Key Performance Indicator Process Monitoring Method for Efficient Adaptive Nonlinear Model Updating

Abstract

The present invention discloses a key performance indicator process monitoring method for efficient adaptive nonlinear model updating, including: preprocessing the monitoring indicators to generate preprocessed indicators; mapping the preprocessed process variables to a high-dimensional space to generate a high-dimensional mapped input nonlinear matrix, constructing a Gaussian kernel function matrix, and generating a normalized Gaussian kernel function matrix; constructing an orthogonal projection nonlinear model based on the normalized Gaussian kernel function matrix and the preprocessed indicators reflecting the core changes of the equipment; based on the orthogonal projection nonlinear model, determining the statistic and control limit according to the normalized input nonlinear matrix and the preprocessed process variables for online monitoring, updating the orthogonal projection nonlinear model based on the current monitoring indicators, updating the statistic and control limit, and determining the current operating state of the complex equipment according to the updated statistic and the updated control limit. The present invention can improve the real-time performance of online monitoring.

Description

Technical Field

[0001] The present invention relates to the field of large equipment and complex industrial process monitoring, and particularly to a key performance index process monitoring method for efficient adaptive nonlinear model updating. Background Art

[0002] In the monitoring of large equipment and complex industrial processes, a large amount of data monitored by a large number of sensors usually exhibits the characteristics of high dimension, multi-variable input and output, high coupling, and non-linear distribution. Therefore, how to extract features that can reflect the key performance indicators of the system from the complex changes of massive data is an urgent problem to be solved. The non-linear change of data is a common phenomenon in the complex process of large equipment, usually reflected in the non-linear distribution between input variables, and the non-linear distribution between process variables and key performance indicators. Therefore, how to extract non-linear features reflecting the changes of key performance indicators from non-linearly distributed process data is a difficult problem in research.

[0003] In addition, in large and complex equipment, due to equipment aging and slight changes in the working environment, the working point will slowly drift, resulting in slow time-varying changes in the system. Therefore, it is necessary to update the model regularly to track the changes of the system and avoid serious false alarms. In non-linear processes, traditional model update methods require a large number of accumulated normal samples. Although the construction of kernel functions in non-linear process monitoring avoids the calculation of non-linear functions, the computational complexity will gradually increase with the increase in the number of samples, thereby reducing the model update efficiency and affecting the real-time performance of online monitoring. Summary of the Invention

[0004] The purpose of the present invention is to provide a key performance index process monitoring method for efficient adaptive non-linear model updating to solve the problem of poor real-time performance of online monitoring.

[0005] To achieve the above object, the present invention provides the following solution:

[0006] A key performance index process monitoring method for efficient adaptive non-linear model updating includes:

[0007] Obtain the monitoring indicators of complex equipment, and preprocess the monitoring indicators to generate preprocessed indicators; the monitoring indicators include process variables and indicators reflecting the core changes of the equipment; the preprocessed indicators include preprocessed process variables and preprocessed indicators reflecting the core changes of the equipment; the process variables include temperature, flow rate, and pressure; the indicators reflecting the core changes of the equipment include servo mechanism nozzles and product concentrations;

[0008] Map the preprocessed process variables to a high-dimensional space to generate a high-dimensional mapped input non-linear matrix;

[0009] Construct a Gaussian kernel function matrix based on the input non - linear matrix, and perform normalization processing on the Gaussian kernel function matrix to generate a normalized Gaussian kernel function matrix;

[0010] Construct an orthogonal projection non - linear model based on the normalized Gaussian kernel function matrix and the index reflecting the core changes of the equipment after pre - processing;

[0011] Based on the orthogonal projection non - linear model, determine the statistic and control limit according to the normalized input non - linear matrix and the pre - processed process variables;

[0012] Perform online monitoring according to the statistic and the control limit to obtain the current monitoring index of the online monitoring;

[0013] Update the orthogonal projection non - linear model based on the current monitoring index to determine the updated orthogonal projection non - linear model;

[0014] Update the statistic and the control limit according to the updated orthogonal projection non - linear model, and determine the current operating state of the complex equipment according to the updated statistic and the updated control limit; the current operating state is that the complex equipment has a quality - related fault or the complex equipment is operating normally.

[0015] Optionally, pre - process the monitoring index to generate a pre - processed index, specifically including:

[0016] Calculate the mean and standard deviation of the monitoring index;

[0017] Perform standardization processing on each sample in the monitoring index to unify the data scale and generate a pre - processed index.

[0018] Optionally, the normalized Gaussian kernel function matrix is:

[0019]

[0020] where, 1 n is the all - one column vector of n is the identity matrix of x is the Gaussian kernel function matrix, is the 1 - dimensional real number set, is the n - dimensional real number set, and n is the number of training data samples.

[0021] Optionally, an orthogonal projection non-linear model is constructed based on the normalized Gaussian kernel function matrix and the pre-processed indicators reflecting the core changes of the equipment, specifically including:

[0022] Determine the input latent variable vector of the s-th iteration, the output projection vector of the s-th iteration, and the output latent variable vector of the s-th iteration according to the normalized Gaussian kernel function matrix and the pre-processed indicators reflecting the core changes of the equipment; s is the number of iterations;

[0023] Determine the output load matrix according to the output projection vector of the s-th iteration;

[0024] Determine the output estimation matrix according to the input latent variable vector of the s-th iteration, the output projection vector of the s-th iteration, and the output latent variable vector of the s-th iteration;

[0025] Determine the quality-related orthogonal projection vector of the s-th iteration according to the output estimation matrix;

[0026] Determine the load vector of the s-th iteration of the input matrix and the orthogonal score vector of the s-th iteration according to the quality-related orthogonal projection vector;

[0027] Determine the input load matrix according to the load vector of the s-th iteration;

[0028] Determine the orthogonal input score matrix according to the orthogonal score vector;

[0029] Construct an orthogonal projection non-linear model according to the input non-linear matrix after high-dimensional mapping, the pre-processed indicators reflecting the core changes of the equipment, the input load matrix, the orthogonal input score matrix, and the output load matrix.

[0030] Optionally, the orthogonal projection non-linear model is:

[0031]

[0032] where Ψ x is the input non-linear matrix after high-dimensional mapping, is the quality-related matrix, is the residual space matrix, P x is the input load matrix, T or is the orthogonal input score matrix, Y * is the pre-processed indicator reflecting the core changes of the equipment, is the input predictable matrix, is the output residual matrix, T p is the original score matrix, Q is the output load matrix, and T is the transpose operation.

[0033] Optionally, based on the orthogonal projection nonlinear model, determine the statistic and the control limit according to the normalized input nonlinear matrix and the preprocessed process variable, specifically including:

[0034] Determine the quality-related orthogonal projection matrix according to the quality-related orthogonal projection vector;

[0035] Based on the orthogonal projection nonlinear model, determine the statistic according to the quality-related orthogonal projection matrix, the normalized input nonlinear matrix, the preprocessed process variable, and the orthogonal input score matrix;

[0036] Calculate the variance and mean of the statistic;

[0037] Determine the control limit according to the variance and mean of the statistic.

[0038] Optionally, determine the current operating state of the complex device according to the updated statistic and the updated control limit, specifically including:

[0039] When the updated statistic is greater than or equal to the updated control limit, determine that the current operating state is that the complex device has a quality-related fault;

[0040] When the updated statistic is less than the updated control limit, determine that the current operating state is that the complex device is operating normally.

[0041] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects: The present invention provides a key performance index process monitoring method for efficient adaptive nonlinear model updating. By constructing an orthogonal projection nonlinear model, the process monitoring of nonlinear orthogonal projection is realized, and the false alarm rate of quality-unrelated faults is reduced. At the same time, the current monitoring index of online monitoring is used to replace the original data, and a recursive model for nonlinear adaptive updating is constructed, that is, the orthogonal projection nonlinear model is updated to achieve efficient model updating, track the parameter changes of the system, and improve the real-time performance of online monitoring. Description of the Drawings

[0042] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0043] Figure 1 It is a flowchart of the key performance index process monitoring method for efficient adaptive nonlinear model updating provided by the present invention;

[0044] Figure 2 Quality-related fault detection diagram provided by the present invention;

[0045] Figure 3 Quality-unrelated fault detection diagram provided by the present invention;

[0046] Figure 4 Schematic diagram of the fluctuation of variable 3 over time provided by the present invention;

[0047] Figure 5 Schematic diagram of the quality-related fault detection situation provided by the present invention. Detailed implementation manners

[0048] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0049] The purpose of the present invention is to provide a key performance indicator process monitoring method for efficient adaptive nonlinear model update, which can improve the real-time performance of online monitoring.

[0050] To make the above objects, features and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific implementation manners.

[0051] Embodiment 1

[0052] Figure 1 Flowchart of the key performance indicator process monitoring method for efficient adaptive nonlinear model update provided by the present invention, as Figure 1 shown, a key performance indicator process monitoring method for efficient adaptive nonlinear model update includes:

[0053] Step 101: Obtain the monitoring indicators of the complex equipment, and preprocess the monitoring indicators to generate preprocessed indicators; the monitoring indicators include process variables and indicators reflecting the core changes of the equipment; the preprocessed indicators include preprocessed process variables and preprocessed indicators reflecting the core changes of the equipment; the process variables include temperature, flow rate, and pressure; the indicators reflecting the core changes of the equipment include servo mechanism nozzles and product concentrations.

[0054] In the health state management of large and complex equipment (such as inertial measurement units, servo mechanisms, safety control systems, etc.), a large amount of process data can be measured by various sensors such as temperature sensors, vibration sensors, gyroscopes, and electrical signals. Among a large number of monitoring indicators, process variables are selected as input X (such as temperature, flow rate, pressure, etc.), and indicators reflecting the core changes of the equipment (such as servo mechanism nozzles, product concentrations, etc.) are selected as output variable Y. Suppose there are m input monitoring indicators and p output monitoring indicators, and the first n samples of the initial operation of the equipment are used as training data and

[0055] Calculate the mean and standard deviation of the training data X and Y

[0056]

[0057]

[0058] where, x i,j is the j-th sampling sample of the i-th variable in X, and y i,j is the j-th sampling sample of the i-th variable in Y. is the mean of the first n samplings of the j-th variable, is the mean of the first n samplings of the s-th variable. δ x,i is the variance of the first n samplings of the i-th variable in X, and δ y,i is the variance of the first n samplings of the i-th variable in Y.

[0059] Standardize each sample x i,j and y i,j in X and Y respectively to unify the data scale,

[0060]

[0061]

[0062] Denote the standardized input and output data by symbols X * = [x * 1,..., x * m and Y * = [y * 1,..., y * p , where

[0063] In practical applications, the monitoring indicators are preprocessed to generate preprocessed indicators, specifically including: calculating the mean and standard deviation of the monitoring indicators; performing standardization processing on each sample in the monitoring indicators to unify the data scale and generate preprocessed indicators.

[0064] Step 102: Map the preprocessed process variables to a high-dimensional space to generate a high-dimensional mapped input non-linear matrix.

[0065] In practical applications, due to the fact that large-scale equipment usually faces complex working conditions, the standardized data still has a non-linear distribution, and there is also a non-linear relationship between the process variables and the key performance indicators. In order to extract non-linear features related to the key performance indicators from the process data, the preprocessed process data is mapped to a high-dimensional space X * →Ψ x , where the high-dimensional mapped input non-linear matrix Ψ x has no actual numerical value and is only represented by symbols.

[0066] Step 103: Construct a Gaussian kernel function matrix based on the input non-linear matrix and perform normalization processing on the Gaussian kernel function matrix to generate a normalized Gaussian kernel function matrix.

[0067] In practical applications, based on the input non-linear matrix, a Gaussian kernel function matrix is constructed:

[0068] K x (e,j)=ψ(x e )ψ(x j ) T (5)

[0069] where ψ(·) represents the non-linear mapping function of the sample, and K x (e,j) represents the kernel function of the e-th sampling sample and the j-th sampling sample of Ψ x . After solving the calculation of the kernel function between each sample of the input data, the kernel function matrix of Ψ x is

[0070] Specifically, the calculation formula of the kernel function is where exp() represents the exponential function operation, and c is the kernel parameter, which is determined by optimization.

[0071] After the kernel function K x is constructed, it needs to be normalized, and the calculation is as follows:

[0072]

[0073] where, 1 n is All - one column vector, I n is the identity matrix of

[0074] Step 104: Construct an orthogonal projection non - linear model according to the normalized Gaussian kernel function matrix and the pre - processed index reflecting the core changes of the equipment.

[0075] In practical applications, Step 104 specifically includes: determining the input latent variable vector of the s - th iteration, the output projection vector of the s - th iteration, and the output latent variable vector of the s - th iteration according to the normalized Gaussian kernel function matrix and the pre - processed index reflecting the core changes of the equipment; s is the number of iterations; determining the output load matrix according to the output projection vector of the s - th iteration; determining the output estimation matrix according to the input latent variable vector of the s - th iteration, the output projection vector of the s - th iteration, and the output latent variable vector of the s - th iteration; determining the quality - related orthogonal projection vector of the s - th iteration according to the output estimation matrix; determining the load vector of the s - th iteration of the input matrix and the orthogonal score vector of the s - th iteration according to the quality - related orthogonal projection vector; determining the input load matrix according to the load vector of the s - th iteration; determining the orthogonal input score matrix according to the orthogonal score vector; constructing an orthogonal projection non - linear model according to the high - dimensional mapped input non - linear matrix, the pre - processed index reflecting the core changes of the equipment, the input load matrix, the orthogonal input score matrix, and the output load matrix.

[0076] To construct a non - linear model of orthogonal projection, the non - linear orthogonal regression modeling method is constructed as follows:

[0077] Initialize the number of iterations s = 1, and arbitrarily select a column y in Y * as the initial output load vector u1, u s = y.

[0078] Step 1) Iteration of the quality - related projection direction:

[0079] Calculate the input latent variable vector t s of the s - th iteration, and normalize it: t s = t s / ||t s ||; where is the input kernel function in the s - th iteration.

[0080] Calculate the output projection vector q s of the s - th iteration, and normalize it: q s = q s / ||q s ||.

[0081] Calculate the output latent variable vector u for the s-th iteration s , and normalize it: u s = Y * q s , u s = u s / ||u s ||.

[0082] Repeat step 1) until the above process converges.

[0083] Step 2) Calculate the orthogonal projection direction:

[0084] Output the estimation matrix where is the correlation coefficient matrix of the input and output. Construct the correlation eigenmatrix MM T as follows:

[0085]

[0086] H is a transition matrix (without practical meaning), that is, let Perform singular value decomposition on H to obtain

[0087]

[0088] where is the quality-related orthogonal projection vector for the s-th iteration, is the sub-component projection matrix for the s-th iteration, Λ o is the eigenvalue matrix.

[0089] Step 3) Update the parameters:

[0090] Calculate the load vector of the input matrix Ψ for the s-th iteration:

[0091]

[0092] The orthogonal score vector for the s-th iteration is calculated as follows:

[0093]

[0094] Update the kernel function matrix of Ψ:

[0095]

[0096] Update the output matrix:

[0097]

[0098] Let s = s + 1, and return to step 1).

[0099] Repeat the above steps until A principal components are extracted to obtain the orthogonal input score matrix T or =[t or,1 ,...,t or,A , where t or,s is the latent variable of Ψ x extracted by the s-th sub-component.

[0100] Construct the orthogonal projection non-linear model as follows:

[0101]

[0102] where is the quality-related matrix, is the residual space matrix, P x is the input load matrix, P x =[p x,1 ,...,p x,A , T or is the orthogonal input score matrix, is the input predictable matrix, is the output residual matrix, Q is the output load matrix, Q = [q x,1 ,...,q x,A , T p =[t1,...,t A is the original score matrix, and T is the transpose operation.

[0103] Step 105: Based on the orthogonal projection non-linear model, determine the statistic and control limit according to the normalized input non-linear matrix and the pre-processed process variable.

[0104] Construct the coefficient matrix R of the pre-processed non-linear data Ψ x and the orthogonal input score matrix:

[0105]

[0106] Then the orthogonal input score matrix T or can be directly calculated as follows:

[0107]

[0108] The score vector t of a single sample after non-linear mapping is calculated as follows:

[0109]

[0110] where V is the quality-related orthogonal projection matrix, obtained by the iterative regression process, k is and Ψ xKernel function

[0111] Construct T 2 Statistic

[0112] T 2 = t T Λ -1 t(13)

[0113] Where is the feature matrix

[0114] Construct the control limit J

[0115]

[0116] where g = ξ / 2μ and h = 2μ 2 / ξ, ξ and μ represent the variance and mean of all sample T statistics in the training set respectively 2 Statistic

[0117] Step 106: Perform online monitoring based on the statistic and the control limit to obtain the current monitoring index of the online monitoring

[0118] At this time, the current operating state of the complex device can be determined through the statistic and the control limit, and the fault diagnosis logic is

[0119] If T 2 ≥ J, a quality-related fault occurs

[0120] If T 2 < J, the complex device is operating normally

[0121] Step 1: Update the orthogonal projection nonlinear model based on the current monitoring index to determine the updated orthogonal projection nonlinear model

[0122] In practical applications, the adaptive nonlinear recursive iteration process of the updated orthogonal projection nonlinear model is as follows

[0123] When the large complex equipment is in operation, the current monitoring index of the online monitoring will be projected along the constructed model and a statistic will be constructed to determine whether a fault occurs. Let the online test sample be Map it to a high-dimensional space to get φ(x new ), the test sample score vector t new and the statistic T 2 The calculation formulas are as follows

[0124] t new = R T φ(x new ) (15)

[0125]

[0126] where \(R\) is the projection coefficient matrix obtained from the offline process training, and it is the feature matrix.

[0127] The fault diagnosis logic is used to judge whether the test sample is abnormal. If it is normal, the input and output test data are stored in \(X\) new =\([X new x new \), \(Y\) new =\([Y new y new \). After storing \(W\) normal test samples, due to the influence of slow time-varying, the model needs to be updated regularly. At this time

[0128] From the training model, when the number of principal components \(A = m\) is taken, the following relationship can be obtained:

[0129]

[0130] where \(T\) T \(T = I\).

[0131] Then equation (17) can be written as

[0132]

[0133] Therefore, the non-linear input matrix \(\varPsi\) x can be represented by the input load matrix .

[0134]

[0135] From equation (19), \(Y\) can be represented by the output load complex \(Q\) T .

[0136] Combining the model parameters and the stored test data, the model update input matrix \(X\) m and the output matrix \(Y\) m can be constructed as follows:

[0137]

[0138] Map \(X\) m to a high dimension to obtain the non-linear mapping input matrix \(\varPsi\) m , then the kernel function \(K\) m of \(\varPsi\) m is calculated as follows:

[0139]

[0140] ① First, calculate \(P\) m in \(K\) TP:

[0141]

[0142] Among them, is the load vector in the s-th iteration of step 1, and the non-linear input matrix in the (s + 1)-th iteration Therefore, the following relationship exists:

[0143]

[0144] ② Calculate K m in

[0145]

[0146] K new is the kernel function of Ψ new .

[0147] ③ Calculate P in K m Ψ T Ψ new and

[0148]

[0149] From the above can be calculated as

[0150]

[0151] Among them, K r represents the kernel function matrix of Ψ and Ψ new .

[0152] Based on ①, ② and ③, K m is solved.

[0153] Substitute Ψ m , Y new and K m into the non-linear orthogonal iteration in Section B to obtain the model update parameters T or , the quality-related orthogonal projection matrix V and the R projection coefficient matrix. Establish a recursive update model:

[0154]

[0155] Construct the model update statistic and control limit from formulas (11)-(14) to complete the model update.

[0156] Step 108: Update the statistic and the control limit according to the updated orthogonal projection non-linear model, and determine the current operating state of the complex device according to the updated statistic and the updated control limit; the current operating state is that the complex device has a quality-related fault or the complex device is operating normally.

[0157] Specifically, for the newly measured test samples, the statistic and the control limit will be constructed along the updated orthogonal projection non-linear model to achieve fault detection.

[0158] Embodiment 2

[0159] A. Tennessee - Eastman Experiment

[0160] In the process monitoring of large complex equipment, the system is usually a multi-input multi-output time-varying system, which is characterized by large samples, high dimensions, high coupling, etc. Analyzing the above process, its data characteristics are similar to the Tennessee - Eastman process (TEP). Therefore, TEP is used to verify the effectiveness of the proposed method. TEP is a typical benchmark experiment, a classic simulation experiment for verifying multi-input multi-output process anomaly detection methods. It is a small industrial process model developed in 1993, consisting of five operating units, including a chemical reactor, a condenser, a compressor, a vapor / liquid separator, and a separator. Its purpose is to monitor whether the product content after multi-stage reaction meets the standards.

[0161] TEP contains a training data set and a test data set. The training data set contains 480 normal samples, and the test data set contains 1920 samples, of which the first 1120 are normal samples and the last 800 are fault samples. In each data set, there are a total of 33 input variables and 5 output variables. In addition, the test data contains a total of 11 types of faults, of which 6 faults are quality-related faults and 5 faults are quality-unrelated faults.

[0162] Note: 1. Quality-related faults are fault situations where abnormal process data input will affect the output change; 2. Quality-unrelated faults are fault situations where abnormal process data input will not affect the output change.

[0163] Next, experiments will be carried out based on TEP data. Let the process data in the training data be The output data in the training data is

[0164] First, calculate the means u x,j , u y,j and variances δ x , δ y , and perform standardization:

[0165]

[0166]

[0167] Then, perform non - linear orthogonal regression modeling to obtain the training model parameters T or , V, and R.

[0168] Construct the T 2 statistic:

[0169] T 2 = t T Λ -1 t

[0170] Where

[0171] Construct the control limit J:

[0172]

[0173] Where g = ξ / 2μ and h = 2μ 2 / ξ, and ξ and μ represent the variance and mean of the T - statistics of each sample in the training set respectively.

[0174] Online monitoring:

[0175] Collect a single sample of the test data to obtain x new , and standardize it

[0176]

[0177] Calculate the statistic of x new :

[0178]

[0179] Perform fault detection:

[0180] If T 2 ≥ J, a quality - related fault occurs;

[0181] If T 2 < J, the system is operating normally, and store the current normal data X new = [X new x new , Y new = [Y new y new .

[0182] After W data are online - monitored, update the model. First, construct the model update matrices X m and Y m , where

[0183] Calculate the kernel function matrix of the computational model update matrix

[0184]

[0185] Calculate K from Equation (24) - Equation (26) m Substitute Ψ m , Y new and K m into the non - linear orthogonal iteration in Section B to obtain the model update parameters T or , V and R.

[0186] The test samples for the next acquisition will calculate the statistic based on the obtained parameters to achieve fault detection after model update.

[0187] Figure 2 is the quality - related fault detection diagram provided by the present invention, Figure 3 is the quality - unrelated fault detection diagram provided by the present invention. The experimental results are as Figure 2 - Figure 3 shown:[[]]

[0188] (1) Quality-related faults:

[0189] Figure 2 is the result of quality - related fault detection. It can be seen that before 1120 samples, the model was updated three times. The model showed significant anomalies in the samples after 1120 faults, far exceeding the control limit. Therefore, effective alarm for quality - related faults can be achieved.

[0190] (2) Quality - unrelated faults:

[0191] Figure 3 shows the result of the proposed method for quality - unrelated fault detection. For quality - unrelated faults, although there are anomalies in the process data X, they do not affect the change of the output. Since online monitoring only judges whether the output is abnormal by constructing the statistic of the input data, for quality - unrelated faults, if the T2 statistic gives an alarm, it is a false alarm. False alarm is a phenomenon that seriously affects the normal operation of large complex equipment. Once it occurs, it will delay the operation of the equipment and conduct fault troubleshooting. From Figure 3 it can be seen that after 1120, they are all quality - unrelated fault samples, and there are no false alarms in the monitoring space, indicating good detection performance.

[0192] B. Numerical simulation experiment

[0193] Since in the actual process, the influence of slow time - varying usually requires a long period and high time cost, therefore, numerical simulation experiments are used to simulate the influence of slow time - varying on the system in the non - linear process and verify the performance of the proposed non - linear adaptive update method in the slow time - varying process.

[0194] In the numerical simulation, it is set that the training data X and Y contain 500 samples, and each sample consists of 5 variables. The test data contains 1500 samples, among which the first 1000 are normal data and the last 500 are faulty samples. In the numerical simulation, a time-varying factor is set, and the fluctuation of the system will gradually increase with time. Figure 4 It is a schematic diagram showing the fluctuation of variable 3 over time provided by the present invention. The change of the 3rd variable in the test data is as Figure 4 shown, and it can be seen from Figure 4 that the fluctuation of variable 3 also gradually increases with time.

[0195] Figure 5 It is a schematic diagram showing the detection of quality-related faults provided by the present invention. The detection results of quality-related faults are as Figure 5 shown, and it can be seen from Figure 4 that the first 1000 samples are updated 5 times, and after 1000, the occurrence of quality-related faults is significantly detected.

[0196] Taking large-scale complex equipment as the research object, a key performance index method for efficient adaptive nonlinear model updating is explored to realize the updating of the slow time-varying nonlinear process model and the detection of quality-related faults.

[0197] The present invention provides a key performance index process monitoring method for efficient adaptive nonlinear model updating, which takes into account both the computational complexity of model updating and the detection performance of quality-related faults, effectively reduces the computational complexity of model updating, improves the online updating efficiency of the model, and has a more excellent quality-related fault detection rate and a lower false alarm rate. It provides a theoretical basis and technical support for the online fault monitoring of large-scale complex equipment and industrial process monitoring, thereby saving expenditure and avoiding unnecessary economic losses, and has good engineering application value.

[0198] In this specification, each embodiment is described in a progressive manner. The key point of each embodiment is to illustrate the differences from other embodiments. The same or similar parts among the embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the description of the method part.

[0199] In this article, specific examples are used to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, based on the idea of the present invention, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to the present invention.

Claims

1. A key performance indicator process monitoring method for efficient adaptive non-linear model updating, characterized in that, Including: Obtain the monitoring indicators of complex equipment, and preprocess the monitoring indicators to generate preprocessed indicators; The monitoring indicators include process variables and indicators reflecting the core changes of the equipment; The preprocessed indicators include preprocessed process variables and preprocessed indicators reflecting the core changes of the equipment; the process variables include temperature, flow rate, and pressure; the indicators reflecting the core changes of the equipment include servo mechanism nozzles and product concentrations; Map the preprocessed process variables to a high-dimensional space to generate a high-dimensional mapped input non-linear matrix; Construct a Gaussian kernel function matrix based on the input non-linear matrix, and perform normalization processing on the Gaussian kernel function matrix to generate a normalized Gaussian kernel function matrix; Construct an orthogonal projection non-linear model based on the normalized Gaussian kernel function matrix and the preprocessed indicators reflecting the core changes of the equipment, specifically including: Determine the input latent variable vector of the s-th iteration, the output projection vector of the s-th iteration, and the output latent variable vector of the s-th iteration according to the normalized Gaussian kernel function matrix and the preprocessed indicators reflecting the core changes of the equipment; s is the number of iterations; Determine the output load matrix according to the output projection vector of the s-th iteration; Determine the output estimation matrix according to the input latent variable vector of the s-th iteration, the output projection vector of the s-th iteration, and the output latent variable vector of the s-th iteration; Determine the quality-related orthogonal projection vector of the s-th iteration according to the output estimation matrix; Determine the load vector of the s-th iteration of the input matrix and the orthogonal score vector of the s-th iteration according to the quality-related orthogonal projection vector; Determine the input load matrix according to the load vector of the s-th iteration; Determine the orthogonal input score matrix according to the orthogonal score vector; Construct an orthogonal projection non-linear model based on the high-dimensional mapped input non-linear matrix, the preprocessed indicators reflecting the core changes of the equipment, the input load matrix, the orthogonal input score matrix, and the output load matrix; The orthogonal projection non-linear model is: Among them, Ψ x is the input non-linear matrix after high-dimensional mapping, is the quality-related matrix, is the residual space matrix, P x is the input load matrix, T or is the orthogonal input score matrix, Y * is the index reflecting the core changes of the equipment after preprocessing, is the input predictable matrix, is the output residual matrix, T p is the original score matrix, Q is the output load matrix, and T is the transpose operation; Based on the orthogonal projection non-linear model, determine the statistic and control limit according to the normalized input non-linear matrix and the preprocessed process variables; Perform online monitoring according to the statistic and the control limit to obtain the current monitoring indicators of the online monitoring; [[ID=********]]Update the orthogonal projection non-linear model based on the current monitoring indicators to determine the updated orthogonal projection non-linear model; [[ID=********]]Update the statistic and the control limit according to the updated orthogonal projection non-linear model, and determine the current operating state of the complex equipment according to the updated statistic and the updated control limit; the current operating state is that the complex equipment has a quality-related fault or the complex equipment is operating normally.

2. The key performance indicator process monitoring method for efficient adaptive nonlinear model updating according to claim 1, characterized in that Preprocess the monitoring indicators to generate preprocessed indicators, specifically including: Calculate the mean and standard deviation of the monitoring indicators; Perform standardization processing on each sample in the monitoring indicators to unify the data scale and generate preprocessed indicators. It should be noted that there are some potential issues in the original text where the same variable naming and description seem a bit repetitive and could be further optimized for clarity. Also, the two parts marked with "********" in the translation might need to be adjusted according to more specific and correct content in the original Chinese if there are inaccuracies in the provided text.

3. The key performance indicator process monitoring method for efficient adaptive non-linear model updating according to claim 1, characterized in that The Gaussian kernel function matrix after the normalization process is as follows: Among them, 1 n is a column vector of all 1s, I n is the identity matrix, K x is the Gaussian kernel function matrix, is the set of 1-dimensional real numbers, is the set of n-dimensional real numbers, where n is the number of training data samples.

4. The key performance indicator process monitoring method for efficient adaptive non - linear model updating according to claim 1, characterized in that, Based on the orthogonal projection non-linear model, determine the statistic and the control limit according to the normalized input non-linear matrix and the preprocessed process variable, specifically including: Determine the quality-related orthogonal projection matrix according to the quality-related orthogonal projection vector; Based on the orthogonal projection non-linear model, determine the statistic according to the quality-related orthogonal projection matrix, the normalized input non-linear matrix, the preprocessed process variable, and the orthogonal input score matrix; Calculate the variance and the mean of the statistic; Determine the control limit according to the variance and the mean of the statistic.

5. The key performance indicator process monitoring method for efficient adaptive non - linear model updating according to claim 1, characterized in that, Determine the current operating state of the complex device according to the updated statistic and the updated control limit, specifically including: When the updated statistic is greater than or equal to the updated control limit, determine that the current operating state is that the complex device has a quality-related fault; When the updated statistic is less than the updated control limit, determine that the current operating state is that the complex device is operating normally.

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