Deep sea energy system life prediction method

Abstract

The invention provides a deep sea energy system life prediction method, and relates to the technical field of life prediction, and the method specifically comprises the steps: collecting the electrical characteristics of a battery and deep sea environment stress, and carrying out the standardization processing; constructing a deep sea environment degradation model, and constraining the physical characteristics based on the deep sea environment model; inputting the data into a physical branch network to extract consistency constraint features and physical initial priori; the standardized data, the physical enhancement features and the consistency constraint features are input into a lightweight data branch network, and deep residual information formed after the lightweight data branch network is pre-trained is transmitted to a physical branch network; and the RUL priori estimation output by the physical branch network and the data correction item output by the data branch form a final prediction, the final prediction is input into a Bayesian framework to derive posteriori distribution, and uncertainty quantization is carried out. According to the technical scheme, the problems of low service life prediction accuracy and relatively high computing resources of the deep sea energy system in the prior art are solved.

Description

Technical Field

[0001] The present invention relates to the technical field of life prediction, and particularly relates to a method for predicting the life of a deep-sea energy system. Background Art

[0002] As the core power unit of the deep-sea equipment system, the research on the life prediction of the deep-sea energy system is directly related to the mission reliability and strategic effectiveness of key equipment such as the seafloor observatory network, autonomous underwater vehicles, and stealth weapon platforms. The life prediction technology of the deep-sea energy system has become the core foundation for ensuring its reliable operation throughout the life cycle. Existing research shows that deep-sea pressure fluctuations will accelerate the growth rate of the solid electrolyte interface membrane (SEI) of lithium-ion batteries, and the synergistic effect of low-temperature environment and high-pressure hydrogen permeation may cause irreversible attenuation of the catalytic layer of proton exchange membrane fuel cells. More complexly, the attachment of microbial films on the surface of metal electrodes will change the local electrochemical environment, inducing multi-mode failures such as pitting corrosion and stress corrosion cracking. These degradation processes are characterized by strong time-variability and multi-scale coupling, making the traditional life assessment method based on a single stress accelerated aging experiment difficult to apply, and there is an urgent need to establish a life prediction theory system under special deep-sea working conditions.

[0003] Although existing research has preliminarily explored the correlation mechanism between electrochemical aging and capacity decay through the Arrhenius equation and stochastic processes (Wiener / Gamma processes), the systematic life prediction research on deep-sea energy systems is still blank, and there are significant deficiencies in the existing models in quantifying the reconstruction effect of high-pressure environment on the activation energy of materials and the pressure-temperature dynamic coupling mechanism. In addition, in the field of data-driven, although deep learning algorithms have shown advantages in predicting the health state of lithium batteries, due to the inherent defects of deep-sea in-situ monitoring data such as small sample size, strong noise interference, and high working condition discreteness, the generalization ability of the model will be insufficient.

[0004] Therefore, there is a need for a method for predicting the life of a deep-sea energy system that can accurately capture the multi-scale spatio-temporal correlation of the influence of deep-sea high-pressure and low-temperature environmental factors on battery degradation, has high prediction accuracy, and requires low computing resources. Summary of the Invention

[0005] The main object of the present invention is to provide a method for predicting the life of a deep-sea energy system to solve the problems of low accuracy and high computing resources in predicting the life of a deep-sea energy system in the prior art.

[0006] To achieve the above object, the present invention provides a method for predicting the life of a deep-sea energy system, which specifically includes the following steps:

[0007] S1, collect the electrical characteristics of the battery and deep-sea environmental stress, and perform standardization processing.

[0008] S2. Based on the Arrhenius equation, Weibull distribution, and Wiener process, a deep - sea environmental degradation model is constructed, and the physical characteristics are constrained based on the deep - sea environmental model.

[0009] S3. Input the data processed in step S1 into the physical branch network to extract the consistency - constraint features and physical initial priors.

[0010] S4. Input the standardized data, physical enhancement features, and consistency - constraint features processed in step S1 into the lightweight data branch network. The lightweight data branch network includes: a main network and an auxiliary network. The deep - layer residual information formed after pre - training of the lightweight data branch network is transmitted to the physical branch network.

[0011] S5. The RUL prior estimate output by the physical branch network and the data correction term output by the data branch form the final prediction, which is input into the Bayesian framework to deduce the posterior distribution for uncertainty quantification.

[0012] Further, step S3 is specifically: Input the data processed in step S1 into the 2D fully - connected layer, hidden layer, and fully - connected layer connected in sequence in the physical branch network. The hidden layer outputs physical enhancement features , and the fully - connected layer outputs consistency - constraint features and physical initial priors .

[0013] Further, step S2 specifically includes the following steps:

[0014] S2.1. The deep - sea environmental degradation model is : ; ; ; ; where is the initial battery capacity, is the degradation rate model, is the temperature, is the pressure, is the time, is the basic amplitude factor of the degradation rate, is the activation energy at normal temperature and pressure, is the pressure - sensitive coefficient, is the Weibull distribution probability density function, is the Weibull scale parameter, is the Weibull shape parameter, is the capacity fluctuation caused by Brownian noise, is the capacity baseline offset, is the temperature compensation coefficient, is the temperature non - linear exponent, is the pressure compensation coefficient, is the pressure non - linear exponent.

[0015] S2.2, Define the first - hitting time of the standard Brownian motion as: ; where, is the infimum of the set, is the battery failure threshold.

[0016] S2.3, Convert the degradation process into a first - hitting time problem of the standard Brownian motion, and define the standardized threshold : ; where, .

[0017] Obtain the approximate probability density of RUL : ; where, is the natural exponential function.

[0018] Furthermore, both the main network and the auxiliary network in step S4 include, connected in sequence: an input layer, a linear layer, a multi - head sparse self - attention module, a feature concatenation layer, a linear fusion layer, a DRC&CLN layer, a gated feed - forward network, a DRC&Norm layer, and a linear prediction layer. Step S4 specifically includes the following steps: S4.1, Obtain query, key, and value vectors through the linear transformation of the linear layer: ; where, , and are the projection parameter matrices.

[0019] S4.2, In the multi - head sparse self - attention module, for the th query vector , the sparsity metric is defined as follows: ; where, is the total length of the key sequence, is the normalization factor when scaling dot - product attention, is the th key, is to take the maximum.

[0020] S4.3, Construct a sparse query matrix , only keep the dot products between each query vector and the keys vectors with the largest sparsity, and set the rest to zero, define the multi-head sparse self-attention layer: ; where is the feature representation obtained after sparse attention calculation by the th attention head, and

[0021] is the SoftMax function applied row-wise. ; where represents the total length of the query sequence, and is the natural logarithm.

[0022] Furthermore, step S4 also includes the following steps: S4.4, Subsequently, pass through the feature concatenation layer and the linear fusion layer and enter the DRC&CLN layer. In the DRC&CLN layer, the scaling factor and the offset of the normalization parameter are generated by the time step feature : ; where , represent the weight matrices of the linear transformations for generating the scaling factor and the offset respectively, and and represent the corresponding bias vectors respectively.

[0023] The normalization operation is expressed as: ; where and are the mean and standard deviation of the current time step respectively, is the matrix dot product, and represents the feature of the current time step.

[0024] S4.5, Adopt cross-layer dense residual connection DRC. In the output calculation of each layer, in addition to the multi-head sparse self-attention, the outputs of all previous layers are also concatenated together: ; where represents layer normalization, represents multi-head sparse self-attention, represents concatenation, Represents the features extracted through the DRC&CLN layer.

[0025] S4.6, realizing the adaptive regulation of the feature flow through the gated feed-forward network GLU: ; Among them, is the projection matrix, is the Sigmoid function, is the element-wise multiplication, and are the bias terms corresponding to the projection matrix respectively.

[0026] Furthermore, step S4 also includes the following steps: S4.7, passing through the DRC&Norm layer and the linear prediction layer again, and obtaining the potential feature representation of the training data extracted by the main network feature extractor : ; Among them, is the potential feature extracted by the main network training data at time step , is the total length of the time series of the current training sample, is the number of time steps for future prediction, is the dimension of the potential feature extracted at each time step, is the length of the historical window of the input sequence.

[0027] S4.8, taking the output by the main network as the input and feeding it into the prediction network of the residual MLP to predict the future potential representation: ; Among them, is the prediction result of the potential feature at time step , is the predicted end time point of the current test sequence.

[0028] The output result of the auxiliary network is , among which, is the test data.

[0029] S4.9, calculating the feature similarity using the cosine similarity, and calculating the similarity degree between the predicted feature and the actual feature in the th incremental learning IL: ; Among them, is the average cosine similarity of the th incremental learning, indicating the

[0030] Furthermore, step S4 further includes the following steps: S4.10, define the contrastive loss as: .

[0031] The test loss function during the th incremental learning training process is defined as follows: ; where, is the system health state at the prediction time step , and is the adjustment coefficient.

[0032] S4.11, when the predicted health state is lower than the failure threshold for the first time, it is considered that the system is about to fail, and the remaining useful life RUL is defined as: ; where, m is the length of historical data, and 𝑟 represents the prediction step from the current moment to the health state lower than the failure threshold; when , the system is still in a healthy state; when , the system is determined to have degraded and failed, and the RUL prediction ends; is the failure threshold.

[0033] Furthermore, step S5 includes the following steps: S5.1, the final predicted output , construct the Bayesian likelihood function form:

[0034] where, is the uncertainty of the data-driven model prediction error, is proportional to. At the same time, the uncertainty of the physical branch network parameters is described by the prior distribution . After combining the likelihood function, the Bayesian posterior fusion distribution can be obtained: ; where, is the RUL value to be estimated, is the prior information from the physical branch network, is the likelihood function from the lightweight data branch network.

[0035] S5.2. Let the reliability index be , and the posterior -th raw moment is expressed as: ; where is the update factor, is the prior PDF, and is the l-th raw moment estimate under the Bayesian framework.

[0036] S5.3. Under the SGNI framework, use orthogonal polynomials and nested sampling points to construct a sparse expression for the multiple integral, which is further rewritten as: ; where represents the sum of the multi-indices, the non-negative integer represents the precision level, the set is the multi-dimensional grid point set under the SGNI rule, is the parameter space dimension, is the likelihood function, represents the prior CDF of the distribution parameter and the inverse normal transformation operator between the standard normal CDF , represents the standard normal random vector, and represent the grid points of SGNI and their corresponding weights in the standard normal space, respectively.

[0037] Furthermore, step S5 includes the following steps: S5.4. After obtaining the first three raw moments of the posterior reliability index, further calculate the statistical characteristics of the posterior RUL distribution: ; ; ; where is the mean, is the standard deviation, and is the skewness.

[0038] S5.5. The location , scale , and shape parameter satisfy the following relationships: ; ; .

[0039] S5.6. According to the SLN distribution characteristics, when the RUL threshold corresponds to the preset safe life, its expected failure probability can be directly calculated from the cumulative distribution function: ; where , is the probability density function, is the cumulative distribution function, is the standard normal distribution CDF.

[0040] Correspondingly, the lower limit of RUL at the confidence level of can be calculated by the inverse transformation of the SLN distribution: ; thus obtaining the failure probability at the confidence level of .

[0041] S5.7. The probability density function PDF of the failure probability is expressed as : ; where is the independent variable.

[0042] The present invention has the following beneficial effects: The present invention proposes a method for predicting the remaining useful life (RUL) of a lithium-ion battery in a deep-sea environment, which is used for predicting the remaining useful life of a lithium-ion battery in a deep-sea environment. The lightweight data branch network can operate as an independent deep learning model. The physical branch network realizes the mechanism modeling of the battery degradation process by embedding the degradation modeling formula based on physical principles, and enhances the feature expression ability of the data-driven branch through physical consistency constraints, thereby improving the prediction accuracy and interpretability of the model, and making the final prediction result have both the self-adaptability of data-driven and the reliability of physical modeling. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained according to these drawings. In the drawings: Figure 1 shows the flowchart of a method for predicting the remaining useful life of a deep-sea energy system according to the present invention.

[0044] Figure 2The figure shows the RUL prediction results of the deep - sea energy system. Detailed implementation manners

[0045] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some but not all of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the protection scope of the present invention.

[0046] As Figure 1 shown, a method for predicting the life of a deep - sea energy system specifically includes the following steps: S1, Multi - modal data input: Collect battery electrical characteristics and deep - sea environmental stresses, and perform standardization processing. The battery electrical characteristics include voltage and current; the deep - sea environmental stresses include temperature and pressure; after standardization processing, the high - voltage and low - temperature characteristics are combined.

[0047] S2, Based on the Arrhenius equation, Weibull distribution, and Wiener process, construct a deep - sea environmental degradation model, and constrain the physical characteristics based on the deep - sea environmental model.

[0048] Compared with the degradation model under constant - temperature conditions, the degradation of lithium - ion batteries in the deep - sea high - pressure and low - temperature environment has more complex characteristics. The coupling effect of temperature fluctuations and hydrostatic pressure changes the ion mobility in the electrolyte, the phase - change kinetics of electrode materials, and the growth mechanism of the solid electrolyte interface (SEI) film, resulting in the multi - scale spatio - temporal correlation between the degradation rate and the random fluctuation of the discharge capacity. Therefore, two core problems need to be solved when constructing a degradation model in this environment: First, how to accurately establish the mathematical relationship between the degradation rate and the changes in deep - sea environmental temperature and pressure; second, how to map the battery capacity degradation under random environmental variables to the equivalent capacity loss under the reference environment (i.e., normal temperature and pressure). For this reason, the present invention couples and corrects the pressure - temperature factors based on the Arrhenius equation, and combines the time - dependent Weibull distribution and Wiener process to construct a degradation model of lithium - ion batteries suitable for the deep - sea environment.

[0049] S3, Input the data processed in step S1 into the physical branch network to extract consistency - constraint features and physical initial priors.

[0050] S4, Input the standardized data, physical enhancement features, and consistency - constraint features processed in step S1 into the lightweight data branch network. The lightweight data branch network includes a main network and an auxiliary network. The deep - layer residual information formed after pre - training of the lightweight data branch network is transmitted to the physical branch network; the lightweight data branch network uses the iSparC - Former network for feature extraction and time - series modeling.

[0051] The final prediction, which consists of the prior RUL estimate output by the physical branch network and the data correction term output by the data branch, is input into the Bayesian framework to derive the posterior distribution for uncertainty quantification.

[0052] Specifically, S3 is as follows: The data processed in step S1 is input into the 2D fully connected layer, hidden layer, and fully connected layer connected in sequence in the physical branch network, and the hidden layer outputs physical enhancement features , and the fully connected layer outputs consistency constraint features and the physical initial prior .

[0053] Specifically, step S2 specifically includes the following steps:

[0054] S2.1, the deep-sea environment degradation model is : ; ; ; ; Among them, is the initial battery capacity, is the degradation rate model, is the temperature, is the pressure, is the time, is the base amplitude factor of the degradation rate, following the Gaussian distribution , is the activation energy at normal temperature and pressure, is the pressure sensitivity coefficient, is the Weibull distribution probability density function, is the Weibull scale parameter, is the Weibull shape parameter (reflecting the degradation mode), is the capacity fluctuation caused by Brownian noise, is the capacity baseline offset, following the Gaussian distribution, used to correct the capacity measurement deviation caused by environmental changes, making the model comparable under different environments. is the temperature compensation coefficient, is the temperature nonlinear exponent, is the pressure compensation coefficient, is the pressure nonlinear exponent; reflects the degradation mode: represents early rapid degradation, corresponds to a constant degradation rate, while This means accelerated degradation in the later stage. This distribution can well describe the full-life cycle degradation trajectory of lithium batteries from the initial stage (formation of SEI film), slow degradation in the middle stage to accelerated degradation of the material structure in the later stage.

[0055] S2.2, Define the first passage time of the standard Brownian motion as: ; where is the infimum of the set, is the battery failure threshold.

[0056] S2.3, Convert the degradation process into the first passage time problem of the standard Brownian motion, and define the standardized threshold : ; where .

[0057] Obtain the approximate probability density of RUL : ; where is the natural exponential function. Among them, the first term characterizes the influence of the threshold distance on the failure probability, and the second term characterizes the contribution of the degradation rate at a specific time. This result provides a closed solution for RUL assessment in the deep-sea environment.

[0058] At the data stream level, the fusion of the output features of the physical branch network PI and the data-driven branch is divided into two levels. First, PI provides the physical enhanced feature 𝑝 at the hidden layer level. This feature is extracted through a 2D fully connected layer and injected into the encoder of the iSparC-Former structure to optimize the representation ability of the data-driven features. Second, at the final output stage, PI outputs the physical consistency constraint , which is used to guide the RUL prediction of the lightweight data branch network to make it conform to the physical prior knowledge.

[0059] Specifically, both the main network and the auxiliary network in step S4 include, connected in sequence: an input layer, a linear layer, a multi-head sparse self-attention module, a feature splicing layer, a linear fusion layer, a DRC&CLN layer, a gated feed-forward network, a DRC&Norm layer, and a linear prediction layer. Step S4 specifically includes the following steps: S4.1, Obtain query, key, and value vectors through the linear transformation of the linear layer: ; where 、 and is the projection parameter matrix.

[0060] S4.2. In view of the long sequence characteristics of deep-sea sensor data, the present invention introduces a Sparse Multi-Head Attention (SMHA) module into the data branch network, aiming to filter redundant calculations and highlight key associations by screening dominant attention pairs based on sparsity metrics. Redundant calculations are trimmed through a key feature screening strategy, while retaining the feature focusing ability of information-sensitive regions, thereby ensuring the prediction accuracy and generalization ability of the model while reducing computational complexity.

[0061] In the sparse multi-head self-attention module, for the th query vector , the sparsity metric is defined as follows: ; where is the total length of the key sequence, is the normalization factor when scaling dot-product attention, is the th key, is to take the maximum. The first term in the formula represents the maximum dot-product value calculated by the query over all keys , while the second term represents their weighted average. This metric reflects the degree of bias of the attention distribution towards a few key key vectors. If is large, it means that the attention distribution significantly deviates from the uniform distribution and depends on a few key vectors, and thus can be sparsified.

[0062] S4.3. Therefore, a sparse query matrix is constructed, and only the dot-products between each query vector and the first key vectors with the largest sparsity are retained, and the rest are set to zero. The multi-head sparse self-attention layer is defined as: ; where is the feature representation obtained after sparse attention calculation by the th attention head, is the SoftMax function performed row-wise, which is used to normalize the sparse attention scores into a probability distribution.

[0063] Basis for selecting the sparsity 𝑢: ; where represents the total length of the query sequence, is to take the logarithm.

[0064] In most practical application scenarios, the length of the key sequence is equal to that of the query sequence, that is . Under the premise of maintaining effective attention, this strategy reduces the computational complexity to . At the same time, in the multi-head mechanism, each attention head independently constructs its own sparse query matrix , realizing the sparse expression and enhancement of features in different subspaces.

[0065] To further improve the adaptability of iSparC-Former to the dynamic non-stationary data distribution in the deep-sea environment, the present invention introduces conditional layer normalization (CLN) in the encoder, enabling the model to dynamically adjust the normalization parameters according to the context information of the current time step.

[0066] Specifically, step S4 further includes the following steps: S4.4, Subsequently, it enters the DRC&CLN layer through a feature concatenation layer and a linear fusion layer in sequence. In the DRC&CLN layer, the scaling factor and the offset of the normalization parameters are generated by the time-step feature : ; wherein, , respectively represent the linear transformation weight matrices for generating the scaling factor and the offset, and respectively represent the corresponding bias vectors.

[0067] The normalization operation is expressed as: ; wherein, and are respectively the mean and standard deviation of the current time step, is matrix dot product, represents the feature of the current time step. Through this design, the model can adaptively adjust the normalization strategy. For example, when the baseline drift of sensor measurements is caused by changes in deep-sea environmental pressure or temperature, CLN can effectively correct the distribution shift and improve the stability of the model.

[0068] S4.5, In addition, to enhance the feature transfer ability of the deep network, iSparC-Former adopts cross-layer dense residual connection DRC to alleviate the problem of gradient disappearance and retain the fine-grained information of the shallow layers. Specifically, in the output calculation of each layer, in addition to the multi-head sparse self-attention, the outputs of all previous layers are concatenated together: ; wherein, represents layer normalization, represents multi-head sparse self-attention, Indicates splicing, Represents the features extracted by the DRC&CLN layer.

[0069] This design ensures information sharing between different layers, so that shallow features can directly affect deep feature extraction, thereby improving the perception of weak degradation signals. Weak signals in the long-term operation of deep-sea energy system life prediction may carry key degradation information, and dense residual connections can ensure that this information will not be forgotten in the deep network.

[0070] S4.6, adaptive control of feature flow is achieved through the gated feedforward network GLU: ; in, is the projection matrix, is the Sigmoid function, is element-wise multiplication, and are the bias terms corresponding to the projection matrix. This design allows the model to assign feature-level weights to input features, such as giving higher transmission weights to sensors with high signal-to-noise ratios, while suppressing signals contaminated by environmental noise. In the early degradation stage of energy systems, abnormal features of sensor signals are often weak and easily drowned by noise. Through this mechanism, GLU can dynamically control the flow of information, making the network more selective for different input features and improving the sensitivity of early degradation warning.

[0071] Specifically, step S4 also includes the following steps: During the long-term operation of deep-sea energy systems, the data collected by sensors will be affected by environmental changes, equipment aging, and operating condition fluctuations, resulting in drift in data distribution. If a statically trained model is used directly for prediction, the model may not be able to adapt to the new data distribution, resulting in a decrease in prediction accuracy. Therefore, in order to enhance the generalization ability and adaptability of the model, an online incremental learning mechanism is introduced so that the data branch can dynamically update parameters while continuously receiving new data, thereby reducing the impact of error accumulation and improving the prediction accuracy of long-term degradation trends.

[0072] S4.7, when new data with distribution drift is obtained, the prediction of the degradation state in the system is inevitably affected by the error accumulation effect. In order to solve this problem, the present invention introduces a contrastive learning mechanism in the iSparC-Former network to maximize the similarity between the predicted latent features and the future latent features, thereby improving the model's adaptability to incremental data and the robustness of prediction. After the DRC&Norm layer and the linear prediction layer, the incremental data is passed through the main network feature extractor. The training data is extracted of the potential feature representation : ; Among them, is the potential feature extracted from the main network training data at time step , is the total length of the time series of the current training sample, is the number of time steps for future prediction, is the dimension of the potential feature extracted at each time step, is the historical window length of the input sequence; The incremental data refers to the newly introduced data samples used to improve the model's generalization ability or adapt to new tasks / states relative to the existing training data. S4.8, taking the output by the main network as the input, and sending it into the prediction network of the residual MLP for predicting the future potential representation: ; Among them, is the prediction result of the potential feature at time step , is the predicted end time point of the current test sequence.

[0073] To provide a supervision signal, an auxiliary network is introduced. The network structure is the same as that of the main network, but its parameters are frozen, that is, they do not participate in the gradient update. The auxiliary network is responsible for extracting the potential features of the real future samples , and participating in the optimization as a comparison target. To ensure that the model learns only from the current training data, gradient truncation (stopgradient) is set, and this operation is applied to the potential feature encoding path of the future test data, that is: the output result of the auxiliary network is statically encoded, and the gradient cannot be backpropagated, and it only participates in the supervision as a target vector. Among them, is the test data.

[0074] S4.9, since the potential representation of the future time series is learned from the historical sequence, the future features predicted by the model should have a high similarity with the real future features in the representation space. For this reason, the cosine similarity is used to calculate the feature similarity, and calculate the similarity degree between the predicted feature and the actual feature in the th incremental learning IL: ; Among them, is the Average cosine similarity of incremental learning denotes norm. The larger this value is, the closer the potential representation predicted by the model is to the true potential representation , which means that the model has successfully captured the future structure evolution trend hidden in historical features. By minimizing the difference between potential representations, the main network is guided to optimize its modeling ability for future degradation states without relying on future labels, thereby enhancing the model's adaptability and robustness to distribution drift and unknown data.

[0075] Specifically, step S4 further includes the following steps: S4.10, Since the test data cannot be used for the th IL process network update, the contrast loss is defined as: .

[0076] Based on this, the test loss function in the 𝑘-th incremental learning training process is defined as follows: ; where is the system health state at the prediction time step , and is the adjustment coefficient.

[0077] In the actual online life prediction process, the iSparC-Former main network trained by online incremental learning is used as the degradation trend prediction model for deep-sea energy systems.

[0078] To construct training data, window sliding sampling is performed on the RMS feature sequence to form the input sequence , each window length is , and the prediction target is the future . The model outputs the predicted value , which is added to the sequence for prediction at the next moment.

[0079] S4.11, When the predicted health state is first lower than the failure threshold , it is considered that the system is about to fail, and the remaining useful life RUL is defined as: ; where m is the length of historical data, and 𝑟 represents the prediction step from the current moment to the health state lower than the failure threshold; when , the system is still in a healthy state; when When this occurs, the system is determined to have experienced degradation failure and the RUL prediction ends; is the failure threshold.

[0080] Specifically, step S5 includes the following steps: S5.1, in the prediction of the remaining useful life (RUL) of the deep - sea energy system, in the face of challenges such as high - dimensionality, complex degradation mechanisms, and environmental uncertainties, the present invention proposes a physics - data fusion method based on the Bayesian probability framework for realizing dynamic, interpretable RUL prediction and uncertainty quantification. This method is based on a dual - parallel architecture, where the physical branch network calculates the initial RUL estimate based on a hybrid mechanism of the pressure - corrected Arrhenius model - Weibull distribution - non - linear Wiener process , while the deep - time - series model iSparC - Former learns the sensor data features to form a residual correction term , which together constitute the final prediction output , to achieve a reasonable fusion of these two parts of information, the present invention proposes a Bayesian inference fusion framework, regarding the data branch as a statistical correction of the prediction error of the physical branch network, assuming that the prediction residual follows a Gaussian noise model, and thus constructing the form of the Bayesian likelihood function: ; where is the uncertainty of the data - driven model prediction error, is proportional to, usually obtained by estimating the variance of historical residuals. At the same time, the uncertainty of the physical branch network parameters is described by the prior distribution , and such prior information usually comes from laboratory data calibration or domain expert experience.

[0081] Combined with the likelihood function, the Bayesian posterior fusion distribution can be obtained: ; where is the RUL value to be estimated, is the prior information from the physical branch network, is the likelihood function from the lightweight data branch network.

[0082] However, the high - dimensional characteristics of the deep - sea energy system model make the above integral difficult to analyze. Therefore, the present invention adopts the sparse grid numerical integration (SGNI) method to efficiently approximate the statistical moments of the posterior reliability index through the Smolyak formula.

[0083] S5.2, let the reliability index be , and the th original moment of the posterior is expressed as: ; where is the update factor, is the prior PDF, Bayesian evidence As a normalization constant, it needs to be calculated by integration over the prior space. is the l-th raw moment estimate under the Bayesian framework.

[0084] S5.3. Under the SGNI framework, using orthogonal polynomials and nested sampling points to construct a sparse expression of the multiple integral, the above formula can be further rewritten as: ; where , represents the sum of the multi-index, non-negative integers represents the precision level, the set is the multi-dimensional grid point set under the SGNI rule, is the parameter space dimension, is the likelihood function, represents the distribution parameter the prior CDF and the standard normal CDF of the inverse normal transformation operator between represents the standard normal random vector, and represent the grid points of SGNI and their corresponding weights in the standard normal space respectively, is the sampling point coordinate in the standard normal distribution space of the -th nested sampling point in the h-th dimension, are the Gauss-Hermite quadrature points, the weighted coefficients corresponding to the sampling points, used for the linear combination when approximating the multi-dimensional integral, are the weights of the Gauss-Hermite quadrature points, and these weights can be determined using the Gauss-Hermite formula related to the weight .

[0085] Specifically, step S5 includes the following steps: S5.4. After obtaining the first three raw moments of the posterior reliability index, further calculate the statistical characteristics of the posterior RUL distribution: ; ; ; where is the mean, is the standard deviation, is the skewness.

[0086] S5.5. To achieve a closed - form expression for the posterior RUL distribution, the present invention uses the Shifted - LogNormal (SLN) distribution for fitting. Its probability density function realizes a flexible description of the degradation process with a non - zero lower limit through an additional displacement parameter 𝜆. Its location , scale , shape parameter and statistical characteristics satisfy the following relationships: ; ; .

[0087] A step - by - step optimization strategy is adopted for solving: First, the initial value of the displacement parameter (such as the intercept of the degradation curve fitting) is set according to experience, and then and are updated by the Newton - Raphson iteration method to minimize the moment error and ensure the consistency of the statistical moments.

[0088] S5.6. According to the SLN distribution characteristics, when the RUL threshold corresponds to the preset safe life, its expected failure probability can be directly calculated by the cumulative distribution function: ; where, , is the probability density function, is the cumulative distribution function, is the standard normal distribution CDF.

[0089] Correspondingly, the lower limit of RUL at a confidence level of can be calculated by the inverse transformation of the SLN distribution: .

[0090] Thus, the failure probability at a confidence level of is obtained.

[0091] S5.7. The probability density function PDF of the failure probability is expressed as : ; where, is the independent variable.

[0092] This Bayesian fusion scheme combines a physical branch network and a data-driven model, uses the SGNI method to calculate the posterior distribution moments, and fits them with a shifted lognormal distribution to achieve efficient calculation of the posterior failure probability. This method not only improves the prediction accuracy but also provides uncertainty quantification, providing theoretical support for the reliability analysis of deep-sea energy systems.

[0093] In the prediction stage, the Bayesian fusion module takes the RUL prediction output by the physical branch as the prior and the prediction residual of the data branch as the observation, and jointly establishes the posterior RUL distribution. To overcome the difficulty of high-dimensional integration, the present invention uses sparse grid integration (SGNI) to efficiently approximate the posterior moments and fits the prediction results with a shifted lognormal distribution (SLN), and further derives the failure probability and confidence life index, providing an interpretable and uncertainty-quantified health state assessment method for deep-sea energy systems.

[0094] Figure 2 The blue solid line in the figure is the actually measured capacity curve, the red solid line is the capacity change trend predicted by the model, the black dashed line is the capacity failure threshold (2.1 Ah), and the blue shaded area on the left represents the initial training data window (the first 200 days). From the perspective of prediction performance, the error between the overall red line and the true blue line remains within ±0.03 Ah, and the fluctuation period is consistent, indicating that the model has strong long-term trend modeling ability. Its mean absolute error (MAE) is about 0.015 Ah, and the loss rate is less than 2%, which shows that the model not only has high accuracy in health state assessment but also has a certain ability to resist noise, and can achieve reliable inference of the remaining useful life (RUL) of deep-sea battery systems.

[0095] The method for predicting the remaining useful life (RUL) of lithium-ion batteries proposed by the present invention based on a dual parallel framework of a physical branch network and a lightweight data branch network is particularly suitable for battery management and remaining life prediction in the deep-sea high-pressure and low-temperature environment. In the deep-sea environment, the battery faces the coupled action of multiple environmental stresses such as high pressure and low temperature. By constructing a modified Arrhenius-Weibull-Wiener hybrid model for the deep-sea environment and an incremental sparse contrast learning network (iSparC-Former), this method can accurately capture the multi-scale spatio-temporal correlation of environmental factors (such as temperature and pressure) on battery degradation, effectively making up for the deficiencies of traditional methods in modeling battery degradation under extreme working conditions. Secondly, the introduction of the physical branch network enhances the physical consistency of the model, ensuring the reliability and interpretability of the RUL prediction results, thereby improving the prediction accuracy of the battery in high-pressure and low-temperature environments such as the deep sea. At the same time, the Bayesian fusion dynamically quantifies the prediction uncertainty, providing more comprehensive and reliable health state assessment and decision support for the deep-sea battery management system.

[0096] Certainly, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by those skilled in the art within the scope of the essence of the present invention shall also fall within the protection scope of the present invention.

Claims

1. A method for predicting the lifespan of a deep - sea energy system, characterized in that, Specifically, it includes the following steps: S1. Collect the electrical characteristics of the battery and the deep-sea environmental stress, and perform standardization processing; S2. Based on the Arrhenius equation, Weibull distribution, and Wiener process, construct a deep-sea environmental degradation model, and constrain the physical characteristics based on the deep-sea environmental model. S3. Input the data processed in step S1 into the physical branch network to extract the consistency constraint features and physical initial priors. S4. Input the standardized data, physical enhancement features, and consistency constraint features processed in step S1 into the lightweight data branch network. The lightweight data branch network includes a main network and an auxiliary network. The deep residual information formed after pre-training of the lightweight data branch network is transmitted to the physical branch network. S5. The prior estimate of RUL output by the physical branch network and the data correction term output by the data branch form the final prediction, which is input into the Bayesian framework to derive the posterior distribution for uncertainty quantification.

2. The method for predicting the service life of a deep-sea energy system according to claim 1, wherein, Step S3 specifically is: Input the data processed through Step S1 into the 2D fully connected layer, hidden layer, and fully connected layer connected in sequence in the physical branch network, and the hidden layer outputs physical enhancement features , and the fully connected layer outputs consistency constraint features and physical initial priors .

3. A method for predicting the lifespan of a deep-sea energy system according to claim 1, characterized in that, Step S2 specifically includes the following steps: S2.1, the deep - sea environment degradation model is : ； ； ； ； Among them, is the initial battery capacity, is the degradation rate model, is the temperature, is the pressure, is the time, is the basic amplitude factor of the degradation rate, is the activation energy under normal temperature and pressure, is the pressure sensitivity coefficient, is the Weibull distribution probability density function, is the Weibull scale parameter, is the Weibull shape parameter, is the capacity fluctuation caused by Brownian noise, is the capacity baseline offset, is the temperature compensation coefficient, is the temperature nonlinear exponent, is the pressure compensation coefficient, is the pressure nonlinear exponent; S2.2, Define the first passage time of the standard Brownian motion as follows: ； wherein, is the infimum of the set, is the battery failure threshold; S2.

3. Convert the degradation process into a first passage time problem of a standard Brownian motion and define a standardized threshold : ； Among them, ; Obtain the approximate probability density of RUL : ； Among them, is the natural exponential function.

4. A method for predicting the lifespan of a deep - sea energy system according to claim 1, characterized in that, Both the main network and the auxiliary network in step S4 include, in sequence: an input layer, a linear layer, a multi-head sparse self-attention module, a feature splicing layer, a linear fusion layer, a DRC&CLN layer, a gated feed-forward network, a DRC&Norm layer, and a linear prediction layer. Step S4 specifically includes the following steps: S4.

1. Obtain query, key, and value vectors through the linear transformation of the linear layer: ； Among them, , and are projection parameter matrices; S4.2, in the multi-head sparse self-attention module, for the th query vector , the sparsity metric is defined as follows: ； Among them, is the total length of the key sequence, is the normalization factor during scaled dot-product attention, is the th key, is to take the maximum; S4.3, Construct a sparse query matrix , only retain the dot products between each query vector and the key vectors with the largest sparsity, and set the rest to zero, and define the multi-head sparse self-attention layer: ； Among them, is the feature representation obtained after sparse attention calculation by the th attention head, is the SoftMax function performed by row; Basis for selecting the sparsity 𝑢: ； Among them, represents the total length of the query sequence, is the logarithm taking.

5. A method for predicting the service life of a deep - sea energy system according to claim 4, characterized in that, Step S4 also includes the following steps: S4.4, and then enter the DRC&CLN layer through the feature concatenation layer and the linear fusion layer in sequence. In the DRC&CLN layer, the scaling factor and the offset are generated by the time-step feature : ； Among them, , respectively represent the linear transformation weight matrices for generating the scaling factor and the offset, and respectively represent the corresponding bias vectors; The normalization operation is expressed as: ； Among them, and are the mean and standard deviation of the current time step respectively, is the matrix dot product, represents the feature of the current time step; S4.

5. Adopt cross-layer dense residual connection DRC. In the output calculation of each layer, in addition to the multi-head sparse self-attention, the outputs of all previous layers are also spliced together. ； Among them, represents layer normalization, represents multi-head sparse self-attention, represents concatenation, represents the features extracted through the DRC&CLN layer; S4.

6. Achieve adaptive regulation of the feature flow through the gated feed-forward network GLU. ； Among them, is the projection matrix, is the Sigmoid function, is the element-wise multiplication, and are the bias terms corresponding to the projection matrix, respectively.

6. A method for predicting the lifespan of a deep-sea energy system according to claim 5, characterized in that, Step S4 also includes the following steps: S4.7, and then through the DRC&Norm layer and the linear prediction layer, the incremental data is obtained and passed through the main network feature extractor The training data is extracted The latent feature representation of : ； Among them, is the latent feature extracted from the main network training data at time step The total length of the time series of the current training sample is The number of time steps for future prediction is The dimensionality of the latent feature extracted at each time step is The length of the historical window of the input sequence is ; S4.8, take the output from the main network as input and feed it into the prediction network of the residual MLP for predicting future latent representations: ； wherein, is the prediction result of the potential feature at the time step , and is the predicted end time point of the current test sequence; Auxiliary network The output result of is , where is test data; S4.9, calculate the feature similarity using cosine similarity, and calculate the similarity between the predicted feature and the actual feature in the th incremental learning IL: ； Among them, is the average cosine similarity of the th incremental learning, denotes norm.

7. A method for predicting the lifespan of a deep-sea energy system according to claim 6, characterized in that Step S4 also includes the following steps: S4.10, define the contrastive loss as: ； The test loss function during the 𝑘-th incremental learning training process is defined as follows: ； wherein, is the predicted time step of the system health state, is the adjustment coefficient; S4.11, when the predicted health state is lower than the failure threshold for the first time it is considered that the system is about to fail, and the remaining useful life RUL is defined as: ； where m is the length of historical data, and 𝑟 represents the prediction step from the current moment to the state where the health state is lower than the failure threshold; when the system is still in a healthy state; when the system is determined to have degraded failure and the RUL prediction ends; is the failure threshold.

8. A method for predicting the service life of a deep-sea energy system according to claim 1, characterized in that Step S5 includes the following steps: S5.1, Final prediction output , construct the Bayesian likelihood function form: ； Among them, is the uncertainty of the prediction error of the data-driven model, is proportional to. At the same time, the uncertainty of the physical branch network parameters is described by the prior distribution After combining with the likelihood function, the Bayesian posterior fusion distribution can be obtained: ； Among them, is the RUL value to be estimated, is the prior information from the physical branch network, is the likelihood function from the lightweight data branch network; S5.2, let the reliability index be , and the posterior th raw moment is expressed as: ； where is the update factor, is the prior PDF, is the l-th order raw moment estimate under the Bayesian framework; S5.

3. Under the SGNI framework, construct a sparse expression of the multiple integral by using orthogonal polynomials and nested sampling points, which is further rewritten as: ； wherein, represents the sum of the multiple indices, a non - negative integer represents the precision level, a set is a multi - dimensional grid point set under the SGNI rule, is the dimension of the parameter space, is the likelihood function, represents the distribution parameter the inverse normal transformation operator between the prior CDF of and the standard normal CDF represents a standard normal random vector, and respectively represent the grid points of SGNI and their corresponding weights in the standard normal space.

9. A method for predicting the lifespan of a deep-sea energy system according to claim 8, characterized in that Step S5 includes the following steps: S5.4, after obtaining the first three raw moments of the posterior reliability index further calculate the statistical characteristics of the posterior RUL distribution: ； ； ； wherein, is the mean value, is the standard deviation, is the skewness; S5.5, position , ratio , shape parameter and the statistical features satisfy the following relationship: ； ； ； S5.

6. According to the SLN distribution characteristics, when the RUL threshold corresponds to the preset safe life, its expected failure probability can be directly calculated by the cumulative distribution function: ； Among them, , is the probability density function, is the cumulative distribution function, is the standard normal distribution CDF; Accordingly, the lower limit of RUL at a confidence level of can be calculated by the inverse transformation of the SLN distribution: ； Thus, the failure probability at the confidence level is obtained; S5.7, the probability density function PDF of the failure probability is expressed as :[[]]END]] ； Among them, is the independent variable.

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