Width learning-based water quality index BOD5 monitoring method for efficiently extracting data feature information

Abstract

The invention discloses a water quality index BOD5 monitoring method for efficiently extracting data feature information based on width learning. According to the method, under the inspiration of a loop network structure, recursive cascading is carried out on feature windows of a width learning system to extract time correlation features of process data. On this basis, a non-Gaussian feature extraction window is added, non-Gaussian features of sewage data are extracted by using an over-complete independent component analysis method, the ability of the model to extract different features of the data is enriched, and the accuracy of the model is improved. The method comprises an off-line training stage and an on-line monitoring stage. Besides, aiming at the condition that the model precision is insufficient in a severe environment and an operation condition in the sewage treatment process, the model provided by the invention can be reconstructed in an increment mode, the whole network does not need to be retrained from the beginning, and the network training can be completed in a very short time; therefore, the water quality index of the sewage can be rapidly monitored in time.

Description

Technical Field

[0001] The present invention relates to the field of data-driven quality indicator monitoring technology, and in particular to a water quality indicator BOD5 monitoring technology for sewage treatment processes. Specifically, the present invention relates to a width learning model based on feature enhancement extraction, which is used to monitor water quality indicators in sewage treatment processes. In the sewage treatment process, accurate monitoring of the water quality indicator Five-Day Biochemical Oxygen Demand (BOD5) is crucial. Traditional water quality indicator monitoring methods are difficult to apply to complex sewage treatment processes, so a novel data-driven method is needed to improve the performance and accuracy of water quality indicator monitoring methods. The present invention aims to improve the performance and accuracy of water quality indicator monitoring methods through 2 Background Art

[0002] Sewage treatment plants effectively treat sewage and reduce the concentration of pollutants in water bodies. They minimize water pollution and protect the sustainable use of water resources in accordance with strict effluent discharge standards. Among them, the water quality indicator five-day biochemical oxygen demand (BOD5) is one of the key parameters for measuring the effect of sewage treatment, reflecting the concentration of biodegradable organic matter in water. By monitoring the BOD5 concentration of effluent, the efficiency of sewage treatment plants in treating organic pollutants can be effectively evaluated to ensure that the treated water quality meets environmental protection standards and can safely re-enter natural water bodies or be reused. However, the BOD5 measurement methods currently used in practice have certain limitations, including long measurement cycles (usually 5 days), cumbersome operations, and high dependence on environmental conditions, all of which may affect the efficiency and accuracy of the measurement. Therefore, although BOD5 is an important indicator for evaluating the effect of sewage treatment, its measurement characteristics limit its application in real-time monitoring and rapid decision-making. Faced with these challenges, soft sensing technology has been proposed as an alternative. The core of this technology is to estimate performance indicators that are difficult to measure directly by constructing mathematical models with easily measurable process variables. In the field of sewage, soft sensor modeling methods are mainly divided into two methods: process mechanism analysis-based and data-driven. When establishing a mechanism model, it usually requires an in-depth understanding of the sewage treatment process and involves complex biological, chemical or physical equation descriptions, so the modeling process is both complex and time-consuming. In contrast, the data-driven soft sensor model only identifies the mapping relationship between input and output by analyzing historical data, and has received widespread attention in the field of sewage soft measurement for its fast modeling speed and high accuracy.

[0003] At present, the data-driven water quality indicator monitoring models applied to sewage treatment processes and other complex industrial processes include classic methods such as principal component regression (PCR), kernel partial least squares (KPLS), support vector machine (SVM) and artificial neural network (ANN). However, the above methods are limited by the shallow network structure and are not ideal when processing complex sewage treatment process data. Recent studies have shown that methods based on deep neural networks have stronger expressive power than shallow neural networks and can better capture the nonlinear characteristics of complex input data in modeling. Common deep neural networks including stacked autoencoders, convolutional neural networks and deep belief networks have achieved superior performance in modeling sewage treatment processes and other complex industrial processes. However, the above deep neural networks usually assume that samples are independent and ignore the time-related characteristics of sewage treatment process time series data. In addition, due to its deep network structure and complex hyperparameters, the model is also very time-consuming in the training process and cannot meet the needs of real-time measurement of water quality indicators in sewage treatment processes.

[0004] In view of the above-mentioned shortcomings of deep learning, the emergence of Broad Learning System (BLS) provides a solution to the time-consuming problem of deep neural network training and updating. The basic idea of ​​BLS is to map data into feature nodes and enhancement nodes, and merge them into a layer directly connected to the output layer. Unlike deep neural networks that improve model accuracy by superimposing network layers, BLS horizontally expands the network by increasing the number of nodes and only needs to train the connection weights between this layer and the output layer. This flattened network structure allows BLS to avoid complex training processes and greatly reduces the time cost of network training. In addition, the trained BLS can quickly update and add nodes to improve model accuracy without retraining the network, and its universal approximation ability and nonlinear feature extraction ability are also guaranteed in theory. However, although BLS guarantees the time cost of network training and can quickly update the network structure online, it cannot effectively handle the nonlinear, time-related and non-Gaussian characteristics of sewage data at the same time. If the multiple feature information of the data is ignored, it will lead to insufficient data feature extraction and reduced monitoring accuracy of the model. In addition, the above analysis shows that the structure of BLS is flexible. Therefore, in order to obtain better network performance, this method improves the feature window of BLS by cyclic connection to RBLS, and constructs a monitoring method for water quality index BOD5 of width learning system based on feature enhancement extraction through OICA algorithm. This method improves the monitoring accuracy of water quality index BOD5 by learning the time correlation characteristics and non-Gaussian characteristics of sewage data, and then extracting effective process information from the data. The water quality index monitoring technology of the present invention can be widely used in sewage treatment plants and related fields for online monitoring of water quality indicators. Through this technology, operators can better understand the water quality status in the treatment process and take necessary measures in time to ensure the efficient operation of the sewage treatment process and the compliance of water quality. Summary of the invention

[0005] In order to solve the problem of inaccurate monitoring results of water quality index BOD5 caused by nonlinear, time-correlated and non-Gaussian characteristics of sewage treatment process data, the present invention proposes a water quality index monitoring method based on feature augmented extraction broad learning system (FAE-BLS). Inspired by the deep recurrent network RNN, the feature window of BLS is recursively cascaded to form RBLS to effectively extract the time-correlated characteristics of sewage data. At the same time, in order to enhance the extraction of non-Gaussian features of sewage data by RBLS, the OICA algorithm is used to construct the extraction window of non-Gaussian features to enrich the learning ability of the BLS model for the process characteristics of sewage data. In addition, the nonlinear activation function of the width learning system can also extract the nonlinear characteristics of the data. Finally, when the prediction accuracy of the network continues to decline and does not meet the actual industrial needs when facing changes in the sewage treatment environment or abnormal conditions, the network can be horizontally expanded to add enhanced nodes to quickly adjust the model structure, and the monitoring accuracy of the model can be improved without retraining the network. In summary, the present invention provides a new water quality indicator monitoring technology for sewage treatment process, which realizes accurate real-time monitoring of BOD5, a water quality indicator in sewage treatment process, based on feature-enhanced width learning system. The application of this technology will help improve the operating efficiency of water treatment plants and the reliability of water quality monitoring.

[0006] The present invention adopts the following technical solutions and implementation steps:

[0007] Assume that the input process variable raw data is X∈R n×d , n represents the number of samples, and d is the number of process variables contained in each sample. The corresponding water quality index output data is Y∈R n×M , M is the number of water quality indicators.

[0008] A. Offline training phase:

[0009] 1) Use the time window to serialize the original data X to obtain the serialized data set X p =[X1, ..., X t ],t=1,…,p. X t ∈R (n-p+1)×d is the input data of each feature window, p is the number of feature windows, and m=n-p+1 is the step size of the time window.

[0010] 2) The data X after time window scanning is processed p Input into the feature window based on the loop structure,

[0011] The construction formula for generating the tth window is as follows:

[0012] Z t =σ(X t W Z +Z t-1 U+b0) (1)

[0013] Among them, the t-th feature window Z t Not only from the current input X t Extract shallow features and learn the t-1th feature window Z t-1 To extract the time correlation features of data at different time steps,

[0014] The feature window of the ring structure. σ is the activation function sigmoid, and the initial state Z0 is set to 0. Each feature window

[0015] The weights and biases associated with the recursive cascade are shared, that is, the weights W generated randomly using uniform distribution Z , weight U and bias b0.

[0016] 3) Repeat step 2 to complete the feature window Z of all extracted data time correlations t The generation of these windows is represented by connecting them as Z P =[Z1,Z2,…,Z p ], p represents the total number of feature windows contained in the network.

[0017] Subsequently, in order to enhance the model’s learning of different process characteristics of the data, a non-high-resolution OICA-based

[0018] The core idea of ​​the OICA algorithm applied in this window is to transform the d-dimensional process variables of the training data X through the mixing matrix D∈R d×k Decompose into k independent elements with high-order features (k>d)

[0019] To extract the non-Gaussian information.

[0020] X T =Dα (2)

[0021] Among them, X T ∈R d×n is the transposed matrix of X, α=[α1,…,α k ] is the independent element matrix, k is the independent element dimension after the d-dimensional process variable decomposition, represents the ith independent element, and n is the number of samples.

[0022] 4) Solving the mixing matrix D is mainly divided into two steps. First, construct an approximate subspace W = Span {N1, N2, ..., Ns}, Span is a mathematical symbol representing the space spanned by the matrix. Then, the approximate calculation Atoms in

[0023] right Perform eigenvalue decomposition, where the eigenvector corresponding to the maximum eigenvalue is the mixing matrix D

[0024] The approximate solution of the vector in , can be combined in the order of number i = 1, ... k to obtain the mixing matrix D.

[0025] After taking the mixing matrix D, the non-Gaussian feature extraction of the data is as follows:

[0026] G=XD (3)

[0027] Among them, G∈R n×k Represents the non-Gaussian information of the data extracted by the feature window based on OICA. 5) After creating the feature window for extracting the time correlation and non-Gaussianity of the data, in order to ensure that the method can

[0028] The original nonlinear features of the input data are extracted. Therefore, unlike the classic BLS which maps the feature window to the enhancement window, this method inputs the original data X into the enhancement window to extract the nonlinear features.

[0029] The body is as follows:

[0030] H j =ξ(XW hj +β hj )j=1,2,…,J (4)

[0031] 6) Where ξ is the nonlinear activation function tanh, W hj and β hj The weights and biases are randomly generated from a uniform distribution

[0032] Repeat step 5 to complete the generation of all nonlinear enhancement windows for the extracted data, and connect these windows to represent H J =[H1,H2,…,H J ], J represents the total number of enhancement windows contained in the network.

[0033] Finally, all windows that extract different data features are combined into the input layer:

[0034] A J =[Z1,Z2,…,Z p |G|H1,H2,…,H J ] (5)7) After obtaining the input layer, a width learning system for multiple feature enhancement extraction is constructed, which can be expressed by the following formula:

[0035] Y=A J W J (6)

[0036] Among them, W J =[W Z |W G |W H ] is the output connection weight of the network, W Z , W G and W H They represent the output weights of the time correlation characteristics, non-Gaussian characteristics and nonlinear characteristic information of sewage data respectively. Connection weight W J =[A J ] + Y, [·] + It means to find the pseudo-inverse of a matrix. The specific calculation process is as follows:

[0037]

[0038] Among them, λ2 is the L2 regularization parameter, I is the unit matrix, and the output network weight W of the width learning system can be obtained J , thereby obtaining the monitoring results of the water quality indicator BOD5.

[0039] B. Online monitoring stage:

[0040] 8) Collect sample data x at the current moment new , refer to step 1 to use the time window for the newly collected data

[0041] Serialized to

[0042] 9) Then, The input is into the trained feature enhancement extraction width learning system, where the model parameters are obtained by offline modeling training, and the final output of the model is the water quality index of the sewage treatment process.

[0043] 10) When the method is applied to the online prediction accuracy of sewage treatment sites and is not accurate enough, it can be quickly updated to add enhanced nodes to improve the model accuracy without retraining the network. The addition of enhanced nodes does not require complex calculations, and the weights can be simply obtained through pseudo-inversion. Input layer after adding enhanced nodes

[0044] Expressed as:

[0045] A J+1 =[A J ∣∣ξ(XW hJ+1 +β hJ+1 )] (8)

[0046] The weight WhJ+1 and β hJ+1 The weights and biases are randomly generated.

[0047] 11) The connection expression between the new input layer and the output layer is Y = A J+1 W J+1 , connection weight W J+1 =[A J+1 ] + Y where [A J +1 ] + The calculation process is as follows:

[0048]

[0049] C=ξ(XW hJ+1 +β hJ+1 )-A J D

[0050] Finally, increase the new connection weight W of the enhanced node J+1 for:

[0051]

[0052] 12) Update the network parameters through step 11 and save them, input the online data into the updated network, and the final output of the model is the measurement results of the water quality indicators.

[0053] Beneficial Effects

[0054] Compared with the prior art, the present invention uses a width learning model with multiple feature enhancement extraction to perform offline training on the normal data collected, and then uses the model parameters obtained through training to measure the online water quality indicators. Different from the prior art, the method proposed in the present invention can simultaneously learn the non-Gaussian characteristics, time correlation characteristics, and nonlinear characteristics of sewage treatment data, making up for the shortcomings of BLS in extracting multiple features of sewage treatment process data, and achieving high-precision monitoring of water quality indicators in sewage treatment processes. In addition, the method can quickly update the method online. When the accuracy of the model decreases in the face of a sewage treatment industrial process with complex environmental dynamics, the efficiency of the model can be improved by quickly updating the model without retraining the network, which is more suitable for application in actual sewage treatment industrial processes. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is an overall view of the sewage treatment plant defined by the experimental platform BSM1 of the present invention;

[0056] Figure 2 This is a structural diagram of the width learning soft measurement model based on feature enhancement of the present invention.

[0057] Figure 3 This is a flow chart of width learning soft measurement based on feature enhancement of the present invention.

[0058] Figure 4 It is a schematic diagram of the effect of applying the present invention and traditional technology to the prediction of sewage quality indicators.

[0059] Figure 5 It is a schematic diagram of the effect of applying the present invention and traditional technology to the prediction of sewage quality indicators. DETAILED DESCRIPTION

[0060] The core technology of the urban sewage treatment process is the biological reaction based on the activated sludge method, which achieves the effect of phosphorus and nitrogen removal by decomposing organic pollutants by microorganisms under anaerobic, anoxic and aerobic conditions. In 2001, the International Water Association developed a benchmark simulation platform based on the activated sludge method (Benchmark Simulation Model 1, BSM1) to simulate the actual sewage treatment process. BSM1 has a total of five activated sludge reactors (biological reactors) (6000m3) and a secondary sedimentation tank (4m deep, 10 layers, 6000m3). Two of the five activated sludge reactors are anoxic links and the rest are aeration links. In addition, based on the actual operating data of the sewage treatment plant, BSM1 simulates the operation of the sewage treatment plant in different weather (sunny days, rainy days). The specific structure of BSM1 consists of Figure 1 Shown

[0061] In reality, sewage treatment plants are affected by environmental changes and abnormal operating conditions, which causes significant changes in process data such as sewage inflow flow and component concentration, and sewage treatment is in an unstable operating state. Therefore, in order to verify the stability of the water quality index monitoring model, this paper introduces common toxic shock faults in sewage treatment plants under different environments (dry and rain) of normal operation of BSM1. The sampling period of the simulation data is 15 minutes, and 96 samples can be collected every day. The sampling lasted for 14 days and a total of 1344 sets of sample data were obtained. The environmental changes and abnormal operating conditions simulated in this paper occurred from the 7th day and lasted for three days. The sewage inflow flow and microbial concentration changed dramatically. Therefore, the first 1056 sets of 1344 sets of sample data were used to train the model, and the remaining 288 sets were used to test the performance of the model. The specific parameter settings of the data used in the experiment are shown in Table 1. All state variables in the variables provided by BSM1 are selected as auxiliary variables, as shown in Table 2.

[0062] Table 1 Process variables input to the model

[0063]

[0064]

[0065]

[0066] Table 2 Fault setting

[0067] The application process of the present invention in the above-mentioned BSM1 simulation platform is specifically described as follows:

[0068] Offline Modeling:

[0069] The BSM1 simulation platform is used to collect three batches of operating data under normal working conditions and three batches of operating data under fault conditions according to the parameter settings in Table 2. Each batch of sampling data is set to contain 13 process variables and 1344 samples at each moment, which is recorded as X∈R n×d , where d and n represent the 13 process variables and the number of samples 1344 in Table 1, respectively. The five-day biochemical oxygen demand is an important indicator for characterizing the content of organic pollutants in sewage. However, the detection of the five-day biochemical oxygen demand is currently mostly determined by manual testing, which is time-consuming and laborious. Therefore, in the present invention, the five-day biochemical oxygen demand of the effluent is used as the test object to verify the method proposed in the present invention. Y∈R n×1 , represents the five-day biochemical oxygen demand, a water quality indicator in the sewage treatment process. After obtaining the training data, data preprocessing is performed.

[0070] Step 1: Scan the original data X using a time window to obtain a serialized data set X p =[X1,S2,…,X t ],t=1,…,p. X t ∈R (n-p+1)×d is the input data of each feature window, p is the number of feature windows, and n-p+1 is the step size of the time window. The parameters of the model are determined based on knowledge and actual training results. In the present invention, p is set to 10.

[0071] Step 2: Scan the data X after the time window in step 1 p Input into the feature window based on the cyclic structure, the construction formula of the generated t-th window is as follows:

[0072] Z t =σ(X t Wz+Z t-1 U+b0) (11)

[0073] Among them, the t-th feature window Z t Not only from the current input X t Extract shallow features and learn the t-1th feature window Z t-1To extract the time correlation features of data at different time steps, to form a feature window with a cyclic structure. σ is the activation function sigmoid, and the initial state Z0 is set to 0. The weights and biases associated with each feature window during recursive cascading are shared, that is, the weights W randomly generated by uniform distribution Z , weight U and bias b0.

[0074] Step 3: Repeat step 2 to complete the generation of all feature windows for extracting the time correlation of data, and connect these windows to represent Z P =[Z1,Z2,…,Z p ], p = 10 represents the total number of cyclic feature windows contained in the network. Subsequently, in order to enhance the model's learning of different process characteristics of the data, a non-Gaussian feature extraction window based on OICA was created. The core idea of ​​the OICA algorithm applied in this window is to transform the d-dimensional process variables of the training data X through the mixing matrix D∈R d×k Decompose it into k independent components (k>d) with high-order features to extract the non-Gaussian information.

[0075] X T =Dα (12)

[0076] Among them, X T ∈R d×n is the transposed matrix of X, α=[α1,…,α k ] is the independent element matrix, k is the independent element dimension after the d-dimensional process variable decomposition, represents the ith independent element, n is the number of samples. In the present invention, k=40.

[0077] Step 4: Solving the mixing matrix D is mainly divided into two steps. First, construct an approximate subspace W = Span {N1, N2, ..., N s}, Span is a mathematical symbol representing the space spanned by the matrix. Then, the approximate calculation Atoms in right Perform eigenvalue decomposition, where the eigenvector corresponding to the maximum eigenvalue is the approximate solution of the vector in the mixing matrix D. Combining in the order of number i=1,…k can obtain the mixing matrix D. All the steps for solving the D matrix are given below.

[0078] Step 5: First, for the estimated subspace W, it is necessary to construct s (s>d) matrices N1, N2, …, N by calculating the Hessian matrix of the Cumulant Generating Function (CGF) s ∈R d×d In the present invention, s = k = 40, the cumulative amount generating function is defined as follows:

[0079]

[0080] Where E(·) represents the mathematical expectation, t∈R d .Will Substitute (zero vector) into the second-order cumulant generating function and perform Hessian evaluation to obtain X T The covariance matrix cov(X T ), the formula is as follows:

[0081]

[0082] When t is a non-zero vector, Hessian evaluation of the cumulant generating function can be obtained as X T The generalized covariance matrix of

[0083]

[0084] In order to represent X in the context of independent meta-analysis T The generalized covariance matrix of T t, X T =Dα is substituted into the above formulas (15) and (16) to obtain:

[0085]

[0086] Where α=[α1,...,α k ],α i represents the ith independent element, C α (y) represents the generalized covariance matrix of independent variables, which is similar to solving X T The generalized covariance matrix of independent variables can be further expressed as:

[0087]

[0088] Independent element generalized covariance matrix C α (y) is a diagonal matrix due to its independence. Therefore, can be rewritten as:

[0089]

[0090] where ω i (t) = [C α (D T t)] ii Represents α i The covariance of Can be XT The generalized covariance matrix of is represented by enough (s>d) vectors T1, T2, …, t S ∈R d , we get the same matrix N j =C X (t j ),j=1,…s. The obtained s N j The space spanned by the matrix is ​​an approximation of the subspace W.

[0091] W∈Span{N1,N2,…,N s} (twenty two)

[0092] The above analysis is done through s N j The matrix approximation obtains the subspace W. The next step is to approximate the atoms The solution is approximated by the semi-positive definite optimization shrinkage method. The following steps are to solve the semi-positive definite problem As an example, take the solution for an atom:

[0093]

[0094] Among them, argmaxx represents the matrix G∈R that determines the shrinkage direction among all matrices belonging to the set subspace W. d×d Find a matrix B with the largest value and solve the constraint formula as follows:

[0095] K={B∈W:Tr(B)=1,B≥0} (24)

[0096] Tr(B) = 1 means that the trace of the matrix B to be solved is equal to 1, and B ≥ 0 means that the matrix B to be solved is a semi-positive definite matrix. The above are the steps to calculate a single optimal atom. In order to obtain all the atoms, first use the clustering method to select the cluster center with the smallest class variance as the selected atom, and then remove the optimal atom from W and continue to solve using adaptive shrinkage. Iterate k times to obtain all the atoms Then all atomic matrices Perform eigenvalue decomposition, select the eigenvector corresponding to the maximum eigenvalue as the mixing component in the mixing matrix D, and combine them in the order of numbers to obtain the mixing matrix D. After taking the mixing matrix D, the non-Gaussian feature extraction of the data is as follows:

[0097] G=XD (25)

[0098] Among them, G∈R n×k Represents the non-Gaussian information of the data extracted by the feature window based on OICA.

[0099] Step 6: After creating the feature window for extracting the time correlation and non-Gaussianity of the data, in order to ensure that the method can extract the original nonlinear features of the input data, this method is different from the classic BLS that maps the enhanced window through the feature window. The original data X is input into the enhanced window for nonlinear feature extraction, as follows:

[0100] H j =ξ(XW hj +β hj )j=1,2,…,J (26)

[0101] Where ξ is the nonlinear activation function tanh, W hj and β hj are weights and biases randomly generated by uniform distribution. Repeat step 6 to complete the generation of all nonlinear enhancement windows for extracted data, and connect these windows to represent H J =[H1,H2,…,H J ],j=1...J,H j represents an enhanced window contained therein. In the present invention, the number of enhanced windows J is selected as 5, and there are 50 enhanced nodes in total. Finally, all windows that extract different data features are merged into the input layer:

[0102] A J =[Z1,Z2,…,Z p |G|H1,H2,…,H J ] (27) After obtaining the input layer, a width learning system for multiple feature enhancement extraction is constructed, which can be expressed by the following formula:

[0103] Y=A J W J (28)

[0104] Among them, W J =[W Z |W G |W H ] is the output connection weight of the network, W Z , W G and W H They represent the output weights of the time correlation characteristics, non-Gaussian characteristics and nonlinear characteristic information of sewage data respectively. Connection weight W J =[A J ] + Y, [·] + It means to find the pseudo-inverse of a matrix. The specific calculation process is as follows:

[0105]

[0106] Wherein, λ2 is the L2 regularization parameter, which is taken as 2 in the present invention.-30 , I is the unit matrix, and the output network weight W of the width learning system can be obtained J , thereby obtaining the monitoring results of the water quality indicator BOD5.

[0107] Online monitoring:

[0108] Step 7: When performing online measurement, collect the sample data x at the current moment new And perform data preprocessing X new , refer to step 1 to serialize the newly collected data using the time window as The time step is consistent with the offline training model.

[0109] Step 8: Serialize the data The input is used to generate a feature window with a cyclic structure in the width learning system of multiple feature enhancement extraction, and the time correlation characteristics of the test data are extracted. At the same time, the original data X new The non-Gaussian feature window and the enhancement window are generated by the width learning system with transposed input into the multiple feature enhancement extraction, and the non-Gaussian and nonlinear information of the test data are extracted. Subsequently, the final output of the model is calculated with reference to the parameters of the offline model, which is the measurement result of the water quality index.

[0110] The above steps are the specific practical application of the method of the present invention on the sewage treatment BSM1 simulation platform. In order to better quantify the performance of the proposed method, this experiment uses two indicators, root mean square error (RMSE) and root mean square absolute error (MAE), to qualitatively evaluate the five water quality index monitoring models. The formulas are defined as follows:

[0111]

[0112] Where T is the size of the data set, is the predicted value estimated by the model at time t, y t is the true value at time t. To reduce the impact of randomness on the experimental results, all algorithms will be repeated twenty times, and the average values ​​of RMSE and MAE of the twenty times will be used for comparison.

[0113] First, the performance of the method proposed in the present invention and other classical methods were compared in a test environment under normal operation of the sewage treatment plant in all weather conditions. Table 3 shows the RMSE and MAE results of different models under normal and abnormal conditions. It can be seen that in a test environment under normal operation in all weather conditions (dry and rainy days), the model performance of the method proposed in the present invention is the best, and its RMSE and MAE are the lowest, respectively. In addition, the performance of the OBLS model is second only to the method proposed in the present invention, which is normal considering that the OBLS model fails to capture the strong time-correlation characteristics of the sewage treatment process.

[0114] In the environment of abnormal working conditions with toxic shock, the performance of the three models all tends to decline, which indirectly shows that the sewage treatment plant is in an unstable operating state under abnormal working conditions, which puts a greater test on the model. Compared with normal working conditions, the process variables, that is, the input of the model, are unstable under abnormal working conditions with faults. It is difficult for the model to capture comprehensive process variable feature information, so the performance of the model will also decline slightly. However, it can be seen from Table 3 that the breadth learning system (FAE-BLS) based on feature enhancement extraction still performs well, with the lowest average RMSE and MAE of the model, excellent performance and high applicability, thanks to the window in the FAE-BLS model responsible for extracting different process characteristics of the data. Specifically, the feature window with a recursive loop structure in FAE-BLS is responsible for extracting the time correlation characteristics of the data, the feature window based on independent component analysis is responsible for extracting the non-Gaussian characteristics of the data, and the enhanced window is responsible for extracting the nonlinear characteristics of the data. These three parallel windows expand the model's focus on different process characteristics of the data, making its feature expression ability more diversified, and can fully extract unstable process data feature information, thereby better stabilizing the model performance to adapt to environmental changes. It also indirectly shows that the water quality indicator monitoring model proposed in this paper is more suitable for actual industrial processes.

[0115] Table 3 Measurement index results of different models under six working conditions

[0116]

Claims

1. A water quality indicator BOD5 monitoring method based on width learning to efficiently extract data feature information, Its characteristics include two stages: "offline training" and "online monitoring", which are characterized by The specific steps are as follows: Offline Modeling: Three batches of operating data under normal conditions and three batches of fault conditions are collected respectively. Each batch of sampling data contains 13 process variables and 1344 samples at different times, denoted as X∈R n*d , where d and n represent the 13 process variables and the number of samples 1344 in Table 1 respectively; BOD5, the five-day biochemical oxygen demand of the effluent BOD5 is the test object; Y∈R n×1 , represents the five-day biochemical oxygen demand of the water quality indicator in the sewage treatment process. After obtaining the training data, data preprocessing is performed; Table 1 Process variables input to the model Step 1: Scan the original data X using a time window to obtain a serialized data set X p =[X1,X2,…,X t ],t=1,…,p;X t ∈R (n-p+1)×d is the input data of each feature window, p is the time step and the number of feature windows, and n-p+1 is the step of the time window; the parameters of the model are determined based on knowledge and actual training results, and p is set to 10; Step 2: Scan the data X after the time window in step 1 p =[X t ] is input into the feature window based on the loop structure, and the construction formula of the generated t-th window is as follows: WITH t =σ(X t IN Z +Z t-1 U+b0) (1) Among them, the t-th feature window Z t Not only from the current input X t Extract shallow features and learn the t-1th feature window Z t-1 To extract the time correlation features of data at different time steps to form a feature window with a cyclic structure; σ is the nonlinear activation function sigmoid, and the initial state Z0 is set to 0; the weights and biases associated with each feature window during recursive cascading are shared, that is, the randomly generated weights W that conform to the uniform distribution Z , weight U and bias b0; Step 3: Repeat step 2 to complete the generation of all feature windows for extracting the time correlation of data, and connect these windows to represent Z P =[Z1,Z2,…,Z p ], p = 10 represents the total number of cyclic feature windows contained in the network; then, in order to enhance the model's learning of different process characteristics of the data, a non-Gaussian feature extraction window based on OICA was created; the core idea of ​​the OICA algorithm applied to this window is to transform the d-dimensional process variables of the training data X through the mixing matrix D∈R d×k Decompose into k independent elements with high-order features (k>d) to extract non-Gaussian information; X T =Dα (2) Among them, X T ∈R d×n is the transposed matrix of X, α=[α1,…,α k ] is the independent element matrix, k is the independent element dimension after the d-dimensional process variable decomposition, represents the ith independent element, n is the number of samples; in the present invention, k=40; Step 4: Solving the mixing matrix D is mainly divided into two steps. First, construct an approximate subspace W = Span {N1, N2, ..., N s }, Span is a mathematical symbol representing the space spanned by the matrix; then, the approximate calculation Atoms in Finally, The atomic matrix is ​​decomposed by eigenvalues, where the eigenvector corresponding to the largest eigenvalue is the approximate solution of the vector in the mixing matrix D. The mixing matrix D can be obtained by combining them in the order of number i=1,…k. All the steps for solving the D matrix are given below. Step 5: First, for the estimated subspace W, it is necessary to construct s (s>d) matrices N1, N2, …, N by calculating the Hessian matrix of the cumulant generating function CGF s ∈R d×d ,s=k=40,cumulant generation function is defined as follows: Where E(·) represents the mathematical expectation, t∈R d ;Will That is, the zero vector is substituted into the second-order cumulant generating function, and the Hessian evaluation is performed to obtain X T The covariance matrix cov(X T ), the formula is as follows: When t is a non-zero vector, the Hessian evaluation of the cumulant generating function is obtained as X T The generalized covariance matrix of In order to represent X in the context of independent meta-analysis T The generalized covariance matrix of T t, X T =Dα is substituted into formula (5) and (6), and we obtain: Where α=[α1,...,α k ],α i represents the ith independent element, C α (y) represents the generalized covariance matrix of the independent element, and the generalized covariance matrix of the independent element is expressed as: Due to the independence of independent elements, the generalized covariance matrix C of independent elements α (y) is a diagonal matrix; therefore, is rewritten as: where ω i (t) = [C α (D T t)] ii Represents α i The covariance of By X T The generalized covariance matrix of is represented by a sufficiently large number (s>d) of vectors t1, t2, …, t s ∈R d , we get the same matrix The number of N obtained is sufficient j The space spanned by the matrix is ​​an approximation of the subspace W; W∈Span{N1,N2,…,N s } (12) The above analysis is done through s N j The matrix approximation obtains the subspace W. The next step is to calculate the atoms contained in the subspace W. The solution is approximated by the semi-positive definite optimization shrinkage method; the following steps are to solve the semi-positive definite problem As an example, take the solution for an atom: Among them, argmax means that among all matrices belonging to the set subspace W, according to the matrix G∈R that determines the shrinkage direction d×d Find a matrix B with the largest value and solve the constraint formula as follows: K={B∈W:Tr(B)=1,B≥0} (14) Tr(B) = 1 means that the trace of the matrix B to be solved is equal to 1, and B ≥ 0 means that the matrix B to be solved is a semi-positive definite matrix. The above are the steps for calculating a single atom. In order to obtain all the atoms, the clustering method is first used to select the cluster center with the smallest class variance as the selected atom, and then the optimal atom is removed from the W subspace and the solution is continued using adaptive shrinkage. All the atoms can be obtained by iterating k times. Finally, The matrix is ​​decomposed by eigenvalues, and the eigenvector corresponding to the maximum eigenvalue is selected as the mixed component in the mixing matrix D, and the mixing matrix D can be obtained by combining them in the order of numbers; after taking the mixing matrix D, the non-Gaussian feature extraction of the data is as follows: G=XD (15) Among them, G∈R n×k Represents the non-Gaussian information of the data extracted by the feature window based on OICA; Step 6: After creating the feature window for extracting the time correlation and non-Gaussianity of the data, in order to ensure that the method extracts the original nonlinear features of the input data, this method is different from the classic BLS that maps the enhanced window through the feature window. The original data X is input into the enhanced window for nonlinear feature extraction, as follows: H j =ξ(XW hj +β hj )j=1,2,…,J (16) Where ξ is the nonlinear activation function tanh, W hj and β hj are weights and biases randomly generated by uniform distribution; repeat step 6 to complete the generation of all nonlinear enhancement windows for extracted data, and connect these windows to represent H J =[H1,H2,…,H J ],j=1...J,H j represents an enhanced window contained therein. In the present invention, the total number of enhanced windows J is selected as 5, and there are 50 enhanced nodes in total. Finally, all windows that extract different data features are merged into the input layer: A J =[Z1,Z2,…,Z p |G|H1,H2,…,H J ] (17) After obtaining the input layer, a width learning system for multiple feature enhancement extraction is constructed, which is expressed by the following formula: Y=A J W J (18) Among them, W J =[W Z |W G |W H ] is the output connection weight of the network, W Z , W G and W H Represent the output weights of the time correlation characteristics, non-Gaussian characteristics and nonlinear characteristic information of sewage data respectively; the connection weight W J =[A J ] + Y, [·] + It means to find the pseudo-inverse of a matrix. The specific calculation process is as follows: Wherein, λ2 is the L2 regularization parameter, which is taken as 2 in the present invention. -30 , I is the unit matrix, and the output network weight W of the width learning system is obtained J , thus obtaining the water quality index BOD5 result; Online monitoring: Step 7: When performing online measurement, collect the sample data x at the current moment new And perform data preprocessing X new , refer to step 1 to serialize the newly collected data using the time window as The time step is consistent with the offline training model; Step 8: Serialize the data Input into the trained multiple feature enhancement extraction width learning system to generate a feature window with a cyclic structure and extract the time correlation characteristics of the test data; at the same time, use the original data X after data preprocessing new and its transposed input into the width learning system of multiple feature enhancement extraction to generate non-Gaussian feature windows and enhancement windows, extracting non-Gaussian and nonlinear information of the test data; then, the final output of the model is calculated with reference to the parameters of the offline model as the measurement results of the water quality indicators.

2. According to claim 1, a method for monitoring water quality indicators in a sewage treatment process based on a width learning system with feature enhancement extraction is characterized in that: The number of cyclic feature windows of the FAE-BLS model during offline training is 10, the number of nodes in each window is 10, and the number of feature nodes is 100 in total. The number of feature windows of the overcomplete independent component analysis is 1, the number of nodes is 40, and the number of enhanced nodes is 50.

Images