An unmanned ship modeling and prediction method based on an improved nonlinear reservoir computing model

Abstract

The application discloses an unmanned ship modeling prediction method based on an improved nonlinear reservoir pool calculation model, relates to the technical field of unmanned ship modeling, and comprises the following steps: collecting motion state data of an unmanned ship at a historical moment, forming an input data set, and corresponding future moment state data forming an output data set; optimizing the time delay order of the nonlinear reservoir pool calculation model through an improved genetic algorithm to obtain an optimal time delay order; constructing a feature matrix based on the optimal time delay order; performing feature selection based on a statistical quantity F and retaining features with higher importance; training an output weight matrix by using a ridge regression method, performing multi-step prediction, and estimating the uncertainty of the prediction result. The application realizes high-precision multi-step prediction of the motion state of the unmanned ship, significantly improves the prediction accuracy and calculation efficiency, introduces the uncertainty estimation and multi-step prediction mechanism, provides forward-looking decision support for the unmanned ship in different operation environments, and effectively enhances the navigation safety and control reliability.

Description

Technical Field

[0001] This invention relates to the field of unmanned vessel motion control and state prediction technology, and in particular to a method for unmanned vessel state modeling and multi-step prediction based on an improved nonlinear reservoir calculation model. Background Technology

[0002] Accurate forecasting of the motion state of unmanned surface vessels (USVs) performing monitoring and sampling tasks in the marine environment is crucial for navigation safety and mission execution. Traditional state forecasting methods are insufficient in handling the strong nonlinearity and time-varying characteristics of the marine environment, resulting in limited forecast accuracy. While existing reservoir calculation methods can process time-series data, there is still room for improvement in areas such as multi-step prediction accuracy and feature selection optimization. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of the prior art and provide an unmanned vessel modeling and forecasting method based on an improved nonlinear reservoir calculation model, which can effectively handle nonlinear interference in complex marine environments and improve the accuracy and computational efficiency of multi-step forecasting.

[0004] The technical solution adopted by this invention to solve its technical problem is: an unmanned vessel modeling and forecasting method based on an improved nonlinear reservoir calculation model, comprising the following steps:

[0005] Step 1: Collect historical motion state data of the unmanned vessel to form the input dataset, and the corresponding future state data to form the output dataset.

[0006] Step 2: Optimize the time delay order of the nonlinear reservoir calculation model using an improved genetic algorithm. To obtain the optimal time delay order ;

[0007] Step 3, based on the optimal time delay order Construct the feature matrix;

[0008] Step 4: Select features based on the statistic F, retaining features with higher importance;

[0009] Step 5: Use the ridge regression method to train the output weight matrix and perform multi-step prediction;

[0010] Step 6: Estimate the uncertainty of the prediction results.

[0011] The aforementioned unmanned vessel modeling and forecasting method based on an improved nonlinear reservoir calculation model, wherein step 1 specifically includes:

[0012] Set the input matrix as follows:

[0013] ;

[0014] in, This refers to the total number of time steps, i.e., the total number of moments in data collection. for Constant oscillation speed; for The speed of constant oscillation; for Constant bow roll rate; for The rudder at all times;

[0015] Set the output matrix as follows:

[0016] ;

[0017] in, for Constant oscillation speed; for The speed of constant oscillation; for Constant bow roll rate;

[0018] Input state vector Output state vector ;

[0019] The training set accounts for 0.7%, the validation set accounts for 0.15%, the test set accounts for 0.13%, and the multi-step prediction set accounts for 0.02%.

[0020] The above-mentioned unmanned vessel modeling and forecasting method based on an improved nonlinear reservoir calculation model, specifically includes step 2:

[0021] Step 2.1: Randomly generate an initial population, where each individual represents a possible time delay order. The population is initialized as follows: ;

[0022] The initial population in a genetic algorithm; Refers to the first The time delay order for each individual; Population size; This refers to the minimum time delay order; This refers to the maximum time delay order;

[0023] Step 2.2: Calculate the fitness value for each individual, taking into account both single-step prediction accuracy and multi-step prediction performance;

[0024] ;

[0025] in, This refers to the individual's fitness value; The coefficient of determination for a single-step prediction; ; Refers to the first The true value of each sample; Refers to the first Predicted values ​​for each sample; The mean of the true values ​​in the validation set; The coefficient of determination in multi-step prediction; ; The number of samples in the validation set; This refers to the number of samples in a multi-step prediction process. Refers to the number of steps in multi-step prediction; Refers to the first The sample at the th The true value of the step; Refers to the first The sample at the th The predicted value of the step; Refers to the first The average of the actual values;

[0026] Step 2.3: Generate a new generation of population through genetic operations;

[0027] Step 2.4: Repeat steps 2.1-2.3 until the optimal time delay order is obtained. .

[0028] The aforementioned unmanned vessel modeling and forecasting method based on an improved nonlinear reservoir calculation model, specifically includes step 3 as follows:

[0029] Step 3.1, for the optimal time delay order Construct linear feature vectors:

[0030] ;

[0031] in, Refers to time The linear feature vector contains all state information from the current and past time points; This refers to the optimal time delay order; This refers to the dimension of the linear eigenvector, with 4 state variables at each time step;

[0032] Step 3.2, construct the linear feature matrix:

[0033] ;

[0034] in, Refers to the linear characteristic matrix. The subscript from The initial purpose was to eliminate the influence of transient effects caused by the initial state of the reserve pool; each row is a linear feature vector at a point in time.

[0035] Step 3.3, construct the nonlinear characteristic matrix:

[0036] ;

[0037] in, The nonlinear characteristic matrix contains all quadratic terms, i.e., time-major characteristics. No. The and the first Interaction terms of linear features, index ; This indicates element-wise multiplication; The first linear eigenvector One element; The first linear eigenvector One element;

[0038] Dimensions of the nonlinear feature matrix:

[0039] ;

[0040] in, The dimension of the linear feature matrix. ; Refers to the dimension of the nonlinear feature matrix;

[0041] Step 3.4, construct the complete feature matrix:

[0042] .

[0043] The above-mentioned unmanned vessel modeling and forecasting method based on an improved nonlinear reservoir calculation model, specifically includes step 4:

[0044] Step 4.1, Feature selection analysis, feature selection based on statistic F:

[0045] ;

[0046] ;

[0047] in, Refers to the first The feature is related to the first The regression sum of squares of each output reflects the variation in the feature interpretation;

[0048] Pointing to the first The feature is related to the first The sum of squared residuals of each output reflects the unexplained variation;

[0049] Step 4.2, Feature Importance Score:

[0050] ;

[0051] in, Refers to the first The importance score of each feature Refers to the first The feature is related to the first The test statistic F for each output; Refers to the total number of features;

[0052] Select important features:

[0053] ;

[0054] in, Refers to the set of feature indices selected; Refers to the first The importance score of each selected feature; This refers to the cumulative importance threshold; This refers to the number of features selected.

[0055] The above-mentioned unmanned vessel modeling and forecasting method based on an improved nonlinear reservoir calculation model, specifically includes step 5:

[0056] Step 5.1, Standardization Process:

[0057] ;

[0058] in, Refers to the standardized feature matrix; The selected feature matrix contains only important features. The mean of the characteristic matrix; The standard deviation of the characteristic matrix; Refers to the standardized output matrix; The mean of the output matrix; The standard deviation of the output matrix; Refers to the first Arrive at the The output matrix of the row;

[0059] Step 5.2, the ridge regression solution is:

[0060] ;

[0061] in, Refers to the output weight matrix; Ridge regression regularization parameters; Refers to the identity matrix, with dimensions of ;

[0062] Step 5.3, the predicted value is:

[0063] ;

[0064] in, Standardized forecast value; The final predicted value after destandardization;

[0065] Step 5.3, during multi-step prediction, the state sequence needs to be updated: ;

[0066] ;

[0067] ;

[0068] in, Refers to the first The complete state vector, including the predicted velocity vector. and the rudder angle of the step ; The updated state sequence involves removing the oldest state and adding the latest predicted state. This is the rudder angle attenuation coefficient.

[0069] The aforementioned unmanned vessel modeling and forecasting method based on an improved nonlinear reservoir calculation model, specifically includes step 6:

[0070] Step 6.1, Uncertainty estimation:

[0071] ;

[0072] in, This refers to the uncertainty estimate, which reflects the reliability of the forecast; Refers to the first One standardized feature value; Refers to the first The weights of each feature are equal to the feature importance scores. ;

[0073] Step 6.2, Uncertainty Smoothing:

[0074] ;

[0075] ;

[0076] in, The smoothing weighting coefficient; The smoothed predicted value; This refers to the predicted value from the previous step.

[0077] The beneficial effects of this invention are that by improving the nonlinear reservoir calculation model, it achieves high-precision multi-step prediction of the motion state of unmanned vessels, can adaptively optimize time delay parameters and screen key features, significantly improving prediction accuracy and computational efficiency; at the same time, by introducing uncertainty estimation and multi-step prediction mechanisms, it provides forward-looking decision support for unmanned vessels in different operating environments such as narrow waterways and complex sea conditions, effectively enhancing navigation safety and control reliability, and has important engineering application value. Attached Figure Description

[0078] Figure 1 This is a flowchart of the invention;

[0079] Figure 2 This is a simulation diagram of the genetic algorithm optimization according to an embodiment of the present invention;

[0080] Figure 3 This is a simulation diagram of feature analysis and selection in an embodiment of the present invention;

[0081] Figure 4 This is a simulation diagram of multi-step prediction of state information in an embodiment of the present invention, wherein (a) is a comparison between the predicted and actual values ​​of the sway velocity for the next two steps; (b) is a comparison between the predicted and actual values ​​of the sway velocity for the next two steps; and (c) is a comparison between the predicted and actual values ​​of the bow roll rate for the next two steps. Detailed Implementation

[0082] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0083] like Figure 1 As shown in the figure, this embodiment discloses an unmanned vessel modeling and forecasting method based on an improved nonlinear reservoir calculation model, as detailed below:

[0084] Step 1: The motion state data of the unmanned vessel at historical moments, including sway velocity u, roll velocity v, bow roll rate r, and rudder angle δ, constitute the input dataset; the corresponding future moment state data constitute the output dataset.

[0085] Step 1 specifically includes:

[0086] Set the input matrix as follows:

[0087] ;

[0088] in, This refers to the total number of time steps, i.e., the total number of moments in data collection. for Constant oscillation speed; for The speed of constant oscillation; for Constant bow roll rate; for Timing and rudder angle; a total of 997 moments;

[0089] Set the output matrix as follows:

[0090] ;

[0091] in, for Constant oscillation speed; for The speed of constant oscillation; for Timing of bow roll rate; a total of 997 time points;

[0092] Input state vector Output state vector ;

[0093] Training set percentage: 0.7%; Validation set percentage: 0.15%; Test set percentage: 0.13%; Multi-step prediction set percentage: 0.02%.

[0094] Step 2: Optimize the time delay order of the nonlinear reservoir calculation model using an improved genetic algorithm. .

[0095] Step 2 specifically includes:

[0096] Step 2.1: Select a suitable genetic algorithm. The initial population is randomly generated, and each individual in the population represents a possible time delay order. The population is initialized as follows: ;

[0097] The initial population in a genetic algorithm; Refers to the first The time delay order for each individual; Population size, valued at 8; This refers to the minimum time delay order, with a value of 1. This refers to the maximum time delay order, with a value of 6.

[0098] Step 2.2: Calculate the fitness value for each individual, taking into account both single-step prediction accuracy and multi-step prediction performance;

[0099] ;

[0100] in, This refers to the individual's fitness value; The coefficient of determination for a single-step prediction; ; Refers to the first The true value of each sample; Refers to the first Predicted values ​​for each sample; The mean of the true values ​​in the validation set; The coefficient of determination in multi-step prediction; ; The number of samples in the validation set; This refers to the number of samples in a multi-step prediction process. Refers to the number of steps in multi-step prediction; Refers to the first The sample at the th The true value of the step; Refers to the first The sample at the th The predicted value of the step; Refers to the first The average of the actual values.

[0101] Step 2.3: Generate a new generation population through genetic operations such as selection, crossover, and mutation.

[0102] Selection: Select superior individuals based on fitness values;

[0103] ;

[0104] in, This refers to selecting outstanding individuals. This refers to selecting a threshold value of 0.8.

[0105] cross: ;

[0106] in, The parameter values ​​refer to those of the parent individual; The parameter value refers to the parameter value of the offspring individual; the parameter value is randomly selected from two parents as the parameter value of the offspring, and the probability of each parent being selected is 50%.

[0107] Mutation: in terms of probability Variation of individuals:

[0108] ;

[0109] in, Refers to the parameter value after mutation; This refers to randomly sampling a value from a uniform distribution within this interval; This refers to the mutation probability, with a value of 0.1.

[0110] Step 2.4: Repeat steps 2.1-2.3 until the optimal time delay order is obtained. The value is 2.

[0111] Simulation diagram of genetic algorithm optimization as follows Figure 2 As shown, the algorithm starts searching from the initial population. The optimal fitness value obtained at this point is low (approximately 0.10), indicating a significant gap between the initial solution and the optimization objective. Through genetic operations such as selection, crossover, and mutation, the optimal fitness value is dramatically increased. Once the optimal fitness reaches approximately 0.40, the fitness value no longer changes significantly, indicating that the algorithm has successfully converged to an optimal solution. The optimal time delay order is also discussed. The value is 2.

[0112] Step 3, based on the optimal time delay order Construct a feature matrix, including linear and nonlinear features.

[0113] Step 3 specifically includes:

[0114] Step 3.1, for the optimal time delay order Construct linear feature vectors.

[0115] ;

[0116] in, Refers to time The linear feature vector contains all state information from the current and past time points; This refers to the optimal time delay order; This refers to the dimension of the linear eigenvector, with 4 state variables at each time step.

[0117] Step 3.2, construct the linear feature matrix:

[0118] ;

[0119] in, Refers to the linear characteristic matrix. The subscript from The initial purpose was to eliminate the influence of transient effects caused by the initial state of the reservoir. Each row is a linear feature vector at a point in time.

[0120] Step 3.3, construct the nonlinear characteristic matrix:

[0121] ;

[0122] in, The nonlinear characteristic matrix contains all quadratic terms, i.e., time-major characteristics. No. The and the first Interaction terms of linear features, index ; This indicates element-wise multiplication (Hadamard product). The first linear eigenvector One element; The first linear eigenvector One element;

[0123] Dimensions of the nonlinear feature matrix:

[0124] ;

[0125] in, The dimension of the linear feature matrix. ; This refers to the dimension of the nonlinear feature matrix.

[0126] Step 3.4, construct the complete feature matrix:

[0127] ;

[0128] Where 1 refers to the constant term (a vector of all 1s); The complete feature matrix contains constant terms, linear features, and nonlinear features, totaling 43 features. The constant features are the constant vectors from step 3.4, the linear features are the linear feature matrix from step 3.2, and the nonlinear features are the nonlinear feature vectors formed by element-wise multiplication of the linear features from step 3.3. The optimal time delay order is 2, the number of linear features is 2*4=8, the number of nonlinear features is 8*9 / 2=36, and the number of constant terms is 1, totaling 8+36+1=45. However, due to the need to remove the influence of the initial state, it needs to start from a time delay of 2, thus including a total of 43 features.

[0129] Step 4: Select features based on the statistic F, retaining features with higher importance.

[0130] Step 4 specifically includes:

[0131] Step 4.1, Feature selection analysis, feature selection based on statistic F:

[0132] ;

[0133] ;

[0134] in, Refers to the first The feature is related to the first The regression sum of squares of each output reflects the variation in the feature interpretation;

[0135] Pointing to the first The feature is related to the first The sum of squared residuals of each output reflects the unexplained variation.

[0136] Step 4.2, Feature Importance Score:

[0137] ;

[0138] in, Refers to the first The importance score of each feature is a factor, with a higher value indicating that the feature is more important. Refers to the first The feature is related to the first The test statistic F for each output; Refers to the total number of features;

[0139] Select important features:

[0140] ;

[0141] in, This refers to the set of selected feature indices that contains the most important features; Refers to the first The importance score of each selected feature; The cumulative importance threshold is set to 0.8. This refers to the minimum number of features selected that satisfy the condition that cumulative importance is ≥80%. After selecting the features, Become Fourteen features were selected.

[0142] Feature analysis and selection simulation results are as follows Figure 3 As shown, the optimal time delay order The initial value is 2, therefore the total number of features is 45, which becomes 43 after removing the initial transient effect of the reserve pool. Based on the statistic F and feature importance scores, 14 important features were selected.

[0143] Step 5: Use the ridge regression method to train the output weight matrix and perform multi-step prediction.

[0144] Step 5 specifically includes:

[0145] Step 5.1, Standardization Process:

[0146] ;

[0147] in, This refers to the standardized feature matrix, with a mean of 0 and a standard deviation of 1. The selected feature matrix contains only important features. The mean of the characteristic matrix; The standard deviation of the characteristic matrix; Refers to the standardized output matrix; The mean of the output matrix; The standard deviation of the output matrix; Refers to the first Arrive at the The output matrix of the row;

[0148] Step 5.2, the ridge regression solution is:

[0149] ;

[0150] in, The output weight matrix has dimensions of 1. ; Ridge regression regularization parameters; Refers to the identity matrix, with dimensions of ;

[0151] Step 5.3, the predicted value is:

[0152] ;

[0153] in, Standardized forecast value; The final predicted value after destandardization;

[0154] Step 5.3, during multi-step prediction, the state sequence needs to be updated: ;

[0155] ;

[0156] ;

[0157] in, Refers to the first The complete state vector, including the predicted velocity vector. and the rudder angle of the step ; This refers to the updated state sequence, where the oldest state is removed and the latest predicted state is added. The rudder angle attenuation coefficient is 0.95.

[0158] State information modeling, multi-step prediction, simulation results, such as Figure 4 As shown, Figure (a) compares the predicted and actual values ​​of the sway velocity for the next two steps, with the gray area representing the prediction error; Figure (b) compares the predicted and actual values ​​of the sway velocity for the next two steps, with the gray area representing the prediction error; Figure (c) compares the predicted and actual values ​​of the bow roll rate for the next two steps, with the gray area representing the prediction error; all correspond to the prediction of the next two steps in step 5.3, requiring the state sequence to be updated twice.

[0159] Step 6: Estimate the uncertainty of the prediction results.

[0160] Step 6 specifically includes:

[0161] Step 6.1, Uncertainty estimation:

[0162] ;

[0163] in, This refers to the uncertainty estimate, which reflects the reliability of the forecast; Refers to the first One standardized feature value; Refers to the first The weights of each feature are equal to the feature importance scores. ;

[0164] Step 6.2, Uncertainty Smoothing:

[0165] ;

[0166] ;

[0167] in, This refers to the smoothing weighting coefficient; the greater the uncertainty, the smaller the weight. This refers to the smoothed predicted value, which reduces prediction jitter. This refers to the predicted value from the previous step, used to smooth the current prediction. By introducing uncertainty estimation and multi-step prediction mechanisms, unmanned vessels can provide forward-looking decision support in different operating environments such as narrow waterways and complex sea conditions, effectively enhancing navigation safety and control reliability, and has significant engineering application value.

[0168] The above embodiments are merely exemplary embodiments of the present invention and are not intended to limit the present invention. Those skilled in the art can make various modifications or equivalent substitutions to the present invention within its scope and protection, and such modifications or equivalent substitutions should also be considered to fall within the protection scope of the present invention.

Claims

1. A method for modeling and forecasting unmanned surface vessels based on an improved nonlinear reservoir calculation model, characterized in that, Includes the following steps: Step 1: Collect historical motion state data of the unmanned vessel to form the input dataset, and the corresponding future state data to form the output dataset. Step 2: Optimize the time delay order of the nonlinear reservoir calculation model using an improved genetic algorithm. To obtain the optimal time delay order ; Step 3, based on the optimal time delay order Construct the feature matrix; Step 4: Select features based on the statistic F, retaining features with higher importance; Step 5: Use the ridge regression method to train the output weight matrix and perform multi-step prediction; Step 6: Estimate the uncertainty of the prediction results; Step 2 specifically includes: Step 2.1: Randomly generate an initial population, where each individual represents a possible time delay order. The population is initialized as follows: ; The initial population in a genetic algorithm; Refers to the first The time delay order for each individual; Population size; This refers to the minimum time delay order; This refers to the maximum time delay order; Step 2.2: Calculate the fitness value for each individual, taking into account both single-step prediction accuracy and multi-step prediction performance; ; in, This refers to the individual's fitness value; The coefficient of determination for a single-step prediction; ; Refers to the first The true value of each sample; Refers to the first Predicted values ​​for each sample; The mean of the true values ​​in the validation set; The coefficient of determination in multi-step prediction; ; The number of samples in the validation set; This refers to the number of samples in a multi-step prediction process. Refers to the number of steps in multi-step prediction; Refers to the first The sample at the th The true value of the step; Refers to the first The sample at the th The predicted value of the step; Refers to the first The average of the actual values; Step 2.3: Generate a new generation of population through genetic operations; Step 2.4: Repeat steps 2.1-2.3 until the optimal time delay order is obtained. ; Step 4 specifically includes: Step 4.1, Feature selection analysis, feature selection based on statistic F: ; ; in, Refers to the first The feature is related to the first The regression sum of squares of each output reflects the variation explained by the features, and N represents the total number of time steps; Pointing to the first The feature is related to the first The sum of squared residuals of each output reflects the unexplained variation; Step 4.2, Feature Importance Score: ; in, Refers to the first The importance score of each feature Refers to the first The feature is related to the first The test statistic F for each output; Refers to the total number of features; Select important features: ; in, Refers to the set of feature indices selected; Refers to the first The importance score of each selected feature; This refers to the cumulative importance threshold; This refers to the number of features selected.

2. The unmanned vessel modeling and forecasting method based on an improved nonlinear reservoir calculation model according to claim 1, characterized in that, Step 1 specifically includes: Set the input matrix as follows: ; in, This refers to the total number of time steps, i.e., the total number of moments in data collection. for Constant oscillation speed; for The speed of constant oscillation; for Constant bow roll rate; for The rudder at all times; Set the output matrix as follows: ; in, for Constant oscillation speed; for The speed of constant oscillation; for Constant bow roll rate; Input state vector Output state vector ; The training set accounts for 0.7%, the validation set accounts for 0.15%, the test set accounts for 0.13%, and the multi-step prediction set accounts for 0.02%.

3. The unmanned surface vessel modeling and forecasting method based on an improved nonlinear reservoir calculation model according to claim 1, characterized in that, Step 3 specifically includes: Step 3.1, for the optimal time delay order Construct linear feature vectors: ; in, Refers to time The linear feature vector contains all state information from the current and past time points; This refers to the optimal time delay order; This refers to the dimension of the linear eigenvector, with 4 state variables at each time step; Step 3.2, construct the linear feature matrix: ; in, Refers to the linear characteristic matrix. The subscript from The initial purpose was to eliminate the influence of transient effects caused by the initial state of the reserve pool. Each row is a linear feature vector at a time point, and N represents the total number of time steps. Step 3.3, construct the nonlinear characteristic matrix: ; in, The nonlinear characteristic matrix contains all quadratic terms, i.e., time-major characteristics. No. The and the first Interaction terms of linear features, index ; This indicates element-wise multiplication; The first linear eigenvector One element; The first linear eigenvector One element; Dimensions of the nonlinear feature matrix: ; in, The dimension of the linear feature matrix. ; Refers to the dimension of the nonlinear feature matrix; Step 3.4, construct the complete feature matrix: 。 4. The unmanned surface vessel modeling and forecasting method based on an improved nonlinear reservoir calculation model according to claim 1, characterized in that, Step 5 specifically includes: Step 5.1, Standardization Process: ; in, Refers to the standardized feature matrix; The selected feature matrix contains only important features. The mean of the characteristic matrix; The standard deviation of the characteristic matrix; Refers to the standardized output matrix; The mean of the output matrix; The standard deviation of the output matrix; Refers to the first Arrive at the The output matrix of the row; Step 5.2, the ridge regression solution is: ; in, Refers to the output weight matrix; Ridge regression regularization parameters; Refers to the identity matrix, with dimensions of ; Step 5.3, the predicted value is: ; in, Standardized forecast value; The final predicted value after destandardization; Step 5.4, during multi-step prediction, the state sequence needs to be updated: ; ; ; in, Refers to the first The complete state vector, including the predicted velocity vector. and the rudder angle of the step ; The updated state sequence involves removing the oldest state and adding the latest predicted state. This is the rudder angle attenuation coefficient.

5. The unmanned surface vessel modeling and forecasting method based on an improved nonlinear reservoir calculation model according to claim 1, characterized in that, Step 6 specifically includes: Step 6.1, Uncertainty estimation: ; in, This refers to the uncertainty estimate, which reflects the reliability of the forecast; Refers to the first One standardized feature value; Refers to the first The weights of each feature are equal to the feature importance scores. ; Step 6.2, Uncertainty Smoothing: ; ; in, The smoothing weighting coefficient; The smoothed predicted value; This refers to the predicted value from the previous step.

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