CN111209973B - Process monitoring method based on mixed kernel PCA-CCA and kernel density estimation - Google Patents

Abstract

The invention relates to a process monitoring method based on mixed kernel PCA-CCA and kernel density estimation, in a modeling stage, input and output data collected under a normal working condition are used, a corresponding weighting matrix is obtained through a mixed kernel PCA-CCA model, then T2 statistic is established based on model residual errors in a state space, and finally a corresponding statistic threshold value is obtained through a kernel density estimation method; in the real-time monitoring stage, samples input and output in real time are collected and mapped into a high-dimensional feature space by using a mixed kernel, real-time residual errors and statistic thereof are calculated according to a model obtained in the modeling stage, and then the obtained real-time statistic is compared with a threshold value to judge whether the output of the liquefying device is abnormally changed. The method focuses on the cross correlation between the process input and the process output, effectively improves the monitoring effect on the nonlinear process, determines the threshold value by using the kernel density estimation method, and more accurately determines the statistic threshold value of the non-Gaussian process.

Description

Process monitoring method based on hybrid kernel PCA-CCA and kernel density estimation

Technical field:

The present invention relates to the field of process monitoring technology, and in particular to a process monitoring method based on hybrid kernel PCA-CCA and kernel density estimation.

Background technology:

Nowadays, environmental protection has become a major livelihood issue that my country needs to solve urgently. Natural gas, as a high-quality clean energy, has the advantages of high efficiency and no pollution, and plays an indelible role in the development of my country's clean energy system. Compared with gaseous natural gas, the volume of liquefied natural gas is greatly reduced (about 1/600), so the natural gas liquefaction device is an indispensable equipment in the storage and application of natural gas. In recent years, with the substantial increase in the demand for natural gas resources, the construction of natural gas liquefaction devices has been greatly promoted, and the development of my country's low-carbon economy has been promoted.

At present, the natural gas liquefaction process is mainly divided into: cascade liquefaction process, mixed refrigerant liquefaction process, liquefaction process with expander and propane pre-cooling mixed refrigerant liquefaction process. Among them, the propane pre-cooling mixed refrigerant liquefaction process combines the advantages of the cascade liquefaction process and the mixed refrigerant liquefaction process. The process is simple and efficient and has been widely used in various scenarios. The propane pre-cooling mixed refrigerant liquefaction process is mainly divided into two links: light hydrocarbon recovery and fractionation process and refrigerant circulation process. The light hydrocarbon recovery and fractionation process mainly passes the pre-treated raw gas through the deethanizer, depropanizer and debutanizer in sequence to recover and fractionate light hydrocarbons, obtain propane refrigerant and other high value-added by-products, and adjust the calorific value of natural gas condensate. The refrigerant circulation process mainly converts natural gas and mixed refrigerant into liquefied natural gas products through heat exchangers, and the mixed refrigerant is exported for recycling at a certain stage.

Since the natural gas liquefaction device needs to operate under high pressure and low temperature for a long time, and the external gas source is not constant and the equipment design and structural parameters are unreasonable, it is very easy to be damaged, which will lead to reduced natural gas liquefaction efficiency and accelerated equipment damage. In serious cases, major safety accidents may occur. Therefore, it is necessary to conduct real-time process monitoring of the natural gas liquefaction device in order to detect equipment failures in time and carry out maintenance. Through process monitoring, the safety of personnel and equipment is guaranteed, and the service life of components is also increased.

There are some methods for process monitoring of input and output links in industrial processes, such as multivariate statistical process monitoring and fault diagnosis technology represented by PCA (principal component analysis) and PLS (partial least squares method), which have been successfully applied. However, such methods usually assume that the measured data obeys Gaussian distribution and comes from a single stable working condition. However, the actual industrial production process is often not operated under a single working condition. Changes in production load, product characteristics, raw material composition, etc. will lead to changes in working conditions. In this case, using a traditional single PCA model to monitor the process will weaken the statistical characteristics of each under different working conditions, which will inevitably lead to inaccurate process performance analysis and underreporting of process failures. In view of this, this case was born.

Summary of the invention:

The present invention discloses a process monitoring method based on hybrid kernel PCA-CCA and kernel density estimation, which combines the hybrid kernel PCA-CCA (CCA is a typical correlation analysis) modeling method with the process monitoring method, focuses on the mutual correlation between process input and output, and is applicable to the kernel technique to effectively improve the monitoring effect of nonlinear processes, especially for initial faults. In addition, the present invention uses the kernel density estimation (KDE) method in determining the threshold, which can more accurately determine the statistical threshold of non-Gaussian processes.

In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

The process monitoring method based on hybrid kernel PCA-CCA and kernel density estimation includes the following steps:

Step 1: Collect process input and output sample data under normal working conditions, obtain the 1×m input vector u _k and the 1×q output vector y _k at sampling time k, and after n samplings, obtain input data U = [u ₁ ,u ₂ … _un ] ^T ∈R ^n×m and output data Y = [y ₁ ,y ₂ …y _n ] ^T ∈R ^n×q ;

Step 2: Map the input data U and the output data Y to the high-dimensional feature space using a hybrid kernel, respectively, to obtain an input hybrid kernel matrix _Ku and an output hybrid kernel matrix _Ky , wherein the hybrid kernel is composed of a Gaussian kernel and a radial basis;

Step 3: Establish a hybrid kernel PCA-CCA model, calculate the weighted matrix J of _Ku and the weighted matrix L of _Ky , and obtain the residual r according to the weighted matrices J and L;

Step 4: Calculate the ^T2 statistic;

用下式计算：Step 5: Calculate the statistical threshold using the kernel density estimation method

Use the following formula to calculate:

表示

的概率，p(T²)表示T²统计量的概率密度，α为 给定置信度，其中，p(T²)按照下式计算：In the above formula,

express

The probability of T 2 , p(T ² ) represents the probability density of T ² statistic, α is the given confidence level, where p(T ² ) is calculated as follows:

In the above formula, N is the number of statistical samples, h is the kernel function width, K() is the kernel density function, let

和实时输 出数据核向量

所述混合核是由高斯核与径向基组合而成；Step 6: Collect online real-time input data and output data, and standardize the collected real-time data to obtain the real-time input data vector u _new and the real-time output data vector y _new . Use hybrid kernels to map u _new and y _new to the high-dimensional feature space to obtain the real-time input data kernel vector

and real-time output data kernel vector

The hybrid kernel is composed of a Gaussian kernel and a radial basis;

Step 7: Based on the weighted matrices J and L obtained in step 3 and the hybrid kernel PCA-CCA model trained in step 3, calculate the new real-time data residual variable r _new and calculate the real-time monitoring statistics

是否小于阈值

若小于阈值则判断设备运行正常 无需维护，若大于阈值则判断设备发生故障需要维护。Step 8: Real-time comparison

Is it less than the threshold?

If it is less than the threshold, it is judged that the equipment is operating normally and does not need maintenance. If it is greater than the threshold, it is judged that the equipment has failed and needs maintenance.

Further, the Gaussian kernel in step 2 is expressed as follows:

n》q或m，其中，

c₁和c₂均为高斯核参数；

n》q or m, where

c ₁ and c ₂ are Gaussian kernel parameters;

The radial basis kernel in step 2 is expressed as follows:

其中，

d₁和d₂均为径向基核参数；

in,

d ₁ and d ₂ are radial basis kernel parameters;

为系数，用于权衡核函数的分配。By integrating the Gaussian kernel function with the radial basis function, we can get:

is a coefficient used to weigh the distribution of the kernel function.

Furthermore, the hybrid kernel PCA-CCA model in step 3 is established according to the following objective function:

表示输入的协方差；

表示输出的协方差；

表示交叉协方差；in,

represents the covariance of the input;

represents the covariance of the output;

represents the cross covariance;

The objective function in formula 3 is obtained by performing singular value decomposition on Ψ, and the expression of Ψ is as follows:

Ψ＝∑ _U ^1/2 ∑ _UY ∑ _Y ^1/2 ＝ΓΛΔ ^T (Formula 4)

In the above formula, Γ is the data matrix containing left singular vectors, Δ is the data matrix containing right singular vectors, and Λ is the singular value matrix;

The weighting matrices J and L are calculated as follows: J = ∑ _U ^1/2 Γ, L = ∑ _Y ^1/2 Δ; residual r = J ^T K _u - Λ L ^T K _y .

Furthermore, in step 4, T ² = r ^T (I-Λ ² )r, wherein I is the identity matrix.

其中I为单位矩阵。Further, in step 7

Where I is the identity matrix.

The present invention combines the hybrid kernel PCA-CCA modeling method with the process monitoring method, focuses on the cross-correlation between process input and output, and is applicable to the kernel technique to effectively improve the monitoring effect of the nonlinear process, so that the monitoring accuracy is higher, especially for the initial fault. In addition, the present invention uses the kernel density estimation method in the determination of the threshold, which can more accurately determine the statistical threshold of the non-Gaussian process, and improves the accuracy of nonlinear process monitoring through multiple means of improvement.

The present invention is further described below through the accompanying drawings and specific embodiments.

Description of the drawings:

FIG1 is a flow chart of a process monitoring method according to an embodiment of the present invention;

FIG. 2 is a graph showing monitoring index results using a specific example of the monitoring method of the present invention.

Specific implementation method:

This embodiment discloses a process monitoring method based on hybrid kernel PCA-CCA and kernel density estimation, which is mainly used in natural gas liquefaction devices. It is necessary to install various sensors (flow sensors, temperature sensors, concentration sensors, etc.) in the process input and output components that need to be monitored in the natural gas liquefaction device to collect process input and output sample data under normal working conditions. The specific monitoring method includes the following steps (as shown in Figure 1):

Step 1: Collect process input and output sample data under normal operating conditions. Each sampling can obtain a 1×m input vector _uk and a 1×q output vector _yk . The subscript k in the above parameters represents the sampling time. After n samplings, the input data U＝[u ₁ ,u ₂ … _un ] ^T ∈R ^n×m and the output data Y＝[y ₁ ,y ₂ … _yn ] ^T ∈R ^n×q can be obtained. The sampling data of the liquefaction equipment under normal operating conditions should be selected as training data.

Step 2: Use a mixed kernel to map the above input data U and output data Y to a high-dimensional feature space, respectively, to obtain an input mixed kernel matrix _Ku and an output mixed kernel matrix _Ky . Here, the mixed kernel is a combination of a Gaussian kernel and a radial basis. The Gaussian kernel is represented as follows:

n》q或m，其中，

c₁和c₂均为高斯核参数；

n》q or m, where

c ₁ and c ₂ are Gaussian kernel parameters;

The radial basis kernel is expressed as follows:

其中，

d₁和d₂均为径向基核参数。

in,

_d1 and _d2 are radial basis kernel parameters.

为系数，用于权衡核函数的分配。By integrating the above Gaussian kernel function with the radial basis function, we can get:

is a coefficient used to weigh the distribution of the kernel function.

Step 3: According to the objective function given below, a hybrid kernel PCA-CCA model based on process input and output is established, and the weight matrix J of _Ku and the weight matrix L of _Ky are calculated, and then the residual r is obtained according to the weight matrices J and L; wherein the hybrid kernel PCA-CCA model is established according to the following objective function:

表示输入的协方差；

表示输出的协方差；

表示交叉协方差；in,

represents the covariance of the input;

represents the covariance of the output;

represents the cross covariance;

The objective function in formula 3 is obtained by performing singular value decomposition on Ψ, and the expression of Ψ is as follows:

Ψ＝∑ _U ^1/2 ∑ _UY ∑ _Y ^1/2 ＝ΓΛΔ ^T (Formula 4)

In the above formula, Γ is the data matrix containing left singular vectors, Δ is the data matrix containing right singular vectors, and Λ is the singular value matrix;

The weighting matrices J and L are calculated as follows: J = ∑ _U ^1/2 Γ, L = ∑ _Y ^1/2 Δ; residual r = J ^T K _u - Λ L ^T K _y .

Step 4: Calculate the T ² statistic, T ² = r ^T (I-Λ ² )r, where I is the identity matrix.

用下式计算：Step 5: Calculate the statistical threshold using the kernel density estimation method

Use the following formula to calculate:

表示

的概率，p(T²)表示T²统计量的概率密度，α为 给定置信度，其中，p(T²)按照下式计算：In the above formula,

express

The probability of T 2 , p(T ² ) represents the probability density of T ² statistic, α is the given confidence level, where p(T ² ) is calculated as follows:

In the above formula, N is the number of statistical samples, h is the kernel function width, K() is the kernel density function, let

和实时输出数据核向量

混合核是由高斯核与径向基组 合而成。Step 6: Collect online real-time input data and output data, and standardize the collected real-time data to obtain the real-time input data vector u _new and the real-time output data vector y _new . Referring to the method in step 2 above, u _new and y _new are respectively mapped to the high-dimensional feature space using a hybrid kernel to obtain the real-time input data kernel vector

and real-time output data kernel vector

The hybrid kernel is a combination of a Gaussian kernel and a radial basis.

其中I为单位矩阵。Step 7: Based on the weighted matrices J and L obtained in step 3 and the hybrid kernel PCA-CCA model trained in step 3, calculate the new real-time data residual variable r _new and calculate the real-time monitoring statistics

Where I is the identity matrix.

是否小于阈值

若小于阈值则判断设备运行正常无需维护，若大于阈值则判断设备发生故障 需要维护。Step 8: Real-time judgment of the operating status of the equipment, that is, real-time comparison

Is it less than the threshold?

If it is less than the threshold, it is judged that the equipment is operating normally and does not need maintenance. If it is greater than the threshold, it is judged that the equipment has failed and needs maintenance.

实线 表示实时统计量

从图2中的结果显示可以看出，本发明所提供的监测方 法可以快速、准确的捕捉到故障的发生，能够为天然气液化装置的稳定工作 保驾护航。In order to verify the monitoring effect of the monitoring method disclosed in the present invention, the method of the present invention is used under the condition of confidence level α=0.001, 250 normal data are used as training samples to establish the model and threshold, and the real-time data of the subsequent 480 moments are monitored (the fault is artificially injected after 80 samples). The monitoring indicators are shown in Figure 2, and the dotted line in Figure 2 represents the statistical threshold

Solid lines represent real-time statistics

It can be seen from the results shown in FIG2 that the monitoring method provided by the present invention can quickly and accurately capture the occurrence of faults and can ensure the stable operation of the natural gas liquefaction device.

The above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Other modifications or equivalent substitutions made to the technical solution of the present invention by ordinary technicians in this field should be included in the scope of the claims of the present invention as long as they do not depart from the spirit and scope of the technical solution of the present invention.

Claims (5)

1. A process monitoring method based on hybrid kernel PCA-CCA and kernel density estimation, characterized in that it comprises the following steps: Step 1: Collect process input and output sample data under normal working conditions, obtain the 1×m input vector u _k and the 1×q output vector y _k at sampling time k, and after n samplings, obtain input data U = [u ₁ ,u ₂ … _un ] ^T ∈R ^n×m and output data Y = [y ₁ ,y ₂ …y _n ] ^T ∈R ^n×q ; Step 2: Map the input data U and the output data Y to the high-dimensional feature space using a hybrid kernel, respectively, to obtain an input hybrid kernel matrix _Ku and an output hybrid kernel matrix _Ky , wherein the hybrid kernel is composed of a Gaussian kernel and a radial basis; Step 3: Establish a hybrid kernel PCA-CCA model, calculate the weighted matrix J of _Ku and the weighted matrix L of _Ky , and obtain the residual r according to the weighted matrices J and L; Step 4: Calculate the ^T2 statistic; Step 5: Calculate the statistical threshold using the kernel density estimation method

Use the following formula to calculate:

In the above formula,

express

The probability of T 2 , p(T ² ) represents the probability density of T ² statistic, α is the given confidence level, where p(T ² ) is calculated as follows:

In the above formula, N is the number of statistical samples, h is the kernel function width, K() is the kernel density function, let

Step 6: Collect online real-time input data and output data, and standardize the collected real-time data to obtain the real-time input data vector u _new and the real-time output data vector y _new . Use hybrid kernels to map u _new and y _new to the high-dimensional feature space to obtain the real-time input data kernel vector

and real-time output data kernel vector

The hybrid kernel is composed of a Gaussian kernel and a radial basis; Step 7: Based on the weighted matrices J and L obtained in step 3 and the hybrid kernel PCA-CCA model trained in step 3, calculate the new real-time data residual variable r _new and calculate the real-time monitoring statistics

Step 8: Real-time comparison

Is it less than the threshold?

If it is less than the threshold, it is judged that the equipment is operating normally and does not need maintenance. If it is greater than the threshold, it is judged that the equipment has failed and needs maintenance. 2. The process monitoring method based on hybrid kernel PCA-CCA and kernel density estimation according to claim 1, characterized in that: the Gaussian kernel in step 2 is expressed as follows:

n>>q or m, where

c ₁ and c ₂ are Gaussian kernel parameters; The radial basis kernel in step 2 is expressed as follows:

in,

d ₁ and d ₂ are radial basis kernel parameters; By integrating the Gaussian kernel function with the radial basis function, we can get:

is a coefficient used to weigh the distribution of the kernel function. 3. The process monitoring method based on hybrid kernel PCA-CCA and kernel density estimation according to claim 1 is characterized in that: the hybrid kernel PCA-CCA model in step 3 is established according to the following objective function:

in,

represents the covariance of the input;

represents the covariance of the output;

represents the cross covariance; The objective function in formula 3 is obtained by performing singular value decomposition on Ψ, and the expression of Ψ is as follows: Ψ＝∑ _U ^1/2 ∑ _UY ∑ _Y ^1/2 ＝ΓΛΔ ^T (Formula 4) In the above formula, Γ is the data matrix containing left singular vectors, Δ is the data matrix containing right singular vectors, and Λ is the singular value matrix; The weighting matrices J and L are calculated as follows: J = ∑ _U ^1/2 Γ, L = ∑ _Y ^1/2 Δ; residual r = J ^T K _u - Λ L ^T K _y . 4 . The process monitoring method based on hybrid kernel PCA-CCA and kernel density estimation according to claim 3 , characterized in that: in step 4 , T ² =r ^T (I-Λ ² )r, wherein I is a unit matrix. 5. The process monitoring method based on hybrid kernel PCA-CCA and kernel density estimation according to claim 3, characterized in that: in step 7

Where I is the identity matrix.

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