DO concentration prediction method of double-circulation neural network based on improved FHO

Abstract

The invention discloses a DO concentration prediction method based on an improved FHO dual-cycle neural network. The method comprises the following steps: collecting and preprocessing multi-dimensional data of a water body; decomposing the preprocessed multi-dimensional data of the water body into an intrinsic mode function by adopting improved variational mode decomposition; constructing a dual-circulation neural network; performing hyper-parameter optimization on the bicirculating neural network through an optimization algorithm to obtain an optimal bicirculating neural network, inputting the decomposed intrinsic mode function into the optimal bicirculating neural network, and outputting a prediction result; according to the method, a new joint gate FUGate is defined, a forgetting gate of LSTM and an updating gate of GRU are fused, in the forward propagation process, the hidden state and the cell state are updated through the FUGate, and more efficient information flow control is achieved; through combination of VMD-ADMM decomposition, LSTM, GRU, a self-attention mechanism and other technologies, a dual-circulation neural network is constructed, and the modeling capability of complex time series data is significantly improved.

Description

Technical Field

[0001] The present invention relates to the technical field of DO concentration prediction, and in particular to a DO concentration prediction method based on a double-circulation neural network of an improved FHO. Background Art

[0002] Dissolved oxygen concentration is one of the important indicators for evaluating water quality health. It directly affects the survival of aquatic organisms and the self-purification capacity of water bodies. Dissolved oxygen is a key indicator of biological activity in water bodies, especially in aquaculture, rivers, lakes and groundwater. The dissolved oxygen concentration affects the survival and reproduction of aquatic organisms. Accurately predicting dissolved oxygen concentration helps to detect water quality changes in a timely manner, take corresponding management measures, and ensure the health of the ecosystem. In sewage treatment plants or other industrial processes, dissolved oxygen is an important factor in determining the efficiency of sewage treatment. By predicting the dissolved oxygen concentration, the operation of aeration equipment can be controlled in real time to improve treatment efficiency and reduce energy consumption.

[0003] Traditional DO concentration prediction methods mainly rely on models based on empirical formulas, statistical regression analysis or physical and chemical reaction models. These methods have low prediction accuracy under complex environmental conditions and usually require a large amount of historical data for modeling and verification.

[0004] In recent years, with the development of deep learning technology, researchers have gradually applied it to environmental data analysis, but most existing deep learning models lack effective capture of the complexity of water quality changes, and are not efficient enough in processing multivariate time series data. For example, in the EEMD-LSTM prediction model, EEMD may introduce additional uncertainty when noise is introduced, especially in the case of low signal-to-noise ratio, which is prone to redundant overfitting and other problems. The calculation process of the hybrid MIC-BP neural network model involves a lot of data analysis and matrix operations. When the input data dimension is very high, the complexity and time cost of MIC calculation will increase significantly. The calculation method of MIC depends on the relationship between the data, and the BP neural network is prone to overfitting in complex tasks. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention provides a DO concentration prediction method based on a double-circulation neural network of an improved FHO, which aims to solve the problems in the background technology.

[0006] To achieve the above object, the present invention provides the following technical solution: a DO concentration prediction method based on a double-circulation neural network of an improved FHO, comprising the following steps: Step S1: Collect multi-dimensional water data of the sewage treatment plant and perform pre-processing; Step S2: using improved variational mode decomposition to decompose the preprocessed water body multi-dimensional data into intrinsic mode functions; Improved variational mode decomposition is to optimize variational mode decomposition using alternating direction multiplier method ADMM; Step S3: construct a double recurrent neural network; The specific structure of the double recurrent neural network is: convolution layer, batch normalization layer, maximum pooling layer, discard layer, joint gate, long short-term memory network LSTM, gated recurrent unit GRU, attention mechanism layer, fully connected layer, output layer; Step S4: Optimize the hyperparameters of the double recurrent neural network through the optimization algorithm to obtain the optimal double recurrent neural network, input the decomposed intrinsic mode function into the optimal double recurrent neural network, and the intrinsic mode function passes through the convolution layer, batch normalization layer, maximum pooling layer, discard layer, joint gate, long short-term memory network LSTM, gated recurrent unit GRU, attention mechanism layer, fully connected layer, and output layer in the optimal double recurrent neural network in turn to output the DO concentration prediction result; In step S3, the control logic of the forget gate of the long short-term memory network LSTM and the update gate of the gated recurrent unit GRU are merged into a joint gate FUGate, which manages the forget gate of the long short-term memory network LSTM and the update gate of the gated recurrent unit GRU at the same time.

[0007] Furthermore, the joint gate FUGate controls the forget gate of the long short-term memory network LSTM and the update gate of the gated recurrent unit GRU at the same time, which is expressed as: ; In the formula, express The output of the combined gate at all times; Represents the Sigmoid activation function; and Respectively represent the weight matrix and bias parameters shared by the joint gate, The dimension is , used to generate the forget gate of the long short-term memory network LSTM and the update gate of the gated recurrent unit GRU, The dimension is , represents the input dimension, represents the hidden state dimension; express Input of time; Indicates the hidden state at the previous moment; is a two-dimensional vector, expressed as: , Represents the forget gate of the long short-term memory network LSTM, Represents the update gate of the gated recurrent unit GRU; Reset gate calculation: ; In the formula, Indicates the gate The output of the reset gate of the time-controlled recurrent unit GRU; and Represent the weight matrix and bias term of the reset gate respectively; Generate candidate memories: ; In the formula, express The content of the candidate memory at each moment; represents element-wise multiplication; and Respectively The weight matrix and bias term of ; The cell state update of the long short-term memory network LSTM: ; In the formula, express The cell state at a given moment; express The cell state at a given moment; The hidden state update of the gated recurrent unit GRU: ; In the formula, express The hidden state of the moment; represents the hyperbolic tangent function.

[0008] Furthermore, the specific process of optimizing the variational mode decomposition using the alternating direction multiplier method ADMM is as follows: Construct augmented Lagrangian function; The objective function is: ; In the formula, Indicates Intrinsic mode functions; Indicates The frequency parameters associated with the eigenmode functions; represents the total number of eigenmode functions; Indicates time The partial derivative of represents the Dirac function; represents an imaginary unit; represents a natural constant; represents the frequency parameter; The constraints are: ; In the formula, Represents the original input signal, i.e., the multi-dimensional data of water body after preprocessing; The constraints are expressed through Lagrange multipliers Introducing the objective function and adding the quadratic penalty term, we get the augmented Lagrangian function , expressed as: ; In the formula, For penalty items; represents the Lagrange multiplier; Alternating direction updates; renew : ; In the formula, express After the iteration Updated values ​​of the intrinsic mode functions in the frequency domain; express Representation in the frequency domain; Indicates Updated values ​​of the intrinsic mode functions in the frequency domain; Denote the representation of Lagrange multipliers in the frequency domain; renew : ; In the formula, Indicates The eigenmode function is in the The value after iterations; Express Integral operation; renew : ; In the formula, express Moment After iterations The value of express Moment After the iteration Intrinsic mode functions; Alternate Update , , , set two stop conditions, and stop alternating update when any one of the stop conditions is met; The stopping conditions are: Check All Is the update amount less than the preset threshold? , calculate the sum of squared Euclidean distances between two consecutive iterations, when , express After the iteration If there are no intrinsic mode functions, the iteration stops; When the number of iterations exceeds the preset maximum number of iterations, the iteration stops.

[0009] Furthermore, the hyperparameters of the dual recurrent neural network include: the number of filters in the convolutional layer , Number of LSTM units , the number of units of the gated recurrent unit GRU and the dropout rate of the dropout layer ; The optimization algorithm adopts the improved Fire Eagle optimization algorithm. The specific process of optimizing the hyperparameters of the double recurrent neural network using the improved Fire Eagle optimization algorithm is as follows: Encode the hyperparameters of the double recurrent neural network into a unified solution vector: ; Randomly generate an initial fire eagle population, each fire eagle individual in the fire eagle population represents a solution vector ; Calculate the fitness value of each fire eagle individual in the fire eagle population, and re-divide the fire eagle individuals in the fire eagle population into fire eagle individuals and prey according to the fitness value; Simulate arson, driving away and capturing strategies to update the locations of individual fire hawks and prey; Perform local search for the best fire eagle individual in the current population; When local search satisfies: , or the current number of iterations reaches the preset maximum number of iterations, the current optimal solution is output And the corresponding objective function value , the current optimal solution As the optimal hyperparameter; Indicates The location of each Fire Eagle individual, Indicates The position of each Fire Eagle individual after local search optimization; Represents the fitness function value.

[0010] Furthermore, the arson strategy is simulated: the leader fire eagle individual, that is, the best fire eagle individual in the current fire eagle set, generates the fire source location: ; In the formula, Indicates The location of the fire source; Indicates The location of the leader Fire Hawk individuals; It indicates the fire source control coefficient; Indicates A random perturbation vector; Simulated expulsion strategy: prey fleeing from fire: ; In the formula, Indicates The position of each prey after the expulsion strategy is updated; express The current location of the prey; represents the escape intensity coefficient; Represents a randomly generated safe location; represents the disturbance amplitude; represents a random vector; Simulated capture strategy: Fire hawk individuals move towards prey and fire: ; In the formula, Indicates The positions of individual fire eagles after the simulated capture strategy update; Indicates The current location of each Fire Hawk individual; Represents the weight coefficient of the fire eagle individual moving towards the current optimal prey position; The weight coefficient that indicates the movement of individual fire eagles toward the fire source; Indicates the current optimal prey location.

[0011] Furthermore, in the capture strategy, the inertia weight is introduced Control search criteria: .

[0012] Furthermore, the triggering conditions for local search include: Periodic trigger: Every The iteration triggers a local search: ; In the formula, Represents a trigger signal, which is used to decide whether to perform a local search; Indicates the current iteration number; Indicates the periodic interval that triggers local search; Fitness stagnation trigger: The best Fire Eagle individual continues No improvement triggers a local search: ; In the formula, Represents the fitness function value of the best fire eagle individual in the current iteration; Represents the fitness function value of the best fire eagle individual in the previous iteration; Before The fitness function value of the best fire eagle individual in the iteration; Diversity trigger: Firehawk population standard deviation falls below set threshold Trigger a local search: ; In the formula, The fire eagle population is The standard deviation of the dimension; Indicates the total number of dimensions; When the local search is triggered, the best Fire Eagle individual is selected to perform local search optimization: ; In the formula, represents the local learning rate; When the optimal solution after local search optimization is better than the current optimal solution, the current optimal solution is replaced.

[0013] Furthermore, the multi-dimensional data of water bodies include temperature, pH value, flow rate, mixed liquor suspended solids concentration MLSS, effluent total nitrogen, effluent ammonia nitrogen, and DO of the anoxic section of the oxidation ditch; The preprocessing process includes: cleaning the collected multi-dimensional water body data to remove missing values ​​and outliers; and normalizing the cleaned multi-dimensional water body data.

[0014] Furthermore, the performance of the optimal double recurrent neural network is evaluated using mean square error, root mean square error, and mean absolute error.

[0015] Compared with the existing technology, the present invention has the following beneficial effects:

[0016] (1) The present invention improves the prediction accuracy and efficiency of DO concentration and enhances the robustness to noise and outliers. It is suitable for various scenarios such as water quality monitoring, ecological protection and industrial process control, and provides more reliable technical support for intelligent water quality management systems. It can effectively solve the technical problems in signal decomposition, feature selection, nonlinear modeling, hyperparameter optimization and other aspects of existing dissolved oxygen concentration prediction methods.

[0017] (2) The present invention constructs a dual recurrent neural network by combining VMD-ADMM decomposition, LSTM, GRU, self-attention mechanism and other technologies, which significantly improves the modeling ability of complex time series data, especially in processing long-term dependencies, local feature extraction, global relationship capture and other aspects. The present invention integrates the control logic of the forget gate of the long short-term memory network LSTM and the update gate of the gated recurrent unit GRU into a joint gate FUGate by sharing the gated parameters through gated collaboration, and manages the forget gate of the long short-term memory network LSTM and the update gate of the gated recurrent unit GRU at the same time. In the forward propagation process, it is used to update the hidden state and cell state to achieve more efficient information flow control; the hyperparameters of the model are further adjusted through the local search Firehawk optimization algorithm, the model performance is optimized, and the prediction accuracy and generalization ability are improved. The present invention can effectively overcome the limitations of traditional technologies, especially in processing complex sewage treatment data and other environmental monitoring data, showing strong potential and advantages. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 The figure is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0019] like Figure 1 As shown, the present invention provides a technical solution: a DO concentration prediction method based on a double-circulation neural network of an improved FHO, comprising the following steps:

[0020] Step S1: Collect multi-dimensional water data of the sewage treatment plant through sensors and monitoring equipment and perform pre-processing. The multi-dimensional water data include temperature, pH value, flow rate, mixed liquor suspended solids concentration (MLSS), effluent total nitrogen, effluent ammonia nitrogen, and DO of the anoxic section of oxidation ditch A.

[0021] The preprocessing process includes: cleaning the collected multi-dimensional water body data to remove missing values ​​and outliers; normalizing the cleaned multi-dimensional water body data: ; In the formula, It is the multi-dimensional data of the cleaned water body; is the minimum value of the multi-dimensional data of the water body after cleaning; It is the maximum value of the multi-dimensional data of the water body after cleaning; After normalization .

[0022] Step S2: The preprocessed water multidimensional data is decomposed into five intrinsic mode functions using improved variational mode decomposition. Each intrinsic mode function represents the components of the original signal at different frequencies and amplitudes, and has better local feature representation. Improved variational mode decomposition uses the alternating direction multiplier method (ADMM) to optimize variational mode decomposition.

[0023] The improved variational mode decomposition decomposes the original problem into multiple sub-problems through the alternating direction multiplier method (ADMM) and solves them alternately. The core of the improved variational mode decomposition is to decompose the signal (pre-processed multi-dimensional water body data) into multiple intrinsic mode functions by constructing a constrained optimization problem: Construct augmented Lagrangian function; The objective function is: ; In the formula, Indicates Intrinsic mode functions; Indicates The frequency parameters associated with the eigenmode functions; represents the total number of eigenmode functions; Indicates time The partial derivative of represents the Dirac function; represents an imaginary unit; represents a natural constant; Represents the frequency parameter.

[0024] The constraints are: ; In the formula, Represents the original input signal, that is, the multi-dimensional data of water body after preprocessing.

[0025] The constraints are expressed through Lagrange multipliers Introducing the objective function and adding the quadratic penalty term, we get the augmented Lagrangian function , expressed as: ; In the formula, is a penalty term used to control the strictness of the constraint; represents the Lagrange multiplier.

[0026] Alternating direction updates; renew : Derivative of the Lagrangian function, fixed and , solve in the frequency domain: ; In the formula, express After the iteration Updated values ​​of the intrinsic mode functions in the frequency domain; express Representation in the frequency domain; Indicates Updated values ​​of the intrinsic mode functions in the frequency domain; Denotes the representation of Lagrange multipliers in the frequency domain.

[0027] renew :right Derivative, and set to 0, by minimizing the frequency domain energy center of the mode to obtain : ; In the formula, Indicates The eigenmode function is in the The value after iterations; Express Integral operation; represents the weighted integral of the modal power spectrum; represents the total energy of the eigenmode function.

[0028] renew :Adjust according to the reconstruction error : ; In the formula, express Moment After iterations The value of express Moment After the iteration An intrinsic mode function.

[0029] Alternate Update , , ,Set two stop conditions, and stop alternating updates when any one of the stop conditions is met.

[0030] The stopping conditions are:

[0031] 1. The modal update amount is small enough: Check all Is the update amount less than the preset threshold? , calculate the sum of squared Euclidean distances between two consecutive iterations, if , express After the iteration eigenmode function, the iteration is stopped; in this embodiment, = .

[0032] 2. Reaching the maximum number of iterations: If the number of iterations exceeds the preset maximum number of iterations, the iteration will be stopped even if the condition of the modal update amount is not met; in this embodiment, the maximum number of iterations is set to 1000.

[0033] The improved variational mode decomposition (VMD-ADMM) decomposes the signal (preprocessed multi-dimensional water body data) into several intrinsic mode functions through an optimization process, and there will be a residual term, which is the error between the sum of the decomposed intrinsic mode functions and the signal. Specifically, the improved variational mode decomposition (VMD-ADMM) decomposes the signal into multiple intrinsic mode functions, each of which represents the local characteristics of the signal at different frequency components. It can be expressed as: ; In the formula, Represents the signal, i.e., the multi-dimensional data of the water body after preprocessing; Indicates IMFs, each of which represents a different frequency component of the signal; Represents the residual term.

[0034] Step S3: Construct a double recurrent neural network.

[0035] Among them, the specific structure and processing flow of the double recurrent neural network are as follows:

[0036] The convolutional layer (Conv1D) receives the input data (eigenmode function obtained by modified variational mode decomposition (VMD-ADMM)) and extracts local features in the input data.

[0037] Batch Normalization layer normalizes the output of the convolutional layer to reduce internal covariate shift, speed up the training process, and improve the generalization ability of the model.

[0038] The maximum pooling layer (MaxPooling1D) reduces the feature dimension of the output of the batch normalization layer, thereby reducing the amount of computation and extracting the most important features.

[0039] Dropout layer: The output of the maximum pooling layer is sent to the dropout layer, which randomly discards the output of some neurons to reduce overfitting and improve the generalization ability of the model.

[0040] Long Short-Term Memory Network LSTM, the output of the discard layer is fed into the Long Short-Term Memory Network LSTM. The Long Short-Term Memory Network LSTM processes sequence data through its gating mechanism (input gate, forget gate, output gate) to capture long-term dependencies.

[0041] The output of the LSTM is fed into the GRU. The GRU simplifies the structure of the LSTM through its update gate and reset gate while maintaining the ability to capture long-term dependencies.

[0042] Attention Layer: The output of the gated recurrent unit GRU is fed into the attention layer. This layer enables the model to assign different attention weights according to the importance of different parts of the input, thereby focusing on the most important parts of the input data.

[0043] Fully connected layer (Dense), the output of the attention mechanism layer is sent to the fully connected layer. This layer integrates the features extracted by the previous layer and is usually used for classification or regression tasks.

[0044] Output Layer: The output of the fully connected layer is fed into the output layer. The output layer generates the final prediction result based on the output of the fully connected layer. The structure and activation function of the output layer depend on the specific task (for example, for a binary classification task, a sigmoid activation function may be used; for a multi-classification task, a softmax activation function may be used).

[0045] Among them, since the forget gate of the long short-term memory network LSTM and the update gate of the gated recurrent unit GRU are complementary in function, the present invention merges the control logic of the forget gate of the long short-term memory network LSTM and the update gate of the gated recurrent unit GRU into a joint gate FUGate through gated collaborative sharing of gating parameters, and simultaneously manages the forget gate of the long short-term memory network LSTM and the update gate of the gated recurrent unit GRU to achieve more efficient information flow control.

[0046] The joint gate FUGate controls the forget gate of the long short-term memory network LSTM and the update gate of the gated recurrent unit GRU at the same time, expressed as: ; In the formula, express The output of the combined gate at all times; Represents the Sigmoid activation function, with an output range of [0,1]; and Respectively represent the weight matrix and bias parameters shared by the joint gate, The dimension is , used to generate the forget gate of the long short-term memory network LSTM and the update gate of the gated recurrent unit GRU, The dimension is , represents the input dimension, represents the hidden state dimension; express Input of time; Indicates the hidden state at the previous moment; is a two-dimensional vector, expressed as: , Represents the forget gate of the long short-term memory network LSTM, which is used to control the proportion of old memory retention. Represents the update gate of the gated recurrent unit GRU, which is used to control the proportion of new memory integration.

[0047] Reset gate calculation: ; In the formula, Indicates the gate The output of the reset gate of the time-controlled recurrent unit GRU; and Represent the weight matrix and bias term of the reset gate respectively, The dimension is , The dimension is .

[0048] Generate candidate memory, fuse the current input and historical state, expressed as: ; In the formula, express The content of the candidate memory at each moment; represents element-wise multiplication; and Respectively The weight matrix and bias term of .

[0049] The cell state update of the long short-term memory network LSTM: ; In the formula, express The cell state at a given moment; express The cell state at a given moment.

[0050] The hidden state update of the gated recurrent unit GRU: ; In the formula, express The hidden state of the moment; represents the hyperbolic tangent function.

[0051] The update of long-term memory (cell state of LSTM) and short-term state (hidden state of GRU) is done by the same joint gate. Coordinate to avoid logical conflicts. The forget gate of the long short-term memory network LSTM determines how to update the hidden state and generate new output. The reset gate of the gated recurrent unit GRU determines how to forget the information of the previous moment, and the update gate determines the fusion ratio of new and old information; control The retention ratio is adjusted while adjusting the current information integration ratio.

[0052] Step S4: Optimize the hyperparameters of the double recurrent neural network through the optimization algorithm to obtain the optimal double recurrent neural network, input the decomposed intrinsic mode function into the optimal double recurrent neural network, and the intrinsic mode function passes through the convolution layer, batch normalization layer, maximum pooling layer, discard layer, joint gate, long short-term memory network LSTM, gated recurrent unit GRU, attention mechanism layer, fully connected layer, and output layer in the optimal double recurrent neural network in turn to output the DO concentration prediction result.

[0053] Among them, the optimization algorithm adopts the improved Fire Eagle optimization algorithm. The improved Fire Eagle optimization algorithm is obtained by combining the original Fire Eagle optimization algorithm (FHO) with local search and adding adaptive inertia weight.

[0054] Among them, the specific process of optimizing the hyperparameters of the double recurrent neural network using the improved Fire Eagle optimization algorithm is as follows: Optimize the hyperparameters of the double recurrent neural network. The hyperparameters of the dual recurrent neural network include: the number of filters in the convolutional layer , Number of LSTM units , the number of units of the gated recurrent unit GRU and the dropout rate of the dropout layer ,in, , , is a discrete parameter, is a continuous parameter.

[0055] Encode the hyperparameters of the double recurrent neural network into a unified solution vector: .

[0056] right , , Perform neighborhood search to generate candidate solutions .

[0057] Select the better solution by comparing the evaluation indicators.

[0058] like Can be guided, then Fine-tune using gradient directions.

[0059] like If it is not differentiable, then Use Pattern Search.

[0060] Initialize the population: Randomly generate an initial population of fire eagles. Each fire eagle individual in the population represents a solution vector. .

[0061] Calculate the fitness value of each fire eagle individual in the fire eagle population, and re-divide the fire eagle individuals in the fire eagle population into fire eagle individuals and prey according to the fitness value.

[0062] The arson, driving away and capturing strategies are simulated to update the positions of individual fire hawks and prey.

[0063] Simulating arson strategy: The leader fire eagle individual (the best fire eagle individual in the current fire eagle set) generates the fire source location: ; In the formula, Indicates The location of the fire source; Indicates The location of the leader Fire Hawk individuals; Indicates the fire source control coefficient, which is used to control the search range; Indicates A random perturbation vector.

[0064] Simulated expulsion strategy: prey fleeing from fire: ; In the formula, Indicates The position of each prey after the expulsion strategy is updated; express The current location of the prey; represents the escape intensity coefficient (decreasing with iteration); represents a randomly generated safe location, i.e., a new location that prey may choose when trying to escape from the fire; represents the disturbance amplitude; represents a random vector.

[0065] Simulated capture strategy: Fire hawk individuals move towards prey and fire: ; In the formula, Indicates The positions of individual fire eagles after the simulated capture strategy update; Indicates The current location of each Fire Hawk individual; The weight coefficient of the fire eagle individual moving towards the current optimal prey position is used to control the step length of the fire eagle individual moving towards the prey direction; The weight coefficient of the fire eagle moving towards the fire source is used to control the step length of the fire eagle moving towards the fire source. Indicates the current optimal prey location.

[0066] Since the algorithm may reduce the search accuracy due to excessive step size in the later stage, inertia weight is introduced in the capture strategy. Control search criteria: . Perform a local search for the best fire eagle individual in the current population.

[0067] The trigger conditions for local search include: Periodic trigger: Every The iteration triggers a local search: ; In the formula, Represents a trigger signal, which is used to decide whether to perform a local search; Indicates the current iteration number; Indicates the periodic interval that triggers the local search.

[0068] Fitness stagnation trigger: The best Fire Eagle individual continues No improvement triggers a local search: ; In the formula, Represents the fitness function value of the best fire eagle individual in the current iteration; Represents the fitness function value of the best fire eagle individual in the previous iteration; Before The fitness function value of the best fire eagle individual in the iteration.

[0069] Diversity trigger: Firehawk population standard deviation falls below set threshold Trigger a local search: ; In the formula, The fire eagle population is The standard deviation of the dimension; Indicates the total number of dimensions.

[0070] When the local search is triggered, the best Fire Eagle individual is selected to perform local search optimization: ; In the formula, Indicates The position of each Fire Eagle individual after local search optimization; Indicates The location of each Fire Hawk individual; represents the local learning rate; Represents the fitness function value.

[0071] When the optimal solution after local search optimization is better than the current optimal solution, the current optimal solution is replaced.

[0072] When local search satisfies: Or the current number of iterations reaches the preset maximum number of iterations, output the current optimal solution And the corresponding objective function value , the current optimal solution as the optimal hyperparameter.

[0073] Among them, the performance of the optimal double recurrent neural network is evaluated, and the evaluation indicators include mean square error (MSE), root mean square error (RMSE) and mean absolute error (MAE).

[0074] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. The DO concentration prediction method based on the double-circulation neural network of improved FHO is characterized by: The steps include: Step S1: Collect multi-dimensional water data of the sewage treatment plant and perform pre-processing; Step S2: using improved variational mode decomposition to decompose the preprocessed water body multi-dimensional data into intrinsic mode functions; Improved variational mode decomposition is to optimize variational mode decomposition using alternating direction multiplier method ADMM; Step S3: construct a double recurrent neural network; The specific structure of the double recurrent neural network is: convolution layer, batch normalization layer, maximum pooling layer, discard layer, joint gate, long short-term memory network LSTM, gated recurrent unit GRU, attention mechanism layer, fully connected layer, output layer; Step S4: Optimize the hyperparameters of the double recurrent neural network through the optimization algorithm to obtain the optimal double recurrent neural network, input the decomposed intrinsic mode function into the optimal double recurrent neural network, and the intrinsic mode function passes through the convolution layer, batch normalization layer, maximum pooling layer, discard layer, joint gate, long short-term memory network LSTM, gated recurrent unit GRU, attention mechanism layer, fully connected layer, and output layer in the optimal double recurrent neural network in turn to output the DO concentration prediction result; In step S3, the control logic of the forget gate of the long short-term memory network LSTM and the update gate of the gated recurrent unit GRU are merged into a joint gate FUGate, which manages the forget gate of the long short-term memory network LSTM and the update gate of the gated recurrent unit GRU at the same time.

2. The DO concentration prediction method based on the double-circulation neural network of improved FHO according to claim 1 is characterized in that: The joint gate FUGate controls the forget gate of the long short-term memory network LSTM and the update gate of the gated recurrent unit GRU at the same time, expressed as: ； In the formula, express The output of the combined gate at all times; Represents the Sigmoid activation function; and Respectively represent the weight matrix and bias parameters shared by the joint gate, The dimension is , used to generate the forget gate of the long short-term memory network LSTM and the update gate of the gated recurrent unit GRU, The dimension is , represents the input dimension, represents the hidden state dimension; express Input of time; Indicates the hidden state at the previous moment; is a two-dimensional vector, expressed as: , Represents the forget gate of the long short-term memory network LSTM, Represents the update gate of the gated recurrent unit GRU; Reset gate calculation: ； In the formula, Indicates the gate The output of the reset gate of the GRU; and Represent the weight matrix and bias term of the reset gate respectively; Generate candidate memories: ； In the formula, express The content of the candidate memory at every moment; represents element-wise multiplication; and Respectively The weight matrix and bias term of ; represents the hyperbolic tangent function; The cell state update of the long short-term memory network LSTM: ； In the formula, express The cell state at a given moment; express The cell state at a given moment; The hidden state of the gated recurrent unit GRU is updated: ； In the formula, express The hidden state of the moment.

3. The DO concentration prediction method based on the double-circulation neural network of improved FHO according to claim 2 is characterized in that: The specific process of optimizing variational mode decomposition using the alternating direction multiplier method ADMM is as follows: Construct augmented Lagrangian function; The objective function is: ； In the formula, Indicates Intrinsic mode functions; Indicates The frequency parameters associated with the eigenmode functions; represents the total number of eigenmode functions; Indicates time The partial derivative of represents the Dirac function; represents an imaginary unit; represents a natural constant; represents the frequency parameter; The constraints are: ； In the formula, Represents the original input signal, i.e., the multi-dimensional data of water body after preprocessing; The constraints are expressed through Lagrange multipliers Introducing the objective function and adding the quadratic penalty term, we get the augmented Lagrangian function , expressed as: ； In the formula, For penalty items; represents the Lagrange multiplier; Alternating direction updates; renew : ； In the formula, express After the iteration Updated values ​​of the intrinsic mode functions in the frequency domain; express Representation in the frequency domain; Indicates Updated values ​​of the intrinsic mode functions in the frequency domain; Denote the representation of Lagrange multipliers in the frequency domain; renew : ； In the formula, Indicates The eigenmode function is in the The value after iterations; Express Integral operation; renew : ； In the formula, express Moment After iterations The value of express Moment After the iteration Intrinsic mode functions; Alternate Update , , ,Set two stop conditions, and stop alternating updates when any one of the stop conditions is met; The stopping conditions are: Check All Is the update amount less than the preset threshold? , calculate the sum of squared Euclidean distances between two consecutive iterations, when , express After the iteration If there are no intrinsic mode functions, the iteration stops; When the number of iterations exceeds the preset maximum number of iterations, the iteration stops.

4. The DO concentration prediction method based on the double-circulation neural network of improved FHO according to claim 3 is characterized in that: The hyperparameters of the dual recurrent neural network include: the number of filters in the convolutional layer , Number of LSTM units , the number of units of the gated recurrent unit GRU and the dropout rate of the dropout layer ; The optimization algorithm adopts the improved Fire Eagle optimization algorithm. The specific process of optimizing the hyperparameters of the double recurrent neural network using the improved Fire Eagle optimization algorithm is as follows: Encode the hyperparameters of the double recurrent neural network into a unified solution vector: ; Randomly generate an initial fire eagle population, each fire eagle individual in the fire eagle population represents a solution vector ; Calculate the fitness value of each fire eagle individual in the fire eagle population, and re-divide the fire eagle individuals in the fire eagle population into fire eagle individuals and prey according to the fitness value; Simulate arson, driving away and capturing strategies to update the locations of individual fire hawks and prey; Perform local search for the best fire eagle individual in the current population; When local search satisfies: , or the current number of iterations reaches the preset maximum number of iterations, output the current optimal solution And the corresponding objective function value , the current optimal solution As the optimal hyperparameter; Indicates The location of each Fire Eagle individual, Indicates The position of each Fire Eagle individual after local search optimization; Represents the fitness function value.

5. The DO concentration prediction method based on the double-circulation neural network of improved FHO according to claim 4 is characterized in that: Simulate arson strategy: The leader fire eagle individual, that is, the best fire eagle individual in the current fire eagle set, generates the fire source location: ； In the formula, Indicates The location of the fire source; Indicates The location of the leader Fire Hawk individuals; It indicates the fire source control coefficient; Indicates A random perturbation vector; Simulated expulsion strategy: prey fleeing from fire: ； In the formula, Indicates The position of each prey after the expulsion strategy is updated; express The current location of the prey; represents the escape intensity coefficient; Represents a randomly generated safe location; represents the disturbance amplitude; represents a random vector; Simulated capture strategy: Fire hawk individuals move towards prey and fire: ； In the formula, Indicates The positions of individual fire eagles after the simulated capture strategy update; Indicates The current location of each Fire Hawk individual; Represents the weight coefficient of the fire eagle individual moving towards the current optimal prey position; The weight coefficient that indicates the movement of individual fire eagles toward the fire source; Indicates the current optimal prey location.

6. The DO concentration prediction method based on the double-circulation neural network of improved FHO according to claim 5 is characterized in that: In the capture strategy, inertia weight is introduced Control search criteria: 。 7. The DO concentration prediction method based on the double-circulation neural network of improved FHO according to claim 6 is characterized in that: The trigger conditions for local search include: Periodic trigger: Every The iteration triggers a local search: ； In the formula, Represents a trigger signal, which is used to decide whether to perform a local search; Indicates the current iteration number; Indicates the periodic interval that triggers local search; Fitness stagnation trigger: The best Fire Eagle individual continues No improvement triggers a local search: ； In the formula, Represents the fitness function value of the best fire eagle individual in the current iteration; Represents the fitness function value of the best fire eagle individual in the previous iteration; Before The fitness function value of the best fire eagle individual in the iteration; Diversity trigger: Firehawk population standard deviation falls below set threshold Trigger a local search: ； In the formula, The fire eagle population is The standard deviation of the dimension; Indicates the total number of dimensions; When the local search is triggered, the best Fire Eagle individual is selected to perform local search optimization: ； In the formula, represents the local learning rate; When the optimal solution after local search optimization is better than the current optimal solution, the current optimal solution is replaced.

8. The DO concentration prediction method based on the double-circulation neural network of improved FHO according to claim 7 is characterized in that: Multi-dimensional water data include temperature, pH value, flow rate, mixed liquor suspended solids concentration (MLSS), effluent total nitrogen, effluent ammonia nitrogen, and DO of the anoxic section of the oxidation ditch; The preprocessing process includes: cleaning the collected multi-dimensional water data to remove missing values ​​and outliers; The multi-dimensional data of the cleaned water body are normalized.

9. The DO concentration prediction method based on the double-circulation neural network of improved FHO according to claim 8 is characterized in that: The performance of the optimal double recurrent neural network is evaluated using mean square error, root mean square error, and mean absolute error.

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