A process monitoring method and device based on residual whiteness

Abstract

The present application relates to the technical field of statistical process monitoring, in particular to a process monitoring method and device based on residual whiteness. The present application model is suitable for processes with obvious dynamic characteristics, can effectively mine the dynamic characteristics of the process, and has better physical interpretability compared with traditional dynamic process monitoring models. The present application proposes a new W statistic, which can not only monitor the changes of principal component and residual subspace distribution, but also effectively monitor the dynamic characteristic changes of the process based on the whiteness of the residual principal component. Compared with traditional data-driven process monitoring methods, the present application can not only sensitively reflect the dynamic characteristic abnormalities of the process and reduce the false negative rate, but also effectively distinguish non-dynamic characteristic abnormal factors such as normal shift of working point and disturbance expansion, thereby providing more accurate information for the operator and having strong practical value.

Description

Technical Field

[0001] This invention relates to the field of statistical monitoring technology, and in particular to a process monitoring method and device based on residual whiteness. Background Technology

[0002] Many abnormal factors affect the normal operation of industrial processes, such as model mismatch, disturbances, and valve sticking. Real-time monitoring of the process, enabling timely alarms for anomalies, is crucial for the safe, stable, and efficient operation of the process. However, due to the generally complex mechanisms of industrial processes, modeling based on specific mechanisms is often difficult, thus limiting the applicability of model-based performance monitoring methods in real-world production scenarios. In recent years, multivariate statistical process monitoring (MSPM) has gained widespread attention due to its advantage of requiring only historical data collected from the industrial field without relying on extensive process mechanisms, making it applicable to various complex and variable industrial processes. Therefore, MSPM is receiving increasing attention.

[0003] Actual industrial processes are often dynamic, resulting in data exhibiting both autocorrelation and cross-correlation. To describe the static and dynamic relationships within the data, Dynamic Principal Component Analysis (DPCA) has been widely applied, utilizing T... 2 The Q statistic describes the overall covariance of latent variables, and the Q statistic describes the size of the residual space, thus reflecting the occurrence of anomalies. However, DPCA struggles to obtain time-independent residuals, making the control region of the Q statistic overly conservative and reducing its detection sensitivity. Dynamic latent variable models, represented by DiPCA and DiCCA, sequentially calculate predictable components to improve the decorrelation level of residuals; however, this gradual optimization of latent variables makes it difficult to completely eliminate residual correlations. In fact, time-independent residuals are an important modeling indicator and should be enforced. Furthermore, the traditional Q statistic describes data changes from a variance perspective, lacking sufficient information for alarms regarding anomalies. Shifts in steady-state operating points, changes in dynamic characteristics, and amplification of disturbances can all lead to alarms, leaving operators with little information about the type of anomaly. Therefore, designing interpretable statistics is meaningful. Summary of the Invention

[0004] To address the above problems, this invention provides a process monitoring method and apparatus based on residual whiteness.

[0005] In a first aspect, the present invention provides a process monitoring method based on residual whiteness, the method comprising:

[0006] The online measurement values ​​of the process variables to be monitored are read in, formed into an input vector, and input into the white component model to obtain the online real-time calculation value of the feature vector z(t);

[0007] The statistics T are obtained based on the residual characteristics of the eigenvector z(t). 2 Instantaneous estimates of Q and W;

[0008] Statistic T 2 The instantaneous estimates of Q and W are compared with the corresponding control limits to achieve process monitoring that maximizes residual whiteness.

[0009] Furthermore, the white component model is as follows:

[0010]

[0011] Where m is the dimension of the input vector, x(t) is the m-dimensional input vector discretized at the sampling time, z(t) is the m-dimensional feature vector discretized at the sampling time, and its statistical properties are somewhat similar to white noise; the coefficient matrix P is an m-order square matrix, μ is the m-dimensional input vector, μ represents the bias of the feature vector, and t is the sampling time.

[0012] Furthermore, the structure of the input vector x(t) is as follows:

[0013]

[0014] Where, {x1,x2,…,x n Let} be n input variables, Δt be the sampling interval of the input variables, and d be the length of the historical data contained in the input vector; the dimension m of the input vector satisfies the relation m = n(d + 1).

[0015] Furthermore, based on the residual characteristics of the eigenvector z(t), the statistics T are obtained respectively. 2 Instantaneous estimates of Q and W, including:

[0016] The vector z is composed of the first M residual features in the feature vector z(t). e (t), based on vector z e (t) yields the instantaneous estimate of the statistic Q.

[0017] Furthermore, according to vector z e The instantaneous estimate of the statistic Q is obtained using the following formula:

[0018]

[0019] R = P -T =[r1 r2 … r m ],R e=[r1 r2 … r M ]

[0020]

[0021] Where z e z(t) is the feature vector composed of the first M residual features whose statistical properties are close to white noise, where M is the number of residual features, m is the dimension of the input vector, and r is the number of residual features. k For feature z k The load vector, R is the characteristic load matrix, R e Let Q be a matrix composed of the load vectors of the first M residual features, where t is the sampling time. α Let Q be the control limit and α be the confidence level.

[0022] Furthermore, based on the residual characteristics of the eigenvector z(t), the statistics T are obtained respectively. 2 The instantaneous estimates of Q and W also include:

[0023] The vector z(t) is composed of mM features. p (t), based on vector z p (t) yields the statistic T 2 The instantaneous estimate.

[0024] Furthermore, according to vector z p (t) yields the statistic T 2 The instantaneous estimate is obtained using the following formula:

[0025]

[0026] E{[z k (t)] 2}=λ k M+1≤k≤m

[0027] Λ=diag{λ M+1 ,λ M+2 ,…,λ m}

[0028] Where z p z(t) is the vector composed of mM features following the feature vector z(t); M is the number of residual features; m is the dimension of the input vector, z k (t) represents the value of the k-th feature at time t, E is the mathematical expectation operator, k is the feature index, and λ k For z k The variance of is given by Λ, where Λ is the covariance matrix of the last mM features, and t is the sampling time. For the statistic T 2The control limits are given by α, where α is the confidence level.

[0029] Furthermore, based on the residual characteristics of the eigenvector z(t), the statistics T are obtained respectively. 2 The instantaneous estimates of Q and W also include:

[0030] The calculated values ​​are based on the first M residual features from the L+1 most recent time steps in the eigenvector z(t). We obtain an instantaneous estimate of the statistic W.

[0031] Furthermore, based on the calculated values ​​of the first M residual features at the most recent L+1 times in the eigenvector z(t)... The instantaneous estimate of the statistic W is obtained using the following formula:

[0032]

[0033]

[0034] Where t is the sampling time, z k (t) represents the value of the k-th feature at time t, where k is the feature index, Δt is the sampling interval of the input variable, and M is the number of residual features; W α α represents the control limit of the statistic W, α represents the confidence level, ρ(·) represents the whiteness index operator for the scalar time series, and L+1 represents the length of historical data used to calculate the whiteness index.

[0035] Furthermore, ρ(y) is calculated as follows:

[0036]

[0037]

[0038] θ t =[1 e -j2πt / N … e -j2πt(N-1) / N ] T ,

[0039] y is an N-dimensional vector, consisting of a scalar time series of length N, where k is the frequency point number, and Q... k To calculate the kernel matrix representing the degree to which the cumulative energy spectrum deviates from the ideal at the k-th frequency point, Re is the real part operator, t is the sampling time, I is the identity matrix, and θ... t Let θ be the coefficient vector of the discrete Fourier transform. t H For θ t The conjugate transpose of .

[0040] Furthermore, the statistic T 2The instantaneous estimates of Q and W are compared with the corresponding control limits, including:

[0041] like This indicates that the process has deviated from its steady-state operating point; if W ≥ W α This indicates that the process undergoes a change in dynamic characteristics; if Q≥Q α But W <W α This indicates that interference or noise has increased in the process, but the control performance has not changed significantly. 2 Q and W are the statistics to be monitored, and their control limits are respectively... Q α and W α , where α is the confidence level.

[0042] Furthermore, the online database collects relevant measurable auxiliary variables in ascending order of sampling time to form a sample set C. A confidence level α is selected, and the sample set C is input into the white component model to calculate T. 2 For the statistical control charts of Q and W, their upper α quantiles were selected as control limits. Q α and W α .

[0043] Furthermore, the process of establishing the white component model:

[0044] A sample set C is constructed by collecting relevant measurable auxiliary variables from an online database in ascending order of sampling time.

[0045] C={x(t),x(t+Δt),…,x(t+(N-1)Δt)}

[0046] The number of samples is N, and the sampling period Δt satisfies Shannon's sampling theorem;

[0047] Using samples from C, construct the sample matrix X and the augmented sample matrix X:

[0048]

[0049] Where N is the number of samples, 1 is a vector with all elements being 1, and its dimension is the same as the number of rows in X; m is the dimension of the input vector;

[0050] Let U=I, Let i be an empty matrix, i = 1; define matrix Φ = U(:, i: m), that is, the i-th to m-th columns of U, and solve the following optimization problem:

[0051]

[0052] stq T q=1

[0053] Where ρ is the whiteness operator, X is the augmented sample matrix, q is the optimization variable, Φ is the transition matrix, Φ is composed of a set of orthonormal bases in the residual space, and Φq is the augmented projection vector based on X; the optimal solution q is obtained. * and the optimal value ρ * Whiteness level threshold ρ ε Determined based on the value of N;

[0054] If ρ * ≤ρ ε If the value of M is 1, perform singular value decomposition; otherwise, let M = i-1 and perform eigenvalue decomposition.

[0055] Singular Value Decomposition: Update Φq * To optimize the obtained augmented projection vector, singular value decomposition is performed on the updated P:

[0056]

[0057] This updates the U matrix, where U is the left eigenvector matrix, Σ is the singular value matrix, and V is the right eigenvector matrix; if i = m, normalization is performed; otherwise, i = i + 1, and the optimization problem is solved again.

[0058] Eigenvalue decomposition: for a matrix Perform eigenvalue decomposition:

[0059]

[0060] Where V is an orthogonal eigenvector matrix, Λ=diag{λ1,λ2,…,λ m} is a diagonal matrix containing the eigenvalues; update

[0061] Normalization: For all 1≤i≤m, The i-th column Split into Where p i yes The first m elements, μ i yes The last element; perform the following normalization:

[0062]

[0063] The coefficient matrix and vectors that constitute the white component model:

[0064] P = [p1 p2 … p] m ], μ=[μ1 μ2 … μ m ] T

[0065] Once the coefficient matrix P and vector μ are determined, the white component model is established.

[0066] Furthermore, the optimal solution q is obtained by using the alternating direction multiplier method. * and the optimal value ρ * The alternating direction multiplier method includes:

[0067] Selecting γ≥1, we define:

[0068]

[0069]

[0070] in Let Φ be the augmented sample matrix, Φ be the transition matrix, and Q be the variable. k Let I be the kernel matrix used to calculate the whiteness index, where I is the identity matrix, N is the number of samples, and k is the traversal index.

[0071] Select a suitable penalty factor β, an initial point q0, and calculate...

[0072]

[0073]

[0074]

[0075]

[0076] Where ζ is an intermediate variable in the same direction as q, τ is an intermediate variable positively correlated with feature whiteness, w, w', u are optimization variables of the alternating direction multiplier method, and Θ and Ω are... k As intermediate variables to aid in solving the optimization problem; define the Lagrange augmenting function:

[0077] L β (w,w',u)=w T Θw+β(||w-w'+u|| 2 -||u|| 2 )

[0078] Where β is the penalty factor for the alternating direction multiplier method;

[0079] Solve the following quadratic programming problem to update w:

[0080]

[0081] The w, w', and u on the right side of the equation are the most recent iteration values ​​of the optimization variables in the alternating direction multiplier method, while the w on the left side of the equation is the updated value after solving the quadratic programming problem.

[0082] The following convex optimization problem is solved by solving the dual problem to update w':

[0083]

[0084] The w' on the left side of the equation is the updated value after solving the convex optimization problem;

[0085] Update u = u + w - w';

[0086] Determine if convergence has occurred; if not, recalculate the quadratic programming problem and update w.

[0087] If convergent, then calculate...

[0088]

[0089] Where ζ is an intermediate variable in the same direction as q, and τ is an intermediate variable positively correlated with the feature whiteness, the solution and optimal value of the optimization problem can be obtained:

[0090]

[0091] q * This is the solution to the whiteness optimization problem, and the corresponding Φq * That is, the augmented projection vector obtained through optimization, ρ * The whiteness of the obtained feature.

[0092] Secondly, this invention provides a process monitoring device based on residual whiteness, comprising a characteristic variable calculation unit, a statistical quantity calculation unit, and a comparison monitoring unit.

[0093] The feature variable calculation unit is used to read in the online measurement values ​​of the process variables to be monitored, form an input vector and input it into the white component model to obtain the online real-time calculation value of the feature vector z(t);

[0094] The statistics calculation unit is used to obtain the statistics T based on the residual characteristics of the eigenvector z(t). 2 Instantaneous estimates of Q and W;

[0095] The comparison monitoring unit is used to compare the statistical quantity T. 2 The instantaneous estimates of Q and W are compared with the corresponding control limits to achieve process monitoring that maximizes residual whiteness.

[0096] Thirdly, the present invention provides an electronic device, including a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus;

[0097] Memory, used to store computer programs;

[0098] When the processor executes the program stored in memory, it implements the above-mentioned process monitoring method based on residual whiteness.

[0099] Fourthly, the present invention provides a computer-readable storage medium having a computer program stored thereon, characterized in that the computer program, when executed by a processor, implements the above-described process monitoring method based on residual whiteness.

[0100] The present invention has at least the following beneficial effects:

[0101] The model of this invention is applicable to process monitoring problems with obvious dynamic characteristics. It can effectively mine the dynamic characteristics of the process and has better physical interpretability compared with traditional dynamic process monitoring models.

[0102] This invention proposes a novel W statistic that can not only monitor changes in the distribution of principal components and residual subspaces, but also effectively monitor changes in the dynamic characteristics of the process through the whiteness of residual principal components. Compared with traditional data-based process monitoring methods, this method can more sensitively reflect process dynamic anomalies and reduce the false negative rate. Furthermore, it can effectively help distinguish between normal shifts in the operating point and the amplification of disturbances, providing operators with richer and more accurate information, thus possessing strong practical value.

[0103] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures pointed out in the description and the drawings. Attached Figure Description

[0104] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0105] Figure 1 This is a flowchart of the process monitoring method according to an embodiment of the present invention;

[0106] Figure 2 This is a schematic diagram of the process monitoring device according to an embodiment of the present invention;

[0107] Figure 3 This is a schematic diagram of the solution implemented by a host computer in an industrial setting according to the present invention;

[0108] Figure 4 This is a schematic diagram of the test results for disturbance 1;

[0109] Figure 5 This is a schematic diagram of the test results for Disturbance 2. Detailed Implementation

[0110] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0111] In existing technologies, DPCA struggles to obtain time-independent residuals, leading to an overly conservative control region for the Q statistic and reduced detection sensitivity. Traditional Q statistics describe data variations from a variance perspective, lacking sufficient information for alarms related to anomalies. Offsets to the steady-state operating point, changes in dynamic characteristics, and amplification of interference or noise can all trigger alarms, leaving operators with limited information about the type of anomaly.

[0112] To this end, the present invention proposes a process monitoring method and apparatus based on residual whiteness, including a process monitoring method based on residual whiteness, a process monitoring apparatus based on residual whiteness, an electronic device, and a computer-readable storage medium.

[0113] This invention defines a whiteness index for finite-length time series and derives time-independent white components based on it, thereby characterizing the most essential dynamic relationships and corresponding residuals of the process. Then, monitoring statistics are constructed using the distribution of the white components and the whiteness index. Finally, the process monitoring model based on white component analysis is implemented in a production process control system.

[0114] Firstly, such as Figure 1 As shown, the present invention provides a process monitoring method based on residual whiteness, the method comprising:

[0115] The online measurement values ​​of the process variables to be monitored are read in, formed into an input vector, and input into the white component model to obtain the online real-time calculation value of the feature vector z(t);

[0116] The statistics T are obtained based on the residual characteristics of the eigenvector z(t). 2 Instantaneous estimates of Q and W;

[0117] Statistic T 2 The instantaneous estimates of Q and W are compared with the corresponding control limits to achieve process monitoring that maximizes residual whiteness.

[0118] In practical implementation, since the whiteness of residual principal components can be quantified, this method proposes a new W statistic, which can not only monitor the shift of the steady-state operating point but also effectively monitor changes in the dynamic characteristics of the process. Compared with traditional data-driven process monitoring methods, this method has higher sensitivity to dynamic characteristic anomalies, can effectively distinguish between normal shifts in the operating point and disturbances and faults affecting the dynamic characteristics of the process, significantly reduces the false alarm rate of faults, and provides operators with richer and more accurate information, thus having strong practical application value.

[0119] In this embodiment, the white component model is as follows:

[0120]

[0121] Where m is the dimension of the input vector, x(t) is the m-dimensional input vector discretized at the sampling time, z(t) is the m-dimensional feature vector discretized at the sampling time, and its statistical properties are somewhat similar to white noise; the coefficient matrix P is an m-order square matrix, μ is the m-dimensional input vector, μ represents the bias of the feature vector, and t is the sampling time.

[0122] In this embodiment, the structure of the input vector x(t) is as follows:

[0123]

[0124] Where, {x1,x2,…,x n Let} be n input variables, Δt be the sampling interval of the input variables, and d be the length of the historical data contained in the input vector; the dimension m of the input vector satisfies the relation m = n(d + 1).

[0125] In this embodiment, the statistic T is obtained based on the residual features of the feature vector z(t). 2 Instantaneous estimates of Q and W, including:

[0126] The vector z is composed of the first M residual features in the feature vector z(t). e (t), based on vector z e (t) yields the instantaneous estimate of the statistic Q.

[0127] In this embodiment, based on vector z e The instantaneous estimate of the statistic Q is obtained using the following formula:

[0128]

[0129] R = P -T =[r1 r2 … r m ],R e =[r1 r2 … r M ]

[0130]

[0131] Where ze(t) is the feature vector composed of the first M residual features of the feature vector z(t) whose statistical properties are close to white noise, M is the number of residual features, m is the dimension of the input vector, and r k For feature z k The load vector, R is the characteristic load matrix, R e Let Q be a matrix composed of the load vectors of the first M residual features, where t is the sampling time. α Let Q be the control limit and α be the confidence level.

[0132] In this embodiment, the statistic T is obtained based on the residual features of the feature vector z(t). 2 The instantaneous estimates of Q and W also include:

[0133] The vector z(t) is composed of mM features. p (t), based on vector z p (t) yields the statistic T 2 The instantaneous estimate.

[0134] In this embodiment, based on vector z p (t) yields the statistic T 2 The instantaneous estimate is obtained using the following formula:

[0135]

[0136] E{[z k (t)] 2}=λ k M+1≤k≤m

[0137]

[0138] Where z p z(t) is the vector composed of mM features following the feature vector z(t); M is the number of residual features; m is the dimension of the input vector, z k (t) represents the value of the k-th feature at time t, E is the mathematical expectation operator, k is the feature index, and λ k For z k The variance of is given by Λ, where Λ is the covariance matrix of the last mM features, and t is the sampling time. For the statistic T 2 The control limits are given by α, where α is the confidence level.

[0139] In this embodiment, the statistic T is obtained based on the residual features of the feature vector z(t). 2The instantaneous estimates of Q and W also include:

[0140] The calculated values ​​are based on the first M residual features from the L+1 most recent time steps in the eigenvector z(t). We obtain an instantaneous estimate of the statistic W.

[0141] In this embodiment, the calculated values ​​of the first M residual features at the most recent L+1 time points in the feature vector z(t) are used. The instantaneous estimate of the statistic W is obtained using the following formula:

[0142]

[0143]

[0144] Where t is the sampling time, z k (t) represents the value of the k-th feature at time t, where k is the feature index, Δt is the sampling interval of the input variable, and M is the number of residual features; W α α represents the control limit of the statistic W, α represents the confidence level, ρ(·) represents the whiteness index operator for the scalar time series, and L+1 represents the length of historical data used to calculate the whiteness index.

[0145] In this embodiment, ρ(y) is calculated as follows:

[0146]

[0147]

[0148] θ t =[1 e -j2πt / N … e -j2πt(N-1) / N ] T ,

[0149] y is an N-dimensional vector, consisting of a scalar time series of length N, where k is the frequency point number, and Q... k To calculate the kernel matrix representing the deviation of the cumulative energy spectrum from the ideal state at the k-th frequency point, Re is the real part operator, t is the sampling time number, I is the identity matrix, and θ... t Let θ be the coefficient vector of the discrete Fourier transform. t H For θ t The conjugate transpose of .

[0150] In this embodiment, the statistic T 2 The instantaneous estimates of Q and W are compared with the corresponding control limits, including:

[0151] like This indicates that the process has deviated from its steady-state operating point; if W ≥ Wα This indicates that the process undergoes a change in dynamic characteristics; if Q≥Q α But W <W α This indicates that interference or noise has increased in the process, but the control performance has not changed significantly. 2 Q and W are the statistics to be monitored, and their control limits are respectively... Q α and W α , where α is the confidence level.

[0152] In this embodiment, the online database collects relevant measurable auxiliary variables in ascending order of sampling time to form a sample set C. A confidence level α is selected, and the sample set C is input into the white component model to calculate T. 2 For the statistical control charts of Q and W, their upper α quantiles were selected as control limits. Q α and W α .

[0153] In this embodiment, the process of establishing the white component model is as follows:

[0154] A sample set C is constructed by collecting relevant measurable auxiliary variables from an online database in ascending order of sampling time.

[0155] C={x(t),x(t+Δt),…,x(t+(N-1)Δt)}

[0156] The number of samples is N, and the sampling period Δt should satisfy Shannon's sampling theorem;

[0157] Using samples from C, construct the sample matrix X and the augmented sample matrix.

[0158]

[0159] Where N is the number of samples, and 1 is a vector with all elements being 1, and its dimension is the same as the number of rows in X;

[0160] Let U=I, Let i be an empty matrix, i = 1; define matrix Φ = U(:, i: m), that is, the i-th to m-th columns of U, and solve the following optimization problem:

[0161]

[0162] stq T q=1

[0163] Where ρ is the whiteness operator. The sample matrix is ​​the augmented matrix, q is the optimization variable, Φ is a matrix consisting of a set of orthonormal bases of the residual space, called the transition matrix, and Φq is based on The augmented projection vector. The optimal solution q is obtained. * and the optimal value ρ * Whiteness level threshold ρ ε Determined based on the value of N; if ρ * ≤ρ ε If the value of M is 1, perform singular value decomposition; otherwise, let M = i-1 and perform eigenvalue decomposition.

[0164] Singular Value Decomposition: Update Φq * To optimize the obtained augmented projection vector, the updated vector is... Perform singular value decomposition:

[0165]

[0166] This updates the U matrix, where U is the left eigenvector matrix, Σ is the singular value matrix, and V is the right eigenvector matrix; if i = m, normalization is performed; otherwise, i = i + 1, and the optimization problem is solved again.

[0167] Eigenvalue decomposition: for a matrix Perform eigenvalue decomposition:

[0168]

[0169] Where V is an orthogonal eigenvector matrix, Λ=diag{λ1,λ2,…,λ m} is a diagonal matrix containing the eigenvalues; update

[0170] Normalization: For all 1≤i≤m, normalize the i-th column of P. Split into Where p i yes The first m elements, μ i yes The last element; perform the following normalization:

[0171]

[0172] The coefficient matrix and vectors that constitute the white component model:

[0173] P = [p1 p2 … p] m ], μ=[μ1 μ2 … μ m ] T

[0174] Once the coefficient matrix and vectors are determined, the white component model is established.

[0175] In this embodiment, the optimal solution q is obtained using the alternating direction multiplier method.* and the optimal value ρ * The alternating direction multiplier method includes:

[0176] Selecting γ≥1, we define:

[0177]

[0178]

[0179] in Let Φ be the augmented sample matrix, Φ be the transition matrix, and Q be the variable. k Let I be the kernel matrix used to calculate the whiteness index, where I is the identity matrix, N is the number of samples, and k is the traversal index.

[0180] Select a suitable penalty factor β, an initial point q0, and calculate...

[0181]

[0182]

[0183]

[0184]

[0185] Where ζ is an intermediate variable in the same direction as q, τ is an intermediate variable positively correlated with feature whiteness, w, w', u are optimization variables of the alternating direction multiplier method, and Θ and Ω are... k These are intermediate variables used to assist in solving the optimization problem. The Lagrange augmented function is defined as follows:

[0186] L β (w,w',u)=w T Θw+β(||w-w'+u|| 2 -||u|| 2 )

[0187] Where β is the penalty factor for the alternating direction multiplier method.

[0188] Solve the following quadratic programming problem to update w:

[0189]

[0190] The w, w', and u on the right side of the equation are the most recent iteration values ​​of the optimization variables in the alternating direction multiplier method, and the w on the left side of the equation is its updated value.

[0191] The following optimization problem is solved by solving its dual problem to update w':

[0192]

[0193] The w, w', and u on the right side of the equation are the most recent iteration values ​​of the variables optimized by the alternating direction multiplier method, and the w' on the left side of the equation is its updated value.

[0194] Update u = u + w - w';

[0195] Determine if convergence has occurred; if not, recalculate the quadratic programming problem and update w.

[0196] If convergent, then calculate...

[0197]

[0198] Where ζ is an intermediate variable in the same direction as q, and τ is an intermediate variable positively correlated with the feature whiteness, the solution and optimal value of the optimization problem can be obtained:

[0199]

[0200] q * This is the solution to the whiteness optimization problem, and the corresponding Φq * That is, the augmented projection vector obtained through optimization, ρ * The whiteness of the obtained feature.

[0201] Secondly, such as Figure 2 As shown, this invention provides a process monitoring device based on residual whiteness, including a characteristic variable calculation unit, a statistical quantity calculation unit, and a comparison and monitoring unit.

[0202] The feature variable calculation unit is used to read in the online measurement values ​​of the process variables to be monitored, form an input vector and input it into the white component model to obtain the online real-time calculation value of the feature vector z(t);

[0203] The statistics calculation unit is used to obtain the statistics T based on the residual characteristics of the eigenvector z(t). 2 Instantaneous estimates of Q and W;

[0204] The comparison monitoring unit is used to compare the statistical quantity T. 2 The instantaneous estimates of Q and W are compared with the corresponding control limits to achieve process monitoring that maximizes residual whiteness.

[0205] In specific implementation, the implementation processes of the process monitoring device and the process monitoring method based on residual whiteness of the present invention correspond one-to-one, and will not be elaborated here.

[0206] Thirdly, the present invention provides an electronic device, including a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus;

[0207] Memory, used to store computer programs;

[0208] When the processor executes the program stored in memory, it implements the above-mentioned process monitoring method based on residual whiteness.

[0209] Fourthly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the above-described process monitoring method based on residual whiteness.

[0210] The computer-readable storage medium may be included in the device / apparatus described in the above embodiments; or it may exist independently and not assembled into the device / apparatus. The computer-readable storage medium carries one or more programs that, when executed, implement the method according to the embodiments of this disclosure.

[0211] According to embodiments of this disclosure, the computer-readable storage medium can be a non-volatile computer-readable storage medium, such as including, but not limited to: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this disclosure, the computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0212] To enable those skilled in the art to better understand the present invention, the principles of the present invention are explained below in conjunction with the accompanying drawings:

[0213] A process monitoring method based on white component analysis, comprising the following steps:

[0214] Step A1: Read the white component model and monitoring model. The white component model is as follows:

[0215]

[0216] Where m is the dimension of the input vector, x(t) is the m-dimensional input vector discretized at the sampling time, and z(t) is the m-dimensional feature vector discretized at the sampling time, whose statistical properties are somewhat similar to white noise; the coefficient matrix P is an m-order square matrix, μ is the m-dimensional input vector representing the bias of the feature vector, and t is the sampling time. To describe the dynamic characteristics of the process, the input vector x(t) generally contains a certain amount of historical data. Assume there are n input variables {x1, x2, ..., xn}. n}, then the structure of the input vector x(t) is:

[0217]

[0218] Where Δt is the sampling interval of the input variable, and d is the length of the historical data contained in the input vector. The dimension m of the input vector satisfies the relation m = n(d + 1).

[0219] The monitoring model mentioned is

[0220]

[0221] E{[z k (t)] 2}=λ k ,1≤k≤m

[0222] R = P -T =[r1 r2 … r m ],R e =[r1 r2 … r M ]

[0223]

[0224]

[0225]

[0226] Where M is the number of white components considered (usually M <m),z e (t) is a vector composed of the first M features, z p (t) is a vector composed of the last mM features, r k For feature z k The load vector, R is the characteristic load matrix, R e Let λ be a matrix composed of the load vectors of the first M residual characteristics, where t is time t and λ is the load vector. k For z k The variance is given by Λ, where Λ is the covariance matrix of the last mM features. ρ(·) is the whiteness index operator, and L+1 is the length of the historical data used to calculate the whiteness index. For an N-dimensional vector y, ρ(y) is calculated as follows:

[0227]

[0228]

[0229]

[0230] Where k is the frequency point number, Q kTo calculate the kernel matrix representing the degree to which the cumulative energy spectrum deviates from the ideal at the k-th frequency point, Re is the real part operator, t is the time sequence number, I is the identity matrix, and θ... t Let θ be the coefficient vector of the discrete Fourier transform. t H For θ t The conjugate transpose of T. 2 Q and W are the statistics to be monitored, and their control limits are respectively... Q α and W α , where α is the confidence level.

[0231] Step A2: Read the online measurement values ​​of the process variables into the DCS system, form an input vector, and input it into the white component model to obtain the online real-time estimate of the slow feature vector z(t).

[0232] Step A3: Combine the vector z composed of the first M features e (t), the vector z composed of the last mM features p (t) Input into the monitoring model to obtain Q and T 2 Instantaneous estimates of the statistics; the most recent L+1 historical values ​​of the first M features. Inputting 1≤k≤M into the monitoring model yields an instantaneous estimate of the W statistic.

[0233] Step A4: Place T 2 The instantaneous estimates of the Q and W statistics are written into the DCS system for display and reference by operators. If This indicates that the process has deviated from the steady-state operating point; if W ≥ W α This indicates that the process has undergone a change in dynamic characteristics; if Q≥Q α But W <W α This indicates that the process has only experienced interference or increased noise.

[0234] The process of establishing the white component model and monitoring model in step A1 includes:

[0235] Step B1: Select process variables based on the analysis of the production process mechanism or practical experience, and give an estimate of the length d of the historical data.

[0236] Step B2: Complete the collection of relevant data samples. Collect relevant measurable auxiliary variables from the online database in ascending order of sampling time to form sample set C:

[0237] C={x(t),x(t+Δt),…,x(t+(N-1)Δt)}

[0238] The number of samples is N, and the sampling period Δt should satisfy Shannon's sampling theorem.

[0239] Step B3: Construct the sample matrix X and the augmented sample matrix using the samples in C.

[0240]

[0241] Here, 1 is a vector whose elements are all 1s.

[0242] Step B4: Determine the appropriate whiteness level threshold ρ based on the value of N. ε .

[0243] Step B5: Let U = I, It is an empty matrix, i = 1.

[0244] Step B6: Define matrix Φ = U(:,i:m), that is, the i-th to m-th columns of U, and solve the following optimization problem:

[0245]

[0246] stq T q=1

[0247] Where ρ is the whiteness operator. The sample matrix is ​​the augmented matrix, q is the optimization variable, Φ is a matrix consisting of a set of orthonormal bases of the residual space, called the transition matrix, and Φq is based on The augmented projection vector. The optimal solution q is obtained. * and the optimal value ρ * If ρ * ≤ρ ε Proceed to step B7; otherwise, let M = i-1 and proceed to step B8. Methods for solving optimization problems include, but are not limited to, the alternating direction multiplier method. The alternating direction multiplier method includes the following sub-steps:

[0248] Step B6.1: Select γ≥1, define

[0249]

[0250]

[0251] in Let Φ be the augmented sample matrix, Φ be the transition matrix, and Q be the variable. k Let I be the kernel matrix used to calculate the whiteness index, where I is the identity matrix, N is the number of samples, and k is the traversal index.

[0252] Step B6.2: Select a suitable penalty factor β, an initial point q0, and calculate...

[0253]

[0254]

[0255]

[0256]

[0257] Where ζ is an intermediate variable in the same direction as q, τ is an intermediate variable positively correlated with feature whiteness, w, w', u are optimization variables of the alternating direction multiplier method, and Θ and Ω are... k These are intermediate variables used to assist in solving the optimization problem. The Lagrange augmented function is defined as follows:

[0258] L β (w,w',u)=w T Θw+β(||w-w'+u|| 2 -||u|| 2 )

[0259] Where β is the penalty factor for the alternating direction multiplier method.

[0260] Step B6.3: Solve the following quadratic programming problem to update w:

[0261]

[0262] The w, w', and u on the right side of the equation are the most recent iteration values ​​of the optimization variables in the alternating direction multiplier method, and the w on the left side of the equation is its updated value.

[0263] Step B6.4: Solve the following convex optimization problem to update w':

[0264]

[0265] The w, w', and u on the right side of the equation represent the most recent iterative values ​​of the optimization variables using the alternating direction multiplier method, while w' on the left side represents its updated value. It is recommended to solve this by addressing its dual problem.

[0266] Step B6.5: Update u = u + w - w'.

[0267] Step B6.6: Determine if convergence has occurred. If yes, proceed to step B6.7; otherwise, proceed to step B6.3.

[0268] Step B6.7: Calculation

[0269]

[0270] Where ζ is an intermediate variable in the same direction as q, and τ is an intermediate variable positively correlated with the feature whiteness, the solution and optimal value of the optimization problem are then obtained:

[0271]

[0272] q * This is the solution to the whiteness optimization problem, and the corresponding Φq * That is, the augmented projection vector obtained through optimization, ρ * The whiteness of the obtained feature. Step B6 is now complete.

[0273] Step B7: Let And perform singular value decomposition on it:

[0274]

[0275] This updates the U matrix, where U is the left eigenvector matrix, Σ is the singular value matrix, and V is the right eigenvector matrix. If i = m, proceed to step B9; otherwise, let i = i + 1 and proceed to step B6.

[0276] Step B8: For the matrix Perform eigenvalue decomposition:

[0277]

[0278] Where V is an orthogonal eigenvector matrix, Λ=diag{λ1,λ2,…,λ m} is a diagonal matrix containing the eigenvalues.

[0279] renew

[0280] Step B9: For all 1≤i≤m, The i-th column Split into Where p i yes The first m elements, μ i yes The last element. Perform the following normalization:

[0281]

[0282] The coefficient matrix and vectors that constitute the white component model:

[0283] P = [p1 p2 … p] m ], μ=[μ1 μ2 … μ m ] T

[0284] At this point, the white component model has been established.

[0285] Step B10: Calculate T 2 Q and W control limits: Select an appropriate upper quantile α, input the dataset C into the white component model to calculate T. 2The statistical control charts for Q and W were used, and their upper α level quantiles were selected as... Q α and W α .

[0286] The advantages of this invention are: 1) This model is applicable to process monitoring problems with obvious dynamic characteristics, effectively mining the dynamic features of the process, and has better physical interpretability compared with traditional dynamic process monitoring models. 2) Since the whiteness of residual principal components can be quantified, this method proposes a new W statistic, which can not only monitor changes in the distribution of principal components and residual subspaces, but also effectively monitor changes in the dynamic characteristics of the process through the whiteness of residual principal components. Compared with traditional data-based process monitoring methods, this method can sensitively reflect process dynamic anomalies and reduce the false negative rate. Furthermore, it can effectively help distinguish between normal shifts in operating points, amplification of disturbances, and other non-dynamic characteristics, providing operators with richer and more accurate information, and has strong practical value.

[0287] like Figure 3 As shown, data acquisition, processing, optimization modeling, and online prediction in this invention can be implemented via a host computer. The control program acquires process data through a real-time database or via OPC (OLE for Process Control), and the main data processing results are displayed on the host computer after calculation. To approximate the actual production process, the Tennessee-Eastman Process (TE Process) proposed by Eastman Chemical Company was selected. The Tennessee-Eastman Process provides an excellent research platform for process control, playing a benchmark role in process monitoring, soft sensing, and fault diagnosis. The entire process consists of a reactor, condenser, compressor, gas-liquid separator, and stripping tower. Four gaseous reactants A, C, D, and E, along with inert gas B, are fed into the reactor, ultimately yielding two products, G and H, and a byproduct F. The simulation code can be obtained from the website https: / / depts.washington.edu / control / LARRY / TE / download.html.

[0288] In this case, there are 31 monitored process variables, selected as XMV(1-4), XMV(6-8), XMV(10-11), and XMEAS(1-22). XMV(1-4), XMV(6-8), and XMV(10-11) are manipulated variables, and XMEAS(1-22) is a measured variable. The sampling period for the process variables is 36 seconds. A training set of 400 training samples was generated; two test sets were also generated, corresponding to two different process disturbances: Disturbance 1: a step disturbance in the compressor recirculation valve position; Disturbance 2: a step disturbance in the feed temperature (D). Each test set contains 400 test samples, and the disturbance occurs after the 180th sample. The historical data length d is 2.

[0289] The steps for training the monitoring model are as follows:

[0290] Step B2: Complete the collection of relevant data samples. Collect relevant measurable auxiliary variables from the online database in ascending order of sampling time to form sample set C:

[0291] C={x(t),x(t+Δt),…,x(t+(N-1)Δt)}

[0292] The number of samples is N, and the sampling period Δt should satisfy Shannon's sampling theorem.

[0293] Step B3: Construct the sample matrix X and the augmented sample matrix using the samples in C.

[0294]

[0295] Here, 1 is a vector whose elements are all 1s.

[0296] Step B4: Determine the appropriate whiteness level threshold ρ based on the value of N. ε .

[0297] Step B5: Let U = I, It is an empty matrix, i = 1.

[0298] Step B6: Define matrix Φ = U(:,i:m), that is, the i-th to m-th columns of U, and solve the following optimization problem:

[0299]

[0300] stq T q=1

[0301] Where ρ is the whiteness operator, X is the augmented sample matrix, q is the optimization variable, Φ is a matrix composed of a set of orthonormal bases of the residual space, called the transition matrix, and Φq is based on The augmented projection vector. The optimal solution q is obtained. * and the optimal value ρ * If ρ * ≤ρ ε Proceed to step B7; otherwise, let M = i-1 and proceed to step B8. The solution methods for optimization problems include, but are not limited to, the alternating direction multiplier method. Preferably, the alternating direction multiplier method includes the following sub-steps:

[0302] Step B6.1: Select γ≥1, define

[0303]

[0304]

[0305] in Let Φ be the augmented sample matrix, Φ be the transition matrix, and Q be the variable. k Let I be the kernel matrix used to calculate the whiteness index, where I is the identity matrix, N is the number of samples, and k is the traversal index.

[0306] Step B6.2: Select a suitable penalty factor β, an initial point q0, and calculate...

[0307]

[0308]

[0309]

[0310]

[0311] Where ζ is an intermediate variable in the same direction as q, τ is an intermediate variable positively correlated with feature whiteness, w, w', u are optimization variables of the alternating direction multiplier method, and Θ and Ω are... k These are intermediate variables used to assist in solving the optimization problem. The Lagrange augmented function is defined as follows:

[0312] L β (w,w',u)=w T Θw+β(||w-w'+u|| 2 -||u|| 2 )

[0313] Where β is the penalty factor for the alternating direction multiplier method.

[0314] Step B6.3: Solve the following quadratic programming problem to update w:

[0315]

[0316] The w, w', and u on the right side of the equation are the most recent iteration values ​​of the optimization variables in the alternating direction multiplier method, and the w on the left side of the equation is its updated value.

[0317] Step B6.4: Solve the following convex optimization problem to update w':

[0318]

[0319] The w, w', and u on the right side of the equation represent the most recent iterative values ​​of the optimization variables using the alternating direction multiplier method, while w' on the left side represents its updated value. It is recommended to solve this by addressing its dual problem.

[0320] Step B6.5: Update u = u + w - w'.

[0321] Step B6.6: Determine if convergence has occurred. If yes, proceed to step B6.7; otherwise, proceed to step B6.3.

[0322] Step B6.7: Calculation

[0323]

[0324] Where ζ is an intermediate variable in the same direction as q, and τ is an intermediate variable positively correlated with the feature whiteness, the solution and optimal value of the optimization problem are then obtained:

[0325]

[0326] q * This is the solution to the whiteness optimization problem, and the corresponding Φq * That is, the augmented projection vector obtained through optimization, ρ * The whiteness of the obtained feature. Step B6 is now complete.

[0327] The following steps will be based on the established model to implement online model monitoring.

[0328] Step A1: Read the white component model and the monitoring model respectively.

[0329] Step A2: Read the online measurement values ​​of the process variables into the DCS system, form an input vector and input it into the white component model to obtain the online real-time estimate of the eigenvector z(t);

[0330] Step A3: Combine the vector z composed of the first M features e (t), the vector z composed of the last mM features p (t) Input into the monitoring model to obtain Q and T 2 Instantaneous estimates of the statistics; the most recent L+1 historical values ​​of the first M features. Inputting 1≤k≤M into the monitoring model yields an instantaneous estimate of the W statistic.

[0331] Step A4: Place T 2 The instantaneous estimates of the Q and W statistics are written into the DCS system for display and reference by operators. If This indicates that the process has deviated from the steady-state operating point; if W ≥ W α This indicates that the process has undergone a change in dynamic characteristics; if Q≥Q α But W <W α This indicates that the process has only experienced an amplification of interference or noise. In this example, the method based on white component analysis (WCA) is compared with traditional dynamic principal component analysis (DPCA), dynamic internal principal component analysis (DiPCA), and dynamic internal canonical variable analysis (DiCCA). Monitoring results on two perturbation test sets are shown. Perturbation 1 is as follows... Figure 4 As shown, disturbance 2 is as follows Figure 5 As shown.

[0332] The results of the disturbance 1 test are as follows Figure 4 As shown, the first column presents the results of dynamic internal principal component analysis, the second column presents the results of dynamic internal canonical variable analysis, the third column presents the results of dynamic principal component analysis, and the fourth column presents the results of the proposed method. Perturbation 1 can have complex effects on the entire system. The T values ​​of DPCA and WCA... 2 Both the curve and the Q curve increased, indicating that the disturbance affected both the dynamic and static relationships of the process. While DPCA responded somewhat, the Q statistic failed to consistently trigger an alarm. The test statistics for DiPCA and DiCCA exhibited similar behavior, fluctuating around the control limits without triggering a clear alarm. In contrast, the monitoring results provided by WCA are more interpretable. On one hand, the T in WCA... 2 Statistics can highlight new operating conditions, information that DiPCA and DiCCA do not provide. On the other hand, disruptions to dynamic relationships can be sensitively detected by the W indicator, providing a clear alarm relative to Q, thus highlighting the effectiveness of utilizing white-hat information. By integrating the three control charts in WCA, the operating status of the process and the dynamic relationships of change can be clearly understood.

[0333] The results of the disturbance 2 test are as follows Figure 5As shown, the first column presents the results of dynamic internal principal component analysis, the second column presents the results of dynamic internal canonical variable analysis, the third column presents the results of dynamic principal component analysis, and the fourth column presents the results of the proposed method. For perturbation 2, the step change in feed temperature further affects the reactor temperature. To maintain the reactor temperature, feedback control is implemented by increasing the reactor cooling water flow rate, which introduces deviations in operating conditions. Although the statistics of DiPCA, DiCCA, and DPCA show a slight upward trend, they do not trigger continuous alarms. In contrast, the W statistic of WCA has a clearer response and can detect small changes in dynamic features. The W statistic checks the whiteness of the data by moving the window, thus enabling more sensitive detection of unmodeled dynamics. Combined with T... 2 With W control charts, operators can understand the dynamic changes in process characteristics and the shift of operating points that occur simultaneously.

[0334] This invention's model is applicable to processes with significant dynamic characteristics, effectively uncovering their dynamic features and offering better physical interpretability compared to traditional dynamic process monitoring models. By proposing a novel W statistic, this invention not only monitors changes in the distribution of principal components and residual subspaces but also effectively monitors changes in process dynamic characteristics based on the whiteness of residual principal components. Compared to traditional data-driven process monitoring methods, this method can more sensitively reflect abnormal dynamic characteristics of the process, reducing the false negative rate. Furthermore, it can effectively distinguish between factors causing non-dynamic anomalies such as normal shifts in operating points and amplification of disturbances, providing operators with richer and more accurate information, thus possessing strong practical value.

[0335] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A process monitoring method based on residual whiteness, characterized in that, The method includes: The online measured values ​​of the process variables to be monitored are read in, formed into an input vector, and input into the white component model to obtain the feature vector. The online real-time calculated value; Based on the feature vector The residual characteristics are respectively used to obtain the statistics. , and The instantaneous estimate; Statistic , and The instantaneous estimate is compared with the corresponding control limit to achieve process monitoring that maximizes the whiteness of the residual; The white component model is as follows: Where m is the dimension of the input vector, The input vector is discretized at the sampling time. The m-dimensional eigenvectors are discretized at each sampling time; the coefficient matrix is... It is an m-order square matrix. Given an m-dimensional input vector, This represents the bias of the feature vector, where t is the sampling time; The process of establishing the white component model: The sample set is constructed by collecting relevant measurable auxiliary variables from the online database in ascending order of sampling time. : in, N x Number of samples, sampling period Satisfies Shannon's sampling theorem; use C The samples in the sample matrix constitute the sample matrix. X and augmented sample matrix : in, All elements are A vector whose dimension is . X The number of rows is the same; m is the dimension of the input vector; make An empty matrix. Define matrix ,Right now The to The following optimization problem is solved: in For whiteness operator, To augment the sample matrix, To optimize variables, This is the transition matrix. It consists of a set of orthonormal bases in the residual space. For based on The augmented projection vector is obtained; the optimal solution is then derived. and optimal value Whiteness level threshold according to N x The value is determined; if Perform singular value decomposition; otherwise, let eigenvalue decomposition is performed. Singular Value Decomposition: Update , To optimize the obtained augmented projection vector, the updated vector is... Perform singular value decomposition: Thus update Matrix, where The left eigenvector matrix, It is a singular value matrix. The right eigenvector matrix; if Normalize; otherwise, let Solve the optimization problem again; Eigenvalue decomposition: for a matrix Perform eigenvalue decomposition: in The eigenvector matrix is ​​an orthogonal matrix. Create a diagonal matrix containing all eigenvalues; update ; Normalization: for all ,Will The List Split into ,in yes The former One element, yes The last element; perform the following normalization: The coefficient matrix and vectors that constitute the white component model: Determine the coefficient matrix sum vector Complete the establishment of the white component model.

2. The process monitoring method based on residual whiteness according to claim 1, characterized in that, Input vector The structure is as follows: in, For n input variables, Let d be the sampling interval of the input variable, and d be the length of the historical data contained in the input vector; the dimension m of the input vector satisfies the following relation. .

3. The process monitoring method based on residual whiteness according to claim 1, characterized in that, Based on the feature vector The residual characteristics are respectively used to obtain the statistics. , and The instantaneous estimates include: eigenvectors The vector is composed of the first M residual features. According to vector Obtain statistics The instantaneous estimate.

4. The process monitoring method based on residual whiteness according to claim 3, characterized in that, According to the vector Obtain statistics The instantaneous estimate is obtained using the following formula: in For feature vectors forward An eigenvector composed of residual features whose statistical properties are close to white noise. denoted by , where is the number of residual features, and m is the dimension of the input vector. Features The load vector, R The load matrix is ​​characterized by... Let be a matrix composed of the load vectors of the first M residual features, where t is the sampling time. for Control limits, , where is the confidence level.

5. The process monitoring method based on residual whiteness according to claim 1, characterized in that, Based on the feature vector The residual characteristics are respectively used to obtain the statistics. , and The instantaneous estimate also includes: eigenvectors middle The feature vectors According to vector Obtain statistics The instantaneous estimate.

6. The process monitoring method based on residual whiteness according to claim 5, characterized in that, According to the vector Obtain statistics The instantaneous estimate is obtained using the following formula: in For feature vectors back A vector composed of features; The number of residual features; m Let be the dimension of the input vector. For the first Each feature at time The value of , E is the mathematical expectation operator, and k is the feature index. for variance For the future The covariance matrix of each feature. t Sampling time, For statistics Control limits, , where is the confidence level.

7. A process monitoring method based on residual whiteness according to claim 1, characterized in that, Based on the feature vector The residual characteristics are respectively used to obtain the statistics. T 2 , Q and W The instantaneous estimate also includes: Based on the feature vector China recently L +1 time before M Calculated values ​​of individual residual features , and obtain the statistics W The instantaneous estimate.

8. A process monitoring method based on residual whiteness according to claim 7, characterized in that, Based on the feature vector China recently L +1 time before M Calculated values ​​of individual residual features , and obtain the statistics W The instantaneous estimate is obtained using the following formula: in t Sampling time, For the first Each feature at time The value, k For feature serial number, The sampling interval for the input variables. M The number of residual features; For statistics Control limits, Confidence level; For scalar time series, the whiteness index operator, L +1 represents the length of historical data used to calculate the whiteness index.

9. A process monitoring method based on residual whiteness according to claim 8, characterized in that, The calculation method is as follows: for dimensional vector, Composed of scalar time series, with a length of N , l For frequency point ordinal numbers, Q l To calculate the cumulative energy spectrum in the th... l The kernel matrix represents the degree of deviation from the ideal situation at each frequency point, where Re is the real part operator and t is the sampling time. I Let θ be the identity matrix. t Let θ be the coefficient vector of the discrete Fourier transform. t H For θ t The conjugate transpose of .

10. A process monitoring method based on residual whiteness according to claim 1, characterized in that, Statistic T 2 , Q and W The instantaneous estimate is compared with the corresponding control limit, including: like This indicates that the process has deviated from its steady-state operating point; if This indicates that the process has undergone a change in dynamic characteristics; if but This indicates that interference or noise has increased in the process, but the control performance has not changed significantly. T 2 , Q and W The control limits for the statistics to be monitored are as follows: , and ,in , where is the confidence level.

11. A process monitoring method based on residual whiteness according to claim 1, characterized in that, The online database collects relevant measurable auxiliary variables in ascending order of sampling time to form a sample set. C Select confidence level , sample set C The white component model was calculated by inputting it. T 2 , Q and W Statistical control charts, select them in sequence Upper level quantile as control limit , and .

12. The process monitoring method based on residual whiteness according to claim 1, characterized in that, The optimal solution is obtained by using the alternating direction multiplier method. and optimal value The alternating direction multiplier method includes: Selected ,definition: in To augment the sample matrix, This is the transition matrix. This is the kernel matrix used to calculate the whiteness index. I It is the identity matrix. N x For the number of samples, The traversal sequence number; Selecting an appropriate penalty factor initial point ,calculate in To and Intermediate variables in the same direction, As an intermediate variable positively correlated with characteristic whiteness, For the optimization variables of the alternating direction multiplier method, and As intermediate variables to aid in solving the optimization problem; define the Lagrange augmenting function: in This is the penalty factor for the alternating direction multiplier method; Solve the following quadratic programming problem: update : The right side of the equation To optimize the most recent iteration value of the variable using the alternating direction multiplier method, the left side of the equation is... To solve the quadratic programming problem, the updated value is needed; The following convex optimization problem is solved by solving the dual problem to update... : The left side of the equation To solve the convex optimization problem, the updated value is needed; renew ; Determine if convergence has occurred; if not, recalculate the quadratic programming problem and update it. ; If convergent, then calculate... in To and Intermediate variables in the same direction, As an intermediate variable positively correlated with the feature whiteness, the solution and optimal value of the optimization problem can be obtained: ； This is the solution to the whiteness optimization problem, and the corresponding This is the augmented projection vector obtained through optimization. The whiteness of the obtained feature.

13. A process monitoring device based on residual whiteness, characterized in that, It includes a feature variable calculation unit, a statistical quantity calculation unit, and a comparison and monitoring unit. The feature variable calculation unit is used to read in the online measurement values ​​of the process variables to be monitored, form an input vector, and input it into the white component model to obtain the feature vector. The online real-time calculated value; The statistical calculation unit is used to calculate the statistical value based on the eigenvector. The residual characteristics are respectively used to obtain the statistics. T 2 , Q and W The instantaneous estimate; The comparison monitoring unit is used to compare statistics. T 2 , Q and W The instantaneous estimate is compared with the corresponding control limit to achieve process monitoring that maximizes the whiteness of the residual; The white component model is as follows: in, m Let be the dimension of the input vector. The input vector is discretized at the sampling time. Discretization of sampling time m 3D eigenvectors; coefficient matrix It is an m-order square matrix. Given an m-dimensional input vector, This represents the bias of the eigenvector. t Sampling time; The process of establishing the white component model: The sample set is constructed by collecting relevant measurable auxiliary variables from the online database in ascending order of sampling time. : in, N x Number of samples, sampling period Satisfies Shannon's sampling theorem; use C The samples in the sample matrix constitute the sample matrix. X and augmented sample matrix : in, All elements are A vector whose dimension is . X The number of rows is the same; m is the dimension of the input vector; make An empty matrix. Define matrix ,Right now The to The following optimization problem is solved: in For whiteness operator, To augment the sample matrix, To optimize variables, This is the transition matrix. It consists of a set of orthonormal bases in the residual space. For based on The augmented projection vector is obtained; the optimal solution is then derived. and optimal value Whiteness level threshold according to N x The value is determined; if Perform singular value decomposition; otherwise, let eigenvalue decomposition is performed. Singular Value Decomposition: Update , To optimize the obtained augmented projection vector, the updated vector is... Perform singular value decomposition: Thus update Matrix, where The left eigenvector matrix, It is a singular value matrix. The right eigenvector matrix; if Normalize; otherwise, let Solve the optimization problem again; Eigenvalue decomposition: for a matrix Perform eigenvalue decomposition: in The eigenvector matrix is ​​an orthogonal matrix. Create a diagonal matrix containing all eigenvalues; update ; Normalization: for all ,Will The List Split into ,in yes The former One element, yes The last element; perform the following normalization: The coefficient matrix and vectors that constitute the white component model: Determine the coefficient matrix sum vector Complete the establishment of the white component model.

14. An electronic device, characterized in that, It includes a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus; Memory, used to store computer programs; A processor, when executing a program stored in memory, implements a process monitoring method based on residual whiteness as described in any one of claims 1-12.

15. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements a process monitoring method based on residual whiteness as described in any one of claims 1-12.

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