Fish growth prediction method based on deep nonlinear state-space model

Abstract

The application discloses a fish growth prediction method based on a deep nonlinear state space model, and belongs to the technical field of intelligent aquaculture. In the method, a fish growth deep state space model is established, a dynamic stage division mechanism is designed, a stage transition criterion is constructed by fusing allometric growth gradients and environmental cumulative effects, model parameter adaptive switching is realized through a gate network, a stage boundary ambiguity problem 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, a model parameter space is constrained through regularization, and an environment-management factor is coupled to realize explainable modeling; cross-scale causal correlation modeling is realized, a cross-scale causal chain of metabolism-growth is constructed in combination with biological statistics priori, and a bottleneck that a traditional black box model cannot associate micro physiology with macro growth is solved.

Description

Technical Field

[0001] This invention belongs to the field of intelligent aquaculture technology, specifically relating 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 Technology

[0002] Recirculating aquaculture systems (RAS) are a highly efficient and intensive aquaculture model that recycles aquaculture water through a water treatment system, reducing water consumption and environmental pollution. However, fish growth is dynamically influenced by multiple factors such as water temperature, dissolved oxygen, and feed intake, exhibiting complex nonlinear characteristics that pose significant challenges to precise control.

[0003] Traditional state-space models have significant limitations in fish growth modeling. On the one hand, traditional models often employ linear state transition equations, making it difficult to accurately describe the nonlinear interactions between environmental factors (such as dissolved oxygen decrease 6 hours after feeding) and time-delay responses. On the other hand, fish growth exhibits distinct stages (such as larval, rapid growth, and maturity stages), with significant differences in metabolic patterns across these stages. Traditional methods typically rely on fixed thresholds for stage division, leading to blurred regulatory boundaries and difficulty in adapting to individual growth differences. Furthermore, RAS systems have strict safety constraints (such as dissolved oxygen levels below 4 mg / L easily causing fish mortality), but existing black-box models lack biological mechanism embeddings, failing to establish interpretable regulatory decision-making criteria.

[0004] Existing technologies mainly rely on empirical regulation or simple linear models, which have the following defects: (1) The model has insufficient expressive power and it is difficult to capture the complex nonlinear dynamics of fish growth; (2) The stage division mechanism is rigid and cannot accurately identify growth transition points; (3) There is a lack of biological mechanism constraints, and the model 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 micro-metabolic mechanisms and macro-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 invention addresses the nonlinear dynamic characteristics, stage transition features, and safety constraints of fish growth processes in factory-scale recirculating aquaculture systems. It 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. Simultaneously, it constructs a dynamic stage division mechanism, integrating allometric growth gradients and environmental cumulative effects as stage transition criteria, and uses a gating network to achieve adaptive switching of model parameters. Furthermore, it embeds biological mechanism equations such as metabolic rate-temperature response and density inhibition effects into the neural network architecture, ensuring the biological rationality of the model output through regularization constraints, ultimately achieving accurate prediction and intelligent control of the fish growth process.

[0007] The present invention adopts the following technical solution:

[0008] This invention provides a method for predicting fish growth based on a deep nonlinear state-space model, comprising the following steps:

[0009] The system acquires input variables, state variables, and output variables. The input variables include fish biophenotypes, environmental factors, and nutritional parameters related to fish growth. The state variables are fish growth factors. The output variables are fish growth indicators.

[0010] Based on the input variables, state variables, and output variables, a nonlinear state-space model of fish growth depth is established using a gated recurrent neural network. This model includes a dynamic stage discrimination module and a time-delay feature extraction module. The dynamic stage discrimination module determines different growth stages based on allometric growth rate and cumulative environmental stress. The allometric growth rate is calculated using fish biophenotypes related to fish growth from the input variables, and the cumulative environmental stress is obtained from environmental factors in the input variables. The time-delay feature extraction module extracts time-delay features related to the current decision from historical environmental sequences to quantify the delayed impact of environmental factors.

[0011] Train the nonlinear state-space model of the fish's growth depth;

[0012] Fish growth is predicted using a trained nonlinear state-space model of fish growth depth, and fish growth indices are obtained.

[0013] 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 stocking density value; the fish growth factors include metabolic rate, enzyme activity and cortisol concentration; and the fish growth indicators include body length and weight gain.

[0014] Furthermore, the dynamic stage discrimination module The calculation is as follows: ; ; ;in, Indicates time, This serves as a 24-hour historical window. , They represent the time as follows , The water temperature at that time Allometric growth rate, This represents the cumulative amount of environmental stress. The allometric growth coefficient is defined as: , For weight, Body length; , They represent the time as follows , Dissolved oxygen at that time; The parameters of the learnable model are output as a three-stage probability distribution, where the stage with the highest probability value is determined as the current growth stage.

[0015] Furthermore, the time-delay feature extraction module extracts time-delay features from the input environmental factors using a 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 For the input environmental factors, This serves as a 24-hour historical window. , , They represent the time as follows Water temperature, dissolved oxygen, and pH value at that time , , They represent the time as follows Water temperature, dissolved oxygen, and pH value at that time; These are environmental factor variables after time lag correction. , , These represent the time after time delay correction. Water temperature, dissolved oxygen, and pH value at that time Calculate according to the following formula: ;in, As the expansion factor, The kernel size is the convolution kernel size. For learnable parameters, This indicates the characteristics after time delay correction.

[0016] Furthermore, in the nonlinear state-space model of fish growth depth, the depth state-space equation and observation equation established based on the gated recurrent neural network include: ; = ;in, For growth factor vectors, For the input vector, For state transition model, For the state transition model parameter vector, For observation models, For the observation model parameter vector, To observe noise; To incorporate the state equation model of the stage transition criterion, A deep fully connected network design is adopted to achieve nonlinear mapping learning from the key latent variable space to the output space; The length of a fish's body; For body weight.

[0017] Further, training the nonlinear state-space model of fish growth depth includes:

[0018] Using historical aquaculture data and aquaculture experimental data, a loss function for the growth state space model was designed. A fully supervised training paradigm was adopted, and the gradient descent algorithm was used to continuously adjust the model parameters with the goal of minimizing the loss, and finally the solution of the fish growth model parameters was obtained.

[0019] Using the fish growth model parameter solution as the initial parameter solution, a reinforcement learning solution algorithm is established, transforming the fish growth model solution process into a state solution space path planning problem, and expanding the solution space exploration path.

[0020] Furthermore, the loss function includes:

[0021] ;in, To predict loss based on phenotype, ; , This represents the actual change in body length and weight. , The model predicts the changes in body length and weight. For metabolic constraint loss, ,in For reference water temperature The basal metabolic rate was determined through experimental testing. For activation energy, It is the gas constant; Metabolic rate, Water temperature; For biochemical associated losses, ;in and To measure enzyme activity and cortisol concentration; and The model was used to predict the output enzyme activity and cortisol concentration. , , For weight hyperparameters, For model parameter regularization, For the state transition model parameter vector, This is the parameter vector for the observation model.

[0022] Furthermore, using the fish growth model parameter solution as the initial parameter solution, a reinforcement learning solution algorithm is established, transforming the fish growth model solution process into a state solution space path planning problem, and expanding the solution space exploration path, including:

[0023] State space variables Defined as: ;in, This represents the growth factor vector in the state-space model. For the input vector, This is a historical prediction error sequence used to capture dynamic biases in the model; This represents the model's predicted output vector. This represents the historical observation vector.

[0024] Action space variables Defined as: ;in, To set the maximum adjustment step size for the model parameters, These are the adjustment values ​​for the growth state model parameters. .

[0025] The reward function for the reinforcement learning algorithm is designed as follows: ;in, To reduce the error sensitivity of the current step prediction error in the growth model, an exponential decay method is used. As a saturation function, the biological constraint rules are normalized to the interval [-1, 1]. For biological constraint functions, through step functions The biological constraints during fish growth are embedded into the reward function, constraining the search space range of the model parameters. The biological constraints include: non-negative growth. The feed conversion ratio does not exceed the upper limit. Penalties are imposed for violations of constraints; policy entropy Encourage algorithms to explore diverse solutions within the feasible solution space, expand the search space of the growth model solution, and prevent the search strategy from converging to a local optimum too early. , , These are the regularization hyperparameters;

[0026] The training and solution are based on the Actor-Critic reinforcement learning algorithm.

[0027] Compared with existing technologies, this invention has the following advantages: In this invention, a state space model of fish growth depth is established, a dynamic stage division mechanism is designed, and a stage transition criterion is constructed by integrating allometric growth gradient and environmental cumulative effect. The model parameters are adaptively switched through a gating network, breaking through the problem of stage boundary ambiguity caused by traditional fixed threshold division. Biological mechanism equations such as metabolic rate temperature response and density inhibition effect are embedded in the neural network. The model parameter space is constrained by regularization to achieve interpretable coupling modeling of environmental-management factors. Cross-scale causal association modeling is realized. A cross-scale causal chain of metabolism-growth is constructed by combining biostatistical priors, breaking the bottleneck of traditional black box models that cannot link microscopic physiology and macroscopic growth. Attached Figure Description

[0028] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0029] Figure 1 This is a diagram of a depth state space model in an embodiment of the present invention;

[0030] Figure 2 This is a flowchart of the reinforcement learning solution algorithm in an embodiment of the present invention;

[0031] Figure 3 This is a diagram illustrating the coupling relationship between the deep state space model and reinforcement learning in an embodiment of the present invention. Detailed Implementation

[0032] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0033] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0034] 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:

[0035] S1. Obtain the input variables, state variables, and output variables;

[0036] The model variables are divided into input variables, state variables, and output variables. The input variables consist of three aspects related to fish growth: fish biophenotype, environmental factors, and nutritional parameters. The fish biophenotype variable is fish body length. and weight The environmental factor variable is dissolved oxygen. pH value and water temperature The nutritional parameter variable is the amount of feed. and stocking density value wait, For time. Input variable The specific definition is shown in equation (1):

[0037] (1)

[0038] State variables are defined as fish growth factors, that is, variables that play a key role in fish growth but are difficult to measure directly. In this embodiment, the state variable is the metabolic rate. Enzyme activity and cortisol concentration Etc., state variables The specific definition is shown in equation (2):

[0039] (2)

[0040] Output variables are defined as indicators reflecting fish growth, such as body length and weight gain. The specific definition is shown in equation (3):

[0041] (3)

[0042] 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.

[0043] In this embodiment, a fish growth state space model is established. Through fish growth factors, the input variable space of fish farming and the output variable space of fish growth indicators are coupled. By transferring the fish growth state space, the relationship between farming input and fish growth is sought, thereby revealing the laws governing fish growth. Traditional state space equations are shown in equations (4)-(5):

[0044] (4)

[0045] (5)

[0046] in, This is a state transition matrix, describing the state transition patterns of fish growth factors. The input matrix describes the effect of the input variables on the state transition. The output matrix describes the intrinsic relationship between growth factors and fish growth indicators. Furthermore, , and All are linear or simple nonlinear forms (such as polynomials, sigmoids). 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 nonlinearities. 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. This realizes the learning of the inherent laws of fish growth and nonlinear mapping. By establishing a deep learning model with a high number of parameters, the model's feature extraction and nonlinear mapping capabilities are improved, ensuring the correctness of the law learning and avoiding the shortcomings of the original state model which only has linear mapping capabilities. Then, by establishing an observation model, the variable space of factors affecting fish growth is mapped to the variable space of fish growth index output. Similarly, a deep learning nonlinear model is 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):

[0047] (6)

[0048] = (7)

[0049] in, For growth factor vectors, The input vector includes fish phenotype, environmental factors, and nutritional parameters. For state transition model, For the state transition model parameter vector, For observation models, For the observation model parameter vector, , These are system and observation noise, respectively. Considering the characteristics of fish growth stage transitions and causal relationships, a dynamic stage discrimination module and a causal mask matrix (specifically, a causal relationship matrix with growth and biological factors, where 1 indicates a related relationship and 0 indicates an unrelated relationship) are introduced to achieve automatic discrimination of fish growth stage transitions and causal constraints for latent state learning, further optimizing the fish growth state space model.

[0050] (1.1) Dynamic Stage Judgment Module:

[0051] Different growth stages in fish development correspond to different growth patterns. The fish growth cycle can be divided into the juvenile stage, the rapid growth stage, and the adult stage. This embodiment designs an allometric growth rate. and cumulative environmental stress To determine different growth stages, the allometric growth rate is used as an input variable. medium body length and weight Calculations are performed to determine the cumulative amount of environmental stress through... The growth stage division is obtained through calculation of environmental factors, taking into account both sudden changes in growth rate (internal factors) and cumulative environmental stress (external factors), overcoming the limitations of traditional fixed threshold division, and featuring a dynamic stage discrimination module. The calculation formulas are shown in equations (8)-(10).

[0052] (8)

[0053] (9)

[0054] (10)

[0055] in The allometric growth coefficient is defined as:

[0056] (11)

[0057] The parameters of the learnable model are output as a three-stage probability distribution, where the stage with the highest probability value is determined as the current growth stage.

[0058] (1.2) Time Delay Feature Extraction Module:

[0059] In recirculating aquaculture systems, environmental factors (such as water temperature and dissolved oxygen) exhibit significant time-lag effects on fish growth. For instance, dissolved oxygen levels decrease 6-8 hours after feeding, and fish metabolic rates change 12-24 hours after density adjustments. Traditional temporal neural networks (such as RNNs and LSTMs) struggle to effectively capture these long time lags and multi-scale coupling relationships, causing fish growth analysis and decision-making strategies to fail in real-world scenarios due to neglecting delayed feedback. To accurately capture these delayed effects, time-lag features relevant to the current decision are extracted from historical environmental sequences to quantify the delayed impact of environmental factors. In this embodiment, a Temporal Convolutional Network (TCN) is designed to capture the delayed effects of environmental factors, and an expansion factor is designed. By controlling the receptive field and capturing delay patterns at different time scales, the network computing unit is shown in Equation (12):

[0060] (12)

[0061] in, As the expansion factor, The kernel size is the convolution kernel size. Learnable parameters. Specifically, in this embodiment, the input environmental factors are subjected to time-delay feature extraction, thereby aligning them with the discrete human intervention input variables on a time scale, as shown in equations (13)-(15):

[0062] (13)

[0063] (14)

[0064] (15)

[0065] in, This serves as a 24-hour historical window. These are environmental factor variables after time lag correction. The nonlinear time-delay convolutional network is constructed using Equation (12) as the computational unit.

[0066] (1.3) Depth state space model:

[0067] Based on the fusion results of bio-elements, a deep state-space model is established using a gated recurrent unit (GRU). GRU 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 update and reset gates, GRU can dynamically control the retention and forgetting of information, significantly improving training efficiency and model performance while maintaining temporal modeling capabilities. The state equation and observation equation are shown in equations (16)-(17):

[0068] (16)

[0069] = (17)

[0070] in, To incorporate the state equation model of the stage transition criterion, A deep fully connected network design is adopted to achieve nonlinear mapping learning from the key latent variable space to the output space.

[0071] S3. Train the nonlinear state-space model of the fish growth depth;

[0072] First, using historical and experimental aquaculture data, a loss function for the growth state space model is designed. A fully supervised training paradigm is adopted, and the gradient descent algorithm is used to continuously adjust the model parameters with the goal of minimizing the loss, ultimately obtaining the model parameter solution. To further improve the model's accuracy and robustness, the above solution is used as the initial solution to design a reward function. An Actor-Critic optimization strategy is employed to allow free exploration within the solution space, preventing the search strategy under supervised learning from prematurely converging to a local optimum. The training framework diagram for the optimal model solution is shown below. Figure 3 As shown. The loss function is designed as follows:

[0073] (1) Phenotypic prediction loss ( ):

[0074] (18)

[0075] in , This represents the actual change in body length and weight. , To predict the changes in body length and weight for the model, this loss constraint contains latent variables. For macro phenotypes ( , ) mapping capability.

[0076] (2) Metabolic constraint loss ( ):

[0077] (19)

[0078] in For reference water temperature The basal metabolic rate was determined through experimental testing. For activation energy, is the gas constant. Metabolic rate, The water temperature is used. The effect of temperature on the reaction rate is quantified using the Arrhenius equation. This loss is used to constrain biological mechanisms, ensuring that the predicted metabolic rate conforms to biophysical laws.

[0079] (3) Biochemical associated losses ( ):

[0080] (20)

[0081] in and To measure enzyme activity and cortisol concentration, and The model predicts output enzyme activity and cortisol concentration; this loss is used to force the latent variables. The mapping relationship with biochemical indicators (enzyme activity and cortisol concentration) constrains the prediction accuracy of latent variables, and constructs an explainable causal chain between metabolic state (microscopic) and phenotypic traits (macroscopic).

[0082] (4) Total loss ( ):

[0083] (twenty one)

[0084] in , , The weighting hyperparameter balances the importance of each loss. This is a regularization term for model parameters to prevent overfitting. For the state transition model parameter vector, This is the parameter vector for the observation model.

[0085] The core variable in reinforcement learning methods is the current model's observed state-space variable. The model outputs the action space variables. and reward function , For long-term accumulation of rewards, the goal of model learning is to learn a set of strategies through continuous trial and error. ), that is, in the known In the given environment, provide the action to be performed. This allows it to accumulate rewards over a long period of time. maximize.

[0086] In step S2, a fish growth state space model was established, and the model was trained and solved using a fully supervised learning method. The model parameters were continuously adjusted through the gradient backpropagation algorithm. and , making the loss function Minimize the loss function to obtain the model parameter solution. However, the entire growth cycle of fish is a complex dynamic nonlinear system with a long growth cycle (several months to a year per cycle). It is difficult to collect growth data that includes all environmental factors and nutritional parameters within a single growth cycle. The limited dataset restricts the size of the model parameter solution space, while fully supervised training methods stipulate that the model must minimize the loss function. Searching for solutions based on a single objective limits the search path. Therefore, a growth model obtained through fully supervised training using data from a single growth cycle is insufficient to accurately reveal growth patterns and cannot guarantee model accuracy and robustness. To address these issues, this embodiment uses the fish growth model parameters obtained through supervised learning as the initial parameter solution. Based on this, a reinforcement learning algorithm is established to transform the fish growth model solution process into a state-solution space path planning problem. This overcomes the limitations of historical aquaculture / experimental data, expands the solution space exploration path, and thus improves the model's generalization and robustness.

[0087] (3.1) Definition of core variable space:

[0088] State space variables The definition is shown in equation (20):

[0089] (twenty two)

[0090] in, This represents the growth factor vector in the state-space model. For the input vector, Historical prediction error sequences are used to capture dynamic biases in the model. This represents the model's predicted output vector. This represents a historical observation vector. Growth factors encode intrinsic biological laws and are used for aquaculture inputs. Reflecting external intervention, historical errors provide adaptive feedback, and the combination of these three factors ensures the completeness of the state representation.

[0091] Action space variables The definition is shown in equation (23):

[0092] (twenty three)

[0093] in, To set the maximum adjustment step size for the model parameters, These are the adjustment values ​​for the growth state model parameters. .

[0094] (3.2) Reinforcement learning reward function

[0095] The reward function design for the reinforcement learning algorithm is shown in equation (24):

[0096] (twenty four)

[0097] in, To reduce the error sensitivity of the current step prediction error in the growth model, an exponential decay method is used. As a saturation function, the biological constraint rules are normalized to the interval [-1, 1]. For biological constraint functions, through step functions The biological constraints during fish growth are embedded into the reward function, constraining the search space range of the model parameters. The biological constraints are non-negative growth. The feed conversion ratio does not exceed the upper limit. Etc., imposing penalties for violations of constraints. Policy entropy. The algorithm is encouraged to explore diverse solutions within the feasible solution space, thereby expanding the search space of the growth model solution and preventing the search strategy from converging to a local optimum prematurely. , , These are the regularization hyperparameters.

[0098] (3.3) Reinforcement learning optimization solution

[0099] In this embodiment, training and solving are performed 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), aiming to improve learning efficiency and stability through the synergistic effect of the two. Its core principle 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 , guarantee Give the optimal adjustment value under the condition. This maximizes reward accumulation. In this embodiment, the policy function is modeled based on the Transformer architecture to fully guarantee the model's policy feature learning ability. 2) Value Function Network (Critic) Learning The value of state-action pairs is evaluated by calculating the estimated cumulative reward generated by the policy function given by the Actor, providing feedback on the Actor's optimization direction and guiding the Actor's optimization direction.

[0100] The advantage function value at each time step is calculated using generalized advantage estimation:

[0101] (25)

[0102] Among them, TD error (Temporal Difference Error) , This indicates that the current strategy is better than the average expectation over time T, and the action should be strengthened; conversely, if the strategy is worse, the action should be strengthened. This indicates that the current strategy is ineffective and needs to be suppressed.

[0103] Policy loss function:

[0104] (26)

[0105] Importance is expressed as a ratio. Through the clip mechanism, Limit the value to [0.8, 1.2] to prevent policy mutations.

[0106] Value loss function:

[0107] (27)

[0108] Among them, target value .

[0109] By leveraging PPO's stable policy search capabilities and combining them with domain knowledge constraints, efficient adaptive optimization of fish growth model parameters is achieved, providing a solid algorithmic foundation for intelligent aquaculture systems.

[0110] In the above embodiments, a state space model of fish growth depth is established, a dynamic stage division mechanism is designed, and a stage transition criterion is constructed by integrating allometric growth gradient and environmental cumulative effect. The model parameters are adaptively switched through a gating network, overcoming the problem of ambiguous stage boundaries caused by traditional fixed threshold division. Biological mechanism equations such as metabolic rate temperature response and density inhibition effect are embedded in the neural network. The model parameter space is constrained by regularization to achieve interpretable coupling modeling of environmental-management factors. Cross-scale causal association modeling is realized, and a cross-scale causal chain of metabolism-growth is constructed by combining biostatistical priors, breaking the bottleneck of traditional black box models that cannot link microscopic physiology and macroscopic growth.

[0111] To verify the effectiveness of the methods in the above embodiments, the inventors conducted the following experiments and evaluations:

[0112] (a) Data preparation

[0113] Simulation environment setup:

[0114] Based on reinforcement learning simulation platforms such as Gym, a dynamic aquaculture simulation system was constructed to simulate the coupling relationship between water temperature, dissolved oxygen, feeding actions, and fish growth, supporting real-time simulation of multi-factor perturbations (such as sudden temperature changes and sudden drops in dissolved oxygen). The time step was 1 hour, the experimental period was 30 days, the initial fish weight was 500g ± 10%, the water temperature fluctuation range was 24-32℃, and the dissolved oxygen safety threshold was 4 mg / L.

[0115] Actual data collection:

[0116] Establish a practical aquaculture experimental platform at the cooperative aquaculture base to collect data on the entire growth cycle of fish, such as hourly water temperature, dissolved oxygen, pH value, daily feeding amount and density adjustment records (labeling feed brand and feeding time), weekly measurement of body length and weight, and monthly random sampling of growth factor indicators (cortisol concentration, enzyme activity), etc.

[0117] (II) Validation of the growth state space model

[0118] Steady-state validation: A controllable experimental culture environment was established, with fixed water temperature, constant dissolved oxygen, and a standard photoperiod. Data on the body length and weight of the target cultured fish throughout their entire growth cycle were collected. By comparing the traditional Von Bertalanffy model with the Dynamic Energy Budget (DEB) model, the root mean square error of this model in predicting body length / weight was quantified, validating its ability to represent basic growth patterns. Correlation analysis between growth factors and phenotypic traits was combined to analyze the model's interpretability of mechanisms such as energy allocation and allometric growth, ensuring physiological consistency.

[0119] Dynamic Disturbance Validation: Temporal environmental disturbances are injected to simulate dynamic disturbances in aquaculture scenarios. The predictive stability of the model during disturbances and the convergence efficiency of the reinforcement learning algorithm are evaluated. A lag effect test is designed, delaying the input of dissolved oxygen drop data to verify the model's adaptability to time-lag environments. Violation rates of rules such as non-negativity of growth and feed coefficient thresholds are statistically analyzed to ensure the algorithm's biological rationality in dynamic scenarios.

[0120] Extreme Condition Validation: Extreme event scenarios such as sudden drop in dissolved oxygen, high-temperature stress, and feeding interruption were constructed to test the response time of adjusting model parameters to restore prediction accuracy. The physiological rationality of changes in growth factors such as metabolic rate and energy reserves under extreme conditions was analyzed, and the rule violation rate was statistically analyzed. Cross-species stress testing was conducted, transferring model parameters from a single dataset to other fish datasets to verify the generalization error increase, overcoming the limitation of insufficient cross-scenario adaptability of traditional models.

[0121] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions 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 method for predicting fish growth based on a deep nonlinear state-space model, characterized in that, Includes the following steps: The system acquires input variables, state variables, and output variables. The input variables include fish biophenotypes, environmental factors, and nutritional parameters related to fish growth. The state variables are fish growth factors. 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 discrimination module and a time-delay feature extraction module; The dynamic stage judgment module determines different growth stages based on allometric growth rate and cumulative environmental stress. The allometric growth rate is calculated using fish biophenotypes related to fish growth from the input variables, and the cumulative environmental stress is calculated from environmental factors from the input variables. The time-delay feature extraction module extracts time-delay features related to the current decision from historical environmental sequences to quantify the delayed impact of environmental factors. Train the nonlinear state-space model of the fish's growth depth; Fish growth is predicted using a trained nonlinear state-space model of fish growth depth, and fish growth indices are obtained.

2. The fish growth prediction method based on a 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 stocking density; the fish growth factors include metabolic rate, enzyme activity and cortisol concentration; and the fish growth indicators include body length and weight gain.

3. The fish growth prediction method based on a deep nonlinear state-space model according to claim 1, characterized in that, Dynamic stage discrimination module The calculation is as follows: ； ； ； in, Indicates time, This serves as a 24-hour historical window. , They represent the time as follows: , The water temperature at that time Allometric growth rate, This represents the cumulative amount of environmental stress. The allometric growth coefficient is defined as: , For weight, Body length; and They are respectively in and The allometric growth coefficient at time step; , They represent the time as follows: , Dissolved oxygen at that time; For learnable model parameters, output a three-stage probability distribution, where the stage with the highest probability value is determined as the current growth stage; for The growth factor vector at any given moment.

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

5. The fish growth prediction method based on a deep nonlinear state-space model according to claim 4, characterized in that, In the nonlinear state-space model of fish growth depth, the depth state-space equation and observation equation established based on a gated recurrent neural network include: ； = ； in, For growth factor vectors, For observation models, For the observation model parameter vector, To observe noise; To incorporate the state equation model of the stage transition criterion, A deep fully connected network design is adopted to achieve nonlinear mapping learning from the key latent variable space to the output space; The length of a fish's body; For weight, Indicates the output variable. Indicates the amount of feed given. This indicates the stocking density value.

6. The fish growth prediction method based on a deep nonlinear state-space model according to claim 1, characterized in that, Training the nonlinear state-space model of fish growth depth includes: Using historical aquaculture data and aquaculture experimental data, a loss function for the growth state space model was designed. A fully supervised training paradigm was adopted, and the gradient descent algorithm was used to continuously adjust the model parameters with the goal of minimizing the loss, and finally the solution of the fish growth model parameters was obtained. Using the fish growth model parameter solution as the initial parameter solution, a reinforcement learning solution algorithm is established, transforming the fish growth model solution process into a state solution space path planning problem, and expanding the solution space exploration path.

7. The fish growth prediction method based on a deep nonlinear state-space model according to claim 6, characterized in that, The loss function includes: ； in, To predict loss based on phenotype, ; , This represents the actual change in body length and weight. , The model predicts the changes in body length and weight. For metabolic constraint loss, ,in For reference water temperature The basal metabolic rate was determined through experimental testing. For activation energy, It is the gas constant; Metabolic rate, Water temperature; For biochemical associated losses, ;in and To measure enzyme activity and cortisol concentration; and The model was used to predict the output enzyme activity and cortisol concentration. , , For weight hyperparameters, For model parameter regularization, For the state transition model parameter vector, This is the parameter vector for the observation model.

8. The fish growth prediction method based on a deep nonlinear state-space model according to claim 6, characterized in that, Using the fish growth model parameter solutions as initial parameter solutions, a reinforcement learning solution algorithm is established. The fish growth model solution process is transformed into a state solution space path planning problem, expanding the solution space exploration path, including: State space variables Defined as: ;in, This represents the growth factor vector in the state-space model. For the input vector, This is a historical prediction error sequence used to capture dynamic biases in the model; This represents the model's predicted output vector. Represents the historical observation vector; Action space variables Defined as: ;in, To set the maximum adjustment step size for the model parameters, These are the adjustment values ​​for the growth state model parameters. ; The reward function for the reinforcement learning algorithm is designed as follows: ;in, To reduce the error sensitivity of the current step prediction error in the growth model, an exponential decay method is used. As a saturation function, the biological constraint rules are normalized to the interval [-1, 1]. For biological constraint functions, through step functions The biological constraints during fish growth are embedded into the reward function, constraining the search space range of the model parameters. The biological constraints include: non-negative growth. The feed conversion ratio does not exceed the upper limit. Penalties are imposed for violations of constraints; policy entropy Encourage algorithms to explore diverse solutions within the feasible solution space, expand the search space of the growth model solution, and prevent the search strategy from converging to a local optimum too early. , , These are the regularization hyperparameters; The training and solution are based on the Actor-Critic reinforcement learning algorithm.

Images