Water supply network sensor data recovery method based on soft sensor

Abstract

The invention discloses a water supply pipe network sensor data recovery method based on a soft sensor, and the method comprises the steps: constructing the soft sensor, creating analysis redundancy through the time series of other sensors in a pipe network and the historical series obtained by the sensors, and providing rich reference samples for data filling; and the accuracy of data filling is improved. And meanwhile, the data in the soft sensor is screened and strengthened again by adopting the maximum information coefficient and principal component analysis, so that the linear model can efficiently fill the data, and sensor data filling in the water supply network becomes an accurate and rapid process.

Description

Technical Field

[0001] The present invention relates to the technical field of water supply pipe networks, and in particular to a water supply pipe network sensor data recovery method based on soft sensors. Background Art

[0002] As an important part of urban infrastructure, the monitoring and management of water supply networks rely on real-time monitoring data provided by sensors. However, due to the harsh underground humid environment of sensors in water supply networks, data missing and anomalies are common. The incompleteness and inaccuracy of data pose major challenges to the monitoring and control of water supply networks. Incomplete or inaccurate water supply network monitoring data may lead to waste of water resources, increased energy consumption, and increased risk of system failure. Therefore, accurate data filling methods are of great significance to fill missing points or cover up abnormal points.

[0003] There are existing data filling methods, such as "simple interpolation method", "statistical method" and "machine learning prediction method". "Simple interpolation method" directly uses neighboring values ​​or uses neighboring points for linear interpolation. This method is easy to implement and fast to calculate, but it does not make full use of information, resulting in insufficient filling accuracy. "Statistical method" can use statistical characteristics such as trends and cycles of time series to perform filling calculations. However, this method ignores the correlation between sensors in the water supply network and cannot meet the needs of high-precision monitoring. "Machine learning prediction method" uses a time series prediction model to calculate the filling value and supports the input of a large amount of data to construct the filling value. Commonly used machine learning prediction methods include long short-term memory networks, convolutional neural networks, transformer models, etc. However, this algorithm takes a lot of time and is difficult to train with the latest data in real time. The accuracy of the filling calculation is sensitive to the latest neighboring data and the latest change pattern, so this method is hindered in its actual application in the water supply network.

[0004] The invention patent application with publication number CN118332270A discloses a method and software system for repairing missing water supply data based on graph signal sampling theory. The repair method includes: arranging time series data into graph data based on the adjacent correlation and periodicity of hydraulic data of the water supply network; obtaining a time Laplace matrix based on the sorted graph data, and performing characteristic frequency analysis using the low frequency of hydraulic data changes; reconstructing time series data based on the characteristic graph frequency coefficients and characteristic graph frequency bases obtained by Laplace matrix decomposition, and using the reconstructed data to interpolate missing data of the water supply network. The prediction accuracy of the method provided by the above patent needs to be further improved.

[0005] The sensors in the water supply network have hydraulic characteristics that are correlated due to the hydraulic connection of the pipes. This correlation is reflected in the correlation of the time series change patterns monitored by the sensors. On the other hand, since the user's water usage pattern is relatively fixed, the periodic characteristics presented in the historical monitoring data of the sensors in the water supply network are also an important source of information. Reasonably coupling the correlation between real-time sensors with the periodicity within the sensors to construct fill values ​​is a technical gap in the current real-time water supply network monitoring and control. Summary of the invention

[0006] The present invention provides a water supply network sensor data recovery method based on soft sensors, which can efficiently and accurately recover missing data and abnormal data using fewer observation points.

[0007] A specific embodiment of the present invention provides a water supply network sensor data recovery method based on a soft sensor, comprising:

[0008] Based on the latest time series monitored by the current sensor, the local weighted regression method is used to obtain the periodic series. The polynomial function fitted to the periodic series is multi-order differentiated to obtain the derivative time series composed of the characteristic vectors of each observation point. Dynamic time warping is used to calculate the distance between the derivative time series corresponding to different sensors to obtain the time series distance matrix of different sensors. Hierarchical clustering is used to group different sensors based on the time series distance matrix of different sensors.

[0009] The time series matrix of the soft sensor is constructed based on the latest time series monitored by the current sensor, the time series monitored by other sensors in the same group as the current sensor, and the historical subsequences with the smallest time series distance to the latest time series in the historical time series monitored by the current sensor;

[0010] Based on the latest time series, principal component analysis is used to filter out the top m relevant eigenvectors from the time series matrix of the soft sensor, and the multivariate polynomial regression input matrix constructed by the top m relevant eigenvectors is solved to fill the missing values ​​or outliers in the latest time series.

[0011] Preferably, the method for solving the order and coefficients of the polynomial function for periodic sequence fitting includes:

[0012] A polynomial function of order p is constructed based on the periodic sequence, an information criterion is constructed based on the covariance between the polynomial function and the periodic sequence and the order of the polynomial function, and the p value is solved by minimizing the information criterion;

[0013] Based on the sequence points of the periodic sequence corresponding to each observation point and the solution of the polynomial function, the coefficients of the polynomial function are obtained by the least square method.

[0014] Preferably, an information criterion is constructed based on the covariance between the polynomial function and the periodic sequence and the order of the polynomial function. The information criterion IC of the i-th sensor is i for:

[0015] IC i =-NlnCov i +(p+1)ln N

[0016]

[0017] in, represents the mean of the periodic sequence with N observation points of the i-th sensor, represents the polynomial function f of order p for the i-th sensor at time t i The value of (t, p) is is the sample mean of the polynomial function, is the time series at the i-th sensor observation point t.

[0018] The present invention minimizes the information criterion to make the Cov value as large as possible, so that the accuracy of the fitted polynomial is higher, and reduces the consumption by limiting the p value.

[0019] Preferably, the derivative time series of the ith sensor composed of the feature vectors of each observation point is for:

[0020]

[0021]

[0022] in represents the m-th order derivative of the polynomial function at the t-th observation point, is the feature vector of the i-th sensor at the t-th observation point.

[0023] The present invention firstly uses multi-order derivative values ​​of a polynomial function of a time series to characterize the characteristics of the time series, and clusters and groups the time series of different sensors in the same time window.

[0024] Preferably, dynamic time warping is used to calculate the distances between the derivative time series corresponding to different sensors to obtain the time series distance matrix of different sensors, where the distance between the derivative time series corresponding to the i-th sensor and the derivative time series corresponding to the j-th sensor is for:

[0025]

[0026]

[0027] Where N is the number of observation points corresponding to the i-th sensor, is the number of observation points corresponding to the jth sensor.

[0028] The present invention uses dynamic time warping (DTW) to recursively calculate the distance between two derivative time series and accumulate the last element of the distance matrix D, i.e. It is the distance d between the time series corresponding to the two sensors.

[0029] Preferably, before selecting the top m relevant eigenvectors from the time series matrix of the soft sensor by principal component analysis based on the latest time series, the maximum information coefficient between the latest time series and any time series of the time series matrix of the soft sensor is constructed, and the diagonal matrix constructed with the maximum information coefficient is used as a weight to weight the time series matrix of the soft sensor, and the weighted time series matrix of the soft sensor is subjected to principal component analysis.

[0030] Preferably, the principal component analysis is used to filter out the top m relevant feature vectors from the time series matrix of the soft sensor based on the latest time series, including:

[0031] The covariance matrix is ​​obtained by performing principal component analysis on the latest time series, and multiple eigenvectors are obtained by performing singular value decomposition on the covariance matrix, thereby screening out the top m relevant eigenvectors from the multiple eigenvectors to obtain the eigenmatrix after dimensionality reduction.

[0032] Preferably, solving the multivariate polynomial regression input matrix constructed from the first m related eigenvectors includes:

[0033] A multivariate polynomial regression input matrix is ​​constructed based on the first m related eigenvectors, a multivariate polynomial regression function is constructed based on the multivariate polynomial regression input matrix, the regression coefficients of the multivariate polynomial regression function are solved by the least squares method based on the solution of the multivariate polynomial regression function and the data values ​​corresponding to the latest time series, and the missing values ​​or abnormal values ​​of the latest time series are filled based on the multivariate polynomial regression function with the determined regression coefficients.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] This method constructs soft sensors and uses the time series of other sensors in the pipe network and the historical series obtained by the sensors themselves to create analytical redundancy, providing rich reference samples for data filling, which is conducive to improving the accuracy of data filling. At the same time, the maximum information coefficient and principal component analysis are used to screen and strengthen the data in the soft sensor again, so that the linear model can efficiently fill the data, turning the sensor data filling in the water supply pipe network into an accurate and fast process. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 A schematic diagram of local weighted regression provided by a specific embodiment of the present invention, wherein: Figure 1 (a) is the trend sequence diagram of the time series calculated by local weighted regression. Figure 1 (b) is the periodic sequence diagram of the time series;

[0037] Figure 2 A schematic diagram of a polynomial fitting function provided by a specific embodiment of the present invention;

[0038] Figure 3 Schematic diagram of the 1st, 2nd and 3rd order derivative functions of the polynomial fitting function provided in a specific embodiment of the present invention, wherein: Figure 3 (a) is a schematic diagram of the first-order derivative function. Figure 3 (b) is a schematic diagram of the second-order derivative function. Figure 3 (c) is a schematic diagram of the third-order derivative function;

[0039] Figure 4 A schematic diagram of a pipe network example provided for a specific embodiment of the present invention. DETAILED DESCRIPTION

[0040] The purpose of the present invention is to provide a method for filling sensor data of a water supply network based on a soft sensor. The soft sensor is constructed by a clustering method, and data filling with high accuracy and low computing resource consumption is achieved according to the analytical redundancy in the soft sensor. The invention provides data support for modeling, monitoring management and operation control of water supply networks. The specific implementation methods of the present invention are further described in detail below.

[0041] A specific embodiment of the present invention provides a water supply network sensor data recovery method based on a soft sensor, comprising:

[0042] Step S1, grouping different sensors based on the time series distance matrix: based on the latest time series monitored by the current sensor, a local weighted regression method is used to obtain a periodic sequence, and the polynomial function fitted to the periodic sequence is multi-order differentiated to obtain a derivative time series composed of the characteristic vectors of each observation point, and dynamic time warping is used to calculate the distance between the derivative time series corresponding to different sensors to obtain the time series distance matrix of different sensors, and hierarchical clustering is used to group different sensors based on the time series distance matrix of different sensors.

[0043] The specific steps of step S1 provided in the specific embodiment of the present invention include:

[0044] Assume that the clustering reference window size is N. The time series of sensor i Decomposed into trend using the locally weighted regression (LOESS) method and cycle Ingredients. Figure 1 As shown in (a), LOESS calculates the trend by fitting a linear model to the data in a local window and assigning a weight to each observation. like Figure 1 As shown in (b), by subtracting the trend component from the original time series, the cyclical component can be separated

[0045]

[0046] With the original sequence In contrast, the periodic series The similar scale characteristics are shown in different time periods of long time series, which provides a basis for subsequent segmentation processing.

[0047] The piecewise polynomial fitting provided in the specific embodiment of the present invention first converts the sequence Divide into several segments, and use a polynomial function to fit each segment. For a certain segment α, its polynomial function It can be expressed as:

[0048]

[0049] Among them, β0, β1, β2,..., β p are the coefficients of the polynomial, and p is the order of the polynomial. Specifically, Figure 2 A graph showing a polynomial fit function.

[0050] In polynomial fitting, the order p is a key parameter. A small p value will lead to inaccurate fitting, while a large p value will cause overfitting and consume too much computing resources. Covariance (COV) is considered to be a suitable indicator for evaluating the similarity of the trend of the water supply system monitoring time series. A larger COV indicates that the fitting function better preserves the trend changes of the original series.

[0051] Therefore, a specific embodiment of the present invention proposes an information criterion (IC) based on COV to balance the order of the polynomial and the fitting accuracy:

[0052] IC i =-NlnCOV i +(p+1)ln N

[0053] Among them, COV i Represents the polynomial function f i (t, p) and periodic sequence The covariance between them is calculated as follows:

[0054]

[0055] in, Representation sequence The mean of represents the polynomial function f of order p for the i-th sensor at time t i The value of (t, p) is is the sample mean of the fitted function.

[0056] By minimizing the IC value, the difficulty of manually determining the polynomial order p for different time series patterns can be eliminated. The polynomial coefficients are estimated by the least squares method, which minimizes the sum of squared errors between the observations and the polynomial fit:

[0057]

[0058] By solving this minimization problem, the coefficients of the polynomial function can be determined, thereby obtaining the polynomial function f i (t).

[0059] The characteristic vector of the time series provided by the specific embodiment of the present invention is obtained from f i (t), specifically by extracting from f i This is achieved by extracting multi-order derivative values ​​at each observation point in (t), specifically, Figure 3 (a)-3(c) show the schematic diagram of the first, second and third order derivative functions of the polynomial fitting function. For a given observation point t, the characteristic vector of the time series of the i-th sensor is for:

[0060]

[0061] in Represents the m-th derivative of the polynomial function at the t-th observation point.

[0062] The specific embodiment of the present invention calculates multi-order derivatives of the polynomial function at each observation point, and the time series is converted into a derivative time series (DTS). Each observation point in the DTS is represented by a feature vector Indicates that N is the number of observation points, forming the following sequence:

[0063]

[0064] The specific embodiment of the present invention calculates the distance between two DTSs by accumulating the distances between corresponding observation points through dynamic time warping (DTW). and the time series of the jth sensor Any two corresponding points t and The distance between is defined as:

[0065]

[0066] Dynamic time warping (DTW) is used to recursively calculate the distance between two derivative time series. The core concept of the DTW algorithm is to determine a warping path that defines how to correspond points in one sequence to points in another sequence so as to minimize the total distance between all corresponding points.

[0067] For two different sequences and The observation point t>0 and The cumulative distance matrix D is constructed according to the following recursive relationship:

[0068]

[0069] Cumulative distance matrix D ij The last element of The distance d between two time series at observation points ij .

[0070] The distance between the derivative time series corresponding to the i-th sensor and the derivative time series corresponding to the j-th sensor for:

[0071]

[0072]

[0073] Where N is the number of observation points corresponding to the i-th sensor, is the number of observation points corresponding to the jth sensor. The distance d between sensor i and sensor j ij is the distance between the derivative time series corresponding to the i-th sensor and the derivative time series corresponding to the j-th sensor

[0074] After calculating the distances between all sensors, a symmetrical distance matrix is ​​obtained as follows:

[0075]

[0076] where d ij represents the distance between sensor i and sensor j, and q is the number of sensors.

[0077] In order to effectively group sensors based on similarity, the distance matrix is ​​used to cluster them using the hierarchical clustering (HC) method. The HC method initially treats each sensor as an independent cluster, and then iteratively merges the two clusters with the smallest distance in the distance matrix into a new cluster. This process continues until all sensors are successfully grouped into one cluster.

[0078] Step S2: construct a time series matrix of the soft sensor based on the latest time series monitored by the current sensor, the time series monitored by other sensors in the same group as the current sensor, and the historical subsequences with the smallest time series distance to the latest time series in the historical time series monitored by the current sensor.

[0079] Furthermore, the specific steps of step S2 are:

[0080] In the specific embodiment of the present invention, the window size of the soft sensor is set to W. For sensor i, its historical time series is divided into a subsequence every t data points, and the distance calculation between each subsequence is the same as step S1. The l subsequences with the smallest distance to the front q are selected and added to the soft sensor corresponding to sensor i.

[0081] The soft sensor contains its own record sequence, namely the latest time series, the time series of other sensors in the same group, and similar historical subsequences. It is a real-time updated data structure. The specific structure is as follows:

[0082]

[0083] Where W is the window size of the soft sensor, is the time series of length W recently acquired by sensor i c1, c2, ...c k are other sensors that are highly correlated with the time series of sensor i and are grouped into the same group, t1, t2, ...t l is the time series of the current window of sensor i The starting point of the other window sequences in the history of highly correlated sensor i.

[0084] The data in the soft sensor provided by the specific embodiment of the present invention is updated in real time over time, and the sensor groups c1, c2, ...c k With the historical sequence t1, t2, ...t l Reselection is carried out regularly.

[0085] Step S3: Based on the latest time series, principal component analysis is used to filter out the top m relevant eigenvectors from the time series matrix of the soft sensor, and the multivariate polynomial regression input matrix constructed by the top m relevant eigenvectors is solved to fill the missing values ​​or abnormal values ​​in the latest time series.

[0086] Specifically, the specific steps of step S3 are:

[0087] In the case of abnormal values ​​and missing values ​​in the data, data filling is required. Data filling is based on soft sensors. First, calculate any sequence X in the soft sensor j Record sequence X with itself i The maximum information coefficient MIC between:

[0088]

[0089] Where w is the adjacent comparison pane, satisfying w<W; f ij (x i , x j ) is X i With X j The probability density function, f i (x i ) and f j (x j ) are their marginal probability density functions, and Gaussian kernel function is used to perform kernel density estimation on these probability density functions.

[0090] Get the diagonal matrix M composed of the maximum information coefficients i :

[0091]

[0092] With matrix M i Weights for soft sensors To perform weighting:

[0093]

[0094] Perform principal component analysis on the weighted soft sensor, and the covariance matrix C i for:

[0095]

[0096] The covariance matrix C i Perform singular value decomposition:

[0097] C i =V i Λ i (V i ) T

[0098] Where V i is the eigenvector, Λ i is the eigenvalue matrix.

[0099] Select the feature vector V i The first m eigenvectors of are the principal element space, and the reduced dimension feature matrix SP is obtained. i :

[0100]

[0101] According to the feature matrix SP i Construct multivariate polynomial regression input matrix Z i :

[0102]

[0103] where sp j Represents the feature matrix SP i The jth column of .

[0104] The multivariate polynomial regression model is:

[0105] X i =Z i B+ ∈

[0106] Where B is the regression coefficient, ∈ is the error term.

[0107] Use the least squares method to solve the regression coefficient B:

[0108]

[0109] Here, ||·|| represents the Euclidean norm.

[0110] Finally, the polynomial regression function is used to solve the filling value

[0111]

[0112] like Figure 4 A schematic diagram of an actual water supply network is given, which is equipped with 58 pressure sensors and 36 flow sensors. The specific steps are as follows:

[0113] Step 1: Calculate the distance between sensor time series: and use this as the basis for clustering. The length of the time series for cluster distance calculation is the first 10 days of the validation set. After performing local weighted regression on the collected time series, the best fitting order of the piecewise polynomial fitting of all sensors is obtained by the information criterion based on covariance. The calculated best fitting order is shown in Table 1. This order is used to perform piecewise polynomial fitting on the sensor, and the polynomial function is multi-order differentiated. Dynamic time warping is used to calculate the distance based on the derivative value, and hierarchical clustering is used to realize the grouping of sensors. The grouping results are shown in Table 1.

[0114] Table 1 Grouping of sensors and their fitting order p values

[0115]

[0116]

[0117] *#P indicates a pressure sensor; #F indicates a flow sensor.

[0118] Step 2: Select historical subsequences for each sensor: Construct a soft sensor, and set the window size of the soft sensor to 5 days. Divide the sensor time series data into a subsequence every 5 days, and perform polynomial function fitting, multi-order derivative feature extraction, and dynamic time warping distance calculation on each subsequence. Finally, calculate the distance between each subsequence and the current latest window sequence, and select the three subsequences with the smallest distance as the historical reference sequence. Construct the self-recording sequence, sensor group sequence, and historical reference sequence under the current window into a soft sensor. Table 2 shows the construction of some soft sensors.

[0119] Table 2 Soft sensor sequence composition corresponding to some sensors

[0120]

[0121] Step 3: Data filling based on soft sensors: In this case, the data at the same 960 time points in the time series of each sensor are set as blank points, and the accuracy of model filling is tested by calculating the error between the model filling value and the true value. In the experiment, the proposed SMSP method is compared with other commonly used methods in the field of time series prediction. Among them, Holt-Winters is a prediction method based on statistics, and the long short-term neural network (LSTM), multi-scale equidistant convolutional neural network (MICN), and transformer model (Transformer) are prediction methods based on deep learning. Table 3 shows the average value of the error between the filling value and the observed value of each model in the 960-step filling experiment on the pressure sensor and the flow sensor. The mean square error (MSE) and mean absolute error (MAE) are used to evaluate the size of the error. The results in Table 3 show that the filling accuracy of the proposed SMSP method is significantly better than other algorithms.

[0122] Table 3 Average filling errors of different models in 960-step filling experiments

[0123]

[0124]

[0125] In addition, as shown in Table 4, the training and prediction time required by SMSP is significantly reduced compared to other methods, which enhances its applicability in real-time detection data processing. Due to its extremely low computing resource consumption, SMSP can use the latest data for real-time training and prediction, while deep learning models usually require regular offline training. The extremely high operating efficiency makes the SMSP method more practical in real-time scenarios.

[0126] Table 4 Average filling errors of different models in 960-step filling experiments

[0127]

[0128] In order to verify the superiority of the invention, a disassembly experiment was conducted to highlight the contribution of the data set construction method in the invention to the filling accuracy. As shown in Table 4, the average filling errors of different data set construction methods in the pressure sensor and flow sensor in the disassembly experiment are shown. Among them, SMSP-NH means that historical data is removed from the original data set construction method, SMSP-NC means that other sensor data in the same group are removed, SMSP-NM means that the maximum information coefficient is not used to weight the data matrix, and SMSM-NP means that principal component analysis is not performed. The experimental results show that each method contributes to the data filling accuracy of the present invention to varying degrees. By combining these different data set construction methods, superior filling accuracy can be obtained in a polynomial model with relatively low complexity.

[0129] Table 4 Average filling errors of different models in 960-step filling experiments

[0130]

[0131] In summary, the data filling method proposed in the present invention can accurately and efficiently realize the data filling of water supply network sensors.

Claims

1. A water supply network sensor data recovery method based on soft sensors, characterized in that: include: Based on the latest time series monitored by the current sensor, the local weighted regression method is used to obtain the periodic series. The polynomial function fitted to the periodic series is multi-order differentiated to obtain the derivative time series composed of the characteristic vectors of each observation point. Dynamic time warping is used to calculate the distance between the derivative time series corresponding to different sensors, thereby obtaining the time series distance matrix of different sensors. Hierarchical clustering is used to group different sensors based on the time series distance matrix of different sensors. The time series matrix of the soft sensor is constructed based on the latest time series monitored by the current sensor, the time series monitored by other sensors in the same group as the current sensor, and the historical subsequences with the smallest time series distance to the latest time series in the historical time series monitored by the current sensor; Based on the latest time series, principal component analysis is used to filter out the top m relevant eigenvectors from the time series matrix of the soft sensor, and the multivariate polynomial regression input matrix constructed by the top m relevant eigenvectors is solved to fill the missing values ​​or outliers in the latest time series.

2. The water supply network sensor data recovery method based on soft sensor according to claim 1 is characterized in that: The methods for solving the order and coefficients of the polynomial function for periodic sequence fitting include: A polynomial function of order p is constructed based on the periodic sequence, an information criterion is constructed based on the covariance between the polynomial function and the periodic sequence and the order of the polynomial function, and the p value is solved by minimizing the information criterion; Based on the sequence points of the periodic sequence corresponding to each observation point and the solution of the polynomial function, the coefficients of the polynomial function are obtained by the least square method.

3. The water supply network sensor data recovery method based on soft sensor according to claim 2 is characterized in that: The information criterion IC of the i-th sensor is constructed based on the covariance between the polynomial function and the periodic sequence and the order of the polynomial function. i for: IC i =-NlnCov i +(p+1)lnN in, represents the mean of the periodic sequence with N observation points of the i-th sensor, represents the polynomial function f of order p of the i-th sensor at the observation point t i The value of (t,p) is is the sample mean of the polynomial function, is the time series at the i-th sensor observation point t.

4. The water supply network sensor data recovery method based on soft sensor according to claim 1 is characterized in that: The derivative time series of the i-th sensor composed of the feature vectors of each observation point for: in represents the m-th order derivative value of the polynomial function at the t-th observation point, is the feature vector of the i-th sensor at the t-th observation point, and N is the number of observation points.

5. The water supply network sensor data recovery method based on soft sensor according to claim 4 is characterized in that: Dynamic time warping is used to calculate the distance between the derivative time series corresponding to different sensors to obtain the time series distance matrix of different sensors, where the distance between the derivative time series corresponding to the i-th sensor and the derivative time series corresponding to the j-th sensor is for: Where N is the number of observation points corresponding to the i-th sensor, is the number of observation points corresponding to the jth sensor.

6. The water supply network sensor data recovery method based on soft sensor according to claim 1 is characterized in that: Before using principal component analysis to filter out the top m relevant eigenvectors from the time series matrix of the soft sensor based on the latest time series, the maximum information coefficient between the latest time series and any time series of the time series matrix of the soft sensor is constructed, and the diagonal matrix constructed with the maximum information coefficient is used as the weight to weight the time series matrix of the soft sensor, and the weighted time series matrix of the soft sensor is subjected to principal component analysis.

7. The water supply network sensor data recovery method based on soft sensor according to claim 1 is characterized in that: Based on the latest time series, principal component analysis is used to filter out the top m relevant feature vectors from the time series matrix of the soft sensor, including: The covariance matrix is ​​obtained by performing principal component analysis on the latest time series, and multiple eigenvectors are obtained by performing singular value decomposition on the covariance matrix, thereby screening out the top m relevant eigenvectors from the multiple eigenvectors to obtain the eigenmatrix after dimensionality reduction.

8. The water supply network sensor data recovery method based on soft sensor according to claim 7 is characterized in that: Solve the multivariate polynomial regression input matrix constructed from the first m related eigenvectors, including: A multivariate polynomial regression input matrix is ​​constructed based on the first m related eigenvectors, a multivariate polynomial regression function is constructed based on the multivariate polynomial regression input matrix, the regression coefficients of the multivariate polynomial regression function are solved by the least squares method based on the solution of the multivariate polynomial regression function and the data values ​​corresponding to the latest time series, and the missing values ​​or abnormal values ​​of the latest time series are filled based on the multivariate polynomial regression function with the determined regression coefficients.

Images