River and lake water bloom prediction method and system based on integrated diffusion learning model

Abstract

The invention discloses a river and lake water bloom prediction method and system based on an integrated diffusion learning model, and the method comprises the steps: carrying out the preprocessing of an original water quality time sequence according to the water quality monitoring data of a target river and lake region, and constructing a standardized water quality time sequence input data set; disturbing the data set based on a conditional diffusion generation model, and constructing a plurality of initial condition diversified input disturbance sets; a plurality of input disturbances of the disturbance set are sent into a deep neural network prediction model for parallel prediction, so that a plurality of algal bloom prediction orbits are formed to jointly form an integrated prediction result under disturbance driving; and statistical analysis and fusion processing are carried out to form prediction result distribution with uncertainty quantification capability, and visual display is carried out. According to the method, the uncertainty of the prediction result can be quantitatively described while the prediction precision is kept, and a more reliable decision basis can still be provided for water environment scheduling, ecological early warning and emergency response especially under extreme hydrological conditions such as flood and drought.

Description

Technical Field

[0001] This invention belongs to the field of water environment monitoring and intelligent prediction technology, and relates to river and lake algal bloom prediction technology, specifically to a river and lake algal bloom prediction method and system based on an integrated diffusion learning model. Background Technology

[0002] Algal blooms refer to the excessive growth of phytoplankton (especially algae) in aquatic bodies under specific environmental conditions. They typically manifest as an algal aggregate or covering layer on the water surface. Algal blooms mainly occur in eutrophic waters. In waters with high concentrations of nutrients such as nitrogen and phosphorus, factors such as water temperature, light intensity, climate change, and nutrient load work together to promote rapid phytoplankton reproduction, leading to algal blooms. Once an algal bloom occurs, it can have significant impacts on the ecological environment, public health, and the socio-economic situation. The massive algal blooms can cause economic losses for tourism and recreational activities that rely on these water bodies, negatively affecting the local economy. Harmful algal blooms can also produce toxic substances that pollute drinking water sources, posing serious health risks to humans and animals.

[0003] With the increasing impact of climate change and human activities, the frequency and intensity of extreme hydrological conditions such as floods and droughts are becoming more significant. These extreme conditions lead to a series of effects, such as abrupt changes in hydrodynamic processes and significant fluctuations in water quality parameters, which further increase the uncertainty of algal blooms in rivers and lakes. Currently, artificial intelligence technology is developing rapidly, especially machine learning, which is widely used. Algal bloom prediction based on machine learning has become an important direction in current water environment research. Current algal bloom prediction methods are mostly based on deterministic modeling frameworks, such as Long Short-Term Memory (LSTM) networks, Gated Recurrent Units (GRUs), and numerical models driven by various empirical rules or physical mechanisms. Although these methods have achieved some success in trend prediction under general conditions, they often only output a single prediction result due to a lack of ability to characterize input errors, model uncertainties, and extreme hydrological disturbances. It is difficult to quantify the confidence interval and risk probability of the prediction. This limitation is particularly pronounced under extreme hydrological conditions, restricting their application in practical water environment management, extreme event early warning, and emergency response. Summary of the Invention

[0004] Purpose of the invention: In order to overcome the shortcomings of the existing technology, this invention provides a method and system for predicting algal blooms in rivers and lakes based on an integrated diffusion learning model. This method can quantitatively characterize the uncertainty of the prediction results while maintaining the accuracy of the prediction. In particular, under extreme hydrological conditions such as floods and droughts, it can still provide a more reliable decision-making basis for water environment management, ecological early warning and emergency response.

[0005] Technical Solution: To achieve the above objectives, this invention provides a method for predicting algal blooms in rivers and lakes based on an ensemble diffusion learning model, comprising the following steps:

[0006] S1: Based on the collected water quality monitoring data of the target river and lake area, the original water quality time series is preprocessed to construct a standardized water quality time series input dataset for diffusion disturbance modeling and depth prediction;

[0007] S2: Based on the conditional diffusion generation model, the standardized water quality time series input dataset is perturbed to construct multiple sets of diverse initial conditional input perturbations with physical rationality and controllable perturbation amplitude;

[0008] S3: Multiple input perturbations from a diverse set of initial condition input perturbations are fed into a deep neural network prediction model for parallel prediction, so as to form multiple algal bloom prediction trajectories that together constitute an integrated prediction result driven by perturbations.

[0009] S4: Perform statistical analysis and fusion processing on the integrated prediction results to form a prediction result distribution with uncertainty quantification capabilities, and then visualize the results.

[0010] Furthermore, the process of constructing the standardized water quality time-series input dataset in step S1 includes:

[0011] A1: Collect historical monitoring data of river or lake water bodies, align the historical monitoring data in chronological order, and construct a two-dimensional data tensor X∈R with variable dimension D and time step number T. T×D Where R represents the real number field, R T×D It is a matrix space with real numbers as elements and a shape of T×D, where each row represents a multivariate observation at a time point;

[0012] A2: Considering the stability of model training and the elimination of differences in the scale of different variables, standardization is performed according to the variable dimension. For each variable j, its mean μ is calculated. j With standard deviation σ j And perform the following normalization operation:

[0013]

[0014] Where t = 1, 2, ..., T, and δ is a constant to prevent division by zero; The standardized data value represents the value of the j-th variable at time step t after standardization; x t,j μ represents the raw observation value before standardization, indicating the observation value of the j-th variable at time step t; j σ is the mean of the j-th variable in the training dataset, used for centering during standardization; jδ is the standard deviation of the j-th variable in the training dataset, used to scale the data to the same scale; δ is a constant used to prevent calculation instability caused by a denominator of zero or too small a value; t is the time step index; j is the dimension index of different water quality index variables;

[0015] The standardized and normalized data tensor X∈R T×D This serves as the input dataset for the subsequent diffusion perturbation generation module and the deep prediction model.

[0016] Furthermore, the historical monitoring data types in step A1 include:

[0017] Indicators of algal bloom intensity include chlorophyll α concentration;

[0018] Physicochemical indicators, including water temperature, pH, conductivity, dissolved oxygen, and turbidity;

[0019] Nutrient indicators include ammonia nitrogen, total nitrogen, total phosphorus, and total organic carbon;

[0020] And / or, spatial information and timestamp information.

[0021] Furthermore, the construction process of the initial condition diversified input perturbation set in step S2 includes:

[0022] B1: By constructing a conditional diffusion generation model, a multi-step forward noise addition process is performed on the water quality observation sequence x0 extracted from the standardized water quality time-series input dataset to obtain the noisy intermediate state x. t ;

[0023] B2: Train the conditional diffusion generation model by training a neural network function. With t steps of noisy input x t Using conditional input c as input data, the system learns to predict the noise term during the noise addition process. The objective function is to minimize the prediction error.

[0024] ;

[0025] Where θ is The trainable parameters; E is the expected value, representing the average value of the random variable;

[0026] B3: A guiding factor ω is introduced during the generation phase, and a classifier-free guiding mechanism is used to adjust the perturbation intensity. Furthermore, the guiding mechanism... During the inference process, both unconditional and conditional predictions are generated simultaneously and combined to obtain the final perturbation direction; where ω is the guiding factor and Ø represents the unconditional input.

[0027] B4: Based on the generated perturbation sample, repeat the diffusion-anti-diffusion operation several times to advance the perturbation sequence in multiple steps, as expressed by the formula:

[0028] ;

[0029] Where, x (0) The initial perturbation sample is K, which is the maximum number of steps.

[0030] B5: Output N independent input perturbation samples , and constitute the input perturbation set.

[0031] Furthermore, the forward noise addition process in step B1 is a Markov chain with the following conditional distribution:

[0032]

[0033]

[0034] Where x0 is a single initial sample extracted from the standardized water quality time-series input dataset, serving as the initial input for the forward noise addition of the diffusion model; x t This represents the noisy state at step t of the forward diffusion; t is the diffusion step index, t=1,2,…,T d T d Let I be the total number of steps in the diffusion process; let I be the identity matrix, with dimensions equal to x. t Same; N is a Gaussian distribution; Preset noise parameters for each diffusion step, This indicates their cumulative product.

[0035] Furthermore, in step B3, perturbation samples of different intensities are generated by adjusting the guiding factor ω.

[0036] Furthermore, the process of forming the integrated prediction results in step S3 includes:

[0037] C1: Selecting a deep neural network G Φ As a predictor, Φ represents the model parameters, and the input is the perturbated water quality time series samples. The output is the prediction result y for the next time step. t+1 The prediction process is expressed by the following formula:

[0038] ;

[0039] in, This represents the input state of the i-th perturbation track at time t. The corresponding prediction results;

[0040] C2: A multi-step recursive approach using autoregression is employed, expressed by the following formula:

[0041] ;

[0042] The N predicted algal bloom orbits together constitute the integrated prediction result driven by the perturbation, as follows:

[0043] .

[0044] Furthermore, the training objective of the prediction process in step C1 is optimized using the mean squared error (MSE) loss function, expressed as:

[0045] ;

[0046] in, These are the model's predicted values. This represents the actual chlorophyll concentration observed at the corresponding time point.

[0047] Furthermore, the distribution of the prediction results in step S4 includes the prediction mean, standard deviation, confidence interval, and risk probability, specifically:

[0048] Predicted mean: The predicted orbits of all algal blooms are averaged at each time step to obtain the ensemble predicted mean orbit.

[0049] ;

[0050] Standard deviation: The uncertainty measure is the standard deviation. The time-step standard deviation of the integrated orbit is calculated and expressed as:

[0051] ;

[0052] Where, σ t This represents the prediction uncertainty at time step t;

[0053] Confidence Interval: Construct the (1-α) confidence interval based on the central limit theorem, expressed as:

[0054] ;

[0055] Among them, z α / 2 is the confidence coefficient for the standard normal distribution;

[0056] Risk probability: The percentage of orbits exceeding the preset algal bloom risk threshold θ at each time step is defined as the exceedance probability, expressed as:

[0057] ;

[0058] Where I is the indicator function, This indicates the risk level of an algal bloom occurring at time step t.

[0059] This invention also provides a river and lake algal bloom prediction system based on an ensemble diffusion learning model, comprising:

[0060] The data construction module preprocesses the raw water quality time series based on the collected water quality monitoring data of the target river and lake areas to construct a standardized water quality time series input dataset for diffusion disturbance modeling and depth prediction.

[0061] The perturbation set module is used to perturb the standardized water quality time series input dataset based on the conditional diffusion generation model, and construct multiple sets of diverse initial conditional input perturbations with physical rationality and controllable perturbation amplitude.

[0062] The integrated prediction module is used to feed multiple input perturbations from a set of diverse initial conditions into a deep neural network prediction model for parallel prediction, so as to form multiple algal bloom prediction trajectories together to constitute an integrated prediction result driven by perturbations.

[0063] The visualization module is used to perform statistical analysis and fusion processing on the integrated prediction results to form a distribution of prediction results with uncertainty quantification capabilities, and then to visualize the results.

[0064] Beneficial Effects: Compared with existing technologies, this invention proposes a perturbation generation method based on a conditional diffusion model. For the first time, it constructs a physically reasonable input set with controllable perturbation amplitude in water quality time-series prediction, effectively improving the diversity and physical consistency of integrated predictions. Furthermore, this invention can be extended into a prediction framework with uncertain outputs without changing the original neural network structure, achieving complete uncertainty quantification indicators such as confidence intervals, standard deviations, and extreme value risk probabilities, thus improving the reliability and interpretability of the prediction system. Simultaneously, it can still provide risk probability assessments under extreme hydrological conditions, providing technical support for emergency dispatch and extreme climate adaptation. It features parallel inference, high versatility, and easy deployment, making it suitable for various environmental monitoring scenarios, including algal bloom early warning, water pollution prediction, and urban flooding risk assessment. Attached Figure Description

[0065] Figure 1 This is a flowchart of the method of the present invention;

[0066] Figure 2 A trend chart illustrating the central trend of future algal bloom concentrations and the range of its uncertainties;

[0067] Figure 3 The risk probability diagram provided for this invention. Detailed Implementation

[0068] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0069] Example 1:

[0070] like Figure 1 As shown in the figure, this embodiment provides a method for predicting algal blooms in rivers and lakes based on an ensemble diffusion learning model, including the following steps:

[0071] S1: Data Preparation and Standardization

[0072] Historical monitoring data of rivers or lakes are collected, including: chlorophyll α concentration (Chla), as a representative indicator of algal bloom intensity; physicochemical indicators such as water temperature, pH, conductivity, dissolved oxygen, and turbidity; nutrient indicators such as ammonia nitrogen, total nitrogen, total phosphorus, and total organic carbon; and optional spatial information (station latitude and longitude) and timestamp information (such as date and hour).

[0073] Based on the collected water quality monitoring data of the target river and lake areas, the original water quality time series is normalized or standardized to construct a standardized water quality time series input dataset for diffusion disturbance modeling and depth prediction.

[0074] The process of constructing a standardized water quality time-series input dataset includes:

[0075] A1: Collect historical monitoring data of river or lake water bodies, align the historical monitoring data in chronological order, and construct a two-dimensional data tensor X∈R with variable dimension D and time step number T. T×D Where R represents the real number field, R T×D It is a matrix space with real numbers as elements and a shape of T×D, where each row represents a multivariate observation at a time point;

[0076] A2: Considering the stability of model training and the elimination of differences in the scale of different variables, standardization is performed by variable dimension (column). For each variable j, its mean μ is calculated. j With standard deviation σ j And perform the following normalization operation:

[0077]

[0078] Where t = 1, 2, ...,T, and δ is a minimal constant to prevent division by zero; The standardized data value represents the value of the j-th variable at time step t after standardization; x t,jμ represents the raw observation value before standardization, indicating the observation value of the j-th variable at time step t; j σ is the mean of the j-th variable in the training dataset, used for centering during standardization; j δ is the standard deviation of the j-th variable in the training dataset, used to scale the data to the same scale; δ is a very small constant used to prevent calculation instability caused by a zero denominator or a value that is too small; t is the time step index (t=1,2,…,T); j is the dimension index of different water quality index variables (j=1,2,…,D);

[0079] Normalization ensures that each variable in the dataset has a mean of 0 and a variance of 1, which helps the neural network parameters converge at a consistent speed during training.

[0080] The standardized data tensor obtained in this process This is a standardized water quality time series input dataset, which serves as the input dataset for the subsequent diffusion perturbation generation module and depth prediction model.

[0081] If there are multiple monitoring stations, the above standardized process can be performed independently for each station, or the mean and variance of the entire area can be calculated uniformly and normalized.

[0082] S2: Conditional diffusion perturbation generation

[0083] Based on the conditional diffusion generation model, the standardized water quality time series input dataset is perturbed to construct multiple sets of diverse initial conditional input perturbations with physical rationality and controllable perturbation amplitude.

[0084] The construction process of the set of diverse initial input perturbations includes:

[0085] B1: By constructing a conditional diffusion generation model, a multi-step forward noise addition process is performed on the water quality observation sequence x0 extracted from the standardized water quality time-series input dataset to obtain the noisy intermediate state x. t ;

[0086] The forward noise-adding process is a Markov chain with the following conditional distribution:

[0087]

[0088]

[0089] in, A single initial sample extracted from the standardized water quality time-series input dataset is used as the starting input for the forward noise addition of the diffusion model; This represents the noisy state at step t of the forward diffusion; t is the diffusion step index, t=1,2,…,T d T dI represents the total number of steps in the diffusion process (different from the time step T); I is the identity matrix, with dimensions equal to x. t Same; N(μ,σ) 2 The mean is μ and the variance is σ. 2 Gaussian distribution; Preset noise parameters for each diffusion step, This indicates their cumulative product.

[0090] B2: Train the conditional diffusion generation model by training a neural network function. With t steps of noisy input Using conditional input c as input data, the system learns to predict the noise term during the noise addition process. The objective function is to minimize the prediction error.

[0091] ;

[0092] Where θ is The trainable parameters; E is the mathematical expectation, representing the average value of the random variable.

[0093] B3: A guiding factor ω is introduced during the generation phase, and a classifier-free guiding mechanism is used to adjust the perturbation intensity. Furthermore, the guiding mechanism... During the inference process, both unconditional and conditional predictions are generated simultaneously and combined to obtain the final perturbation direction; where ω is the guiding factor and Ø represents the unconditional input.

[0094] By adjusting ω, perturbation samples of different intensities can be obtained:

[0095] When ω is large, the generated samples are closer to the original observations and the perturbation is small, which is suitable for conservative prediction scenarios; when ω is small, the perturbation is stronger and the sample diversity is higher, which is suitable for simulating potential high-risk situations.

[0096] B4: To enhance the diversity of the perturbation space and further support the "random walk" mechanism, that is, based on the generated perturbation samples, several diffusion-anti-diffusion operations are repeatedly applied to advance the perturbation sequence in multiple steps, as expressed by the formula:

[0097] ;

[0098] Where, x (0) The initial perturbation sample is K, which is the maximum number of steps. Through multiple perturbation iterations, the distribution coverage of the samples can be expanded, improving sample diversity and generalization ability.

[0099] B5: Output N independent input perturbation samples , and constitute the input perturbation set.

[0100] S3: Parallel Prediction of Deep Models

[0101] Multiple input perturbations from a diverse set of initial conditions are fed into a deep neural network prediction model for parallel prediction, so as to form multiple algal bloom prediction trajectories that together constitute an integrated prediction result driven by perturbations, thereby achieving diverse inferences about the future state of algal blooms.

[0102] The process of forming integrated prediction results includes:

[0103] C1: Select a deterministic deep neural network G with an arbitrary structure Φ As a predictor, Φ represents the model parameters, and the input is the perturbated water quality time series samples. The output is the prediction result y for the next time step. t+1 The prediction process is expressed by the following formula:

[0104] ;

[0105] in, This represents the input state of the i-th perturbation track at time t. The corresponding prediction result, in this embodiment, is the chlorophyll α concentration value or multivariate water quality status at the next moment;

[0106] The training objective of the prediction process is optimized using the mean squared error (MSE) loss function, expressed as:

[0107] ;

[0108] in, These are the model's predicted values. This represents the actual chlorophyll concentration observed at the corresponding time point.

[0109] C2: To obtain the predicted trajectory for the next T steps, an autoregressive approach is used for multi-step recursion, expressed by the following formula:

[0110] ;

[0111] The N predicted algal bloom orbits together constitute the integrated prediction result driven by the perturbation, as follows:

[0112] ;

[0113] In this embodiment, the predictor G ΦAny deep neural network capable of temporal modeling can be selected, including: Long Short-Term Memory (LSTM) networks, which learn temporal dependencies through gating structures; Transformer networks, which model long-distance dependencies based on self-attention mechanisms; Convolutional Neural Networks (such as U-Net), which are used to capture local-global spatiotemporal features; and other regressive feedforward neural networks (such as multilayer perceptrons).

[0114] S4: Prediction Result Fusion and Distribution Generation

[0115] The integrated prediction results are statistically analyzed and fused to form a prediction result distribution with uncertainty quantification capabilities, and then visualized.

[0116] The distribution of the prediction results includes the prediction mean, standard deviation, confidence interval, and risk probability, as follows:

[0117] Predicted mean: The predicted orbits of all algal blooms are averaged at each time step to obtain the ensemble predicted mean orbit.

[0118] ;

[0119] Standard deviation: The uncertainty measure is the standard deviation. The time-step standard deviation of the integrated orbit is calculated and expressed as:

[0120] ;

[0121] in, This represents the prediction uncertainty at time step t. The larger the value, the greater the discrepancy in the model's predictions at that time.

[0122] Confidence Interval: Construct the (1-α) confidence interval based on the central limit theorem, expressed as:

[0123] ;

[0124] Among them, z α / 2 For example, when α = 0.05, z is the confidence coefficient of the standard normal distribution. 0.025 ≈1.96, this confidence interval can be used to intuitively express the prediction range;

[0125] Risk probability: The percentage of orbits exceeding the preset algal bloom risk threshold θ at each time step is defined as the exceedance probability, expressed as:

[0126] ;

[0127] Where I is the indicator function, This indicates the risk level of an algal bloom occurring at time step t; this indicator can be used in practical applications such as risk level classification and early warning triggering.

[0128] The risk threshold θ for algal blooms can be determined based on environmental management standards, historical monitoring statistics, or expert experience. For example, a chlorophyll α concentration of 15 μg / L can be set as the threshold for mild algal blooms.

[0129] In this embodiment, risk levels are classified according to preset rules. <0.3 is considered low risk, 0.3≤ <0.6 is considered medium risk. A value ≥0.6 is considered high risk.

[0130] The predicted mean, standard deviation, confidence interval, and risk probability obtained from the aforementioned fusion analysis are visualized to enable users to intuitively understand the future evolution trend and potential risk level of algal blooms, thereby providing auxiliary support for early warning issuance, water quality scheduling, and management response.

[0131] In this embodiment, the obtained Figure 2 The trend chart shown and Figure 3 The risk probability diagram shown;

[0132] like Figure 2 As shown, the trend plot output is: a trend plot of the predicted chlorophyll α concentration changing over time, where: the center curve represents the mean trajectory of the integrated prediction. The upper and lower envelopes represent the 95% confidence intervals, and are calculated as follows: A risk threshold line (e.g., Chla = 15 μg / L) is plotted for reference. This figure is used to illustrate the central trend of future algal bloom concentrations and the range of uncertainties.

[0133] like Figure 3 As shown, the risk probability graph output is based on the calculated sequence of exceedance probabilities. The corresponding time series curve is plotted to reflect the probability of algal bloom concentration exceeding a preset threshold at each predicted time step. This curve can be used to identify high-risk periods and, based on this, set early warning thresholds or initiate intervention mechanisms.

[0134] Example 2:

[0135] Based on the method provided in Embodiment 1, this embodiment provides a river and lake algal bloom prediction system based on an ensemble diffusion learning model, including:

[0136] The data construction module preprocesses the raw water quality time series based on the collected water quality monitoring data of the target river and lake areas to construct a standardized water quality time series input dataset for diffusion disturbance modeling and depth prediction.

[0137] The perturbation set module is used to perturb the standardized water quality time series input dataset based on the conditional diffusion generation model, and construct multiple sets of diverse initial conditional input perturbations with physical rationality and controllable perturbation amplitude.

[0138] The integrated prediction module is used to feed multiple input perturbations from a set of diverse initial conditions into a deep neural network prediction model for parallel prediction, so as to form multiple algal bloom prediction trajectories together to constitute an integrated prediction result driven by perturbations.

[0139] The visualization module is used to perform statistical analysis and fusion processing on the integrated prediction results to form a distribution of prediction results with uncertainty quantification capabilities, and then to visualize the results.

Claims

1. A method for predicting algal blooms in rivers and lakes based on an ensemble diffusion learning model, characterized in that, Includes the following steps: S1: Based on the collected water quality monitoring data of the target river and lake area, the original water quality time series is preprocessed to construct a standardized water quality time series input dataset for diffusion disturbance modeling and depth prediction; S2: Based on the conditional diffusion generation model, the standardized water quality time series input dataset is perturbed to construct multiple sets of diverse initial conditional input perturbations with physical rationality and controllable perturbation amplitude; S3: Multiple input perturbations from a diverse set of initial condition input perturbations are fed into a deep neural network prediction model for parallel prediction, so as to form multiple algal bloom prediction trajectories that together constitute an integrated prediction result driven by perturbations. S4: Perform statistical analysis and fusion processing on the integrated prediction results to form a prediction result distribution with uncertainty quantification capabilities, and then visualize the results.

2. The method for predicting algal blooms in rivers and lakes based on an ensemble diffusion learning model according to claim 1, characterized in that, The process of constructing the standardized water quality time-series input dataset in step S1 includes: A1: Collect historical monitoring data of river or lake water bodies, align the historical monitoring data in chronological order, and construct a two-dimensional data tensor X∈R with variable dimension D and time step number T. T×D Where R represents the real number field, R T×D It is a matrix space with real numbers as elements and a shape of T×D, where each row represents a multivariate observation at a time point; A2: Considering the stability of model training and the elimination of differences in the scale of different variables, standardization is performed according to the variable dimension. For each variable j, its mean μ is calculated. j With standard deviation σ j And perform the following normalization operation: ； Where t = 1, 2, ..., T, and δ is a constant to prevent division by zero; The standardized data value represents the value of the j-th variable at time step t after standardization; x t,j μ represents the raw observation value before standardization, indicating the observation value of the j-th variable at time step t; j σ is the mean of the j-th variable in the training dataset, used for centering during standardization; j δ is the standard deviation of the j-th variable in the training dataset, used to scale the data to the same scale; δ is a constant used to prevent calculation instability caused by a denominator of zero or too small a value; t is the time step index; j is the dimension index of different water quality index variables; The standardized and normalized data tensor X∈R T×D This serves as the input dataset for the subsequent diffusion perturbation generation module and the deep prediction model.

3. The method for predicting algal blooms in rivers and lakes based on an ensemble diffusion learning model according to claim 2, characterized in that, The process of constructing the initial condition diversified input perturbation set in step S2 includes: B1: By constructing a conditional diffusion generation model, a multi-step forward noise addition process is performed on the water quality observation sequence x0 extracted from the standardized water quality time-series input dataset to obtain the noisy intermediate state x. t ; B2: Train the conditional diffusion generation model by training a neural network function. With t steps of noisy input x t Using conditional input c as input data, the system learns to predict the noise term during the noise addition process. The objective function is to minimize the prediction error. ； Where θ is The trainable parameters; E is the expected value, representing the average value of the random variable; B3: A guiding factor ω is introduced during the generation phase, and a classifier-free guiding mechanism is used to adjust the perturbation intensity. Furthermore, the guiding mechanism... During the inference process, both unconditional and conditional predictions are generated simultaneously and combined to obtain the final perturbation direction; where ω is the guiding factor and Ø represents the unconditional input. B4: Based on the generated perturbation sample, repeat the diffusion-anti-diffusion operation several times to advance the perturbation sequence in multiple steps, as expressed by the formula: ； Where, x (0) The initial perturbation sample is K, which is the maximum number of steps. B5: Output N independent input perturbation samples , and constitute the input perturbation set.

4. The method for predicting algal blooms in rivers and lakes based on an ensemble diffusion learning model according to claim 3, characterized in that, The forward noise addition process in step B1 is a Markov chain with the following conditional distribution: ； ； Where x0 is a single initial sample extracted from the standardized water quality time-series input dataset, serving as the initial input for the forward noise addition of the diffusion model; x t This represents the noisy state at step t of the forward diffusion; t is the diffusion step index, t=1,2,…,T d T d Let I be the total number of steps in the diffusion process; let I be the identity matrix, with dimensions equal to x. t Same; N is a Gaussian distribution; Preset noise parameters for each diffusion step, This indicates their cumulative product.

5. The method for predicting algal blooms in rivers and lakes based on an ensemble diffusion learning model according to claim 4, characterized in that, In step B3, perturbation samples of different intensities are generated by adjusting the guiding factor ω.

6. The method for predicting algal blooms in rivers and lakes based on an ensemble diffusion learning model according to claim 5, characterized in that, The process of forming the integrated prediction results in step S3 includes: C1: Selecting a deep neural network G Φ As a predictor, Φ represents the model parameters, and the input is the perturbated water quality time series samples. The output is the prediction result y for the next time step. t+1 The prediction process is expressed by the following formula: ； in, This represents the input state of the i-th perturbation track at time t. The corresponding prediction results; C2: A multi-step recursive approach using autoregression is employed, expressed by the following formula: ； The N predicted algal bloom orbits together constitute the integrated prediction result driven by the perturbation, as follows: 。 7. The method for predicting algal blooms in rivers and lakes based on an ensemble diffusion learning model according to claim 6, characterized in that, The training objective of the prediction process in step C1 is optimized using the mean squared error (MSE) loss function, expressed as: ； in, These are the model's predicted values. This represents the actual chlorophyll concentration observed at the corresponding time point.

8. The method for predicting algal blooms in rivers and lakes based on an ensemble diffusion learning model according to claim 7, characterized in that, The distribution of the prediction results in step S4 includes the prediction mean, standard deviation, confidence interval, and risk probability, specifically: Predicted mean: The predicted orbits of all algal blooms are averaged at each time step to obtain the ensemble predicted mean orbit. ； Standard deviation: The uncertainty measure is the standard deviation. The time-step standard deviation of the integrated orbit is calculated and expressed as: ； Where, σ t This represents the prediction uncertainty at time step t; Confidence Interval: Construct the (1-α) confidence interval based on the central limit theorem, expressed as: ； Among them, z α / 2 is the confidence coefficient for the standard normal distribution; Risk probability: The percentage of orbits exceeding the preset algal bloom risk threshold θ at each time step is defined as the exceedance probability, expressed as: ； Where I is the indicator function, This indicates the risk level of an algal bloom occurring at time step t.

9. A river and lake algal bloom prediction system based on an ensemble diffusion learning model, characterized in that, For implementing the method of claim 1, the system comprises: The data construction module preprocesses the raw water quality time series based on the collected water quality monitoring data of the target river and lake areas to construct a standardized water quality time series input dataset for diffusion disturbance modeling and depth prediction. The perturbation set module is used to perturb the standardized water quality time series input dataset based on the conditional diffusion generation model, and construct multiple sets of diverse initial conditional input perturbations with physical rationality and controllable perturbation amplitude. The integrated prediction module is used to feed multiple input perturbations from a set of diverse initial conditions into a deep neural network prediction model for parallel prediction, so as to form multiple algal bloom prediction trajectories together to constitute an integrated prediction result driven by perturbations. The visualization module is used to perform statistical analysis and fusion processing on the integrated prediction results to form a distribution of prediction results with uncertainty quantification capabilities, and then to visualize the results.

Images