A water quality time series prediction method and system based on fusion whale optimization algorithm

Abstract

The present invention relates to the technical field of water quality prediction, and specifically to a water quality time series prediction method and system based on a fusion whale optimization algorithm. The water quality time series prediction method includes: collecting water quality monitoring data and preprocessing the water quality monitoring data to obtain water quality time series data; performing denoising on the water quality time series data by wavelet denoising; optimizing the parameters of EEMD by WOA, decomposing the water quality time series data by EEMD, and obtaining a number of IMFs; using the target water quality index as a prediction index, predicting each IMF by a CNN‑LSTM deep learning model and obtaining a prediction result. The present invention uses WOA to automatically optimize the key parameters in EEMD, overcomes the limitations of manually selecting parameters in traditional methods, and improves prediction accuracy and robustness. The optimized EEMD of the present invention can not only effectively reduce the noise in water quality data, but also realize multi-scale signal analysis.

Description

Technical Field

[0001] The present invention relates to the technical field of water quality prediction, and in particular to a method and system for water quality time series prediction based on a fusion whale optimization algorithm. Background Art

[0002] Traditional water quality prediction methods such as ARIMA, multivariate linear regression, fuzzy mathematics, and grey system theory have the problem of low prediction accuracy and are difficult to meet the needs of modern complex water quality data. In recent years, deep learning technology has been widely used in the field of time series prediction due to its powerful data processing capabilities, especially recurrent neural networks (RNN) and long short-term memory networks (LSTM). Although RNN is good at dealing with long-term dependency problems, it has the problem of gradient explosion. In contrast, LSTM was proposed by Hochreiter et al. and is widely used in the field of water quality prediction due to its excellent processing ability for time series data. Although a single LSTM neural network improves the prediction accuracy compared to traditional methods, it still has the problem of decreased prediction accuracy when dealing with high-dimensional and large data volumes. At the same time, the nonlinear components and multi-scale information in water quality data are difficult to capture, and the noise in the data makes it difficult to effectively improve the accuracy.

[0003] As water quality data often presents characteristics such as multi-scale, nonlinear, and disordered fluctuations, there is an urgent need to develop a water quality time series prediction method that can reduce data noise interference and improve the accuracy of water quality index prediction. Summary of the invention

[0004] The purpose of the present invention is to solve at least one of the technical problems existing in the prior art and to provide a water quality time series prediction method and system based on a fusion whale optimization algorithm.

[0005] To achieve the above object, the technical solution adopted by the present invention is as follows: a water quality time series prediction method based on the fusion whale optimization algorithm, comprising the following steps:

[0006] Step 1, collecting water quality monitoring data and preprocessing the water quality monitoring data to obtain water quality time series data;

[0007] Step 2, denoising the water quality time series data by wavelet denoising;

[0008] Step 3, by integrating the whale optimization algorithm WOA, the parameters of the integrated empirical mode decomposition method EEMD are optimized, and the water quality time series data are decomposed by EEMD to obtain several intrinsic mode functions IMF;

[0009] Step 4: Using the target water quality index as the prediction index, predict each IMF through the CNN-LSTM deep learning model and obtain the prediction results; summarize the prediction results of all IMFs and output the prediction value of the entire water quality time series data.

[0010] In step 3, the parameters of the integrated empirical mode decomposition method EEMD are optimized by integrating the whale optimization algorithm WOA, specifically including:

[0011] Step 301, initializing the population: randomly generating a parameter set, each individual in the parameter set represents a set of parameters, the parameters include the synthetic group size and the noise standard deviation, and the value range of these parameters is defined by the lower bound and the upper bound;

[0012] Step 302, evaluate fitness: calculate the fitness value of each individual, i.e., envelope entropy, through the defined fitness function; if the fitness value is lower, it means that the parameter combination is better;

[0013] Step 303, updating the population: WOA updates the population by simulating the predation behavior of whales, including circling prey, spiral movement, and searching for prey; each step updates the position of the individual through a specific mathematical formula, gradually approaching the optimal solution;

[0014] Step 304, boundary check: after updating the population, ensure that all parameter values ​​are within the allowed setting range;

[0015] Step 305, iteration and convergence: repeat the above steps until the maximum number of iterations is reached; in each iteration, the optimal solution is updated and the optimal fitness value of each iteration is recorded;

[0016] In step 3, the water quality time series data is decomposed by EEMD, specifically including:

[0017] The EEMD parameters optimized by WOA are used to perform EEMD decomposition on the preprocessed water quality time series data to obtain several intrinsic mode functions (IMFs) and a residual error (RMF). :

[0018]

[0019] in, is the preprocessed water quality data, and N is the number of IMFs obtained by decomposition.

[0020] Furthermore, in step 1, the water quality monitoring data includes at least indicators of water temperature, pH, dissolved oxygen content, potassium permanganate content, ammonia nitrogen content, total phosphorus content, total nitrogen content, conductivity, and turbidity.

[0021] Furthermore, in step 1, the water quality monitoring data is preprocessed, specifically including:

[0022] Process missing values, outliers, frequency unification and normalization of water quality monitoring data;

[0023] In the missing value processing, linear interpolation is used to interpolate the missing values. The linear interpolation formula is as follows:

[0024]

[0025] in, represents the time variable, exist between, exist between; for and ,in is the time or position of the nearest non-missing data point to the left of the missing value, yes The corresponding observed value; is the time or position of the nearest non-missing data point on the right, yes The corresponding observed value;

[0026] In the normalization process, the original time series data is assumed to be , where T is the length of the time series; the normalization method is used to convert the original time series data into :

[0027]

[0028] in, is the normalized index value, is the original indicator value, They represent the maximum and minimum values ​​of the indicator respectively. Through normalization operation, the values ​​are mapped to [0,1].

[0029] Furthermore, the step 2 specifically includes:

[0030] Step 201, perform wavelet transform:

[0031] Based on the db4 wavelet basis function in the Daubechies wavelet family, the signal is decomposed into multiple frequency sub-bands through convolution operations;

[0032] It is known that the normalized data is , select db4 wavelet basis function, denoted as , calculate the wavelet transform coefficients for:

[0033]

[0034] in, Refers to the wavelet transform coefficient, which indicates the signal at a specific scale and location The wavelet transform result under ; Refers to the normalized index value; Wavelet basis function A zoomed and translated version of ;

[0035] Step 202, perform multi-resolution analysis:

[0036] The signal is gradually decomposed into a series of approximation coefficients and detail coefficients, thereby obtaining approximation and detail parts of different scales;

[0037] Step 203, perform threshold processing:

[0038] The detail coefficients are processed using the soft threshold method to remove the noise component. The mathematical expression of the soft threshold method is:

[0039]

[0040] in, is the detail factor, is the coefficient after threshold processing, is the threshold value;

[0041] Step 204, threshold selection:

[0042] The general threshold method is used to determine the threshold, and the formula is:

[0043]

[0044] in, is the standard deviation of the noise, estimated by the median absolute deviation; N is the signal length.

[0045] Furthermore, in step 4, the target water quality index is used as a prediction index, and each IMF is predicted by the CNN-LSTM deep learning model to obtain the prediction results, which specifically include:

[0046] Step 401, extract CNN features: input data into the convolutional neural network CNN, set the input sequence The data after sliding window processing is , where S is the window size, the output of the first convolutional layer can be expressed as:

[0047]

[0048] in, It is The feature map elements, is the activation function, is the bias term, is the weight of the convolution kernel, K is the size of the convolution kernel;

[0049] The maximum pooling layer performs the input data After downsampling, the output is ,in, is the length of the sequence after pooling; the pooling process can be expressed as:

[0050]

[0051] in, is the stride of the pooling window, is the size of the pooling window;

[0052] Step 402, analyzing LSTM timing: The calculation of the LSTM layer involves the input gate, the forget gate and the output gate, as well as the cell state; suppose and They are the LSTM units at time The cell state and hidden state of is the input vector, then:

[0053]

[0054]

[0055]

[0056]

[0057]

[0058]

[0059] in, The input gate is at time step The output, The forget gate at time step The output, refers to the new candidate cell state, The output gate at time step The output, , , , , , , , They all represent the corresponding weight matrices, , , , They all represent the corresponding bias vectors, is the sigmoid function, tanh is the hyperbolic tangent function, represents element-wise multiplication;

[0060] Step 403, output fully connected layer: The output layer of the model uses a simple fully connected layer, and its output is expressed as:

[0061]

[0062] in, is the hidden state at the last time step, and are the weights and biases of the output layer, is the final predicted value.

[0063] The present invention also provides a water quality time series prediction system based on the fusion whale optimization algorithm, comprising:

[0064] A data preprocessing module is used to collect and preprocess water quality monitoring data to obtain water quality time series data;

[0065] Noise reduction processing module, used to perform noise reduction processing on water quality time series data by wavelet denoising;

[0066] EEMD decomposition module is used to optimize the parameters of the integrated empirical mode decomposition method EEMD by integrating the whale optimization algorithm WOA, and decompose the water quality time series data through EEMD to obtain several intrinsic mode functions IMF;

[0067] The prediction module is used to use the target water quality index as the prediction index, predict each IMF through the CNN-LSTM deep learning model and obtain the prediction results; summarize the prediction results of all IMFs and output the prediction value of the entire water quality time series data.

[0068] It can be seen from the above description of the present invention that, compared with the prior art, the water quality time series prediction method and system based on the fusion whale optimization algorithm of the present invention includes at least one of the following beneficial effects:

[0069] 1. The present invention adopts the whale optimization algorithm WOA to automatically optimize the key parameters in the ensemble empirical mode decomposition method EEMD, overcomes the limitations of manual parameter selection in traditional methods, and improves prediction accuracy and robustness.

[0070] 2. The optimized EEMD of the present invention can not only effectively reduce the noise in water quality data, but also realize multi-scale signal analysis.

[0071] 3. The present invention inputs the denoised data into a deep learning framework consisting of a convolutional neural network (CNN) and a long short-term memory (LSTM) network, wherein CNN is used to extract local features of water quality data and enhance the processing capabilities of large-scale data sets, while LSTM focuses on parsing long-term dependencies, nonlinear patterns, and dynamic changes in time series in water quality sequence data. This combination lays the foundation for building a more accurate and efficient water quality prediction system.

[0072] 4. The present invention combines the biologically inspired optimization technology WOA, the advanced analysis method EEMD in the field of signal processing, and the artificial intelligence technology CNN-LSTM in the field of computer science to form a comprehensive solution for water quality prediction, demonstrating the powerful potential of interdisciplinary knowledge in solving practical problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 This is a flow chart of the steps of a water quality time series prediction method based on the fusion whale optimization algorithm in a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0074] The technical scheme in the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiment of the present invention. Obviously, the described embodiment is only a part of the embodiment of the present invention, not all of the embodiments. Based on the embodiment of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0075] Reference Figure 1 As shown, a preferred embodiment of the present invention, a water quality time series prediction method based on the fusion whale optimization algorithm, comprises the following steps:

[0076] Step 1, collecting water quality monitoring data and preprocessing the water quality monitoring data to obtain water quality time series data;

[0077] Step 2, denoising the water quality time series data by wavelet denoising;

[0078] Step 3, by integrating the whale optimization algorithm WOA, the parameters of the integrated empirical mode decomposition method EEMD are optimized, and the water quality time series data are decomposed by EEMD to obtain several intrinsic mode functions IMF;

[0079] Step 4: Using the target water quality index as the prediction index, predict each IMF through the CNN-LSTM deep learning model and obtain the prediction results; summarize the prediction results of all IMFs and output the prediction value of the entire water quality time series data.

[0080] In step 3, the parameters of the integrated empirical mode decomposition method EEMD are optimized by integrating the whale optimization algorithm WOA, specifically including:

[0081] Step 301, initializing the population: randomly generating a parameter set, each individual in the parameter set represents a set of parameters, the parameters include the synthetic group size and the noise standard deviation, and the value range of these parameters is defined by the lower bound and the upper bound;

[0082] Step 302, evaluate fitness: calculate the fitness value of each individual, i.e., envelope entropy, through the defined fitness function; if the fitness value is lower, it means that the parameter combination is better;

[0083] Step 303, updating the population: WOA updates the population by simulating the predation behavior of whales, including circling prey, spiral movement, and searching for prey; each step updates the position of the individual through a specific mathematical formula, gradually approaching the optimal solution;

[0084] Step 304, boundary check: after updating the population, ensure that all parameter values ​​are within the allowed setting range;

[0085] Step 305, iteration and convergence: repeat the above steps until the maximum number of iterations is reached; in each iteration, the optimal solution is updated and the optimal fitness value of each iteration is recorded;

[0086] In step 3, the water quality time series data is decomposed by EEMD, specifically including:

[0087] The EEMD parameters optimized by WOA are used to perform EEMD decomposition on the preprocessed water quality time series data to obtain several intrinsic mode functions (IMFs) and a residual error (RMF). :

[0088]

[0089] in, is the preprocessed water quality data, and N is the number of IMFs obtained by decomposition.

[0090] As a preferred embodiment of the present invention, it may also have the following additional technical features:

[0091] In this embodiment, in step 1, the water quality monitoring data includes at least indicators of water temperature, pH, dissolved oxygen content, potassium permanganate content, ammonia nitrogen content, total phosphorus content, total nitrogen content, conductivity, and turbidity.

[0092] In this embodiment, in step 1, the water quality monitoring data is preprocessed, specifically including:

[0093] Process missing values, outliers, frequency unification and normalization of water quality monitoring data;

[0094] In the missing value processing, linear interpolation is used to interpolate the missing values. The linear interpolation formula is as follows:

[0095]

[0096] in, represents the time variable, exist between, exist between; for and ,in is the time or position of the nearest non-missing data point to the left of the missing value, yes The corresponding observed value; is the time or position of the nearest non-missing data point on the right, yes The corresponding observed value;

[0097] In the normalization process, the original time series data is assumed to be , where T is the length of the time series; the normalization method is used to convert the original time series data into :

[0098]

[0099] in, is the normalized index value, is the original indicator value, They represent the maximum and minimum values ​​of the indicator respectively. Through normalization operation, the values ​​are mapped to [0,1].

[0100] In this embodiment, step 2 specifically includes:

[0101] Step 201, perform wavelet transform:

[0102] Based on the db4 wavelet basis function in the Daubechies wavelet family, the signal is decomposed into multiple frequency sub-bands through convolution operations;

[0103] It is known that the normalized data is , select db4 wavelet basis function, denoted as , calculate the wavelet transform coefficients for:

[0104]

[0105] in, Refers to the wavelet transform coefficient, which indicates the signal at a specific scale and location The wavelet transform result under ; Refers to the normalized index value; Wavelet basis function A zoomed and translated version of ;

[0106] Step 202, perform multi-resolution analysis:

[0107] The signal is gradually decomposed into a series of approximation coefficients and detail coefficients, thereby obtaining approximation and detail parts of different scales;

[0108] Step 203, perform threshold processing:

[0109] The detail coefficients are processed using the soft threshold method to remove the noise component. The mathematical expression of the soft threshold method is:

[0110]

[0111] in, is the detail factor, is the coefficient after threshold processing, is the threshold value;

[0112] Step 204, threshold selection:

[0113] The general threshold method is used to determine the threshold, and the formula is:

[0114]

[0115] in, is the standard deviation of the noise, estimated by the median absolute deviation; N is the signal length.

[0116] In this embodiment, in step 4, the target water quality index is used as the prediction index, and each IMF is predicted by the CNN-LSTM deep learning model to obtain the prediction result, which specifically includes:

[0117] Step 401, extract CNN features: input data into the convolutional neural network CNN, set the input sequence The data after sliding window processing is , where S is the window size, the output of the first convolutional layer can be expressed as:

[0118]

[0119] in, It is The feature map elements, is the activation function, is the bias term, is the weight of the convolution kernel, K is the size of the convolution kernel;

[0120] The maximum pooling layer performs the input data After downsampling, the output is ,in, is the length of the sequence after pooling; the pooling process can be expressed as:

[0121]

[0122] in, is the stride of the pooling window, is the size of the pooling window;

[0123] Step 402, analyzing LSTM timing: The calculation of the LSTM layer involves the input gate, the forget gate and the output gate, as well as the cell state; suppose and They are the LSTM units at time The cell state and hidden state of is the input vector, then:

[0124]

[0125]

[0126]

[0127]

[0128]

[0129]

[0130] in, The input gate is at time step The output, The forget gate at time step The output, refers to the new candidate cell state, The output gate at time step The output, , , , , , , , They all represent the corresponding weight matrices, , , , They all represent the corresponding bias vectors, is the sigmoid function, tanh is the hyperbolic tangent function, represents element-wise multiplication;

[0131] Step 403, output fully connected layer: The output layer of the model uses a simple fully connected layer, and its output is expressed as:

[0132]

[0133] in, is the hidden state at the last time step, and are the weights and biases of the output layer, is the final predicted value.

[0134] The present invention also provides a water quality time series prediction system based on the fusion whale optimization algorithm, comprising:

[0135] A data preprocessing module is used to collect and preprocess water quality monitoring data to obtain water quality time series data;

[0136] Noise reduction processing module, used to perform noise reduction processing on water quality time series data by wavelet denoising;

[0137] EEMD decomposition module is used to optimize the parameters of the integrated empirical mode decomposition method EEMD by integrating the whale optimization algorithm WOA, and decompose the water quality time series data through EEMD to obtain several intrinsic mode functions IMF;

[0138] The prediction module is used to use the target water quality index as the prediction index, predict each IMF through the CNN-LSTM deep learning model and obtain the prediction results; summarize the prediction results of all IMFs and output the prediction value of the entire water quality time series data.

[0139] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and improved concepts of the present invention within the technical scope disclosed by the present invention, and they should be covered by the protection scope of the present invention.

Claims

1. A water quality time series prediction method based on the fusion whale optimization algorithm, characterized in that: The following steps are involved: Step 1, collecting water quality monitoring data and preprocessing the water quality monitoring data to obtain water quality time series data; Step 2, denoising the water quality time series data by wavelet denoising; Step 3, by integrating the whale optimization algorithm WOA, the parameters of the integrated empirical mode decomposition method EEMD are optimized, and the water quality time series data are decomposed by EEMD to obtain several intrinsic mode functions IMF; Step 4: Using the target water quality index as the prediction index, predict each IMF through the CNN-LSTM deep learning model and obtain the prediction results; summarize the prediction results of all IMFs and output the prediction value of the entire water quality time series data; In step 3, the parameters of the integrated empirical mode decomposition method EEMD are optimized by integrating the whale optimization algorithm WOA, specifically including: Step 301, initializing the population: randomly generating a parameter set, each individual in the parameter set represents a set of parameters, the parameters include the synthetic group size and the noise standard deviation, and the value range of these parameters is defined by the lower bound and the upper bound; Step 302, evaluate fitness: calculate the fitness value of each individual, i.e., envelope entropy, through the defined fitness function; if the fitness value is lower, it means that the parameter combination is better; Step 303, updating the population: WOA updates the population by simulating the predation behavior of whales, including circling prey, spiral movement, and searching for prey; each step updates the position of the individual through a specific mathematical formula, gradually approaching the optimal solution; Step 304, boundary check: after updating the population, ensure that all parameter values ​​are within the allowed setting range; Step 305, iteration and convergence: repeat the above steps until the maximum number of iterations is reached; in each iteration, the optimal solution is updated and the optimal fitness value of each iteration is recorded; In step 3, the water quality time series data is decomposed by EEMD, specifically including: The EEMD parameters optimized by WOA are used to perform EEMD decomposition on the preprocessed water quality time series data to obtain several intrinsic mode functions (IMFs) and a residual. : ； in, is the preprocessed water quality data, and N is the number of IMFs obtained by decomposition.

2. According to claim 1, a water quality time series prediction method based on fusion whale optimization algorithm is characterized in that: In step 1, the water quality monitoring data includes at least indicators of water temperature, pH, dissolved oxygen content, potassium permanganate content, ammonia nitrogen content, total phosphorus content, total nitrogen content, conductivity, and turbidity.

3. The water quality time series prediction method based on the fusion whale optimization algorithm according to claim 1 is characterized in that: In step 1, the water quality monitoring data is preprocessed, specifically including: Process missing values, outliers, frequency unification and normalization of water quality monitoring data; In the missing value processing, linear interpolation is used to interpolate the missing values. The linear interpolation formula is as follows: ； in, represents the time variable, exist between, exist between; for and ,in is the time or position of the nearest non-missing data point to the left of the missing value, yes The corresponding observed value; is the time or position of the nearest non-missing data point on the right, yes The corresponding observed value; In the normalization process, the original time series data is assumed to be , where T is the length of the time series; the normalization method is used to convert the original time series data into ; ； in, is the normalized index value, is the original indicator value, They represent the maximum and minimum values ​​of the indicator respectively. Through normalization operation, the values ​​are mapped to [0,1].

4. The water quality time series prediction method based on the fusion whale optimization algorithm according to claim 1 is characterized in that: The step 2 specifically includes: Step 201, perform wavelet transform: Based on the db4 wavelet basis function in the Daubechies wavelet family, the signal is decomposed into multiple frequency sub-bands through convolution operations; It is known that the normalized data is , select db4 wavelet basis function, denoted as , calculate the wavelet transform coefficients for: ； in, Refers to the wavelet transform coefficient, which indicates the signal at a specific scale and location The wavelet transform result under ; Refers to the normalized index value; Wavelet basis function A zoomed and translated version of ; Step 202, perform multi-resolution analysis: The signal is gradually decomposed into a series of approximation coefficients and detail coefficients, thereby obtaining approximation and detail parts of different scales; Step 203, perform threshold processing: The detail coefficients are processed using the soft threshold method to remove the noise component. The mathematical expression of the soft threshold method is: ； in, is the detail factor, is the coefficient after threshold processing, is the threshold value; Step 204, threshold selection: The general threshold method is used to determine the threshold, and the formula is: ； in, is the standard deviation of the noise, estimated by the median absolute deviation; N is the signal length.

5. The water quality time series prediction method based on the fusion whale optimization algorithm according to claim 1 is characterized in that: In step 4, the target water quality index is used as the prediction index, and each IMF is predicted by the CNN-LSTM deep learning model to obtain the prediction results, which specifically include: Step 401, extract CNN features: input data into the convolutional neural network CNN, set the input sequence The data after sliding window processing is , where S is the window size, the output of the first convolutional layer can be expressed as: ； in, It is The feature map elements, is the activation function, is the bias term, is the weight of the convolution kernel, K is the size of the convolution kernel; The maximum pooling layer performs the input data After downsampling, the output is ,in, is the length of the sequence after pooling; the pooling process can be expressed as: ； in, is the stride of the pooling window, is the size of the pooling window; Step 402, analyzing LSTM timing: The calculation of the LSTM layer involves the input gate, the forget gate and the output gate, as well as the cell state; suppose and They are the LSTM units at time The cell state and hidden state of is the input vector, then: ； ； ； ； ； ； in, The input gate at time step The output, The forget gate at time step The output, refers to the new candidate cell state, The output gate at time step The output, , , , , , , , They all represent the corresponding weight matrices, , , , They all represent the corresponding bias vectors, is the sigmoid function, tanh is the hyperbolic tangent function, represents element-wise multiplication; Step 403, output fully connected layer: The output layer of the model uses a simple fully connected layer, and its output is expressed as: ； in, is the hidden state at the last time step, and are the weights and biases of the output layer, is the final predicted value.

6. A water quality time series prediction system based on the fusion whale optimization algorithm, used to execute the water quality time series prediction method based on the fusion whale optimization algorithm described in claim 1, characterized in that: include: A data preprocessing module is used to collect and preprocess water quality monitoring data to obtain water quality time series data; Noise reduction processing module, used to perform noise reduction processing on water quality time series data by wavelet denoising; EEMD decomposition module is used to optimize the parameters of the integrated empirical mode decomposition method EEMD by integrating the whale optimization algorithm WOA, and decompose the water quality time series data through EEMD to obtain several intrinsic mode functions IMF; The prediction module is used to use the target water quality index as the prediction index, predict each IMF through the CNN-LSTM deep learning model and obtain the prediction results; summarize the prediction results of all IMFs and output the prediction value of the entire water quality time series data.

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