CN109491338B - Multimode process quality-related fault diagnosis method based on sparse GMM - Google Patents

Abstract

The invention discloses a multimode process quality related fault diagnosis method based on sparse GMM, which is characterized in that a high-quality coefficient weight matrix is obtained by utilizing sparse representation, manifold structure information is fused, a sparse Gaussian mixture model is constructed, probability distribution of Gaussian components smoothly changes along a data manifold structure, local neighbor samples of the Gaussian components are similar, the number of the Gaussian components is automatically obtained, robustness on noise and outliers is achieved, quality related fault detection is obtained, and meanwhile, a root-cause variable of fault occurrence is located according to controlled neighbor of detected faults. Compared with a Gaussian mixture model monitoring method, the method disclosed by the invention represents the sparse relation between the local manifold structure of the process data and the data, obtains the local similarity relation between samples, and reflects the change condition of the multi-modal process. Therefore, the sparse GMM method can obtain better fault detection effect and accurately position the root variable of the fault.

Description

Multimode process quality-related fault diagnosis method based on sparse GMM

Technical Field

The invention relates to the technical field of industrial process monitoring, in particular to a multimode process quality-related fault diagnosis method based on sparse GMM.

Background

The process monitoring in modern industry plays a key role in ensuring production safety, improving yield and the like. With the development of distributed control systems, the production scale and the operational complexity increase dramatically, and a large amount of high-dimensional data is collected in the process. Moreover, as the grade and yield of the produced products can be continuously adjusted according to market demands and seasonal effects, the process parameters such as product components, process set values, feed proportions and the like can fluctuate, and modern industrial processes can be switched among a plurality of different operation modes. These random variations in the production process cause the process data to exhibit non-linear, multi-modal, etc. characteristics. Although the data-driven Multivariate Statistical Process Control (MSPC) method is successfully applied to Process monitoring, the mean value and the covariance of multimode nonlinear data are significantly changed, and the traditional MSPC method ignores the nonlinear and multimode relations between different Process variables, which may cause the degradation of the monitoring result. Moreover, in the actual production process, the yield and the product quality are usually difficult to measure directly on-line, and measurement is required after the production is completed. Therefore, building a relational model between product variables and quality variables is particularly important for quality-related multi-modal process monitoring. A Gaussian Mixture Model (GMM) is used for multi-modal process monitoring, a series of Gaussian components are used for estimating complex data distribution in the multi-modal process, and statistical indexes based on Mahalanobis distance and likelihood probability are constructed to implement process monitoring.

However, GMM assumes that each single mode of a multi-modal process is Gaussian distributed, and it is possible for actual process data to be centrally distributed over a low-dimensional sub-manifold structure. Therefore, the neighborhood samples of each manifold are probably distributed in the same Gaussian component, and the manifold geometric information of the process can be fused to construct the manifold GMM monitoring model. Furthermore, it is difficult to measure these key variables, both the yield of the production process and the product quality, directly on-line, but after the production is complete. Therefore, building a relational model between process variables and quality variables is particularly important for quality-related fault detection and diagnosis.

Recently, horses, etc. (neuron computing,2015(285)) proposed a Robust Gaussian Mixture Model (RGMM) that automatically acquires Gaussian component scores for quality-related fault detection and diagnosis. However, in each gaussian component in the multi-modal process, the similarity of the distribution of neighboring data also needs to be grasped during modeling, the manifold discrimination capability of the multi-modal is fully mined, and the local geometric structural features in the gaussian are maintained. In addition, the weight matrix in the local manifold structure plays an important role in describing the geometry of data, and conventional manifold learning generally adopts a k-nearest neighbor or epsilon-sphere method to determine a neighborhood value given parameters. These methods are sensitive to data noise and outliers.

Disclosure of Invention

The invention provides a multimode process quality-related fault diagnosis method based on sparse GMM, aiming at overcoming the defects of the prior art, the sparse GMM method provided by the invention can fully find the internal change of the multimode process, and selects important fault variables related to quality according to the controlled neighbor of the detected fault; compared with the traditional GMM monitoring method, the method can obtain higher diagnosis precision and stronger fault discrimination capability.

The invention adopts the following technical scheme for solving the technical problems:

the invention provides a multimode process quality-related fault diagnosis method based on sparse GMM, which comprises the following steps:

step A, establishing a sparse representation model between a process variable and a quality variable to obtain a sparse reconstruction weight matrix S of a sample;

b, constructing a sparse Gaussian mixture model: forming a constraint condition of the similarity of neighboring samples around Gaussian components according to a sparse coefficient in a sparse reconstruction weight matrix S obtained by a sparse representation model, adaptively selecting a neighborhood range of a training sample, obtaining the conditional probability distribution of the similarity of the Gaussian components, keeping the locality and the sparsity of a data manifold structure, and automatically identifying the number of the Gaussian components;

and step C, constructing a sparse GMM monitoring index, designing a fault detection and diagnosis index by using an output result of a sparse Gaussian mixture model and the local Mahalanobis distance of each mode, fusing the overall output and the local information of the process, and evaluating the running state of the multi-mode process.

As a further optimization scheme of the multimode process quality-related fault diagnosis method based on the sparse GMM, the step a is specifically as follows:

given N samples from a multimodal process, each sample contains a process variable x ∈ R^mAnd the quality variable y ∈ R, the historical data set D is represented as:

wherein R is^mRepresents an m-dimensional variable, R represents a 1-dimensional variable, [ y (1) x (1)]^TRepresenting quality variable and 1 st process variable, abbreviated to d₁By analogy, [ y (1) x (N)]^TRepresenting quality variable and Nth process variable, abbreviated to d_NThe superscript T is transposition;

sparse representation the sparse representation of the training sample is calculated by jointly optimizing an objective function through the following formula:

in the formula, L1-normal form represents the sum of absolute values of matrix elements, lambda is a regularization parameter positive value, E is a sparse error, and E is a column vector with 1 element; solving sparse reconstruction weight matrix S ═ S by convex optimization method₁,s₂,…,s_N]∈R^N×N，R^{N ×N}Representing storage spaces with rows and columns of N, where s_n＝[s_n1,s_n2,…,s_nn-1,0,s_nn+1,…,s_nN]^T，n＝1,2...，N，s_nFor the nth sample data d_nOf each element s of the sparse coefficient variable_njDenotes d_nFor reconstructed j sample d_jThe degree of contribution of (c).

As a further optimization scheme of the multimode process quality-related fault diagnosis method based on the sparse GMM, the method specifically comprises the following steps of:

step a, constructing a Gaussian mixture model related to quality, wherein a probability density function p (d | Θ) of each sample is represented as:

where d is the sample data, C is the number of Gaussian components, ω_kIs the posterior probability of the kth Gaussian component, satisfies

Gauss parameter theta_k＝{μ_k,Σ_k}，μ_kIs a k-th class mean, Σ_kIs a covariance matrix of class k, theta ═ theta₁,θ₂,...,θ_CIs the set of global Gaussian model parameters, θ₁,θ₂,...,θ_CRespectively represent the 1 st, 2 nd, … th and C th local Gaussian components; for the k-th Gaussian component, its profileRate density function g (d θ)_k) Is shown as

Let Z be { Z ═ Z₁,z₂,…,z_NDenotes missing data of a category, and z_i∈{1,2,...,C}，z_iRepresents a category to which the ith sample belongs; if z is_iK, i-th sample belongs to k-th Gaussian component, and latent variable z_ki1, otherwise z_ki0; m is the dimension of the sample, and the parameters Θ of the quality-related gaussian mixture model are solved by maximizing the following likelihood functions:

wherein L (omega, theta; D, Z) is a likelihood function, omega is a posterior probability;

b, fusing geometric structure knowledge of conditional probability distribution in a GMM target function based on the principle that similar samples in the sparse representation and manifold structures are still close to each other in an embedding space, and constructing a sparse GMM; and realizing the minimized sparse regular term for the pairwise similarity constraint on the Gaussian probability distribution, wherein the constraint term is expressed as:

wherein, γ_n＝p(z_n|d_n) Denotes the nth sample d_nBelong to z_nProbability of class, γ_j＝p(z_j|d_j) Denotes the jth sample d_jBelong to z_jThe probability of the category, H (| ·), measures the similarity of the two distributions, and by adopting KL distance measurement, after minimizing the constraint term, the data are smoothly distributed along manifold geometric distance measurement; fusing the sparse regular term with the likelihood function of the GMM to obtain an objective function J of the sparse GMM:

wherein δ >0 is a regularization parameter; solving the parameters of the sparse GMM by adopting an expected value maximization method;

step c, calculating latent variable z according to original GMM and Bayes law_ki：

Wherein, ω is_lIs the posterior probability of the Gaussian component l, g (d)_i|θ_k) Is a sample d_iIn the Gaussian component theta_kDensity probability of (1), g (d)_i|θ_l) Is a sample d_iIn the Gaussian component theta_l(ii) a density probability of;

step d, updating model parameters:

in the formula (I), the compound is shown in the specification,

is the sum of classes, Ω, of samples of the k-th Gaussian component_nk＝(d_n-μ_k)(d_n-μ_k)^TAnd is the sample covariance of the kth gaussian component.

As a further optimization scheme of the multimode process quality-related fault diagnosis method based on the sparse GMM, the steps of constructing the sparse GMM monitoring index are as follows:

step I, for each monitoring sample d_tAccording to the output result of the global structure information represented by the sparse GMM, the model is used for outputting J_outMeasuring the degree of deviation of the monitoring sample from the controlled training baseline, and measuring the degree of deviation J of the monitoring sample from the controlled training baseline_outExpressed as:

J_out＝-ln p(d_t|Θ) (12)

in the formula, p (d)_t| Θ) represents a monitoring sample d_tBased on the probability density of the training model;

counting the probability that the output value of the monitoring sample is smaller than the output value of the training sample, and designing L_otIndex quantization process state:

L_ot(d_t)＝Pr(J_out(d_t)≤J_out(d_train)) (13)

in the formula, J_out(d_train) Represents the output of the training set, J_out(d_t) Represents the output of the test sample, L_ot(d_t) Is a global information index; pr (J)_out(d_t)≤J_out(d_train) Represents the probability that the test sample output is lower than the training set output;

mahalanobis distance is used to measure quality-related fault detection within a single modality, calculating a monitoring sample d_tTo each modality C_kThe mahalanobis distance MD of (a):

mahalanobis distance follows the approximated χ²Is distributed, i.e.

And is

By fusing the global information index L_ot(d_t) And local information index MD^(k)(d_t|d_tE k), designing a synthetic fault detection index GL, reducing monitoring cost and operation load, wherein GL is expressed as:

given control limit η_αWhen GL of the monitoring sample exceeds the control limit, detecting a fault related to the quality, otherwise, indicating that no fault occurs;

secondly, after detecting the quality-related fault, further determining a root variable of the fault; defining the contribution degree of the process variable as the distance between a fault sample and a controlled neighbor, obtaining the direction of the fault deviating from normal operation by solving the virtual controlled neighbor of the fault, and determining a root variable generated by the fault;

the optimization function that defines the controlled vicinity of the fault is:

wherein d is_faultIs a detected fault sample, d_nicnThe method is characterized in that the method is a virtual controlled neighbor sample of a fault, the sample is randomly selected from training samples to serve as initialization input of a nonlinear programming technology, and the controlled neighbor sample is solved, so that the fault sample is further expressed as:

d_fault＝d_nicn+f (17)

in the formula, f represents an estimated fault vector and is used for evaluating the minimum value of the fault sample adjusted to a normal state; the degree of contribution of each variable is defined as d_faultAnd d_nicnIn euclidean distance CON between_q：

In the formula (I), the compound is shown in the specification,

and f^qRespectively represents d_nicn，d_faultAnd the qth element of f;

redefining the degree of contribution of a variable CONMD using Mahalanobis distances_q：

In the formula, xi_qIs the unit vector with the qth element being 1, will have the maximum CONMD_qIsolation of variable sets of values, setting threshold τ as:

if the variable of the fault exceeds this threshold τ, it is determined that the change in the variable caused a process anomaly, triggering the fault.

As a further optimization scheme of the multimode process quality-related fault diagnosis method based on the sparse GMM, α is 0.05.

Compared with the prior art, the invention adopting the technical scheme has the following technical effects: the method utilizes the weight matrix of the sparse representation manifold structure to keep the local geometric structure characteristics of the data manifold in the Gaussian components, automatically obtains the quantity of the Gaussian components, and has robustness on noise and outliers in the process; the method is based on GMM, combines sparsity and locality of manifold geometry structure, constructs sparse GMM, captures process variable characteristics related to quality variables, reflects state change conditions of the multimode process, and identifies root cause variables of faults according to the detected controlled neighbors of the faults; the method is suitable for quality-related fault detection and diagnosis in the multimode process.

Drawings

FIG. 1 is a flow chart of an embodiment of the method of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in detail with reference to the accompanying drawings and specific embodiments.

The invention adopts a sparse representation method without parameter robustness to construct an intrinsic matrix of a manifold structure and automatically decide the neighborhood range of a sample.

In view of the advantages of the sparse representation and quality-related GMM model in process monitoring, the multimode process quality-related fault diagnosis method based on the sparse GMM is provided, the local similarity and sparsity among samples on the manifold geometry of Gaussian components are kept, the learning performance of the GMM model is enhanced, and the diagnosis capability of the model is improved.

On the basis of a Gaussian mixture model, aiming at potential complex structural characteristics of a multi-mode process related to quality, a weight matrix of a manifold structure is represented in a parameter-free robust mode by sparse representation, a sparse Gaussian mixture model is constructed on the basis of similarity between manifold data samples on Gaussian components, and local features and sparse features of the multi-mode process data are kept. The proposed sparse GMM method can fully discover the intrinsic changes of the multimode process, and select important fault variables related to quality according to the controlled neighbors of the detected faults. Compared with the traditional GMM monitoring method, the method can obtain higher diagnosis precision and stronger fault discrimination capability.

The multimode process quality-related fault diagnosis method based on the sparse GMM utilizes the sparse representation to represent the geometric information distribution condition of Gaussian components, constructs the sparse GMM, analyzes the data distribution characteristics of the multimode process, extracts the process variable characteristics related to the quality, captures the internal change of the multimode process, analyzes the root variable of the fault occurrence and enhances the fault diagnosis capability of the sparse GMM method.

As shown in fig. 1, the present invention relates to a sparse GMM-based multimode process quality-related fault diagnosis method, which comprises the following specific implementation steps:

(1) and establishing a sparse representation model between the process variable and the quality variable to obtain a sparse reconstruction weight matrix S of the sample.

Given N samples from a multimodal process, each sample contains a process variable x ∈R^mAnd the quality variable y ∈ R, the historical data set D is represented as:

wherein R is^mRepresents an m-dimensional variable, R represents a 1-dimensional variable, [ y (1) x (1)]^TRepresenting quality variable and 1 st process variable, abbreviated to d₁By analogy, [ y (1) x (N)]^TRepresenting quality variable and Nth process variable, abbreviated to d_NThe superscript T is transposition;

sparse representation the sparse representation of the training sample is calculated by jointly optimizing an objective function through the following formula:

in the formula, L1-normal form represents the sum of absolute values of matrix elements, lambda is a regularization parameter positive value, E is a sparse error, and E is a column vector with 1 element; solving sparse reconstruction weight matrix S ═ S by convex optimization method₁,s₂,…,s_N]∈R^N×N，R^{N ×N}Representing storage spaces with rows and columns of N, where s_n＝[s_n1,s_n2,…,s_nn-1,0,s_nn+1,…,s_nN]^T，n＝1,2...，N，s_nFor the nth sample data d_nOf each element s of the sparse coefficient variable_njDenotes d_nFor reconstructed j sample d_jThe degree of contribution of (c).

(2) And constructing a sparse Gaussian mixture model. By increasing the constraint condition of the similarity of the neighbor samples around the Gaussian components, the neighborhood range of the training samples is selected in a self-adaptive manner, the conditional probability distribution of the similarity of the Gaussian components is obtained, the locality and the sparsity of a data manifold structure are maintained, the number of the Gaussian components is automatically identified, and the robustness is provided for data noise and outliers. The substeps of solving the sparse gaussian mixture model are as follows:

step a, constructing a Gaussian mixture model related to quality, wherein a probability density function p (d | Θ) of each sample is represented as:

where d is the sample data, C is the number of Gaussian components, ω_kIs the posterior probability of the kth Gaussian component, satisfies

Gauss parameter theta_k＝{μ_k,Σ_k}，μ_kIs a k-th class mean, Σ_kIs a covariance matrix of class k, theta ═ theta₁,θ₂,...,θ_CIs the set of global Gaussian model parameters, θ₁,θ₂,...,θ_CRespectively represent the 1 st, 2 nd, … th and C th local Gaussian components; for the kth Gaussian component, its probability density function g (d θ)_k) Is shown as

Let Z be { Z ═ Z₁,z₂,…,z_NDenotes missing data of a category, and z_i∈{1,2,...,C}，z_iRepresents a category to which the ith sample belongs; if z is_iK, i-th sample belongs to k-th Gaussian component, and latent variable z_ki1, otherwise z_ki0; m is the dimension of the sample, and the parameters Θ of the quality-related gaussian mixture model are solved by maximizing the following likelihood functions:

wherein L (omega, theta; D, Z) is a likelihood function, omega is a posterior probability;

b, fusing geometric structure knowledge of conditional probability distribution in a GMM target function based on the principle that similar samples in the sparse representation and manifold structures are still close to each other in an embedding space, and constructing a sparse GMM; and realizing the minimized sparse regular term for the pairwise similarity constraint on the Gaussian probability distribution, wherein the constraint term is expressed as:

wherein, γ_n＝p(z_n|d_n) Denotes the nth sample d_nBelong to z_nProbability of class, γ_j＝p(z_j|d_j) Denotes the jth sample d_jBelong to z_jThe probability of the category, H (| ·), measures the similarity of the two distributions, and by adopting KL distance measurement, after minimizing the constraint term, the data are smoothly distributed along manifold geometric distance measurement; fusing the sparse regular term with the likelihood function of the GMM to obtain an objective function J of the sparse GMM:

wherein δ >0 is a regularization parameter; solving the parameters of the sparse GMM by adopting an expected value maximization method;

step c, calculating latent variable z according to original GMM and Bayes law_ki：

Wherein, ω is_lIs the posterior probability of the Gaussian component l, g (d)_i|θ_k) Is a sample d_iIn the Gaussian component theta_kDensity probability of (1), g (d)_i|θ_l) Is a sample d_iIn the Gaussian component theta_l(ii) a density probability of;

step d, updating model parameters:

in the formula (I), the compound is shown in the specification,

is the sum of classes, Ω, of samples of the k-th Gaussian component_nk＝(d_n-μ_k)(d_n-μ_k)^TAnd is the sample covariance of the kth gaussian component.

(3) Constructing a sparse GMM monitoring index, designing a reasonable fault detection and diagnosis index by using the output result of the whole model and the local Mahalanobis distance of each mode, fusing the global output and the local information of the process, and evaluating the running state of the multi-mode process. The substep of solving the sparse GMM monitoring index is represented as:

step I, for each monitoring sample d_tAccording to the output result of the global structure information represented by the sparse GMM, the model is used for outputting J_outMeasuring the degree of deviation of the monitoring sample from the controlled training baseline, and measuring the degree of deviation J of the monitoring sample from the controlled training baseline_outExpressed as:

J_out＝-ln p(d_t|Θ) (12)

in the formula, p (d)_t| Θ) represents a monitoring sample d_tBased on the probability density of the training model;

counting the probability that the output value of the monitoring sample is smaller than the output value of the training sample, and designing L_otIndex quantization process state:

L_ot(d_t)＝Pr(J_out(d_t)≤J_out(d_train)) (13)

in the formula, J_out(d_train) Represents the output of the training set, J_out(d_t) Presentation measurementOutput of the test sample, L_ot(d_t) Is a global information index; pr (J)_out(d_t)≤J_out(d_train) Represents the probability that the test sample output is lower than the training set output;

mahalanobis distance is used to measure quality-related fault detection within a single modality, calculating a monitoring sample d_tTo each modality C_kThe mahalanobis distance MD of (a):

mahalanobis distance follows the approximated χ²Is distributed, i.e.

And is

By fusing global information indicators Lo_t(d_t) And local information index MD^(k)(d_t|d_tE k), designing a synthetic fault detection index GL, reducing monitoring cost and operation load, wherein GL is expressed as:

given control limit η_α(α ═ 0.05), when GL of the monitored sample exceeds the control limit, a fault related to quality is detected, otherwise, no fault occurs;

secondly, after detecting the quality-related fault, further determining a root variable of the fault; defining the contribution degree of the process variable as the distance between a fault sample and a controlled neighbor, obtaining the direction of the fault deviating from normal operation by solving the virtual controlled neighbor of the fault, and determining a root variable generated by the fault;

the optimization function that defines the controlled vicinity of the fault is:

wherein d is_faultIs a detected fault sample, d_nicnThe method is characterized in that the method is a virtual controlled neighbor sample of a fault, the sample is randomly selected from training samples to serve as initialization input of a nonlinear programming technology, and the controlled neighbor sample is solved, so that the fault sample is further expressed as:

d_fault＝d_nicn+f (17)

in the formula, f represents an estimated fault vector and is used for evaluating the minimum value of the fault sample adjusted to a normal state; the degree of contribution of each variable is defined as d_faultAnd d_nicnIn euclidean distance CON between_q：

In the formula (I), the compound is shown in the specification,

and f^qRespectively represents d_nicn，d_faultAnd the qth element of f;

redefining the degree of contribution of a variable CONMD using Mahalanobis distances_q：

In the formula, xi_qIs the unit vector with the qth element being 1, will have the maximum CONMD_qIsolation of variable sets of values, setting threshold τ as:

if the variable of the fault exceeds this threshold τ, it is determined that the change in the variable caused a process anomaly, triggering the fault.

The method utilizes the weight matrix of the sparse representation manifold structure to keep the local geometric structure characteristics of the data manifold in the Gaussian components, automatically obtains the number of the Gaussian components, and has robustness to noise and outliers in the process. The method is based on GMM, combines sparsity and locality of manifold geometry structure, constructs sparse GMM, captures process variable characteristics related to quality variables, reflects state change conditions of the multi-mode process, and identifies root cause variables of faults according to the detected controlled neighbors of the faults. Therefore, the method is suitable for quality-related fault detection and diagnosis in a multimode process.

The above description is only for the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.

Claims (5)

1. A multimode process quality related fault diagnosis method based on sparse GMM is characterized by comprising the following steps:

step A, establishing a sparse representation model between a process variable and a quality variable to obtain a sparse reconstruction weight matrix S of a sample;

b, constructing a sparse Gaussian mixture model: forming a constraint condition of the similarity of neighboring samples around Gaussian components according to a sparse coefficient in a sparse reconstruction weight matrix S obtained by a sparse representation model, adaptively selecting a neighborhood range of a training sample, obtaining the conditional probability distribution of the similarity of the Gaussian components, keeping the locality and the sparsity of a data manifold structure, and automatically identifying the number of the Gaussian components;

and step C, constructing a sparse GMM monitoring index, designing a fault detection and diagnosis index by using an output result of a sparse Gaussian mixture model and the local Mahalanobis distance of each mode, fusing the overall output and the local information of the process, and evaluating the running state of the multi-mode process.

2. The sparse GMM-based multimode process quality-related fault diagnosis method according to claim 1, wherein the step A specifically comprises the following steps:

given N samples from a multimodal process, each sample contains a process variable x ∈ R^mAnd the quality variable y ∈ R, the historical data set D is represented as:

wherein R is^mRepresents an m-dimensional variable, R represents a 1-dimensional variable, [ y (1) x (1)]^TRepresenting quality variable and 1 st process variable, abbreviated to d₁By analogy, [ y (1) x (N)]^TRepresenting quality variable and Nth process variable, abbreviated to d_NThe superscript T is transposition;

sparse representation the sparse representation of the training sample is calculated by jointly optimizing an objective function through the following formula:

in the formula, L1-normal form represents the sum of absolute values of matrix elements, lambda is a regularization parameter positive value, E is a sparse error, and E is a column vector with 1 element; solving sparse reconstruction weight matrix S ═ S by convex optimization method₁,s₂,…,s_N]∈R^N×N，R^N×NRepresenting storage spaces with rows and columns of N, where s_n＝[s_n1,s_n2,…,s_nn-1,0,s_nn+1,…,s_nN]^T，n＝1,2...，N，s_nFor the nth sample data d_nOf each element s of the sparse coefficient variable_njDenotes d_nFor reconstructed j sample d_jThe degree of contribution of (c).

3. The sparse GMM-based multimode process quality-related fault diagnosis method according to claim 2, wherein the sparse Gaussian mixture model is constructed by the following specific steps:

step a, constructing a Gaussian mixture model related to quality, wherein a probability density function p (d | Θ) of each sample is represented as:

where d is the sample data, C is the number of Gaussian components, ω_kIs the posterior probability of the kth Gaussian component, satisfies

Gauss parameter theta_k＝{μ_k,∑_k}，μ_kIs a class k mean, Σ_kIs a covariance matrix of class k, theta ═ theta₁,θ₂,...,θ_CIs the set of global Gaussian model parameters, θ₁,θ₂,...,θ_CRespectively represent the 1 st, 2 nd, … th and C th local Gaussian components; for the kth Gaussian component, its probability density function g (d | θ)_k) Is shown as

Let Z be { Z ═ Z₁,z₂,…,z_NDenotes missing data of a category, and z_i∈{1,2,...,C}，z_iRepresents a category to which the ith sample belongs; if z is_iK, i-th sample belongs to k-th Gaussian component, and latent variable z_ki1, otherwise z_ki0; m is the dimension of the sample, and the parameters Θ of the quality-related gaussian mixture model are solved by maximizing the following likelihood functions:

wherein L (omega, theta; D, Z) is a likelihood function, omega is a posterior probability;

b, fusing geometric structure knowledge of conditional probability distribution in a GMM target function based on the principle that similar samples in the sparse representation and manifold structures are still close to each other in an embedding space, and constructing a sparse GMM; and realizing the minimized sparse regular term for the pairwise similarity constraint on the Gaussian probability distribution, wherein the constraint term is expressed as:

wherein, γ_n＝p(z_n|d_n) Denotes the nth sample d_nBelong to z_nProbability of class, γ_j＝p(z_j|d_j) Denotes the jth sample d_jBelong to z_jThe probability of the category, H (| ·), measures the similarity of the two distributions, and by adopting KL distance measurement, after minimizing the constraint term, the data are smoothly distributed along manifold geometric distance measurement; fusing the sparse regular term with the likelihood function of the GMM to obtain an objective function J of the sparse GMM:

wherein δ >0 is a regularization parameter; solving the parameters of the sparse GMM by adopting an expected value maximization method;

step c, calculating latent variable z according to original GMM and Bayes law_ki：

Wherein, ω is_lIs the posterior probability of the Gaussian component l, g (d)_i|θ_k) Is a sample d_iIn the Gaussian component theta_kDensity probability of (1), g (d)_i|θ_l) Is a sample d_iIn the Gaussian component theta_l(ii) a density probability of;

step d, updating model parameters:

in the formula (I), the compound is shown in the specification,

is the sum of classes, Ω, of samples of the k-th Gaussian component_nk＝(d_n-μ_k)(d_n-μ_k)^TAnd is the sample covariance of the kth gaussian component.

4. The sparse GMM-based multimode process quality-related fault diagnosis method according to claim 3, wherein the step of constructing the sparse GMM monitoring index is as follows:

step I, for each monitoring sample d_tAccording to the output result of the global structure information represented by the sparse GMM, the model is used for outputting J_outMeasuring the degree of deviation of the monitoring sample from the controlled training baseline, and measuring the degree of deviation J of the monitoring sample from the controlled training baseline_outExpressed as:

J_out＝-ln p(d_t|Θ) (12)

in the formula, p (d)_t| Θ) represents a monitoring sample d_tBased on the probability density of the training model;

counting the probability that the output value of the monitoring sample is smaller than the output value of the training sample, and designing L_otIndex quantization process state:

L_ot(d_t)＝Pr(J_out(d_t)≤J_out(d_train)) (13)

in the formula, J_out(d_train) Represents the output of the training set, J_out(d_t) Represents the output of the test sample, L_ot(d_t) Is a global information index; pr (J)_out(d_t)≤J_out(d_train) Represents the probability that the test sample output is lower than the training set output;

mahalanobis distance is used to measure quality-related fault detection within a single modality, calculating a monitoring sample d_tTo each modality C_kThe mahalanobis distance MD of (a):

mahalanobis distance follows the approximated χ²Is distributed, i.e.

And is

By fusing the global information index L_ot(d_t) And local information index MD^(k)(d_t|d_tE k), designing a synthetic fault detection index GL, reducing monitoring cost and operation load, wherein GL is expressed as:

given control limit η_αWhen GL of the monitoring sample exceeds the control limit, detecting a fault related to the quality, otherwise, indicating that no fault occurs;

secondly, after detecting the quality-related fault, further determining a root variable of the fault; defining the contribution degree of the process variable as the distance between a fault sample and a controlled neighbor, obtaining the direction of the fault deviating from normal operation by solving the virtual controlled neighbor of the fault, and determining a root variable generated by the fault;

the optimization function that defines the controlled vicinity of the fault is:

wherein d is_faultIs a detected fault sample, d_nicnThe method is characterized in that the method is a virtual controlled neighbor sample of a fault, the sample is randomly selected from training samples to serve as initialization input of a nonlinear programming technology, and the controlled neighbor sample is solved, so that the fault sample is further expressed as:

d_fault＝d_nicn+f (17)

in the formula, f represents an estimated fault vector and is used for evaluating the minimum value of the fault sample adjusted to a normal state; the degree of contribution of each variable is defined as d_faultAnd d_nicnIn euclidean distance CON between_q：

In the formula (I), the compound is shown in the specification,

and f^qRespectively represents d_nicn，d_faultAnd the qth element of f;

redefining the degree of contribution of a variable CONMD using Mahalanobis distances_q：

In the formula, xi_qIs the unit vector with the qth element being 1, will have the maximum CONMD_qIsolation of variable sets of values, setting threshold τ as:

if the variable of the fault exceeds this threshold τ, it is determined that the change in the variable caused a process anomaly, triggering the fault.

5. The sparse GMM-based multimode process quality-related fault diagnosis method according to claim 4, wherein α is 0.05.

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