evaluation based on data is becoming a popular field of research in this year.
Over the past twenty-five years, a great deal of research related to control performance evaluation has emerged, and most of them study the deviation between a controlled variable and its set value (or desired value). They aim to quantify the control deviation by a value. The traditional performance indicators are rise time, stabilization time, overshoot, control error, variance, integral error standard and the like. The most widely used and studied control performance evaluation criterion is variance (or standard deviation). The variance of the controlled variables has a direct relationship to process performance, product quality and product profit. The ratio of the minimum achievable variance of the loop to the variance of the real-time control loop is generally used as an evaluation indicator, ranging from zero to one, where a closer indicator to one means better control performance. Methods based on this evaluation concept require knowledge about the control system and process. For a univariate control loop, the delay information of the loop is needed; for multivariable control loops, more detailed control system interaction matrix information is needed. This information is difficult to obtain by direct measurement or indirect calculation in an actual industrial process, which limits the development and application of conventional control performance evaluation methods. The control performance evaluation method based on data driving is characterized in that corresponding evaluation indexes are designed to indicate the grade or the state of the control performance by mining statistical information in process operation data. The method does not need prior process knowledge, and evaluates the control performance on line and automatically through data modeling. At present, the performance evaluation research results of the multivariable closed-loop control system based on data driving are very limited, and the multivariable closed-loop control system is still in a preliminary exploration phase and needs further deep research.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides a multivariate closed-loop control loop performance evaluation method based on Gaussian process regression.
The multivariate closed-loop control loop performance evaluation method based on Gaussian process regression comprises the following steps:
s1, selecting multivariable closed-loop output data to be evaluated, wherein for the multivariable industrial closed-loop control system, the operation process of the multivariable industrial closed-loop control system is set to contain M controlled variables, and a vector x (t) (x) of 1 × M is obtained by sampling at the time t1(t),x2(t),…,xM(t)), after H times of sampling, obtaining the data matrix X of the controlled variable under the condition of good control performanceM＝(x(t),x(t+1),…,x(t+H))T；
S2, data standardization: data matrix X of controlled variablesMSubtracting the mean value of the column by column and dividing by the standard deviation of the column for normalization to obtain a normalized data matrix
S3, calibrating the data matrix in the step S2
Dividing evaluation segments, wherein the length of the divided evaluation segments is determined according to the lengths of different data sets, and a data matrix of a single evaluation segment containing N data points is marked as X to obtain R evaluation segments;
s4, performing autoregressive modeling on the evaluation fragment data matrix X, constructing training input, training output and test input of a model, and determining model parameters by using a least square method:
s4.1, firstly, determining the length of a non-overlapping sliding window to be L;
s4.2, designing training input, test input and training output of the multivariate autoregressive model in the Gaussian process; the training input data matrix is obtained by using the first (N-L) data points in the evaluation fragment data matrix X as follows:
taking each row of data points in the evaluation fragment data matrix X as input X of a Gaussian process multivariable autoregressive modeltT is time, and the value interval of t is [1, N-L +1 ]]；
Using the last L data points in the evaluation segment data matrix X to obtain a test input data matrix as follows:
X1＝[x(N-L+1) x(N-L+2) … x(N)](2)
by training the input data matrix X0The time corresponding to the first data point in the regression model is used as the output of the regression model:
Y0＝[1 2 ... N-2L+1]T(3)
s4.3, defining prior knowledge of a multivariate autoregressive model of the Gaussian process: definition atIs a white noise sequence, the model order is p, and the coefficient of the Gaussian process multivariable autoregressive model is Fj(j ═ 1, 2.., p), the following gaussian process multivariate autoregressive model was obtained:
Xt(t)＝F1Xt(t-1)+F2Xt(t-2)+…+FpXt(t-p)+at(4)
defining the mean m (x) as a constant 0 and the covariance function K (x, x') as a gaussian process of a gaussian kernel, as follows:
f(x)～GP(m(x),K(x,x′)) (5)
m(x)＝0 (6)
s4.4, calculating a prediction error:
Xt(t|t-i)＝Fia(t-i)+Fi+1Xt(t-2)+…+FpXt(t-p)+at(7)
in the above formula (7) to the above formula (8), p is the model order; t is time, and the value interval of t is [1, N-L +1 ]](ii) a x and x' are any two input samples in the input data matrix,
and
the adjustable parameters in the covariance function are used for adjusting the shape of the covariance function changing on the horizontal axis and the vertical axis;
s4.5, determining the adjustable parameters in the step S4.4 according to the maximized marginal likelihood function
And
the maximum marginal likelihood function is:
in the above formula, N is the number of training samples, and N is N to L + 1;
K＝K(X0,X0) (10)
wherein N is N-L +1, and solving the adjustable parameter
And
optimum value of (2):
s5, testing input X by using the established Gaussian process multivariable autoregressive model1To carry outPredicting to obtain a predicted output y1The prediction mean and the prediction variance are specifically realized by the following steps:
s5.1, obtaining prior distribution of test input based on the prior knowledge of the Gaussian process multivariable autoregressive model determined in the step S4.3:
y1～N(0,K(X1,X1)) (12)
in the above formula, N (0, K (X)1,X1) Denotes a mean of zero and a variance of K (X)1,X1) (ii) a gaussian distribution of; y is1Is the test output to be predicted;
s5.2, according to the known training sample X0And Y0And obtaining a training output and a test output which satisfy the following joint Gaussian distribution:
s5.3, the posterior distribution of the output to be predicted can be directly deduced according to a Bayesian formula:
in the above formula, the first and second carbon atoms are,
represents a mean value of
Variance is ω2(ii) a gaussian distribution of;
is the predicted mean, ω, of the test output2Is the predicted variance of the test output;
s6 using the predicted variance ω of the test output obtained in step S5.32As the control performance index p:
p＝ω2(15)
s7, for a plurality of evaluation segments to be evaluated, repeatedly executing the steps S4 to S6 to obtain the value of the control performance index p of each evaluation segment, and drawing a change trend curve of the control performance index p; evaluating the control performance of the closed-loop control system according to the variation trend of the value of the control performance index p obtained in the step S6; because a control loop with good performance generally has strong immunity and stability, output disturbance caused by various random disturbances generally does not repeatedly appear in a closed loop output periodically, and because the closed loop with poor control performance cannot compensate the disturbance in time, the uncompensated disturbance can continuously propagate in the loop and is presented in the closed loop output at certain time delay, so that the output has large autocorrelation and predictability, and according to the knowledge, the application of the performance evaluation index p is explained as follows:
s7.1, if the performance evaluation index p is increased, the predictability of closed-loop output of the multivariable control loop is reduced, the control performance of the closed-loop is improved, and the controller can effectively resist various random interferences without intervention;
s7.2, if the performance evaluation index p has a decreasing trend, the predictability of the closed-loop output of the multivariable control loop is increased, the control performance of the closed-loop begins to degrade, the capacity of the controller for resisting various random interferences is gradually reduced, and the loop evaluation result is further observed;
and S7.3, if the performance evaluation index p is continuously and stably reduced and is not increased any more, the predictability of the closed-loop output of the multivariable control loop is strong, the control performance of the closed-loop is determined to be degraded, the controller has poor capability of resisting various random interferences, and an operator intervenes to diagnose the degradation reason.
Preferably, the evaluation segment length is divided into 100 to 300 data points in the step S3.
Preferably, the length L of the non-overlapping sliding window in step S4.1 is determined according to a variation characteristic of the controlled variable, where the variation characteristic includes a delay time and a variation speed.
The invention has the beneficial effects that: the method does not need process prior knowledge, utilizes the idea of data driving, can mine performance related information contained in process data on line, carries out performance evaluation on the multivariable closed-loop control system, gives out an evaluation result and an operation suggestion of a comprehensive loop according to the change trend of performance indexes, is convenient for a field engineer to directly carry out operation and maintenance on a performance degradation loop through the evaluation result, can rapidly eliminate loop faults, realizes automatic evaluation of the closed-loop system, and ensures safe and efficient operation of the process.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a flow chart of a thermal power generation process for a specific application of the present invention;
FIG. 3 is a graph of performance index trend results for a thermal power process control performance well data set in accordance with the present invention;
FIG. 4 is a graph of performance index trend results for a thermal power process control performance degradation data set as applied to the present invention;
FIG. 5 is a graph of performance index trend results for a thermal power plant process control performance from good to degraded case data set.
Description of reference numerals: the device comprises a slag pump 1, an induced draft fan 2, a dust remover 3, an air preheater 4, an economizer 5, a blower 6, a steam pocket 7, a powder discharge machine 8, a coal pulverizer 9, a high pressure heater 10, a water feed pump 11, a deaerator 12, a low pressure heater 13, a condensate pump 14, a gas condenser 15, a circulating pump 16, a cooling tower 17, a high pressure cylinder 18, a medium pressure cylinder 19, a low pressure cylinder 20, a generator 21 and a main transformer 22.
Detailed Description
The present invention will be further described with reference to the following examples. The following examples are set forth merely to aid in the understanding of the invention. It should be noted that, for a person skilled in the art, several modifications can be made to the invention without departing from the principle of the invention, and these modifications and modifications also fall within the protection scope of the claims of the present invention.
Aiming at the problem of control performance evaluation of an industrial process multivariable closed-loop control system, the invention provides an algorithm for evaluating the performance of the multivariable closed-loop control system based on Gaussian process regression from the aspect of closed-loop output predictability reaction loop control performance. The method designs a performance measurement method for controlling performance states by the predictability of loop output in a multivariable closed-loop control system of the chemical industrial process, constructs a training input matrix by using historical controlled variables for each operation section to be evaluated, constructs a Gaussian process regression model by taking the time corresponding to a first data point in the input matrix as training output, constructs test input by using the historical controlled variables at subsequent times, and obtains the posterior distribution of the predicted value of the Gaussian process regression model, namely the predicted mean value and the predicted variance. Based on the prediction variance information, a new performance evaluation index is provided as an indication for revealing the enhancement or reduction of the control performance according to the highly predictable control performance of the corresponding degradation of the closed loop output and a huge improvement potential thought. The method can evaluate the grade of the control performance on line, and in addition, due to the combination of the Gaussian process regression algorithm, the method can simultaneously process the inherent nonlinear problem of the complex control system, and shows more reliable and comprehensive evaluation results in the performance evaluation application of the actual industrial multivariable control system.
Example (b):
the thermal power generation process is a large complex industrial process, and as shown in fig. 2, mainly comprises three main devices, namely a boiler, a steam turbine, a generator and corresponding auxiliary devices, which are connected through pipelines or lines to form a main production system, namely a combustion system, a steam-water system and an electrical system. The specific working process is that raw coal is conveyed to a coal hopper in a boiler workshop by a belt, enters a coal mill system for grinding and drying, is prepared into coal powder with certain fineness and moisture requirements, and then is sprayed into a furnace together with air preheated by a preheater for combustion, flue gas is removed of ash content by a dust remover and then is extracted by a draught fan, and the flue gas is discharged into the atmosphere through a tall chimney. The coal powder is fed into a boiler, and then is heated by a boiler system to convert water into steam, the water is heated in the boiler and then is evaporated into steam, the steam is further heated by a heater to become superheated steam with specified pressure and temperature, and then the superheated steam is fed into a steam turbine through a pipeline, so that the chemical energy of the coal is converted into heat energy. In a steam turbine system, steam is constantly expanding and flowing at high speed, impacting the rotor of the turbine, converting thermal energy into mechanical energy at a rated speed (rotation, the thermal energy of combustion is converted into mechanical energy by a steam turbine generator, driving a generator coaxial with the turbine to generate electricity, and the generator converts the mechanical energy into electrical energy.
As shown in fig. 1, the present invention comprises the steps of:
s1, selecting multivariable closed-loop output data to be evaluated, wherein the operation process of the cold and hot air baffle closed-loop control system of the coal mill in the thermal power generation process comprises 2 controlled variables, and a vector x (t) ═ x (x) of 1 × 2 can be obtained by sampling at the time t1(t),x2(t)), obtaining a data matrix X of the controlled variables under the condition of good control performance after multiple samplingM＝(x(t),x(t+1),…,x(t+H))T。
S2, data standardization: data matrix of controlled variables
Subtracting the mean value of the column by column and dividing by the standard deviation of the column for normalization to obtain a normalized data matrix XM。
S3, normalizing the data matrix X in the step S2MEvaluation segment division is carried out, the division standard can be determined according to different data set lengths, generally 100-300 data points are recommended to serve as a segment, and 240 data points are adopted as a segment in the experiment. The data matrix of a single evaluation segment including N data points may be represented as X, and the following evaluation procedure may be repeatedly performed for a plurality of evaluation segments.
S4, performing Gaussian process regression modeling on the evaluation fragment data matrix X, constructing training input, training output and test input of the model, and determining model adjustable parameters by utilizing a maximized marginal likelihood function, wherein the specific process is as follows:
s4.1, firstly determining the length L of the sliding window, wherein L can be determined according to the change characteristics of the controlled variable, such as delay time, change speed and the like, in the experiment, L is 70, the front (N-L) points in X are used for obtaining a training input matrix of a Gaussian process regression model, and the rest L points are used for testing input.
S4.2, designing training input, testing input and training output of the Gaussian process regression model: using X middle and front (N-L) data points, a training input data matrix is obtained as follows:
using the last L data points in X, the test input data matrix is obtained as follows:
X1＝[x(N-L+1) x(N-L+2) … x(N)](2)
by X0The time corresponding to the first data point in the graph is used as the output of the regression model, and the following is shown:
Y0＝[1 2 ... N-2L+1]T(3)
s4.3, defining prior knowledge of a Gaussian process: a priori knowledge defining a multivariate autoregressive model of a gaussian process: definition atIs a white noise sequence, the model order is p, and the coefficient of the Gaussian process multivariable autoregressive model is Fj(j ═ 1, 2.., p), the following gaussian process multivariate autoregressive model was obtained:
Xt(t)＝F1Xt(t-1)+F2Xt(t-2)+…+FpXt(t-p)+at(4)
defining a gaussian process with a constant value of m (x) and a constant value of 0, and a gaussian kernel function of K (x, x') as follows:
f(x)～GP(m(x),K(x,x′)) (5)
m(x)＝0 (6)
s4.4, calculating a prediction error:
Xt(t|t-i)＝Fia(t-i)+Fi+1Xt(t-2)+…+FpXt(t-p)+at(7)
in the above formula (7) to the above formula (8), p is the model order; t is time, and the value interval of t is [1, N-L +1 ]](ii) a x and x' are any two inputs in the input data matrixThe sample is taken from the sample container,
and
the adjustable parameters in the covariance function are used for adjusting the shape of the covariance function changing on the horizontal axis and the vertical axis;
where x and x' are any two input samples in the input data matrix,
and
is an adjustable parameter in the covariance function and is used for adjusting the shape of the covariance function changing on the horizontal axis and the vertical axis.
S4.5, determining adjustable parameters in (4.3) according to the maximized marginal likelihood function
And
the marginal likelihood function can be calculated as follows:
K＝K(X0,X0) (10)
solving for tunable parameters using the following equation
And
optimum value of (2):
s5, testing input X by using the established Gaussian process regression model1Making a prediction to obtain a prediction output y1The prediction mean and the prediction variance are specifically realized by the following steps:
s5.1, the prior distribution of the test input can be directly obtained based on the Gaussian prior determined in the step S4.3 as follows:
y1～N(0,K(X1,X1))(12)
wherein, N (0, K (X)1,X1) Denotes a mean of zero and a variance of K (X)1,X1) Gaussian distribution of (y)1Is the test output to be predicted.
S5.2, according to the known training sample X0And Y0The training output and the test output can be obtained to satisfy the following joint gaussian distribution:
s5.3, the posterior distribution of the output to be predicted can be directly deduced according to a Bayes formula, and the method is as follows:
wherein the content of the first and second substances,
represents a mean value of
Variance is ω2The distribution of the gaussian component of (a) is,
is the predicted mean, ω, of the test output2Is the predicted variance of the test output.
S6, using the predicted variance of the test output obtained in step S5.3 as the control performance index p:
p＝ω2(15)
s7, repeatedly executing the evaluation steps (4-6) for a plurality of segments to be evaluated, wherein each segment can obtain a control performance index, finally a series of control performance index values are obtained, a change trend curve of the indexes can be drawn, and the control performance of the closed-loop control system is evaluated according to the change trend of the performance indexes obtained in the step S6: because a control loop with good performance generally has strong immunity and stability, output disturbance caused by various random disturbances generally does not repeatedly appear in a closed loop output periodically, and because the closed loop with poor control performance cannot compensate the disturbance in time, the uncompensated disturbance can continuously propagate in the loop and is presented in the closed loop output at certain time delay, so that the output has large autocorrelation and predictability, and according to the knowledge, the application of the performance evaluation index p is explained as follows:
s7.1, increasing the performance evaluation index p, which shows that the predictability of closed-loop output of the multivariable control loop is reduced, improving the control performance of the closed-loop control loop, and effectively resisting various random interferences by the controller without intervention;
s7.2, the performance evaluation index p has a decreasing trend, which shows that the predictability of the closed-loop output of the multivariable control loop is increased, the control performance of the closed-loop begins to degrade, the capability of the controller for resisting various random interferences is gradually reduced, and the loop evaluation result needs to be further observed;
3) the performance evaluation index p is continuously and stably reduced and does not increase any more, which shows that the predictability of the closed-loop output of the multivariable control loop is very strong, the control performance of the closed-loop is determined to be degraded, the capability of the controller for resisting various random interferences is poor, and the diagnosis of the degradation reason needs to be performed by the intervention of an operator.
Fig. 3, 4 and 5 are results of evaluation of the control performance of the thermal power generation process by the present method. According to fig. 3, it can be seen that the control performance index obtained by performing the proposed control performance evaluation method under the data set with good control performance varies from 0.2 to 1.4. It can be seen from fig. 4 that the control performance index proposed by the method is calculated under the data set of control performance degradation, the index change range is below 0.2, and the control performance grade can be obviously compared according to the fact that the larger the index is, the better the control performance is. Fig. 5 is a diagram illustrating the results of applying the proposed method to a case of loop control performance degradation caused by valve sticking, and it can be seen that the control performance index fluctuates around 0.4 in the first five evaluation segments, and from the sixth evaluation segment, the index rapidly drops below 0.2, and a smaller performance evaluation index value is continuously maintained, which indicates that the loop has undergone significant loop control performance degradation, and corresponding operation and maintenance and troubleshooting should be performed. The time for identifying the loop performance abnormity is earlier than the time for alarming caused by 75% jamming of the loop valve on site, other prior knowledge is not needed, and the method has universal applicability and higher evaluation accuracy and reliability compared with the traditional performance evaluation method.
Claims (3)
1. A multivariate closed-loop control loop performance evaluation method based on Gaussian process regression is characterized by comprising the following steps:
s1, selecting multivariable closed-loop output data to be evaluated, wherein for the multivariable industrial closed-loop control system, the operation process of the multivariable industrial closed-loop control system is set to contain M controlled variables, and a vector x (t) (x) of 1 × M is obtained by sampling at the time t1(t),x2(t),…,xM(t)), after H times of sampling, obtaining the data matrix X of the controlled variable under the condition of good control performanceM＝(x(t),x(t+1),…,x(t+H))T；
S2, data standardization: data matrix X of controlled variablesMSubtracting the mean value of the column by column and dividing by the standard deviation of the column for normalization to obtain a normalized data matrix
S3, calibrating the data matrix in the step S2
Dividing the evaluation segment into N evaluation segments with different data set lengthsThe data matrix of a single evaluation segment of the data points is marked as X, and R evaluation segments are obtained in total;
s4, performing autoregressive modeling on the evaluation fragment data matrix X, constructing training input, training output and test input of a model, and determining model parameters by using a least square method:
s4.1, firstly, determining the length of a non-overlapping sliding window to be L;
s4.2, designing training input, test input and training output of the multivariate autoregressive model in the Gaussian process; the training input data matrix is obtained by using the first (N-L) data points in the evaluation fragment data matrix X as follows:
taking each row of data points in the evaluation fragment data matrix X as input X of a Gaussian process multivariable autoregressive modeltT is time, and the value interval of t is [1, N-L +1 ]]；
Using the last L data points in the evaluation segment data matrix X to obtain a test input data matrix as follows:
X1＝[x(N-L+1) x(N-L+2) … x(N)](2)
by training the input data matrix X0The time corresponding to the first data point in the regression model is used as the output of the regression model:
Y0＝[1 2 ... N-2L+1]T(3)
s4.3, defining prior knowledge of a multivariate autoregressive model of the Gaussian process: definition atIs a white noise sequence, the model order is p, and the coefficient of the Gaussian process multivariable autoregressive model is Fj(j ═ 1, 2.., p), the following gaussian process multivariate autoregressive model was obtained:
Xt(t)＝F1Xt(t-1)+F2Xt(t-2)+…+FpXt(t-p)+at(4)
defining the mean m (x) as a constant 0 and the covariance function K (x, x') as a gaussian process of a gaussian kernel, as follows:
f(x)～GP(m(x),K(x,x′)) (5)
m(x)＝0 (6)
s4.4, calculating a prediction error:
Xt(t|t-i)＝Fia(t-i)+Fi+1Xt(t-2)+…+FpXt(t-p)+at(7)
in the above formula (7) to the above formula (8), p is the model order; t is time, and the value interval of t is [1, N-L +1 ]](ii) a x and x' are any two input samples in the input data matrix,
and
the adjustable parameters in the covariance function are used for adjusting the shape of the covariance function changing on the horizontal axis and the vertical axis;
s4.5, determining the adjustable parameters in the step S4.4 according to the maximized marginal likelihood function
And
the maximum marginal likelihood function is:
in the above formula, N is the number of training samples, and N is N to L + 1;
K＝K(X0,X0) (10)
wherein N is N-L +1, and solving the adjustable parameter
And
optimum value of (2):
s5, testing input X by using the established Gaussian process multivariable autoregressive model1Making a prediction to obtain a prediction output y1The prediction mean and the prediction variance are specifically realized by the following steps:
s5.1, obtaining prior distribution of test input based on the prior knowledge of the Gaussian process multivariable autoregressive model determined in the step S4.3:
y1～N(0,K(X1,X1)) (12)
in the above formula, N (0, K (X)1,X1) Denotes a mean of zero and a variance of K (X)1,X1) (ii) a gaussian distribution of; y is1Is the test output to be predicted;
s5.2, according to the known training sample X0And Y0And obtaining a training output and a test output which satisfy the following joint Gaussian distribution:
s5.3, the posterior distribution of the output to be predicted can be directly deduced according to a Bayesian formula:
in the above formula, the first and second carbon atoms are,
represents a mean value of
Variance is ω2(ii) a gaussian distribution of;
is the predicted mean, ω, of the test output2Is the predicted variance of the test output;
s6 using the predicted variance ω of the test output obtained in step S5.32As the control performance index p:
p＝ω2(15)
s7, for a plurality of evaluation segments to be evaluated, repeatedly executing the steps S4 to S6 to obtain the value of the control performance index p of each evaluation segment, and drawing a change trend curve of the control performance index p; using the value of the control performance index p obtained in step S6, the control performance of the closed-loop control system is evaluated according to its trend of change:
s7.1, if the performance evaluation index p is increased, the predictability of closed-loop output of the multivariable control loop is reduced, the control performance of the closed-loop is improved, and the controller effectively resists various random interferences without intervention;
s7.2, if the performance evaluation index p has a decreasing trend, the predictability of the closed-loop output of the multivariable control loop is increased, the control performance of the closed-loop begins to degrade, the capacity of the controller for resisting various random interferences is gradually reduced, and the loop evaluation result is further observed;
and S7.3, if the performance evaluation index p is continuously and stably reduced and is not increased any more, the predictability of the closed-loop output of the multivariable control loop is strong, the control performance of the closed-loop is determined to be degraded, the controller has poor capability of resisting various random interferences, and an operator intervenes to diagnose the degradation reason.
2. The multivariate closed-loop control loop performance assessment method based on Gaussian process regression as claimed in claim 1, characterized in that: in the step S3, the length of the evaluation segment is divided into 100-300 data points.
3. The multivariate closed-loop control loop performance assessment method based on Gaussian process regression as claimed in claim 1, characterized in that: in the step S4.1, the length L of the non-overlapping sliding window is determined according to the change characteristic of the controlled variable, where the change characteristic includes delay time and change speed.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010441944.8A CN111679648B (en) | 2020-05-22 | 2020-05-22 | Multivariate closed-loop control loop performance evaluation method based on Gaussian process regression |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010441944.8A CN111679648B (en) | 2020-05-22 | 2020-05-22 | Multivariate closed-loop control loop performance evaluation method based on Gaussian process regression |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN111679648A true CN111679648A (en) | 2020-09-18 |
| CN111679648B CN111679648B (en) | 2021-06-01 |
Family
ID=72452702
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010441944.8A Active CN111679648B (en) | 2020-05-22 | 2020-05-22 | Multivariate closed-loop control loop performance evaluation method based on Gaussian process regression |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN111679648B (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112826120A (en) * | 2021-03-18 | 2021-05-25 | 河南中烟工业有限责任公司 | Feed-forward control method and system for airflow type cut tobacco drying |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108536127A (en) * | 2018-04-20 | 2018-09-14 | 华中科技大学 | A kind of model mismatch diagnostic method of the multivariable control system of data-driven |
| US20190095400A1 (en) * | 2017-09-28 | 2019-03-28 | Sas Institute Inc. | Analytic system to incrementally update a support vector data description for outlier identification |
| US10310371B2 (en) * | 2008-12-18 | 2019-06-04 | Asml Netherlands B.V. | Method and system for lithography process-window-maximizing optical proximity correction |
| CN109978201A (en) * | 2017-12-27 | 2019-07-05 | 深圳市景程信息科技有限公司 | Probability load prediction system and method based on Gaussian process quantile estimate model |
| CN110263585A (en) * | 2019-06-26 | 2019-09-20 | 腾讯科技（深圳）有限公司 | Test monitoring and managing method, device, equipment and storage medium |
| CN111045415A (en) * | 2019-12-03 | 2020-04-21 | 沈阳化工大学 | Multi-modal process fault detection method based on local probability density double subspace |
-
2020
- 2020-05-22 CN CN202010441944.8A patent/CN111679648B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US10310371B2 (en) * | 2008-12-18 | 2019-06-04 | Asml Netherlands B.V. | Method and system for lithography process-window-maximizing optical proximity correction |
| US20190095400A1 (en) * | 2017-09-28 | 2019-03-28 | Sas Institute Inc. | Analytic system to incrementally update a support vector data description for outlier identification |
| CN109978201A (en) * | 2017-12-27 | 2019-07-05 | 深圳市景程信息科技有限公司 | Probability load prediction system and method based on Gaussian process quantile estimate model |
| CN108536127A (en) * | 2018-04-20 | 2018-09-14 | 华中科技大学 | A kind of model mismatch diagnostic method of the multivariable control system of data-driven |
| CN110263585A (en) * | 2019-06-26 | 2019-09-20 | 腾讯科技（深圳）有限公司 | Test monitoring and managing method, device, equipment and storage medium |
| CN111045415A (en) * | 2019-12-03 | 2020-04-21 | 沈阳化工大学 | Multi-modal process fault detection method based on local probability density double subspace |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112826120A (en) * | 2021-03-18 | 2021-05-25 | 河南中烟工业有限责任公司 | Feed-forward control method and system for airflow type cut tobacco drying |
Also Published As
| Publication number | Publication date |
|---|---|
| CN111679648B (en) | 2021-06-01 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110346160B (en) | SVR-based coal mill efficiency abnormity detection and diagnosis method | |
| CN106682814B (en) | Wind turbine generator fault intelligent diagnosis method based on fault knowledge base | |
| CN108681633B (en) | Condensate pump fault early warning method based on state parameters | |
| US5181482A (en) | Sootblowing advisor and automation system | |
| CN101657765B (en) | Method and apparatus for generalized performance evaluation of equipment using achievable performance derived from statistics and real-time data | |
| CN110879580B (en) | Analysis and monitoring method for large-range non-steady transient continuous process | |
| CN109471420B (en) | CVA-SFA-based method for monitoring control performance of air preheater of large coal-fired power generator set of intelligent power plant | |
| CN109238760B (en) | Online monitoring method of coal mill of intelligent power plant coal-fired generator set based on typical correlation analysis and slow characteristic analysis | |
| Santolamazza et al. | Anomaly detection in energy consumption for Condition-Based maintenance of Compressed Air Generation systems: an approach based on artificial neural networks | |
| CN112365045A (en) | Main steam temperature intelligent prediction method based on big data | |
| CN104777830A (en) | Multi-work-condition process monitoring method based on KPCA (kernel principal component analysis) mixture model | |
| CN111679648B (en) | Multivariate closed-loop control loop performance evaluation method based on Gaussian process regression | |
| CN104536439A (en) | Fault diagnosis method based on nested iterative Fisher discriminant analysis | |
| CN113468798A (en) | Medium-speed coal mill fault early warning method and system based on least square support vector machine algorithm | |
| CN110942258B (en) | Performance-driven industrial process anomaly monitoring method | |
| CN109184821B (en) | Online monitoring method for closed-loop information analysis of steam turbine of large-scale generator set | |
| CN111898794B (en) | Abnormal monitoring method for thermal efficiency of large coal-fired boiler | |
| CN105785761A (en) | Method for controlling temperature intelligent switching of cement raw materials in the course of decomposition | |
| CN111624979B (en) | Industrial closed-loop control loop multi-oscillation detection and tracing method based on slow characteristic analysis | |
| Li et al. | Early warning of critical blockage in coal mills based on stacked denoising autoencoders | |
| CN111651910B (en) | Coal mill-oriented sectional probabilistic state monitoring method | |
| CN112560339A (en) | Method for predicting temperature of guide bearing bush of hydroelectric generating set by machine learning | |
| Tutiv'en et al. | Wind turbine main bearing condition monitoring via convolutional autoencoder neural networks | |
| CN111474911B (en) | Gaussian non-Gaussian characteristic collaborative analysis and monitoring method for non-steady operation of high-end coal-fired power generation equipment | |
| CN112101733B (en) | Multi-indicating variable decoupling intelligent monitoring method for coal mill of high-end power generation equipment |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |