Fish growth prediction method based on depth nonlinear state space model

Abstract

The invention discloses a fish growth prediction method based on a depth nonlinear state space model, and belongs to the technical field of intelligent aquaculture. In the method, a fish growth depth state space model is established, a dynamic stage division mechanism is designed, and a different-speed growth gradient and an environmental cumulative effect are fused to construct a stage transition criterion; adaptive switching of model parameters is realized through a gating network, the problem of stage boundary fuzziness caused by traditional fixed threshold division is broken through, biological mechanism equations such as metabolic rate temperature response and density inhibition effect are embedded into a neural network, and interpretable coupling modeling of environment-management factors is realized through regularization constraint of a model parameter space; cross-scale causal association modeling is realized, a metabolism-growth cross-scale causal chain is constructed in combination with biometric prior, and the bottleneck that a traditional black box model cannot associate microscopic physiology and macroscopic growth is broken.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent aquaculture technology, and specifically relates to a fish growth prediction method based on a deep nonlinear state space model, which is particularly suitable for dynamic modeling and prediction of fish growth processes under complex environmental conditions. Background Art

[0002] Recirculating Aquaculture Systems (RAS) is a highly efficient and intensive aquaculture model that recycles aquaculture water through water treatment systems, reducing water resource consumption and environmental pollution. However, the fish growth process is dynamically influenced by multiple factors, such as water temperature, dissolved oxygen, and feed intake, exhibiting complex nonlinear characteristics, making precise regulation a significant challenge.

[0003] Traditional state-space models have significant limitations in modeling fish growth. On the one hand, traditional models often use linear state transition equations, which make it difficult to accurately describe the nonlinear interactions between environmental factors (such as the drop in dissolved oxygen 6 hours after feeding) and time-delayed responses. On the other hand, fish growth has distinct stage characteristics (such as the larval stage, rapid growth period, and mature stage), and the metabolic patterns of each stage vary significantly. Traditional methods usually rely on fixed thresholds to divide the stages, resulting in blurred control boundaries and difficulty in adapting to individual growth differences. In addition, RAS systems have strict safety constraints (for example, dissolved oxygen below 4 mg / L can easily cause fish mortality), but existing black-box models lack the embedded biological mechanisms and cannot establish an explainable basis for regulatory decisions.

[0004] Existing technologies mainly rely on empirical regulation or simple linear models, which have the following defects: (1) The model's expressive power is insufficient, making it difficult to capture the complex nonlinear dynamics of fish growth; (2) The stage division mechanism is rigid, making it impossible to accurately identify growth transition points; (3) There is a lack of biological mechanism constraints, and the model's prediction results may violate the physiological laws of fish; (4) Safety constraints are difficult to integrate into the decision-making process, and the regulation risk is high; (5) There is a lack of quantitative correlation between microscopic metabolic mechanisms and macroscopic growth performance, and the model has poor interpretability.

[0005] Therefore, there is an urgent need for a fish growth prediction method that can integrate deep nonlinear modeling and biological mechanism constraints to improve the precise regulation capability of the RAS system. Summary of the Invention

[0006] This paper addresses the nonlinear dynamic characteristics, stage transition characteristics, and safety constraints of fish growth in industrial recirculating aquaculture, and proposes a fish growth prediction method and system based on a deep nonlinear state-space model. This method replaces the linear structure of traditional state-space models with a deep learning model, establishing a high-dimensional nonlinear mapping relationship that accurately describes the time-varying coupling effects of multiple factors, such as water temperature, dissolved oxygen, and feeding, during fish growth. It also constructs a dynamic stage division mechanism, integrating allometric growth gradients and environmental cumulative effects as stage transition criteria, and achieves adaptive switching of model parameters through a gating network. Furthermore, biological mechanism equations, such as metabolic rate temperature response and density inhibition effects, are embedded in the neural network architecture. Regularization constraints are used to ensure the biological rationality of the model output, ultimately achieving accurate prediction and intelligent regulation of fish growth.

[0007] The present invention adopts the following technical solutions: The present invention provides a fish growth prediction method based on a deep nonlinear state space model, comprising the following steps: Obtaining input variables, state variables, and output variables, wherein the input variables include fish biological phenotypes, environmental factors, and nutritional parameters related to fish growth; the state variables are fish growth factors; and the output variables are fish growth indicators; Based on the input variables, state variables and output variables, a nonlinear state space model of fish growth depth is established based on a gated recurrent neural network; the nonlinear state space model of fish growth depth includes: a dynamic stage judgment module and a time-lag feature extraction module; the dynamic stage judgment module judges different growth stages based on allometric growth rate and cumulative environmental stress, the allometric growth rate is calculated using fish biological phenotypes related to fish growth in the input variables, and the cumulative environmental stress is obtained by calculating environmental factors in the input variables; the time-lag feature extraction module extracts time-lag features related to current decisions from historical environmental sequences to quantify the delayed impact of environmental factors; Training the fish growth depth nonlinear state space model; The trained fish growth depth nonlinear state space model is used to predict fish growth and obtain fish growth indicators.

[0008] Furthermore, the fish biological phenotype includes fish body length and weight, the environmental factors include dissolved oxygen, pH value and water temperature, the nutritional parameters include feed amount and breeding density value; the fish growth factors include: metabolic rate, enzyme activity and cortisol concentration; the fish growth indicators include body length and weight gain.

[0009] Furthermore, the dynamic stage discrimination module The calculation is as follows: ; ; ;in, Indicates time, , is a 24-hour historical window, 、 Respectively indicate the time 、 The water temperature at is the allometric growth rate, is the cumulative amount of link stress, is the allometric coefficient, defined as: , For weight, is the body length; 、 Respectively indicate the time 、 dissolved oxygen at 100 ℃; For the learnable model parameters, a three-stage probability distribution is output, where the stage with the largest probability value is determined as the current growth stage.

[0010] Furthermore, the time-delay feature extraction module extracts the time-delay features of the input environmental factors through the nonlinear time-delay convolutional network TCN, thereby aligning the time scale with the discrete artificial intervention input variables. The calculation formula is as follows: ; ; ;in is the input environmental factor, , is a 24-hour historical window, 、 、 Respectively indicate the time Water temperature, dissolved oxygen and pH value at that time, 、 、 Respectively indicate the time Water temperature, dissolved oxygen and pH value at that time; is the environmental factor variable after time lag correction, 、 、 They represent the time after time lag correction respectively. Water temperature, dissolved oxygen and pH value at that time, Calculate according to the following formula: ;in, is the expansion factor, is the convolution kernel size, Learnable parameters, express, represents the characteristics after time lag correction.

[0011] Furthermore, in the fish growth deep nonlinear state space model, the deep state space equation and observation equation established based on the gated recurrent neural network include: ; = ;in, is the growth factor vector, is the input vector, is the state transition model, is the state transition model parameter vector, is the observation model, is the observation model parameter vector, , are the system and observation noise, respectively; In order to incorporate the state equation model into the phase transition criterion, Adopting a deep fully connected network design to achieve nonlinear mapping learning from the key latent variable space to the output space; is the body length of the fish; For weight.

[0012] Furthermore, training the fish growth depth nonlinear state space model includes: Using historical aquaculture data and aquaculture experimental data, we designed a growth state space model loss function. We adopted a fully supervised training paradigm and a gradient descent algorithm. With the goal of minimizing the loss, we continuously adjusted the model parameters and ultimately obtained the parameter solution for the fish growth model. The parameter solution of the fish growth model is used as the initial parameter solution, a reinforcement learning solution algorithm is established, the fish growth model solution process is converted into a state solution space path planning problem, and the solution space exploration path is expanded.

[0013] Furthermore, the loss function includes: ;in, For phenotype prediction loss, ; , is the actual change in body length and weight, , Output the changes in body length and weight for the model prediction; is the metabolic constraint loss, ,in For reference water temperature The basal metabolic rate under the condition of β is obtained through experimental test calibration. is the activation energy, is the gas constant; is the metabolic rate, is the water temperature; For biochemical related losses, ;in and To measure enzyme activity and cortisol concentration; and Output enzyme activity and cortisol concentration were predicted for the model; , , is the weight hyperparameter, is the model parameter regularization term, is the state transition model parameter vector, is the observation model parameter vector.

[0014] Furthermore, the parameter solution of the fish growth model is used as the initial parameter solution, and a reinforcement learning solution algorithm is established to transform the fish growth model solution process into a state solution space path planning problem, and expand the solution space exploration path, including: State space variables Defined as: ;in, is the growth factor vector in the state space model, is the input vector, Historical forecast error series, used to capture model dynamic deviations; represents the model prediction output vector, represents the historical observation vector.

[0015] Action space variables Defined as: ;in, is the maximum adjustment step of the model parameters, is the growth state model parameter adjustment value, .

[0016] The reward function of the reinforcement learning solution algorithm is designed as: ;in, is the prediction error of the current step of the growth model, and the exponential decay form is used to reduce the error sensitivity. is a saturation function, normalizing the biological constraint rules to the interval [-1, 1], is the biological constraint function, through the step function , embedding biological constraints during fish growth into the reward function, constraining the algorithm to search the range of model parameters, biological constraints include: non-negative growth , the bait coefficient does not exceed the upper limit , impose penalties on violations of constraints; policy entropy Encourage the algorithm to explore diverse solutions within the feasible solution space, expand the growth model solution search space, and prevent the search strategy from converging to the local optimum too early; , , are regularization hyperparameters respectively; Training and solving are performed based on the Actor-Critic reinforcement learning algorithm.

[0017] Compared with the existing technology, the present invention has the following beneficial effects: In the present invention, a fish growth depth state space model is established, a dynamic stage division mechanism is designed, the allometric growth gradient and the environmental cumulative effect are integrated to construct the stage transition criterion, and the model parameters are adaptively switched through the gated network, breaking through the stage boundary fuzzy problem caused by the traditional fixed threshold division, and the biological mechanism equations such as metabolic rate temperature response and density inhibition effect are embedded in the neural network. By regularizing the constraint model parameter space, the interpretable coupling modeling of environment-management factors is realized; cross-scale causal association modeling is realized, and the cross-scale causal chain of metabolism-growth is constructed in combination with biostatistical priors, breaking the bottleneck that the traditional black box model cannot associate microphysiology with macro growth. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0019] Figure 1 A deep state space model diagram according to an embodiment of the present invention; Figure 2 This is a block diagram of a reinforcement learning solution algorithm in an embodiment of the present invention; Figure 3 This is a block diagram of the coupling relationship between the deep state space model and reinforcement learning in an embodiment of the present invention. DETAILED DESCRIPTION

[0020] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0021] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the numbers used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0022] like Figure 1 As shown, in this embodiment, a fish growth prediction method based on a deep nonlinear state space model specifically includes the following steps: S1. Obtain input variables, state variables, and output variables; The model variables are divided into input variables, state variables and output variables. The input variables are composed of three variables related to fish growth: fish biological phenotype, environmental factors and nutritional parameters. The fish biological phenotype variable is the fish body length. and weight etc., and the environmental factor variable is dissolved oxygen , pH value and water temperature etc., and the nutritional parameter variable is the amount of feed and stocking density wait, is time. Input variable The specific definition is shown in formula (1): (1) The state variable is defined as the fish growth factor, which is a variable that plays a key role in the growth of fish but is difficult to measure directly. In this embodiment, the state variable is the metabolic rate , enzyme activity and cortisol concentrations etc., state variables The specific definition is shown in formula (2): (2) Output variables are defined as the growth indicators of fish, such as body length and weight increment, etc. Output variables The specific definition is shown in formula (3): (3) S2. Based on the input variables, state variables and output variables, a nonlinear state space model of fish growth depth is established based on a gated recurrent neural network; In this embodiment, a fish growth state space model is established. Through the fish growth factor, the fish farming input variable space is coupled with the fish growth index output variable space. By transferring the fish growth state space, the relationship between farming input and fish growth is found, thereby revealing the law of fish growth. The traditional state space equations are shown in Equations (4)-(5): (4) (5) in, is the state transition matrix, describing the state transition law of fish growth factors, is the input matrix, describing the influence of input variables on state transition, is the output matrix, describing the intrinsic relationship between growth factors and fish growth indicators. And, , and They are all linear or simple nonlinear forms (such as polynomials, Sigmoid). However, fish growth is a dynamic and complex nonlinear process. Traditional state space models are difficult to capture complex dynamic changes and have limited ability to express high-dimensional nonlinearity. In this regard, in this embodiment, a deep nonlinear state space model is established, and a deep learning model is designed to replace the linear state model in the original state space model to achieve the inherent law learning and nonlinear mapping of the fish growth process. By establishing a deep learning model with a high number of parameters, the model feature extraction and nonlinear mapping capabilities are improved, the correctness of law learning is guaranteed, and the deficiency of the original state model that only has linear mapping capabilities is avoided. Then, by establishing an observation model, the variable space of factors affecting fish growth is mapped to the output variable space of fish growth indicators. A deep learning nonlinear model is also established to ensure the accuracy of the model and explore the nonlinear dynamic laws of fish growth. The deep state space equations are shown in Equations (6)-(7): (6) = (7) in, is the growth factor vector, is the input vector (including fish phenotype, environmental factors, nutritional parameters), is the state transition model, is the state transition model parameter vector, is the observation model, is the observation model parameter vector, , are system and observation noise, respectively. Considering the transitions between fish growth stages and causal associations, a dynamic stage discrimination module and a causal mask matrix (specifically, a causal relationship matrix between growth and biological factors, where relevant values ​​are 1 and irrelevant values ​​are 0) are introduced to automatically discriminate fish growth stage transitions and implement causal constraints for hidden state learning, further optimizing the fish growth state space model.

[0023] (1.1) Dynamic stage discrimination module: Different growth stages of fish correspond to different growth patterns. The fish growth cycle can be divided into juvenile stage, rapid growth stage and adult stage. This embodiment designs the allometric growth rate and cumulative amount of link stress To determine different growth stages, the allometric growth rate uses input variables Medium body length and weight The cumulative amount of environmental stress is calculated by The environmental factors are calculated and the growth stage division comprehensively considers the growth rate mutation (internal factors) and the accumulation of environmental stress (external factors), overcoming the limitations of traditional fixed threshold division and dynamic stage discrimination module. The calculation formulas are shown in (8)-(10).

[0024] (8) (9) (10) in is the allometric coefficient, defined as: (11) For the learnable model parameters, a three-stage probability distribution is output, where the stage with the largest probability value is determined as the current growth stage.

[0025] (1.2) Time-delay feature extraction module: In factory-scale recirculating aquaculture, environmental factors (such as water temperature and dissolved oxygen) have a significant time-lag effect on the regulation of fish growth. For example, after the feeding action is executed, the dissolved oxygen will decrease after 6-8 hours, and after the density is adjusted, the metabolic rate of the fish will be delayed for 12-24 hours. Traditional temporal neural networks (such as RNN and LSTM) are difficult to effectively capture such long time delays and multi-scale coupling relationships, resulting in the failure of fish growth analysis and decision-making strategies in actual scenarios due to ignoring delayed feedback. In order to accurately capture the delay effect, the time-lag features related to the current decision are extracted from the historical environmental sequence to quantify the delayed impact of environmental factors. In this embodiment, a temporal convolutional network (TCN) is designed to capture the delayed effect of environmental factors, and an expansion factor is designed. To control the receptive field and capture the delay patterns of different time scales, the network computing unit is shown in Equation (12): (12) in, is the expansion factor, is the convolution kernel size, Learnable parameters. Specifically, in this embodiment, the input environmental factors are subjected to time-lag feature extraction, thereby aligning the time scale with the discrete human intervention input variables, as shown in Equations (13)-(15): (13) (14) (15) in, , is a 24-hour historical window, is the environmental factor variable after time lag correction, is a nonlinear time-delay convolutional network with Equation (12) as the computational unit.

[0026] (1.3), Deep State Space Model: Based on the results of biological element fusion, a deep state-space model is established based on the gated recurrent unit (GRU). The GRU (Gated Recurrent Unit) is an improved recurrent neural network (RNN) designed to address the long-term dependency learning difficulties and gradient vanishing / exploding problems of traditional RNNs. By introducing the update gate and reset gate, the GRU can dynamically control the retention and forgetting of information, significantly improving training efficiency and model performance while maintaining the ability to model time series. The state equation and observation equation are shown in Equations (16)-(17): (16) = (17) in, In order to incorporate the state equation model into the phase transition criterion, A deep fully connected network design is used to achieve nonlinear mapping learning from the key latent variable space to the output space.

[0027] S3, training the fish growth depth nonlinear state space model; First, we use historical breeding data and breeding experimental data to design the growth state space model loss function, adopt a fully supervised training paradigm, use the gradient descent algorithm, minimize the loss as the goal, continuously adjust the model parameters, and finally obtain the model parameter solution. To further improve the accuracy and robustness of the model, we use the above solution as the initial solution, design the reward function, and use the Actor-Critic optimization strategy to conduct free exploration in the solution space to prevent the search strategy under supervised learning from converging to the local optimum too early. The model optimal solution training framework is shown in the figure below. Figure 3 As shown. Among them, the loss function is designed as follows: (1) Phenotype prediction loss ( ): (18) in , is the actual change in body length and weight, , The model predicts the change in body length and weight, and the loss constrains the latent variable Macroscopic phenotypes ( , ) mapping capabilities.

[0028] (2) Loss of metabolic constraint ( ): (19) in For reference water temperature The basal metabolic rate under the condition of β is obtained through experimental test calibration. is the activation energy, is the gas constant. is the metabolic rate, is the water temperature. The Arrhenius equation is used to quantify the effect of temperature on reaction rates. This loss is used to constrain biological mechanisms and ensure that metabolic rate predictions conform to biophysical laws.

[0029] (3) Loss of biochemical association ( ): (20) in and To measure enzyme activity and cortisol concentration, and The model predicts the output enzyme activity and cortisol concentration; through this loss, the latent variable is forced The mapping relationship with biochemical indicators (enzyme activity and cortisol concentration) constrains the prediction accuracy of latent variables and constructs an interpretable causal chain between metabolic state (micro) and phenotypic traits (macro).

[0030] (4) Total loss ( ): (twenty one) in , , is a weight hyperparameter that balances the importance of each loss. is the model parameter regularization term to prevent the model from overfitting, is the state transition model parameter vector, is the observation model parameter vector.

[0031] The core variable of the reinforcement learning method is the current model observation state space variable , the model outputs the execution action space variable and the reward function , For the long-term accumulation of rewards, the model learning goal is to learn a set of strategies through continuous trial and error ( ), that is, in the known In the environment, give the execution action , so that it accumulates rewards in the long run maximize.

[0032] In step S2, a fish growth state space model is established, and the model is trained and solved using a fully supervised learning method. The model parameters are continuously adjusted through the gradient back propagation algorithm. and , so that the loss function Minimize the loss function to obtain the model parameter solution. However, the fish growth cycle is a complex dynamic nonlinear system with a long growth cycle (several months to a year / cycle). It is difficult to collect growth data that includes all environmental factors and nutritional parameters in one growth cycle. The limited data set limits the size of the model parameter solution space, and the fully supervised training method stipulates that the loss function must be minimized. The search for a solution for the target also limits the search path for the solution. Therefore, based on the data of a growth cycle, the growth model obtained by fully supervised training is difficult to accurately reveal the growth pattern and cannot guarantee the accuracy and robustness of the model. To address the above problems, this embodiment uses the fish growth model parameters obtained by supervised learning as the initial parameter solution. On this basis, a reinforcement learning solution algorithm is established to transform the fish growth model solution process into a state solution space path planning problem, breaking through the limitations of historical breeding / experimental data, expanding the solution space exploration path, and thus improving the generalization and robustness of the model.

[0033] (3.1) Definition of core variable space: State space variables The definition is as shown in formula (20): (twenty two) in, is the growth factor vector in the state space model, is the input vector, Historical forecast error series, used to capture model dynamic deviations. represents the model prediction output vector, Represents the historical observation vector. Growth factors encode the inherent laws of organisms, and cultivation input It reflects external intervention, and historical errors provide adaptive feedback. The three together ensure the completeness of state representation.

[0034] Action space variables The definition is as shown in formula (23): (twenty three) in, is the maximum adjustment step of the model parameters, is the growth state model parameter adjustment value, .

[0035] (3.2) Reinforcement Learning Reward Function The reward function design of the reinforcement learning solution algorithm is shown in formula (24): (twenty four) in, is the prediction error of the current step of the growth model, and the exponential decay form is used to reduce the error sensitivity. is a saturation function, normalizing the biological constraint rules to the interval [-1, 1], is the biological constraint function, through the step function , embed the biological constraints of fish growth into the reward function, constrain the algorithm to search the range of model parameters, and the biological constraints are non-negative growth , the bait coefficient does not exceed the upper limit etc., impose penalties on violations of constraints. Policy entropy The algorithm is encouraged to explore diverse solutions in the feasible solution space, expand the growth model solution search space, and prevent the search strategy from converging to the local optimum too early. , , are the regularization hyperparameters respectively.

[0036] (3.3) Reinforcement learning optimization solution In this embodiment, the training solution is based on the Actor-Critic reinforcement learning algorithm. This algorithm is a hybrid optimization method that combines policy optimization (Actor) and value function estimation (Critic). It aims to improve learning efficiency and stability through the synergy of the two. Its core principles can be divided into the following key parts: 1) The policy optimization network (Actor) learns to find the optimal policy function , according to the current state Select parameter adjustment amount , ensure that Give the best adjustment value under the state , so as to maximize the reward accumulation. In this embodiment, the policy function is modeled based on the Transformer architecture to fully ensure the model's policy feature learning ability. 2) Value Function Network (Critic) Learning , evaluate the value of the state-action pair, and provide feedback on the optimization direction of the Actor by calculating the estimated value of the expected cumulative reward generated by the policy function given to the Actor, thereby guiding the Actor's optimization direction.

[0037] Compute the value of the advantage function at each time step using the generalized advantage estimate: (25) Among them, TD error (Temporal Difference Error) , , indicating that the current strategy is better than the average expectation within time T, the action should be strengthened, otherwise , indicating that the current strategy is not good and needs to be suppressed.

[0038] Policy loss function: (26) Among them, the importance adopts the ratio , through the clip mechanism, Limit it to [0.8, 1.2] to prevent policy mutation.

[0039] Value loss function: (27) Among them, the target value .

[0040] Through the stable strategy search capability of PPO and combined with domain knowledge constraints, efficient adaptive optimization of fish growth model parameters is achieved, providing a solid algorithmic foundation for intelligent aquaculture systems.

[0041] In the above embodiment, a state-space model of fish growth depth is established, a dynamic stage division mechanism is designed, the allometric growth gradient and the environmental cumulative effect are integrated to construct a stage transition criterion, and the adaptive switching of model parameters is realized through a gating network, breaking through the fuzzy stage boundary problem caused by the traditional fixed threshold division, and the biological mechanism equations such as the metabolic rate temperature response and the density inhibition effect are embedded in the neural network. By regularizing the constraint model parameter space, the interpretable coupling modeling of the environment-management factor is realized; cross-scale causal association modeling is realized, and the cross-scale causal chain of metabolism-growth is constructed in combination with biostatistical priors, breaking the bottleneck that the traditional black box model cannot associate microphysiology with macro growth.

[0042] In order to verify the effectiveness of the method in the above embodiment, the inventors conducted the following experiments and evaluations: (1) Data preparation Simulation environment construction: Based on reinforcement learning simulation platforms like Gym, a dynamic aquaculture simulation system was constructed to simulate the coupled relationships between water temperature, dissolved oxygen, feeding behavior, and fish growth. This system supports real-time simulation of multi-factor perturbations (such as sudden temperature changes and sudden drops in dissolved oxygen). The system uses a 1-hour time step and a 30-day experimental period. The initial fish weight is 500g ±10%, the water temperature fluctuates between 24-32°C, and the dissolved oxygen safety threshold is 4 mg / L.

[0043] Actual data collection: An actual breeding experimental platform is established at the cooperative breeding base to collect data on the entire fish growth cycle, such as hourly water temperature, dissolved oxygen, pH value, daily feeding amount, density adjustment records (marked with feed brand and feeding time), weekly measurements of body length and weight, and monthly random inspections of growth factor indicators (cortisol concentration, enzyme activity), etc.

[0044] (2) Verification of the growth state space model Steady-state validation: A controlled experimental aquaculture environment was established with constant water temperature, dissolved oxygen, and a standard photoperiod. Data on the length and weight of the target fish were collected throughout their growth cycle. By comparing the traditional Von Bertalanffy model with the dynamic energy budget (DEB) model, the root mean square error (RMS) of the model's length and weight predictions was quantified, validating its ability to represent basic growth patterns. Combined with correlation analysis between growth factors and phenotypic traits, the model's interpretability of mechanisms such as energy allocation and allometric growth was analyzed to ensure physiological consistency.

[0045] Dynamic Disturbance Verification: Simulate dynamic disturbances in aquaculture scenarios by injecting time-series environmental disturbances. Evaluate the model's predictive stability and the convergence efficiency of the reinforcement learning algorithm during disturbances. Design a hysteresis effect test, inputting dissolved oxygen drop data with a delay, to verify the model's adaptability to time-delayed environments. Statistically analyze violations of rules such as growth non-negativity and feed coefficient thresholds to ensure the algorithm's biological plausibility in dynamic scenarios.

[0046] Validation under extreme conditions: We constructed scenarios involving extreme events such as sudden drops in dissolved oxygen, high temperature stress, and feeding interruptions, testing the response time required to adjust model parameters to restore prediction accuracy. We analyzed the physiological plausibility of changes in growth factors such as metabolic rate and energy reserves under these extreme conditions, and calculated rule violation rates. We conducted cross-species stress testing, migrating model parameters from a single cell to datasets of other fish species to verify the generalization error increase, thereby overcoming the limitations of traditional models' lack of cross-scenario adaptability.

[0047] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A fish growth prediction method based on a deep nonlinear state space model, characterized in that: The following steps are involved: Obtaining input variables, state variables, and output variables, wherein the input variables include fish biological phenotypes, environmental factors, and nutritional parameters related to fish growth; the state variables are fish growth factors; and the output variables are fish growth indicators; Based on the input variables, state variables and output variables, a fish growth depth nonlinear state space model is established based on a gated recurrent neural network; the fish growth depth nonlinear state space model includes: a dynamic stage discrimination module and a time lag feature extraction module; The dynamic stage judgment module determines different growth stages based on the allometric growth rate and the cumulative amount of environmental stress. The allometric growth rate is calculated using the fish biological phenotype related to fish growth in the input variables, and the cumulative amount of environmental stress is calculated using the environmental factors in the input variables. The time lag feature extraction module extracts the time lag features related to the current decision from the historical environmental sequence and quantifies the delayed impact of the environmental factors. Training the fish growth depth nonlinear state space model; The trained fish growth depth nonlinear state space model is used to predict fish growth and obtain fish growth indicators.

2. The fish growth prediction method based on deep nonlinear state space model according to claim 1, characterized in that: The fish biological phenotype includes fish body length and weight, the environmental factors include dissolved oxygen, pH value and water temperature, the nutritional parameters include feed amount and breeding density value; the fish growth factors include metabolic rate, enzyme activity and cortisol concentration; the fish growth indicators include body length and weight gain.

3. The fish growth prediction method based on deep nonlinear state space model according to claim 1, characterized in that: Dynamic stage discrimination module The calculation is as follows: ； ； ； in, Indicates time, , is a 24-hour historical window, 、 Respectively indicate the time 、 The water temperature at is the allometric growth rate, is the cumulative amount of link stress, is the allometric coefficient, defined as: , For weight, is the body length; 、 Respectively indicate the time 、 dissolved oxygen at 100 ℃; For the learnable model parameters, a three-stage probability distribution is output, where the stage with the largest probability value is determined as the current growth stage.

4. The fish growth prediction method based on deep nonlinear state space model according to claim 3, characterized in that: The time-delay feature extraction module extracts the time-delay features of the input environmental factors through the nonlinear time-delay convolutional network (TCN), thereby aligning the time scale with the discrete human intervention input variables. The calculation formula is as follows: ； ； ； in is the input environmental factor, , is a 24-hour historical window, 、 、 Respectively indicate the time Water temperature, dissolved oxygen and pH value at that time, 、 、 Respectively indicate the time Water temperature, dissolved oxygen and pH value at that time; is the environmental factor variable after time lag correction, 、 、 They represent the time after time lag correction respectively. Water temperature, dissolved oxygen and pH value at that time, Calculate according to the following formula: ;in, is the expansion factor, is the convolution kernel size, Learnable parameters, express, represents the characteristics after time lag correction.

5. The fish growth prediction method based on deep nonlinear state space model according to claim 4, characterized in that: In the fish growth deep nonlinear state space model, the deep state space equation and observation equation established based on the gated recurrent neural network include: ； = ； in, is the growth factor vector, is the input vector, is the state transition model, is the state transition model parameter vector, is the observation model, is the observation model parameter vector, , are the system and observation noise, respectively; In order to incorporate the state equation model into the phase transition criterion, Adopting a deep fully connected network design to achieve nonlinear mapping learning from the key latent variable space to the output space; is the body length of the fish; For weight.

6. The fish growth prediction method based on deep nonlinear state space model according to claim 1, characterized in that: Training the fish growth depth nonlinear state space model comprises: Using historical aquaculture data and aquaculture experimental data, we designed a growth state space model loss function. We adopted a fully supervised training paradigm and a gradient descent algorithm. With the goal of minimizing the loss, we continuously adjusted the model parameters and ultimately obtained the parameter solution for the fish growth model. The parameter solution of the fish growth model is used as the initial parameter solution, a reinforcement learning solution algorithm is established, the fish growth model solution process is converted into a state solution space path planning problem, and the solution space exploration path is expanded.

7. The fish growth prediction method based on deep nonlinear state space model according to claim 6, characterized in that: The loss function includes: ; in, For phenotype prediction loss, ; , is the actual change in body length and weight, , Output the changes in body length and weight for the model prediction; is the metabolic constraint loss, ,in For reference water temperature The basal metabolic rate under the condition of β is obtained through experimental test calibration. is the activation energy, is the gas constant; is the metabolic rate, is the water temperature; For biochemical related losses, ;in and To measure enzyme activity and cortisol concentration; and Output enzyme activity and cortisol concentration were predicted for the model; , , is the weight hyperparameter, is the model parameter regularization term, is the state transition model parameter vector, is the observation model parameter vector.

8. The fish growth prediction method based on deep nonlinear state space model according to claim 1, characterized in that: The parameter solution of the fish growth model is used as the initial parameter solution, and a reinforcement learning solution algorithm is established. The fish growth model solution process is transformed into a state solution space path planning problem, and the solution space exploration path is expanded, including: State space variables Defined as: ;in, is the growth factor vector in the state space model, is the input vector, Historical forecast error series, used to capture model dynamic deviations; represents the model prediction output vector, represents the historical observation vector; Action space variables Defined as: ;in, is the maximum adjustment step of the model parameters, is the growth state model parameter adjustment value, ; The reward function of the reinforcement learning solution algorithm is designed as: ;in, is the prediction error of the current step of the growth model, and the exponential decay form is used to reduce the error sensitivity. is a saturation function, normalizing the biological constraint rules to the interval [-1, 1], is the biological constraint function, through the step function , embedding biological constraints during fish growth into the reward function, constraining the algorithm to search the range of model parameters, biological constraints include: non-negative growth , the bait coefficient does not exceed the upper limit , impose penalties on violations of constraints; policy entropy Encourage the algorithm to explore diverse solutions within the feasible solution space, expand the growth model solution search space, and prevent the search strategy from converging to the local optimum too early; , , are regularization hyperparameters respectively; Training and solving are performed based on the Actor-Critic reinforcement learning algorithm.

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