Least square method and window decimation based modeling method for control valve flow rate prediction

Abstract

The present application belongs to the technical field of regulating valve flow prediction, and discloses a regulating valve flow prediction modeling method based on least square method and window down-sampling, considers the basic least square regression problem, and constructs the following objective function: for the feature selection problem, a weight matrix Ξ is introduced on this basis, and the objective function of the optimization problem is the method provided by the present application learns the weights of different models based on the least square method, and takes the weights as the basis for evaluating the performance of the models; in the online prediction process, the performance evaluation results of the various prediction models are comprehensively considered, and finally the current flow prediction value of the valve is obtained. The regulating valve flow prediction accuracy problem in the actual application scene is solved, and the health state of the valve is further effectively diagnosed.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of regulating valve flow prediction, in particular to a regulating valve flow prediction modeling method based on least square method and window downsampling. BACKGROUND

[0002] The regulating valve is also called control valve, which is an important actuator in the petrochemical process control system. It receives the instructions of the controller and adjusts the valve opening to change the medium flow, pressure, liquid level or temperature. The regulating valve is suitable for air, water, steam, various corrosive media, mud, oil and other media. According to the stroke characteristics, the regulating valve can be divided into straight stroke and angular stroke. According to the power used by the actuator, it can be divided into pneumatic regulating valve, electric regulating valve and hydraulic regulating valve. According to its function and characteristics, it can be divided into linear characteristic, logarithmic characteristic and quick opening characteristic. In practice, the linear characteristic and logarithmic characteristic regulating valves are most commonly used.

[0003] During long-term use, the regulating valve is prone to leakage, blockage and jamming due to factors such as valve core wear and medium scaling. These faults may cause the diffusion of toxic substances and the failure of valve regulation, etc. These problems may cause unstable system operation, unqualified product quality, and even safety accidents, threatening the life and property safety of on-site workers. More seriously, it may cause secondary disasters, pollute the environment and cause adverse social impact. Therefore, the fault diagnosis and health status evaluation of the valve are particularly important. One of the common methods to diagnose the leakage and blockage of the regulating valve is to establish a flow prediction model, and to use the error value between the predicted flow and the actual flow as the diagnostic basis for diagnosis. This diagnostic framework requires high modeling accuracy of the flow prediction model.

[0004] For the flow regulating valve with logarithmic characteristics, the general research ideas for fault detection problems such as valve leakage and blockage are divided into two categories: one category is the method based on classification or clustering, which usually needs to collect data of different fault types, extract sensitive classification features from the original data, and then train the corresponding learning machine to classify the faults. However, in the actual industrial scene, the regulating valve is mostly in normal working condition, and it is difficult to obtain fault data, so it is difficult to train an effective diagnostic model, and this method has great limitations in practical application; the other category is the method based on prediction, the main idea of which is to establish a corresponding valve model for the input and output characteristics of the valve, identify the model parameters through the corresponding learning algorithm, and compare the predicted flow with the actual flow value measured by the measuring instrument when the error exceeds the threshold value, to determine whether the valve has leakage or blockage. The identification model can be a mechanism model or a model based on data construction. Compared with the first method, this method has more application prospects. In this study, the flow regulating valve has clear characteristics. Therefore, the mechanism modeling method is simpler and more reliable in practical application. The main method is to identify the flow prediction model by the least square method, but it still cannot well predict the flow, and the fitted curve cannot well describe the valve opening-flow characteristics in the actual production process. The main reasons include the following points:

[0005] 1. In the actual production process, the valve characteristics will have certain parameter variations due to the influence of upstream and downstream working condition fluctuations, system action inertia and other factors;

[0006] 2. In the actual industrial process, the sensor will collect a large amount of data, which contains a large amount of effective, invalid and interference data. Using these data directly for modeling will affect the model accuracy;

[0007] 3. Based on the second factor, the original data is often preprocessed in the actual process, such as removing outliers and noise, and the model performance will be improved to a certain extent after the preprocessing, but the effect is limited. The reason is that the amount of data after preprocessing is still large, and in the model identification process, it is often assumed that all data contain the same amount of information, that is, all data are equal in weight in the identification process, so the prediction model accuracy is still low. SUMMARY

[0008] The present application aims to provide a regulating valve flow prediction modeling method based on least squares and window downsampling to solve the problems described in the prior art.

[0009] In order to achieve the above object, the present application provides the following technical solutions:

[0010] The least square method and the window down-sampling are used to adjust the valve flow prediction modeling method, the basic least square regression problem is considered, and the following objective function is constructed:

[0011]

[0012] In the formula, X and Y are corresponding sample matrices, and W is a parameter matrix to be solved;

[0013] For the feature selection problem, a weight matrix Ξ is introduced based on formula (1), and the objective function of the optimization problem is shown in formula (2):

[0014]

[0015] Further, the specific method for constructing the objective function comprises the following steps:

[0016] S1, data selection and pretreatment: single loop control, cascade control strategy is adopted, the opening degree of valve i is op i , the flow is pv i , the flow set value is sp i , the working mode of the valve is Mode i , first sample screening is carried out from the database, and the sample screening needs to meet the following conditions:

[0017]

[0018] Formula (3) represents that the valve must be in normal working state: when op i =0 and op i =100, the closing state of air opening valve and air closing valve is corresponding, at this time, the valve does not work; At the same time, the data of the valve in automatic control mode is collected, so as to avoid the interference of artificial operation on sample data;

[0019] S2, modeling: the flow regulating valve with logarithmic characteristics is provided, the valve opening degree is op, the flow size is pv, and the valve characteristics are represented as:

[0020] pv=βe α·op (4)

[0021] In the formula, α and β are unknown parameters, which are obtained by least square method and swarm intelligent optimization algorithm identification algorithm;

[0022] Formula (4) is further converted into the linear model of formula (5):

[0023] ln(pv)=α·op+lnβ (5)

[0024] Let formula (5) in Then formula (6) is obtained:

[0025]

[0026] Thus, the transformation from nonlinear model to linear model is completed; meanwhile, in order to make full use of the information contained in the training data, multiple identification models are considered to be established;

[0027] Here, let the number of models be l, and formula (7) is obtained:

[0028]

[0029] In the formula, And A = diag{a1, a2, …, a l};

[0030] In order to evaluate the performance of the l different models, the idea of feature selection in the field of data mining is used to assist the modeling process, and a training sample matrix is constructed, and the specific method is as follows:

[0031] A window with a length of l is selected, and the window sliding step is selected as t. The window is slid n times with a step of t, and n time series with a length of l are obtained;

[0032] The n time series obtained by window downsampling of formula (7) are combined into the corresponding matrix form according to the sampling order, and the following sample matrices can be obtained respectively:

[0033]

[0034]

[0035] Therefore, formula (7) can be arranged as:

[0036]

[0037] For formula (8), the least square method is used to identify the parameter matrix A and the bias vector The following objective function is constructed, where η is a hyperparameter:

[0038]

[0039] By expanding the OP, the parameter is introduced into the A matrix,

[0040]

[0041] The objective function is further simplified to formula (11):

[0042]

[0043] To evaluate the performance of the model, define the weight vector and satisfy σ i > 0, (i = 1, 2, …, l), while defining a diagonal matrix ∑, and Introducing ∑ into the objective function (9), we get:

[0044]

[0045] At this point, let Substitute it into equation (12) as:

[0046]

[0047] So far, the optimization problem is expressed as:

[0048]

[0049] Obviously, equation (14) is a constrained optimization problem, which can be solved by using the Lagrange multiplier method: first construct the corresponding Lagrange function (15):

[0050]

[0051] In the formula, represents the i-th row of the transpose of the matrix , take the partial derivative of L with respect to σ i , and set the partial derivative to 0, we get:

[0052]

[0053] We get And because Further, we get Get equation (17):

[0054]

[0055] Substitute equation (17) into equation (14), and the optimization problem is further transformed,

[0056]

[0057] In the formula:

[0058]

[0059] Since Therefore, the optimization problem described in equation (18) is equivalent to:

[0060]

[0061] The objective function in equation (20) is solved and the derivative is set to 0 to obtain equation (21):

[0062]

[0063] wherein is a diagonal matrix and satisfies:

[0064]

[0065] Here, let Substituting equation (21) into equation (20) gives:

[0066]

[0067] wherein Generally, nl+1 is satisfied, so (OPOP T ) -1 exists; at the same time, the matrix X is related to , so the iterative method is used to solve in equation (23) to obtain A, and other parameters.

[0068] S3, Test: In the test phase, the sampling value op test at each time is input into the l valve models obtained by identification, and is weighted to be the final flow prediction at a certain time, to obtain equation (24):

[0069]

[0070] S4, Convergence analysis: To prove the convergence of the above problem, the following lemma needs to be introduced first:

[0071] Lemma 1: For any two non-zero vectors , it is deduced from the basic inequality (a-b) 2 ≥ 0 that:

[0072]

[0073] From equation (20) and equation (21), the original optimization problem is equivalent to equation (26):

[0074]

[0075] Equation (26) is further converted into equation (27):

[0076]

[0077] The optimization problem described by formula (27) satisfies the following formula at the k+1th iteration:

[0078]

[0079] That is:

[0080]

[0081] Further calculation:

[0082]

[0083]

[0084] According to lemma 1, formula (32) is established:

[0085]

[0086] Combined with formula (31) and formula (32), formula (33) which is necessarily established is obtained:

[0087]

[0088] Further calculation obtains formula (34):

[0089]

[0090] Formula (34) shows that the optimization problem described by formula (27) eventually makes the objective function in formula (20) Converge, and the convergence is proved.

[0091] Principle of the technical scheme: The method adopted by the application mainly learns the weighting idea in the feature selection algorithm: a plurality of flow prediction models are established, and the weights of different models are learned based on the least square method, which is used as the basis for evaluating the performance of the model. In the online prediction process, the performance evaluation results of each prediction model are integrated, and finally the current flow prediction value of the valve is obtained.

[0092] The beneficial effects of the technical scheme are:

[0093] 1. The application proposes a flow regulating valve modeling method based on the least square feature selection principle, which learns the weighting idea in the feature selection algorithm. Meanwhile, a window downsampling technology is also proposed to assist the modeling process, and then the objective function is optimized and solved based on the least square principle.

[0094] 2. The application solves the accuracy problem of the flow prediction of the regulating valve in the actual application scene, thereby providing protection for further effectively diagnosing the health status of the valve.

[0095] 3, The application further proves the convergence of the proposed parameter optimization method;

[0096] 4, The adjustment valve flow prediction scheme proposed in the application is preliminarily tested on part of the flow regulating valve equipment of three sets of catalytic devices in a certain petrochemical company. Compared with the prior art, the method proposed in the application can better fit the opening-flow distribution of the regulating valve in the actual scene, and the practicability is further improved. BRIEF DESCRIPTION OF DRAWINGS

[0097] Figure 1 The flow regulating valve opening and flow change curve for the embodiment of the application;

[0098] Figure 2 The window downsampling method schematic diagram for the embodiment of the application;

[0099] Figure 3 The regulating valve 1 flow prediction graph and fitting distribution graph for the embodiment of the application;

[0100] Figure 4 The regulating valve 2 flow prediction graph and fitting distribution graph for the embodiment of the application;

[0101] Figure 5 The regulating valve 3 flow prediction graph and fitting distribution graph for the embodiment of the application;

[0102] Figure 6 The regulating valve 4 flow prediction graph and fitting distribution graph for the embodiment of the application;

[0103] Figure 7 The regulating valve 5 flow prediction graph and fitting distribution graph for the embodiment of the application;

[0104] Figure 8 The regulating valve 6 flow prediction graph and fitting distribution graph for the embodiment of the application;

[0105] Figure 9 The regulating valve 7 flow prediction graph and fitting distribution graph for the embodiment of the application;

[0106] Figure 10 The regulating valve 8 flow prediction graph and fitting distribution graph for the embodiment of the application;

[0107] In the figure:

[0108] (a) is the graph obtained by the existing least square method;

[0109] (b) is the graph obtained by combining the least square method and the window downsampling method. DETAILED DESCRIPTION

[0110] The application will be further described in detail below in combination with the drawings and embodiments:

[0111] The embodiment selects control valve data of three sets of catalytic devices of a certain petrochemical company, the device contains about 200 control valves, adopts single loop control, cascade control and other control strategies, and a part of representative flow regulating valve data is selected for modeling and testing.

[0112] The regulating valve flow prediction modeling method based on least square method and window downsampling includes the following steps:

[0113] S1, data selection and preprocessing: adopting single loop control and cascade control strategy, the opening of valve i is op i , the flow is pv i , the flow set value is sp i , the working mode of the valve is Mode i , first sample screening is carried out from the database, and the sample screening needs to meet the following conditions:

[0114]

[0115] Formula (3) represents that the valve must be in normal working state: when op i =0 and op i =100, the closing state of air opening valve and air closing valve is corresponding, at this time, the valve does not work; at the same time, the data of the valve in automatic control mode should be collected, so as to avoid the interference of manual operation on sample data, after data screening, further denoising and removing abnormal values are needed, and the regulating valve opening and flow time sequence curve as shown in Figure 1 can be obtained;

[0116] S2, modeling: the flow regulating valve with logarithmic characteristics, the valve opening is op, the flow size is pv, and the valve characteristics are represented as:

[0117] pv=βe α·op (4)

[0118] In the formula, α and β are unknown parameters, which are obtained by least square method and swarm intelligent optimization algorithm identification algorithm; formula (4) is further converted into linear model of formula (5):

[0119] ln(pv)=α·op+lnβ (5)

[0120] Let in formula (5), formula (6) can be obtained:

[0121]

[0122] Thus, the conversion from nonlinear model to linear model is completed; at the same time, in order to fully utilize the information contained in the training data, multiple identification models are considered to be established;

[0123] Here, let the number of models be l, and obtain equation (7):

[0124]

[0125] wherein, and A = diag{a1, a2, …, a l};

[0126] To evaluate the performance of the l different models, the idea of feature selection in the field of data mining is used to assist the modeling process. A window downsampling technique is used to construct the training sample matrix. The data processing process is shown in FIG. 1. Figure 2

[0127] A window of length l is selected, and the window sliding step is selected as t. The window is slid n times with a step of t, and n segments of time series of length l are obtained.

[0128] The n segments of time series obtained by window downsampling of equation (7) are combined into a corresponding matrix form according to the sampling order, and the following sample matrices can be obtained:

[0129]

[0130]

[0131] Therefore, equation (7) can be arranged as:

[0132]

[0133] For equation (8), the least squares method is used to identify the parameter matrix A and the bias vector The following objective function is constructed, where η is a hyperparameter:

[0134]

[0135] By expanding the OP, the parameter is introduced into the A matrix,

[0136]

[0137] The objective function is further simplified to equation (11):

[0138]

[0139] To evaluate the performance of the model, the weight vector is defined and satisfies A diagonal matrix ∑ is defined and satisfies Introducing ∑ into the objective function equation (9) gives:

[0140] ​

[0141] At this time, Substituting it into equation (12) gives:

[0142]

[0143] Therefore, the optimization problem can be expressed as:

[0144]

[0145] Obviously, equation (14) is a constrained optimization problem, which can be solved using the Lagrange multiplier method: First, construct the corresponding Lagrange function equation (15):

[0146]

[0147] In the formula, Representation matrix The i-th row of the transpose of L will be used to pair L with σ. i Taking the partial derivative and setting it to 0, we get:

[0148]

[0149] get And because Further obtain Equation (17) is obtained:

[0150]

[0151] Substituting equation (17) into equation (14), the optimization problem is further transformed.

[0152]

[0153] In the formula:

[0154]

[0155] because Therefore, the optimization problem described in equation (18) is equivalent to:

[0156]

[0157] For the objective function in equation (20) beg Setting the derivative to 0, we obtain equation (21):

[0158]

[0159] In the formula, It is a diagonal matrix and satisfies:

[0160]

[0161] Here, let Substitute equation (21) into equation (20) to obtain:

[0162]

[0163] where Generally, n » l+1, so (OPOP T ) -1 always exists; meanwhile, matrix X is related to Therefore, by solving in equation (23) through an iterative method, the parameters A, and so on can be obtained.

[0164] S3, Testing: In the testing phase, the sampling value op test at each time is input into the l valve models obtained through identification, and is weighted to serve as the final flow prediction at a certain time, obtaining equation (24):

[0165]

[0166] S4, Convergence Analysis: To prove the convergence of the above problem, the following lemma needs to be introduced first:

[0167] Lemma 1: For any two non-zero vectors By the basic inequality (a-b) 2 ≥ 0, it is derived that:

[0168]

[0169] From equation (20) and equation (21), the original optimization problem is equivalent to equation (26):

[0170]

[0171] Equation (26) is further converted into equation (27):

[0172]

[0173] The optimization problem described in equation (27) satisfies the following equation at the k+1th iteration:

[0174]

[0175] That is:

[0176]

[0177] Further calculation shows that:

[0178]

[0179]

[0180] From Lemma 1, formula (32) is established:

[0181]

[0182] Combined with formula (31) and formula (32), formula (33) which is necessarily established is obtained:

[0183]

[0184] Further calculation obtains formula (34):

[0185]

[0186] Formula (34) shows that the optimization problem described in formula (27) will eventually make the objective function in formula (20) converge, and the convergence is proved.

[0187] The specific implementation is as follows:

[0188] The experimental data of some valves of three catalytic devices of a petrochemical company are selected. In order to fully verify the effectiveness of the above method, the experimental data covers multiple representative flow regulating valves in the device, and the detailed information of each regulating valve is shown in Table 1:

[0189] Table 1 Partial control valve information of three catalytic devices

[0190]

[0191] In this embodiment, the sampling period of the field DCS system is 1 min, and the sampling data of the system from April 29, 2022 to May 9, 2022 for a total of 10 days is selected for modeling and testing, and the ratio of training data and test data is set to 7:3. Moreover, the method provided by the present application is compared with the method based on least square regression, as shown in Figures 3 to 10 It can be seen that in the actual industrial scene, the distribution of different valve data is affected by internal and external interference, working condition change and many other factors, and the actual data distribution does not strictly conform to the flow characteristic curve. The single model based on least square regression for flow prediction obviously cannot achieve a relatively ideal prediction effect. In comparison, the regulating valve modeling scheme based on the combination of least square method and window downsampling technology proposed by the present application effectively utilizes the useful information in the training data and filters out the interference by establishing multiple flow prediction models and weighting each model, so that the fitting distribution has higher coincidence degree with the training data distribution, and better prediction effect is achieved.

[0192] Notably, for Figure 4 and Figure 10 valves with frequent flow fluctuations, the method based on least square regression may frequently give false alarms, while the method provided by the present application shows good following performance; in addition, from Figure 7 it can be seen that when the measured flow has a large fluctuation for a short time and the duration is long, both methods can give effective early warning under the condition of reasonable setting of the prediction error threshold.

[0193] The above is only an embodiment of the present application, and common technical solutions or characteristics in the scheme are not described in detail. It should be noted that for those skilled in the art, without departing from the technical solutions of the present application, a number of modifications and improvements can be made, which should also be considered as the protection scope of the present application, and these will not affect the effect and practicality of the present application. The protection scope of the present application should be subject to the content of its claims, and the specific implementation mode and the like in the specification can be used to explain the content of the claims.

Claims

1. A method for predicting and modeling the flow rate of a control valve based on least squares method and window downsampling, characterized in that: Considering the basic least squares regression problem, we construct the following objective function: In the formula, X and Y are the corresponding sample matrices, and W is the parameter matrix to be solved; For the feature selection problem, a weight matrix Ξ is introduced based on equation (1), and the objective function of the optimization problem is shown in equation (2): The specific method for constructing the objective function includes the following steps: S1. Data Selection and Preprocessing: A single-loop control and cascade control strategy is adopted. Let the opening degree of valve i be op. i Traffic is PV i The flow rate setting is sp i The valve's operating mode is Mode i First, samples are screened from the database. The sample screening must meet the following conditions: Equation (3) indicates that the valve must be in normal working condition: when op i =0 and op i When = 100, it corresponds to the closed state of the air-to-open valve and the air-to-close valve. At this time, the valves are not working. At the same time, data of the valves in automatic control mode is collected to avoid interference from human operation on the sample data. S2. Modeling: A flow control valve with logarithmic characteristics, assuming the valve opening is op and the flow rate is pv, its valve characteristics are expressed as: pv=βe α·op (4) In the formula, α and β are unknown parameters, which are obtained by the least squares method and the swarm intelligence optimization algorithm. Equation (4) is further transformed into a linear model of equation (5): ln(pv)=α·op+lnβ (5) In formula (5) lnβ=b, we can obtain equation (6): This completes the transformation from a nonlinear model to a linear model; at the same time, in order to make full use of the information contained in the training data, multiple identification models are considered to be established. Here, let the number of models be l, and we get equation (7): In the formula, And A = diag{α1, α2, ..., α l }; To evaluate the performance of l different models, feature selection from the field of data mining is used to construct a training sample matrix to assist the modeling process. The specific method is as follows: Select a window of length l, and set the window sliding step size to t. Slide the window n times with step size t to obtain n time series segments of length l. Equation (7) uses window downsampling to obtain n time series segments. These segments are combined in the sampling order to form corresponding matrix forms, resulting in the following sample matrices: Therefore, equation (7) can be rearranged as follows: For equation (8), the least squares method is used to identify the parameter matrix A and the bias vector. Construct the following objective function, where η is a hyperparameter: By expanding the dimension of OP, the parameters Introducing matrix A, The objective function can be further simplified to equation (11): To achieve model performance evaluation, a weight vector is defined. And satisfy σ i >0, (i = 1, 2, ..., l), and define a diagonal matrix ∑, and Introducing ∑ into the objective function (9), we get: At this time, Substituting it into equation (12) gives: Therefore, the optimization problem can be expressed as: Obviously, equation (14) is a constrained optimization problem, which can be solved using the Lagrange multiplier method: First, construct the corresponding Lagrange function equation (15): In the formula, Representation matrix The i-th row of the transpose of L will be used to pair L with σ. i Taking the partial derivative and setting it to 0, we get: get And because Further obtain Equation (17) is obtained: Substituting equation (17) into equation (14), the optimization problem is further transformed. In the formula: because Therefore, the optimization problem described in equation (18) is equivalent to: For the objective function in equation (20) beg Setting the derivative to 0, we obtain equation (21): In the formula, It is a diagonal matrix and satisfies: Here, let Substituting into equation (21), we get: In the formula, Usually, n >> l + 1 is satisfied, therefore (OPOP) T ) -1 It must exist; at the same time, matrix X and Therefore, the iterative method is used to solve equation (23). Therefore, we can obtain A. Parameters; S3, Testing: During the testing phase, the sampled value op at each time step is... test The values ​​are input into the identified l valve models respectively, and weighted to obtain the final flow prediction at a certain moment, resulting in equation (24): S4. Convergence Analysis: To prove the convergence of the above problem, we first need to introduce the following lemma: Lemma 1: For any two non-zero vectors From the basic inequality (ab) 2 ≥0 is derived as follows: From equations (20) and (21), the original optimization problem is equivalent to equation (26): Equation (26) is further transformed into equation (27): The optimization problem described in equation (27) satisfies the following in the (k+1)th iteration: Right now: Further calculations: By Lemma 1, equation (32) holds: Combining equations (31) and (32), we obtain equation (33), which is necessarily true: Further calculation yields equation (34): Equation (34) shows that the optimization problem described in equation (27) will eventually result in the objective function in equation (20) being... Convergence, the convergence is proven.

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