Lithium battery remaining service life prediction method

Abstract

The invention relates to the technical field of lithium battery fault prediction, in particular to a lithium battery remaining service life prediction method, which comprises the following steps of S1, collecting degradation data of a lithium battery in a multi-time cyclic charging and discharging process at a constant temperature; s2, standardizing the degradation data; s3, optimizing a BP neural network hyper-parameter based on error minimization; s4, performing forward prediction by using the optimal hyper-parameter; s5, updating parameters by adopting a fractional gradient descent method; s6, judging whether a termination condition is met or not, and outputting a training completion model; s7, performing multi-step capacity prediction by using the training model to obtain a degradation trend; and S8, predicting the number of remaining available cycles of the lithium battery in combination with the capacity threshold. According to the invention, through fusion of multi-source data modeling, fractional gradient optimization and DLH-GWO hyper-parameter tuning technologies, the accuracy, convergence efficiency and model stability of prediction of the remaining service life of the lithium battery are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of lithium battery failure prediction, and in particular to a method for predicting the remaining service life of a lithium battery. Background Art

[0002] With the development of energy storage technology, lithium batteries have become the mainstream energy storage unit widely used in portable electronic devices, electric vehicles and new energy power systems due to their advantages such as high energy density, high operating voltage, high conversion efficiency and long cycle life. However, in actual use, the charging and discharging environment of lithium batteries is complex and changeable, which can easily cause electrochemical corrosion and structural aging, resulting in capacity decay and affecting operational stability and safety. If the performance degradation of lithium batteries cannot be identified in time, sudden power outages may occur during operation, leading to equipment shutdown or system failure. Therefore, accurately predicting the remaining service life of lithium batteries has important engineering value and safety significance.

[0003] At present, data-driven battery life prediction methods have been widely used. By collecting characteristic data of lithium batteries during use, modeling and analysis are carried out with the help of models such as neural networks, support vector machines, and Gaussian process regression, and feedback mechanisms are used to achieve dynamic updates of life trends. However, existing neural network methods still have certain limitations when dealing with lithium battery life prediction tasks: on the one hand, traditional gradient descent algorithms are prone to fall into local optimality in high-dimensional nonlinear problems, affecting the convergence speed and prediction accuracy; on the other hand, the neural network hyperparameter configuration has strong randomness, which may lead to unstable model performance and difficult to reproduce results, reducing its reliability and generalization ability in actual scenarios. Summary of the Invention

[0004] The present invention provides a method for predicting the remaining useful life of lithium batteries, which realizes adaptive optimization of hyperparameters, thereby improving the accuracy, stability and convergence efficiency of the prediction model, enhancing its modeling ability for complex nonlinear degradation processes, and is more suitable for lithium battery health management and life assessment in multiple scenarios.

[0005] A method for predicting the remaining service life of a lithium battery comprises the following steps: S1, data collection and measurement: Under constant temperature conditions, lithium batteries are charged in constant current mode until the battery voltage reaches the voltage threshold for constant current to constant voltage conversion. Charging continues in constant voltage mode until the charging current drops to the current threshold for charging cutoff. After charging is completed, they are discharged at a constant current until different batteries drop to different voltages. Multiple charge and discharge cycles are repeated, and data on capacity degradation over the charge and discharge cycles is collected. S2, data preprocessing: standardize the collected lithium battery degradation data; S3, Preliminary preparation: Iterate and determine the optimal hyperparameters of the BP neural network model through the minimum training set output and input error; S4, forward propagation: The optimal hyperparameters are introduced into the BP neural network model, and the pre-processed lithium battery degradation data is forwarded through the BP neural network model to predict the degradation data and transmit the output; S5, back propagation: compare the predicted value output by the forward propagation of the BP neural network model with the actual measured data, and minimize it through the fractional gradient descent method to update the parameters; S6, stop updating: determine whether the number of iterations in the back propagation reaches the maximum setting or whether the minimum output and measurement error meet the termination conditions, and retain the weights and biases of the fractional-order BP neural network model obtained at this time; S7, lithium battery degradation trend prediction: The weights and biases obtained in S6 are introduced into the BP neural network model. The lithium battery degradation data at time t, t+1, and t+2 are used as the input of the BP neural network model to predict the output at time t+3. Through multi-step prediction, the overall degradation trend of the lithium battery's remaining capacity is inferred. S8, prediction of remaining service life of lithium batteries: Different lithium battery models correspond to different capacity thresholds. By predicting the overall degradation trend of the remaining capacity of the lithium battery, the maximum number of cycles required to reach the capacity threshold is analyzed, and the remaining number of uses is obtained.

[0006] Optionally, the data preprocessing in S2 adopts Z-Score standardization, and the degradation data after standardization conforms to the standard normal distribution, that is, the mean is 0 and the standard deviation is 1.

[0007] Optionally, the pre-preparation uses the DLH-GWO optimization algorithm to determine the optimal hyperparameters of the BP neural network model, specifically including: Initialize the gray wolf population: randomly generate a set of hyperparameter combinations (gray wolf locations); Dynamic hierarchical search: α wolf (optimal solution), β wolf (second-best solution), and δ wolf (third-best solution) guide other wolves (candidate solutions) to update their positions. Dynamic weights are introduced to adjust the search range and balance global exploration and local development. Fitness evaluation: Use the training error (such as MSE) of the BP neural network model as the fitness function to evaluate each set of hyperparameters; Iterative update: until the maximum number of iterations (1000 times) or the error threshold (1e-9) is reached, the optimal hyperparameter combination is output.

[0008] Optionally, the forward propagation of the BP neural network model includes: Input layer: receives the normalized degradation data; Hidden layer: BP neural network model after using the optimal hyperparameters; Output layer: Generates prediction results through a linear activation function.

[0009] Optionally, the fractional gradient descent method includes: Forward propagation: calculate the output of the BP neural network model and obtain the predicted value; Error calculation: Compare the predicted value with the actual measurement data and calculate the loss (such as mean square error); Backpropagation: Calculate the gradient of loss with respect to weights and biases using the chain rule, and update the parameters using the gradient descent optimization method; Iterative training: Repeat forward propagation, error calculation, and backpropagation, checking the termination condition after each iteration.

[0010] Optionally, the gradient descent optimization method is expressed as: .

[0011] Optionally, the termination condition includes a preset error threshold (loss < 0.001) or a maximum number of iterations (1000 times).

[0012] Optionally, the lithium battery degradation trend prediction in S7 includes: Hidden layer output: ; Output layer results: .

[0013] Beneficial effects of the present invention: The present invention constructs a lithium battery remaining service life prediction system architecture by integrating data-driven, big data analysis and neural network algorithms. Based on the input of multi-source battery data, it can evaluate the battery health status and degradation trend in real time, realize intelligent life prediction and fault warning, and significantly improve data processing capabilities and operation and maintenance efficiency.

[0014] The present invention optimizes the BP neural network training process by introducing the fractional-order gradient descent method, utilizes the non-locality of the fractional-order derivative, and dynamically adjusts the iteration direction, effectively overcoming the problem that the ordinary gradient method is prone to falling into the local optimum, thereby improving the modeling accuracy and convergence speed of the complex nonlinear degradation characteristics of lithium batteries.

[0015] The present invention embeds the DLH strategy into the GWO optimization algorithm, strengthens the diversity and global-local balance of hyperparameter search, improves the stability and generalization ability of the fractional-order BP neural network in the hyperparameter optimization stage, and enhances the reliability and repeatability of the model prediction results. It shows better prediction performance than traditional methods under various working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only for the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0017] Figure 1 Schematic diagram of the prediction method flow in an embodiment of the present invention; Figure 2 This is a flow chart of the second stage DLH-GWO hyperparameter optimization of the improved fractional-order BP neural network lithium battery remaining service life prediction method according to an embodiment of the present invention; Figure 3 This is a flow chart of the third stage of the improved fractional-order BP neural network method for predicting the remaining useful life of lithium batteries using the fractional-order gradient descent method for training the BP neural network according to an embodiment of the present invention; Figure 4 This is a flow chart of fractional-order BP neural network training and prediction output in the fourth stage of the improved fractional-order BP neural network lithium battery remaining service life prediction method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0018] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. Those skilled in the art may also adopt other alternatives to implement some known technologies; and the accompanying drawings are only for more specific description of the embodiments and are not intended to specifically limit the present invention.

[0019] like Figures 1-4 As shown, a method for predicting the remaining service life of a lithium battery includes the following steps: Step 1: Data collection and measurement. Under constant temperature conditions, the lithium battery is charged in constant current mode until the battery voltage reaches a preset value. Then, it is charged in constant voltage mode until the charging current drops to a preset value. After charging is completed, it is discharged at a constant current until different batteries drop to different voltages. The charge and discharge behavior is repeated multiple times, and the change data of its capacity over the charge and discharge cycle is collected; Step 2: Data preprocessing: Standardize or normalize the lithium battery degradation data obtained in step 1 to improve the stability and convergence speed of model training and ensure that different features contribute more evenly to the prediction results. Step 3: Preliminary preparation - hyperparameter optimization. By iterating the minimum training set output and input error, the most suitable hyperparameters for the model are found. An optimized hyperparameter can improve the prediction efficiency of the neural network model. Step 4: Forward propagation, bring the optimal hyperparameters obtained in step 3 into the BP neural network, forward transmit the lithium battery data information processed in step 2 through the network, calculate and transmit the data information; Step 5: Back propagation - parameter update, the original integer-order gradient descent method of the BP neural network is improved to the fractional-order gradient descent method. The data output by the forward propagation of the BP neural network in step 4 is compared with the actual measurement data, and the fractional-order gradient descent method is used to minimize it and update the parameters. Step 6: Stop updating, determine whether the number of iterations in step 5 has reached the maximum setting or whether the minimum output and measurement error meet the conditions, and retain the weights and bias of the fractional-order BP neural network obtained at this time; Step 7: Predicting the degradation trend of lithium batteries: The weights and biases obtained in step 6 are introduced into the BP neural network. The degradation data of lithium batteries at time t, t+1, and t+2 are used as the input of the model to predict the output at time t+3. Multi-step prediction is used to infer the overall degradation trend of the remaining capacity of the lithium battery. Step 8: Predict the remaining service life of the lithium battery. Different lithium battery models correspond to different capacity thresholds. Based on the capacity degradation trend of the lithium battery predicted in step 7, the maximum number of cycles that the lithium battery can be used after reaching the capacity threshold is analyzed, and then the remaining number of uses is obtained.

[0020] The data preprocessing method is Z-Score normalization, which normalizes the data by giving the mean and standard deviation of the original data. The processed data conforms to the standard normal distribution, that is, the mean is 0 and the standard deviation is 1. The conversion formula is: .

[0021] Before training the prediction model, the DLH-GWO optimization algorithm is used to determine the optimal hyperparameters for training the neural network model. The first layer searches for the global optimal parameter range, and the second layer performs a local fine search within this range to improve the accuracy of the established model after standardizing and preprocessing the data. DLH-GWO optimization. Hyperparameters of the BP neural network (such as learning rate, number of hidden layer nodes, initial weights and biases, etc.)

[0022] step: 1. Initialize the gray wolf population: randomly generate a set of hyperparameter combinations (gray wolf locations).

[0023] 2. Dynamic hierarchical search: Wolf α (optimal solution), wolf β (second-best), and wolf δ (third-best) guide other wolves (candidate solutions) to update their positions.

[0024] Dynamic weights are introduced to adjust the search range and balance global exploration and local development.

[0025] 3. Fitness evaluation: Use the BP network training error (such as MSE) as the fitness function to evaluate each set of hyperparameters.

[0026] 4. Iterative update: until the maximum number of iterations or error threshold is reached, the optimal hyperparameter combination is output.

[0027] By optimizing the hyperparameters of fractional-order BP neural networks, we can improve the model's efficiency, performance, and practicality at multiple levels. This not only helps improve the model's ability to learn from data, but also reduces resource consumption and enhances the model's reliability and generalization capabilities. Therefore, hyperparameter optimization is a key step in applying neural networks to real-world tasks and is fundamental to ensuring the model's practical applicability.

[0028] The optimal hyperparameters were used as initial values ​​to train the FOGD-BP remaining useful life prediction model. This neural network's iterative training algorithm, after accurately acquiring historical lithium battery data, forward-propagates the training data through a fractional-order neural network. Using fractional-order gradient descent, the error between the model output and the actual output is minimized, further updating the parameters to better align with the model.

[0029] Forward BP neural network structure: Input layer: receives standardized feature data.

[0030] Hidden layer: Use the optimized number of nodes and activation function.

[0031] Output layer: Outputs the prediction results (such as linear activation function for regression tasks).

[0032] BP neural network with fractional order gradient descent (FOGD-BP): 1: Forward propagation: Calculate the network output and get the predicted value.

[0033] 2: Error calculation: Compare the predicted value with the true value and calculate the loss (such as mean square error).

[0034] 3: Backpropagation: Calculate the gradient of loss with respect to weights / biases using the chain rule, and use the gradient descent optimization method to update the parameters: .

[0035] 4: Iterative training: Repeat the forward propagation, error calculation, and backpropagation process. After each iteration, check the termination condition: a preset error threshold (such as loss < 0.001) or a maximum number of iterations (such as 1000).

[0036] Model prediction and output. After the best trained and optimized model meets the termination criteria, the fractional-order BP neural network model with the optimal weights is saved. New data is input into the trained model to obtain the standardized prediction results, which are then denormalized and output as the final prediction value.

[0037] Hidden layer output: Output layer results: .

[0038] Figure 2 This is a flow chart of the DLH-GWO hyperparameter optimization process in step 3 of the improved fractional-order BP neural network lithium battery remaining service life prediction method provided by the present invention. The detailed calculation steps are as follows.

[0039] In this example, the initial hyperparameters of the neural network are processed according to the DLH-GWO method to obtain the parameters that best match the model. This solves the problem of insufficient search space coverage caused by the relatively low optimization efficiency of the neural network and the strong randomness of the neural network parameters. This improves the model's generalization ability on new data to a certain extent and improves prediction accuracy. The main calculation process is as follows: The gray wolf approaches its prey during hunting. In order to mathematically model this behavior, the equation for the gray wolf's position update is: ; ; in, Indicates the number of current iterations, represents the position vector of the prey, represents the wolf's position vector.

[0040] and are coefficient vectors, and their expressions are as follows: ; ; in, 、 represents a random vector of

[01] , It is randomly linearly reduced from 2 to 0 during the iteration process.

[0041] After the gray wolf uses its own ability to identify the location of the prey, it will guide the entire wolf pack to hunt the prey. This update process can be described by the following formula: ; ; In the above calculation, the best three wolves are selected, and the positions of these three wolves are considered in the equation to determine the surrounding situation of the prey. Finally, the equation is used to calculate the first Sekiro A new candidate solution position for the iteration .

[0042] In DLH-GWO, a hunting strategy of learning from neighbors is added, which will also generate a new candidate solution. First calculate the current position and candidate solutions Distance between: ; ; in, Indicates the Sekiro iterations, represents the distance between two neighbor wolves, Represents the entire wolf pack. Once formed The neighborhood of can be learned through multiple neighborhoods to form a new candidate solution: ; in, Indicates that in the neighborhood A random neighborhood is chosen, Indicates By comparing the fitness values ​​of two candidate solutions, the better candidate is selected: ; In this example, the parameters in the initial BP neural network model are adjusted using the above method and then introduced into the model. Since the fractional order gradient weight matrix can reflect the deviation of the parameters in the initial fractional order gradient BP neural network model with high accuracy, the fractional order algorithm is used to train the initial fractional order gradient BP neural network model, and a BP neural network model with high judgment accuracy can be obtained.

[0043] Before describing the method of using the fractional order algorithm to perform classification training on the initial fractional order gradient-based BP neural network model, the fractional order gradient descent method is first explained: For the traditional Caputo fractional derivative, when The definition of when is as follows: (1) in, represents the upper bound of the differential equation, represents the lower bound of the differential equation, , , represents the order of the differential equation, , Represents the gamma function, and after optimizing it, we can get the following expansion: (2) in, Assume that the objective function is , then the traditional gradient descent iterative process is: (3) in, Represents the iterative step size. The iterative process of converting Equation (3) into the fractional gradient descent method is: (4) in, Expand the FOGD formula to: (5) In order to keep Equation (5) consistent with the integer-order gradient descent method, it is further optimized as follows: (6) In the above fractional gradient descent method, by Perform multiple iterations to obtain the final fractional gradient descent algorithm.

[0044] Since the fractional-order gradient descent method uses fractional-order derivatives for iterative processing, compared with the commonly used integer-order gradient descent method, the fractional-order gradient descent method has a wider processing range and higher accuracy of the results.

[0045] Figure 3 This is a flow chart of an embodiment of the present invention for training an initial BP neural network model based on fractional order gradient using a fractional order algorithm.

[0046] In this embodiment, an error function is used to calculate the fractional gradient of each node and use this to update the weight matrix. Through iterative optimization, the parameters of the initial fractional gradient BP neural network are adaptively adjusted, ultimately achieving a fully trained, high-precision network model. This fractional gradient weight update mechanism can more accurately characterize the dynamic deviations of network parameters, significantly improving the model's convergence accuracy.

[0047] A typical three-layer BP network, in which The corresponding numbers represent the number of neurons in the input layer, hidden layer and output layer respectively. The output is determined by the attribute dimensional real-valued vector. The connection weights between the input layer and the hidden layer are , the activation function is ; The connection weight between the hidden layer and the output layer is , the activation function is .

[0048] Hidden layer input and output Calculated separately: (7) (8) Input to the output layer and output Calculated separately: (9) (10) Mean squared error loss function for evaluating neural networks It can be defined as: (11) in, Indicates the The ideal output of the sample is After substitution, formula (11) can be written as: (12) For any initial connection weight matrix and , No. The update formula of the secondary weight connection matrix is ​​as follows: (13) (14) The fractional order gradient descent method is now applied to the BP neural network. On the basis of integer order, it is replaced by the gradient descent based on Caputo fractional order derivative. The updated formulas of Equation (13) and Equation (14) are as follows: (15) (16) in, represents the learning rate of the neural network, represents the fractional order, Indicates the label of each sample.

[0049] In the above method, the BP neural network model is trained using the fractional-order algorithm. Since the fractional-order algorithm can more accurately obtain the parameter values ​​in the fractional-order gradient update weight matrix during the processing process, it can enhance the performance of the final BP neural network model based on the fractional-order gradient and improve the judgment accuracy.

[0050] In order to combine the above methods, such as Figure 4 As shown, the present invention also provides a schematic diagram of the flow of training and prediction output of the improved fractional-order BP neural network lithium battery remaining service life prediction method.

[0051] In the back propagation neural network, the commonly used activation function is the sigmoid function. In the experimental configuration, the model usually constructs a set of (in ) to another end time point (in ) The corresponding numerical arrays in these arrays are used as model features for input, which can be expressed as 、 … .

[0052] By using the fractional-order back-propagation neural network as the training function and taking the above-constructed feature array as the input of the model, the predicted output of the model is obtained . Then, the obtained will serve as The numerical input at the moment continues the multi-step training prediction. The method is applied recursively. The specific formula is as follows: ; ; in, Indicates time arrive The corresponding data vector, Represents the input layer and the The weights between the neurons in the hidden layer, Indicates the hidden layer neurons and the The weights between the output neurons, (in ) indicates that at time The predicted output.

[0053] Repeat the above steps until the preset minimum error or maximum number of iterations is reached. At this time, the output is predicted based on the historical lithium battery test set data, and the robustness of the model is verified through early and late predictions.

[0054] The main innovation of this paper lies in combining the DLH-GWO algorithm with the fractional-order BP algorithm. Through a collaborative optimization mechanism, the performance of the neural network is comprehensively improved, achieving high-precision life prediction. This method combines global optimization capabilities with dynamic adjustment of model parameters, providing an effective engineering approach for solving complex nonlinear prediction problems.

[0055] The present invention encompasses any alternatives, modifications, equivalents, and solutions that fall within the spirit and scope of the present invention. To provide a thorough understanding of the present invention, specific details are described in detail below in connection with the preferred embodiments of the present invention, but those skilled in the art will be able to fully understand the present invention without these detailed descriptions. Furthermore, to avoid unnecessary confusion regarding the essence of the present invention, well-known methods, processes, procedures, components, and circuits have not been described in detail.

[0056] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A method for predicting the remaining service life of a lithium battery, characterized in that: The following steps are involved: S1, data collection and measurement: Under constant temperature conditions, lithium batteries are charged in constant current mode until the battery voltage reaches the voltage threshold for constant current to constant voltage conversion. Charging continues in constant voltage mode until the charging current drops to the current threshold for charging cutoff. After charging is completed, they are discharged at a constant current until different batteries drop to different voltages. Multiple charge and discharge cycles are repeated, and data on capacity degradation over the charge and discharge cycles is collected. S2, data preprocessing: standardize the collected lithium battery degradation data; S3, Preliminary preparation: Iterate and determine the optimal hyperparameters of the BP neural network model through the minimum training set output and input error; S4, forward propagation: The optimal hyperparameters are introduced into the BP neural network model, and the pre-processed lithium battery degradation data is forwarded through the BP neural network model to predict the degradation data and transmit the output; S5, back propagation: compare the predicted value output by the forward propagation of the BP neural network model with the actual measured data, and minimize it through the fractional gradient descent method to update the parameters; S6, stop updating: determine whether the number of iterations in the back propagation reaches the maximum setting or whether the minimum output and measurement error meet the termination conditions, and retain the weights and biases of the fractional-order BP neural network model obtained at this time; S7, lithium battery degradation trend prediction: The weights and biases obtained in S6 are introduced into the BP neural network model. The lithium battery degradation data at time t, t+1, and t+2 are used as the input of the BP neural network model to predict the output at time t+3. Through multi-step prediction, the overall degradation trend of the lithium battery's remaining capacity is inferred. S8, prediction of remaining service life of lithium batteries: Different lithium battery models correspond to different capacity thresholds. By predicting the overall degradation trend of the remaining capacity of the lithium battery, the maximum number of cycles required to reach the capacity threshold is analyzed, and the remaining number of uses is obtained.

2. The method for predicting the remaining service life of a lithium battery according to claim 1, wherein: The data preprocessing in S2 adopts Z-Score standardization, and the degradation data after standardization conforms to the standard normal distribution, that is, the mean is 0 and the standard deviation is 1.

3. The method for predicting the remaining service life of a lithium battery according to claim 2, wherein: The preliminary preparation uses the DLH-GWO optimization algorithm to determine the optimal hyperparameters of the BP neural network model, specifically including: Initialize the gray wolf population: randomly generate a set of hyperparameter combinations; Dynamic hierarchical search: α-wolves, β-wolves, and δ-wolves guide other wolves to update their positions. Dynamic weights are introduced to adjust the search range and balance global exploration and local development. Fitness evaluation: Use the training error of the BP neural network model as the fitness function to evaluate each set of hyperparameters; Iterative update: until the maximum number of iterations or error threshold is reached, the optimal hyperparameter combination is output.

4. The method for predicting the remaining service life of a lithium battery according to claim 3, wherein: The forward propagation of the BP neural network model includes: Input layer: receives the normalized degradation data; Hidden layer: BP neural network model after using the optimal hyperparameters; Output layer: Generates prediction results through a linear activation function.

5. The method for predicting the remaining service life of a lithium battery according to claim 4, wherein: The fractional gradient descent method includes: Forward propagation: calculate the output of the BP neural network model and obtain the predicted value; Error calculation: compare the predicted value with the actual measurement data and calculate the loss; Backpropagation: Calculate the gradient of loss with respect to weights and biases using the chain rule, and update the parameters using the gradient descent optimization method; Iterative training: Repeat forward propagation, error calculation, and backpropagation, checking the termination condition after each iteration.

6. A method for predicting the remaining service life of a lithium battery according to claim 5, characterized in that: The gradient descent optimization method is expressed as: 。 7. A method for predicting the remaining service life of a lithium battery according to claim 6, characterized in that: The termination condition includes a preset error threshold or a maximum number of iterations.

8. The method for predicting the remaining service life of a lithium battery according to claim 7, wherein: The lithium battery degradation trend prediction in S7 includes: Hidden layer output: ; Output layer results: .

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