Flood season water quality monitoring data complementation method and device based on Log regular tensor decomposition

Abstract

The invention discloses a flood season water quality monitoring data complementing method and device based on Log regular tensor decomposition. The flood season water quality monitoring data complementing method specifically comprises the following steps: S1, acquiring historical flood season water quality monitoring data from a server and storing the data; s2, constructing a water quality data tensor according to the historical flood season water quality monitoring data; s3, a target loss function is constructed according to the water quality data tensor, iterative training is carried out, and a hidden feature moment is extracted; and S4, calculating missing flood season water quality prediction data according to the extracted hidden feature matrix.

Description

Technical Field

[0001] The present invention relates to the technical field of data processing, and particularly to a method and device for completing flood season water quality monitoring data based on Log regular tensor decomposition. Background Art

[0002] Water quality monitoring is an important part of environmental protection and water resource management. Especially during the flood season, due to the increase in rainfall and the sharp rise in river flow, the water environment changes violently, and water quality parameters (such as dissolved oxygen, pH value, turbidity, ammonia nitrogen, etc.) are prone to abnormal fluctuations or data missing. These missing or abnormal data will affect the accuracy of water quality assessment, and further have an adverse impact on water environment management and decision-making. Therefore, how to effectively complete flood season water quality monitoring data has become an important challenge in the current water quality monitoring field.

[0003] Traditional data completion methods are mainly based on statistical or machine learning techniques, such as interpolation method, regression analysis, matrix decomposition, etc. However, these methods have the following limitations when dealing with multi-dimensional and high-dimensional data: Data dimension limitation: Water quality monitoring data usually contains multiple dimensions such as time, location, and monitoring indicators. Traditional methods are difficult to effectively process this high-dimensional data structure; Non-negativity constraint: Water quality monitoring data (such as pollutant concentration, dissolved oxygen, etc.) is usually non-negative. Traditional methods cannot ensure that the completed data meets the non-negativity constraint; Data sparsity: There are often a large number of missing values in flood season water quality monitoring data. Traditional methods have poor completion effects in the case of data sparsity; Insufficient capture of local features: Traditional methods are difficult to capture local features and complex relationships in data, resulting in inaccurate completion results.

[0004] In recent years, tensor decomposition technology, as an emerging multi-dimensional data processing method, has gradually attracted attention. Tensor decomposition can effectively process high-dimensional data and capture global and local features in the data. Among them, non-negative tensor decomposition is a special tensor decomposition method, which forcibly constrains the decomposition result to be non-negative during the decomposition process, and is very suitable for processing non-negative data such as water quality monitoring data. Summary of the Invention

[0005] Aiming at the problem of a large number of missing values in flood season water quality monitoring data in the prior art, the present invention proposes a method and device for completing flood season water quality monitoring data based on Log regular tensor decomposition.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A method for completing flood season water quality monitoring data based on Log regular tensor decomposition specifically includes the following steps:

[0008] S1: Obtain historical flood season water quality monitoring data from the server and store it;

[0009] S2: Construct a water quality data tensor based on historical flood season water quality monitoring data;

[0010] S3: Construct an objective loss function based on the water quality data tensor and perform iterative training to extract the hidden feature matrix;

[0011] S4: Calculate the missing flood season water quality prediction data based on the extracted hidden feature matrix.

[0012] Preferably, in the S1, the historical water quality monitoring data is stored in a five-tuple X = (y, d, s, p, v), where y represents the monitoring year, d represents the number of days of monitoring time, s represents the site, p represents the pollutant in the water, and v represents the index value of the p pollutant measured during the monitoring period of site s on the dth day of year y.

[0013] Preferably, in the S2, the water quality data tensor is Y I×J×K×P , where I represents the number of years covered by the monitoring data, J represents the number of days covered by the monitoring data, K represents the number of sites where the pollutant is collected, and P is the number of types of pollutants monitored by sensors at all sites.

[0014] Preferably, the S3 includes:

[0015] S3-1: Construct an objective loss function based on the water quality data tensor;

[0016] S3-2: Perform training iteration on the objective loss function according to single hidden feature dependence non-negative and multiplicative update;

[0017] S3-3: Determine whether the objective loss function reaches the termination condition. If not, continue training iteration; if so, stop training iteration and output the hidden feature tensor.

[0018] Preferably, in the S3-1, the objective loss function is:

[0019]

[0020] In formula (1), ε represents the objective loss function; A represents the hidden feature matrix of the monitoring year; B represents the hidden feature matrix of the monitoring days; C represents the hidden feature matrix of the water quality monitoring sites; D represents the hidden feature matrix of the monitored pollutant types; e represents the bias vector of the monitoring year; f represents the bias vector of the monitoring days; y ijkp ∈Λ represents the known entity in the water quality data tensor Y, indicating the specific observed value of the water quality monitoring site k for the monitored pollutant type p during the time period of the ith year and jth day; α ir represents the value of the rth column in the ith row of the hidden feature matrix A of the monitoring year; b jr represents the value of the rth column in the jth row of the hidden feature matrix B of the days; c krrepresents the value of row k and column r in the hidden feature matrix C of the monitoring station; d pr represents the value of the pth row and rth column in the latent feature matrix D of the monitored pollutant type; λ represents the regularization parameter of the latent feature matrix, λ b represents the bias vector regularization parameter; R represents the dimension of the latent feature matrix; e i represents the i-th row in the bias vector e of the monitoring year; f j represents the jth row in the bias vector of the monitoring days; τ represents a constant.

[0021] Preferably, in S3-2, the target loss function training iteration formula is:

[0022]

[0023] In formula (2), α ir b represents the value of row i and column r in the latent feature matrix A of the monitoring year; jr represents the value of the jth row and rth column in the latent feature matrix B of the number of days; c kr represents the value of row k and column r in the hidden feature matrix C of the monitoring station; d pr The value of the pth row and rth column in the latent feature matrix D of the monitored pollutant type; y ijkp ∈Λ represents a known entity in the water quality data tensor Y, which represents the specific observation value of the pollutant type p monitored by the water quality monitoring station k in the time period of day j in year i; represents the entity in the complete water quality data tensor after completion, that is, the predicted data value of the observation indicator j at the i-th observation station on the k-th day and the l-th hour; λ represents the regularization parameter of the latent feature matrix; e i represents the i-th row in the bias vector e of the monitoring year; f j The jth row in the bias vector representing the number of monitoring days; b represents the bias vector regularization parameter; Λ(i), Λ(j), Λ(k), and Λ(p) represent the subsets linked to entities i∈I, j∈J, k∈K, and p∈P, respectively; τ represents a constant.

[0024] Preferably, in S3-3, the termination condition of the training iteration process is: the total number of iterations reaches the set maximum value N, or the difference between the value of the target loss function ε calculated in the current round and the value of the target loss function ε in the previous round is less than the threshold δ for five consecutive rounds.

[0025] Preferably, in said S4, the calculation formula for the missing flood season water quality prediction data is:

[0026]

[0027] In formula (3), Represents the entity in the complete water quality data tensor after completion, that is, the predicted data value of the observation index j at the i-th observation site on the k-th day and the l-th hour; α ir Represents the value of the i-th row and r-th column in the latent feature matrix A of the monitoring year; b jr Represents the value of the j-th row and r-th column in the latent feature matrix B of the number of days; c kr Represents the value of the k-th row and r-th column in the latent feature matrix C of the monitoring site; d pr Represents the value of the p-th row and r-th column in the latent feature matrix D of the types of monitored pollutants; e i Represents the i-th row in the bias vector e of the monitoring year; f j Represents the j-th row in the bias vector of the monitoring days.

[0028] The present invention also provides a flood season water quality monitoring data completion device based on Log regular tensor decomposition, including a data acquisition module, a storage module, a tensor construction module, a latent feature extraction module, and an output module; wherein,

[0029] The data acquisition module is used to obtain historical water quality monitoring data from the server and store it;

[0030] The storage module is used to store the received historical water quality monitoring data and the missing water quality prediction data values;

[0031] The tensor construction module is used to construct a water quality data tensor according to the water quality monitoring data;

[0032] The latent feature extraction module is used to construct an objective loss function according to the water quality data tensor and the historical water quality data, and extract latent features;

[0033] The output module is used to output the missing water quality prediction data values according to the extracted latent features.

[0034] Preferably, the latent feature extraction module includes an initialization unit, an objective loss function construction unit, and a training unit;

[0035] The initialization unit is used to initialize the process parameters involved in the extraction process of the water quality data tensor;

[0036] The objective loss function construction unit is used to construct an objective loss function according to the water quality data tensor, the historical water quality monitoring data, and the process parameters;

[0037] The training unit is used to train and optimize the objective loss function and extract latent features.

[0038] In summary, due to the adoption of the above technical solutions, compared with the prior art, the present invention has at least the following beneficial effects:

[0039] The present invention provides a method and device for completing flood season water quality monitoring data based on non - negative tensor decomposition. By constructing the water quality data of monitoring stations into a tensor model to capture multi - dimensional correlation features, and using tensor decomposition with introduced Log regularization to extract the potential laws of the data, missing or abnormal values can be quickly filled. During the flood season, due to extreme weather (such as heavy rain, floods) or equipment failures, some of the water quality monitoring data may be missing or abnormal. The present invention can utilize the existing complete data to complete the missing part through decomposition and reconstruction, and restore the integrity of the data. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 FIG. is a schematic diagram of a method for completing flood season water quality monitoring data based on Log - regularized tensor decomposition according to an exemplary embodiment of the present invention.

[0041] Figure 2 FIG. is a schematic diagram of a device for completing flood season water quality monitoring data based on Log - regularized tensor decomposition according to an exemplary embodiment of the present invention.

[0042] Figure 3 FIG. is a schematic diagram of a storage module according to an exemplary embodiment of the present invention.

[0043] Figure 4 FIG. is a schematic diagram of a hidden feature extraction module according to an exemplary embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0044] The present invention will be further described in detail below in conjunction with embodiments and specific implementation manners. However, it should not be understood that the scope of the above subject matter of the present invention is limited to the following embodiments. Any technology implemented based on the content of the present invention belongs to the scope of the present invention.

[0045] In the description of the present invention, it should be understood that the orientation or positional relationships indicated by the terms "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. are based on the orientation or positional relationships shown in the drawings. These are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as limiting the present invention.

[0046] As Figure 1 shown, the present invention provides a method for completing flood season water quality monitoring data based on Log - regularized tensor decomposition, which specifically includes the following steps:

[0047] S1: Receive the instruction for completing flood season water quality monitoring data sent by the server, and obtain historical water quality monitoring data from the server.

[0048] The server can send instructions in the following ways: regularly, or according to the notification of the device, or according to the notification of a certain server, send an instruction to the data receiving module to complete the flood season water quality monitoring data.

[0049] In this embodiment, the received historical water quality monitoring data is in the form of a five-tuple X = (y, d, s, p, v), where y represents the monitoring year, d represents the number of days of monitoring time, s represents the site, p represents the pollutant in the water, and v represents the index value of the p pollutant measured during the monitoring period at site s on the dth day of year y.

[0050] S2: Construct a water quality data tensor Y based on the historical water quality monitoring data.

[0051] In this embodiment, all the five-tuples X = (y, d, s, p, v) in the water quality monitoring data storage unit are constructed into a tensor Y I×J×K×P , where I represents the number of years covered by the monitoring data, J represents the number of days covered by the monitoring data, K represents the number of sites where the pollutant is collected, and P is the number of types of pollutants monitored by the sensors at all sites.

[0052] Specifically, the element y in the tensor ijkP represents the specific observed value of the pollutant type p at the water quality monitoring site k during the time period from the ith year to the jth day. Where 1 ≤ i ≤ I, 1 ≤ j ≤ J, 1 ≤ k ≤ K, 1 ≤ p ≤ P. Due to reasons such as equipment failure, transmission interruption, or environmental interference, there must be a certain number of missing values in the tensor A constructed by the water quality monitoring data tensor construction module. Let Λ represent the set of known observed values included in the high-order incomplete tensor A. At the same time, for the abnormal values generated during part of the observations, such as data outside the sensor observation range (such as <0.01, >1000), the values are set to 0 and the sensor upper limit value respectively.

[0053] S3: Construct an objective loss function based on the water quality data tensor and perform iterative training to extract the hidden feature matrix.

[0054] S3-1: Construct an objective loss function ε based on the known data set Λ of the water quality data tensor Y, which is represented by the following formula:

[0055]

[0056] In formula (1), ε represents the objective loss function; A represents the hidden feature matrix of the monitoring year; B represents the hidden feature matrix of the monitoring days; C represents the hidden feature matrix of the water quality monitoring sites; D represents the hidden feature matrix of the monitored pollutant types; e represents the bias vector of the monitoring year; f represents the bias vector of the monitoring days; y ijkp∈Λ represents a known entity in the water quality data tensor Y, which represents the specific observation value of the pollutant type p monitored by the water quality monitoring station k in the jth day of the i-th year; α ir b represents the value of row i and column r in the latent feature matrix A of the monitoring year; jr represents the value of the jth row and rth column in the latent feature matrix B of the number of days; c kr represents the value of row k and column r in the hidden feature matrix C of the monitoring station; d pr represents the value of the pth row and rth column in the latent feature matrix D of the monitored pollutant type; λ represents the regularization parameter of the latent feature matrix, λ b represents the bias vector regularization parameter; R represents the dimension of the latent feature matrix; e i represents the i-th row in the bias vector e of the monitoring year; f j represents the jth row in the bias vector of the monitoring days; τ represents a constant greater than 0, so that the formula satisfies the domain of the logarithmic function.

[0057] In this embodiment, the F norm is used as the optimization target; L2 regularization is used, and λ is the latent feature matrix regularization parameter to constrain the optimization process to prevent overfitting problems during the optimization process.

[0058] S3-2: To minimize the optimization objective loss function ε, the latent feature matrix is trained and calculated based on the non-negative and multiplicative updates of the single latent feature dependency. The training iteration formula is as follows:

[0059]

[0060] In formula (2), α ir b represents the value of row i and column r in the latent feature matrix A of the monitoring year; jr represents the value of the jth row and rth column in the latent feature matrix B of the number of days; c kr represents the value of row k and column r in the hidden feature matrix C of the monitoring station; d pr The value of the pth row and rth column in the latent feature matrix D of the monitored pollutant type; y ijkp ∈Λ represents a known entity in the water quality data tensor Y, which represents the specific observation value of the pollutant type p monitored by the water quality monitoring station k in the time period of day j in year i; represents the entity in the complete water quality data tensor after completion, that is, the predicted data value of the observation indicator j at the i-th observation station on the k-th day and the l-th hour; λ represents the regularization parameter of the latent feature matrix; e i represents the i-th row in the bias vector e of the monitoring year; f j The jth row in the bias vector representing the number of monitoring days; b Represents the bias vector regularization parameter

[0061] Numbers; Λ(i), Λ(j), Λ(k), Λ(p) represent subsets linked to entities i ∈ I, j ∈ J, k ∈ K, and p ∈ P, respectively. τ is a number greater than 0 such that the formula satisfies the domain of the logarithmic function.

[0062] S3-3: Determine whether the training iteration process of the target loss function ε on the known data set Λ reaches the termination condition. If not, continue the training iteration; if so, stop the training iteration and output four hidden feature tensors A, B, C, and D.

[0063] In this step, there are two cases where the training iteration process of the target loss function ε on the known data set Λ reaches the termination condition: the total number of iterations reaches the set maximum value N, or the difference between the value of the target loss function ε calculated in the current round and the value of the target loss function ε in the previous round is less than the threshold δ for five consecutive rounds.

[0064] S4: Calculate the missing water quality data according to the extracted hidden feature matrix:

[0065]

[0066] In formula (3), represents the entity in the complete water quality data tensor after completion, that is, the predicted data value of the observation index j at the i-th observation site on the k-th day and the l-th hour; α ir represents the value of the i-th row and r-th column in the hidden feature matrix A of the monitoring year; b jr represents the value of the j-th row and r-th column in the hidden feature matrix B of the number of days; c kr represents the value of the k-th row and r-th column in the hidden feature matrix C of the monitoring site; d pr represents the value of the p-th row and r-th column in the hidden feature matrix D of the types of monitored pollutants; e i represents the i-th row in the bias vector e of the monitoring year; f j represents the j-th row in the bias vector of the monitoring days.

[0067] The present invention provides a method and device for completing flood season water quality monitoring data based on non-negative tensor decomposition. By constructing the water quality data of the monitoring site into a tensor model to capture multi-dimensional correlation features, and using tensor decomposition technology with an introduced Log regularization term to extract the potential laws of the data, missing or abnormal values are quickly filled. During the flood season, due to extreme weather (such as heavy rain, floods) or equipment failures, some water quality monitoring data may be missing or abnormal. The present invention can utilize the existing complete data to complete the missing part through decomposition and reconstruction, and restore the integrity of the data.

[0068] Based on the above method for completing flood season water quality monitoring data based on Log-regularized tensor decomposition, as Figure 2As shown in the figure, the present invention also provides a flood season water quality monitoring data completion device based on Log regular tensor decomposition, including a data acquisition module 1, a storage module 2, a tensor construction module 3, a hidden feature extraction module 4, and an output module 5.

[0069] The output end of the data acquisition module 1 is connected to the first input end of the storage module 2. The output end of the storage module 2 is respectively connected to the input end of the tensor construction module 3. The output end of the tensor construction module 3 is connected to the input end of the hidden feature extraction module 4. The output end of the hidden feature extraction module 4 is connected to the input end of the output module 5. The output end of the output module 5 is connected to the second input end of the storage module 2.

[0070] Among them, the data acquisition module 1 is used to obtain historical water quality monitoring data from the server and store it.

[0071] The storage module 2 is used to store the received historical water quality monitoring data and the missing water quality prediction data values.

[0072] In this embodiment, as Figure 3 shown, the storage module 2 includes a first storage unit 21 and a second storage unit 22;

[0073] The first storage unit 21 stores the received historical water quality monitoring data in the form of a five-tuple as X = (y, d, s, p, v), where y represents the monitoring year, d represents the number of days of monitoring time, s represents the site, p represents the pollutant in the water, and v represents the index value of the p pollutant measured during the monitoring period of site s on the dth day of year y.

[0074] The second storage unit 22 is used to store the missing water quality prediction data values output by the output module.

[0075] In this embodiment, the tensor construction module 3 is used to construct a water quality data tensor Y according to all the five-tuples X = (y, d, s, p, v) in the water quality monitoring data storage unit I×J×K×P , where I represents the number of years covered by the monitoring data, J represents the number of days covered by the monitoring data, K represents the number of sites where the pollutant is collected, and P is the number of types of pollutants monitored by sensors at all sites.

[0076] Specifically, the element y in the tensor ijkP represents the specific observed value of the water quality monitoring site k for the pollutant type p during the period from the i-th year to the j-th day. Where 1 ≤ i ≤ I, 1 ≤ j ≤ J, 1 ≤ k ≤ K, 1 ≤ p ≤ P. The hidden feature extraction module 4 is used to construct a target loss function according to the water quality data tensor and the historical water quality data, and extract hidden features.

[0077] As Figure 4As shown in the figure, the implicit feature extraction module 4 includes an initialization unit 41, a target loss function construction unit 42, and a training unit 43. The output end of the initialization unit 41 is connected to the input end of the target loss function construction unit 42. The output end of the target loss function construction unit 42 is connected to the input end of the training unit 44. The output end of the training unit 44 is connected to the output module 5.

[0078] The initialization unit 41 is used to initialize the process parameters involved in the extraction process of the water quality data tensor.

[0079] The target loss function construction unit 42 is used to construct a target loss function according to the water quality data tensor, historical water quality monitoring data, and process parameters.

[0080] The training unit 43 is used to train and optimize the target loss function to extract implicit features.

[0081] The output module 5 is used to output the missing water quality prediction data values according to the extracted implicit features.

[0082] The present invention also provides an electronic device, which includes a processor. The processor is used to run a computer program stored in a memory, so that the electronic device implements the steps of the method for supplementing flood season water quality monitoring data based on Log regular tensor decomposition in the above embodiments.

[0083] The present invention also provides a computer-readable storage medium, in which a computer program is stored. When the computer program runs on a processor, it implements the steps of the method for supplementing flood season water quality monitoring data based on Log regular tensor decomposition in the above embodiments.

[0084] The computer program includes computer program code, which can be in the form of source code, object code, executable file, or some intermediate form, etc. The computer-readable medium can at least include: any entity or device capable of carrying the computer program code to an electronic device, a recording medium, a computer memory, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, RandomAccess Memory), an electrical carrier signal, a telecommunication signal, and a software distribution medium. For example, a USB flash drive, a mobile hard disk, a magnetic disk, or an optical disc, etc. In some jurisdictions, according to legislation and patent practice, the computer-readable medium cannot be an electrical carrier signal and a telecommunication signal.

[0085] Those of ordinary skill in the art can understand that the above embodiments are specific embodiments for implementing the present invention. In actual applications, various changes can be made in form and details without departing from the spirit and scope of the present invention.

Claims

1. A method for complementing flood season water quality monitoring data based on Log regular tensor decomposition, characterized in that, Specifically, it includes the following steps: S1: Obtain and store the historical flood season water quality monitoring data from the server; S2: Construct a water quality data tensor based on the historical flood season water quality monitoring data; S3: Construct an objective loss function based on the water quality data tensor and perform iterative training to extract the hidden feature matrix; S4: Calculate the missing flood season water quality prediction data based on the extracted hidden feature matrix.

2. The method for completing flood season water quality monitoring data based on Log regular tensor decomposition according to claim 1, wherein In S1, the historical water quality monitoring data is stored in a five-tuple X = (y, d, s, p, v), where y represents the monitoring year, d represents the number of days of monitoring time, s represents the site, p represents the pollutant in the water, and v represents the index value of the p pollutant measured at the monitoring site s during the monitoring period on the d-th day of the y-th year.

3. The method for completing flood season water quality monitoring data based on Log regular tensor decomposition according to claim 1, characterized in that In the above S2, the water quality data tensor is Y I×J×K×P , where I represents the number of years covered by the monitoring data, J represents the number of days covered by the monitoring data, K represents the number of sites where the pollutant is collected, and P is the number of types of pollutants monitored by sensors at all sites.

4. The method for complementing flood season water quality monitoring data based on Log regular tensor decomposition according to claim 1, characterized in that S3 includes: S3-1: Construct an objective loss function based on the water quality data tensor; S3-2: Perform training iteration on the objective loss function according to the single hidden feature dependence non-negativity and multiplicative update; S3-3: Determine whether the objective loss function reaches the termination condition. If not, continue the training iteration. If so, stop the training iteration and output the hidden feature tensor.

5. The method for completing flood season water quality monitoring data based on Log regular tensor decomposition according to claim 4, wherein In S3-1, the objective loss function is: In formula (1), ε represents the objective loss function; A represents the hidden feature matrix of the monitoring year; B represents the hidden feature matrix of the monitoring days; C represents the hidden feature matrix of the water quality monitoring sites; D represents the latent feature matrix for monitoring pollutant types; e represents the bias vector for monitoring years; f represents the bias vector for monitoring days; y ijkp ∈Λ represents the known entity in the water quality data tensor Y, indicating the specific observed value of the monitoring pollutant type p at the water quality monitoring site k during the time period of the i-th year and the j-th day; α ir represents the value of the i-th row and r-th column in the latent feature matrix A for monitoring years; b jr represents the value of the j-th row and r-th column in the latent feature matrix B for days; c kr represents the value of the k-th row and r-th column in the latent feature matrix C for monitoring sites; d pr represents the value of the p-th row and r-th column in the latent feature matrix D for monitoring pollutant types; λ represents the latent feature matrix regularization parameter, λ b represents the bias vector regularization parameter; R represents the dimension of the latent feature matrix; e i represents the i-th row in the bias vector e indicating the monitoring year; f j represents the j-th row in the bias vector indicating the monitoring days; τ represents a constant.

6. The method for completing flood season water quality monitoring data based on Log regular tensor decomposition according to claim 4, wherein In S3-2, the training iteration formula of the objective loss function is: In formula (2), α ir represents the value of the element in the \(i\)-th row and \(r\)-th column of the latent feature matrix \(A\) for the monitoring year; \(b\ jr represents the value of the element in the \(j\)-th row and \(r\)-th column of the latent feature matrix \(B\) for the number of days; \(c\ kr represents the value of the element in the \(k\)-th row and \(r\)-th column of the latent feature matrix \(C\) for the monitoring site; \(d\ pr represents the value of the element in the \(p\)-th row and \(r\)-th column of the latent feature matrix \(D\) for the types of monitored pollutants; \(y\ ijkp \(\in\Lambda\) represents a known entity in the water quality data tensor \(Y\), indicating the specific observed value of the water quality monitoring site \(k\) for the type of monitored pollutant \(p\) during the period of the \(i\)-th year and \(j\)-th day; represents an entity in the completed complete water quality data tensor, that is, the predicted data value of the observed index \(j\) of the \(i\)-th observation site at the \(k\)-th day and \(l\)-th hour; \(\lambda\) represents the latent feature matrix regularization parameter; \(e\ i represents the \(i\)-th row in the bias vector \(e\) for the monitoring year; \(f\ j represents the \(j\)-th row in the bias vector for the number of monitoring days; \(\lambda\ b represents the bias vector regularization parameter; \(\Lambda(i)\), \(\Lambda(j)\), \(\Lambda(k)\), \(\Lambda(p)\) represent the subsets linked to the entities \(i\in I\), \(j\in J\), \(k\in K\), and \(p\in P\) respectively; \(\tau\) represents a constant.

7. The method for complementing flood season water quality monitoring data based on Log regular tensor decomposition according to claim 4, wherein In S3-3, the termination condition of the training iteration process is: the total number of iterations reaches the set maximum value N, or the difference between the value of the objective loss function ε calculated in the current round and the value of the objective loss function ε in the previous round is less than the threshold δ for five consecutive rounds.

8. The method for completing flood season water quality monitoring data based on Log regular tensor decomposition according to claim 1, characterized in that In S4, the calculation formula for the missing flood season water quality prediction data is: In formula (3), represents the entity in the complete water quality data tensor after completion, that is, the predicted data value of the observation index j at the i-th observation site on the k-th day and the l-th hour; α ir represents the value of the i-th row and the r-th column in the latent feature matrix A of the monitoring year; b jr represents the value of the j-th row and the r-th column in the latent feature matrix B of the number of days; c kr represents the value of the k-th row and the r-th column in the latent feature matrix C of the monitoring site; d pr represents the value of the p-th row and the r-th column in the latent feature matrix D of the types of monitored pollutants; e i represents the i-th row in the bias vector e of the monitoring year; f j represents the j-th row in the bias vector of the monitoring days.

9. A flood season water quality monitoring data completion device based on Log regular tensor decomposition according to the method described in any one of claims 1-8, characterized in that, It includes a data acquisition module, a storage module, a tensor construction module, a hidden feature extraction module, and an output module; among them, The data acquisition module is used to obtain and store the historical water quality monitoring data from the server; The storage module is used to store the received historical water quality monitoring data and the missing water quality prediction data values; The tensor construction module is used to construct a water quality data tensor based on the water quality monitoring data; The hidden feature extraction module is used to construct an objective loss function based on the water quality data tensor and the historical water quality data, and extract the hidden features; The output module is used to output the missing water quality prediction data values according to the extracted hidden features.

10. The flood season water quality monitoring data completion device based on Log regular tensor decomposition according to claim 9, characterized in that, The hidden feature extraction module includes an initialization unit, an objective loss function construction unit, and a training unit; The initialization unit is used to initialize the process parameters involved in the extraction process of the water quality data tensor; The objective loss function construction unit is used to construct an objective loss function based on the water quality data tensor, the historical water quality monitoring data, and the process parameters; The training unit is used to train and optimize the objective loss function and extract the hidden features.

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