A method for predicting the life of deep-sea energy systems

Abstract

The present invention provides a method for predicting the life of a deep-sea energy system, which relates to the technical field of life prediction, and specifically includes: collecting battery electrical characteristics and deep-sea environmental stresses, and performing standardization processing; constructing a deep-sea environmental degradation model, and constraining physical features based on the deep-sea environmental model; inputting data into a physical branch network to extract consistency constraint features and physical initial priors; inputting standardized data, physical enhancement features, and consistency constraint features into a lightweight data branch network, and transmitting the deep residual information formed by the lightweight data branch network after pre-training to the physical branch network; the RUL prior estimate output by the physical branch network and the data correction term output by the data branch constitute the final prediction input into the Bayesian framework to derive the posterior distribution and perform uncertainty quantification. The technical solution of the present invention overcomes the problems of low accuracy and high computing resources in the prior art for predicting the life of deep-sea energy systems.

Description

Technical Field

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

[0002] As the core power unit of deep-sea equipment systems, life prediction research for deep-sea energy systems is directly related to the mission reliability and strategic effectiveness of key equipment such as seafloor observation networks, unmanned underwater vehicles, and stealth weapon platforms. Life prediction technology for deep-sea energy systems is essential for ensuring reliable operation throughout their entire lifecycle. Existing research indicates that deep-sea pressure fluctuations accelerate the growth rate of the solid electrolyte interface (SEI) in lithium-ion batteries, while the synergistic effect of low temperatures and high-pressure hydrogen permeation can trigger irreversible degradation of the catalytic layer of proton exchange membrane fuel cells. Further complicating matters, the attachment of microbial biofilms to metal electrode surfaces alters the local electrochemical environment, inducing multi-mode failure via pitting and stress corrosion cracking. These degradation processes are highly time-varying and multi-scale coupled, making traditional life assessment methods based on single stress-accelerated aging experiments difficult to apply. Therefore, a theoretical framework for life prediction under the unique conditions of the deep sea is urgently needed.

[0003] While existing research has initially explored the link between electrochemical aging and capacity decay using the Arrhenius equation and stochastic processes (Wiener / Gamma processes), systematic lifespan prediction for deep-sea energy systems remains a niche topic. Existing models are significantly inadequate in quantifying the effects of high-pressure environments on the reconfiguration of material activation energies and the dynamic coupling of pressure and temperature. Furthermore, in the data-driven realm, while deep learning algorithms have demonstrated advantages in predicting the health status of lithium batteries, inherent limitations of deep-sea in-situ monitoring data, such as small sample sizes, strong noise interference, and high discreteness of operating conditions, can lead to insufficient model generalization.

[0004] Therefore, there is a need for a deep-sea energy system life prediction method that can accurately capture the multi-scale spatiotemporal correlation 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 purpose of the present invention is to provide a method for predicting the life of a deep-sea energy system, so as to solve the problems of low accuracy and high computing resources in the prior art for predicting the life of a deep-sea energy system.

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

[0007] S1, collects battery electrical characteristics and deep-sea environmental stress and performs standardization.

[0008] S2, based on the Arrhenius equation, Weibull distribution and Wiener process, constructs a deep-sea environmental degradation model, and constrains physical characteristics 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 by step S1 into the lightweight data branch network, which includes: a main network and an auxiliary network. The deep residual information formed by the lightweight data branch network after pre-training is passed 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 constitute the final prediction input into the Bayesian framework to derive the posterior distribution and perform uncertainty quantification.

[0012] Furthermore, step S3 is specifically as follows: inputting the data processed by 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 the physical enhancement feature , the fully connected layer outputs consistency constraint features and physical initial priors .

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

[0014] S2.1, deep-sea environmental degradation model is :

[0015] ;

[0016] ;

[0017] ;

[0018] ;

[0019] in, is the initial battery capacity, is the degradation rate model, is the temperature, For pressure, For time, is the basic amplitude factor of the degradation rate, is the activation energy at room temperature and pressure, is the pressure sensitivity coefficient, is the probability density function of the Weibull distribution, is the Weibull scaling parameter, is the Weibull shape parameter, is the capacity fluctuation caused by Brownian noise, is the capacity reference offset, is the temperature compensation coefficient, is the temperature nonlinear index, is the pressure compensation coefficient, is the pressure nonlinear index.

[0020] S2.2, define the first arrival time of standard Brownian motion for:

[0021] ;

[0022] in, is the infimum of the set, is the battery failure threshold.

[0023] S2.3, transform the degradation process into the first arrival time problem of standard Brownian motion and define the normalization threshold :

[0024] ;

[0025] in, .

[0026] Get the approximate probability density of RUL :

[0027] ;

[0028] in, is the natural exponential function.

[0029] Furthermore, the main network and the auxiliary network in step S4 both include the following sequentially connected layers: input layer, linear layer, multi-head sparse self-attention module, feature splicing layer, linear fusion layer, DRC&CLN layer, gated feedforward network, DRC&Norm layer and linear prediction layer. Step S4 specifically includes the following steps:

[0030] S4.1, after linear transformation of the linear layer, we get query, key and value vectors:

[0031] ;

[0032] in, 、 and is the projection parameter matrix.

[0033] S4.2, in the multi-head sparse self-attention module, for the query vector , the sparsity measure is defined as follows:

[0034] ;

[0035] in, is the total length of the key sequence, is the normalization factor when scaling the dot product attention, For the keys, To take the maximum.

[0036] S4.3, constructing a sparse query matrix , only keep each query vector and the previous The dot product between the key vectors with the largest sparsity and the rest are set to zero to define a multi-head sparse self-attention layer:

[0037] ;

[0038] in, For the The feature representation obtained by the sparse attention calculation of the attention heads is It is the SoftMax function performed row by row.

[0039] The selection basis of sparsity 𝑢 is:

[0040] ;

[0041] in, Indicates the total length of the query sequence, To take the logarithm.

[0042] Furthermore, step S4 further includes the following steps:

[0043] S4.4, then enters the DRC&CLN layer through the feature concatenation layer and the linear fusion layer, and the scaling factor of the normalized parameters in the DRC&CLN layer and offset By time step feature generate:

[0044] ;

[0045] in, 、 Represent the linear transformation weight matrices that generate scaling factors and offsets, respectively. and represent the corresponding bias vectors respectively.

[0046] The normalization operation is expressed as:

[0047] ;

[0048] in, and are the mean and standard deviation of the current time step, is the matrix dot product, Represents the features of the current time step.

[0049] S4.5 uses cross-layer dense residual connections (DRC). In the output calculation of each layer, in addition to multi-head sparse self-attention, the outputs of all previous layers are also spliced ​​together:

[0050] ;

[0051] in, Representation layer normalization, represents multi-head sparse self-attention, Indicates splicing, Represents the features extracted by the DRC&CLN layer.

[0052] S4.6, adaptive control of feature flow is achieved through the gated feedforward network GLU:

[0053] ;

[0054] in, is the projection matrix, is the Sigmoid function, is element-wise multiplication, and are the bias terms corresponding to the projection matrix respectively.

[0055] Furthermore, step S4 further includes the following steps:

[0056] S4.7, then passes through the DRC&Norm layer and the linear prediction layer to obtain the incremental data and pass it through the main network feature extractor Extract training data The latent feature representation :

[0057] ;

[0058] in, is the main network training data at time step The extracted latent features, is the total length of the time series of the current training sample, is the number of time steps into the future, The dimension of the latent features extracted for each time step, is the history window length of the input sequence.

[0059] S4.8, the main network output As input, it is fed into the prediction network of the residual MLP , used to predict future potential representations:

[0060] ;

[0061] in, is the time step The prediction results of the latent features, is the predicted end time point of the current test sequence.

[0062] Auxiliary Network The output result is ,in, For test data.

[0063] S4.9, use cosine similarity to calculate feature similarity, calculate the The similarity between the predicted features and the actual features in the incremental learning IL:

[0064] ;

[0065] in, It is The average cosine similarity of incremental learning, express norm.

[0066] Furthermore, step S4 further includes the following steps:

[0067] S4.10, the contrast loss Defined as:

[0068] .

[0069] Test loss function during the 𝑘th incremental learning training process The definition is as follows:

[0070] ;

[0071] in, is the prediction time step The system health status, is the adjustment coefficient.

[0072] S4.11, when predicting health status First time below the failure threshold When the system is considered to be about to fail, the remaining useful life RUL is defined as:

[0073] ;

[0074] Among them, m is the length of historical data, 𝑟 represents the prediction step from the current moment to the time when the health state is lower than the failure threshold; when When , the system is still in a healthy state; when When , the system is judged to have degraded failure, and the RUL prediction ends; is the failure threshold.

[0075] Furthermore, step S5 includes the following steps:

[0076] S5.1, final prediction output , construct the Bayesian likelihood function form:

[0077]

[0078] in, 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 obtained through the prior distribution Description, combined with the likelihood function, we can get the Bayesian posterior fusion distribution:

[0079] ;

[0080] in, is the RUL value to be estimated, is the prior information from the physical branch network, is the likelihood function from the light data branch network.

[0081] S5.2, let the reliability index be , the posterior The original moments are expressed as:

[0082] ;

[0083] in is the update factor, is the prior PDF, is the l-order raw moment estimate in the Bayesian framework.

[0084] S5.3, in the SGNI framework, using orthogonal polynomials and nested sampling points to construct sparse expressions for multiple integrals, Further rewritten as:

[0085] ;

[0086] in, Represents the sum of multiple indices, a non-negative integer Indicates the level of precision, set is the multidimensional grid point set under the SGNI rule, is the parameter space dimension, is the likelihood function, Represents the distribution parameters The a priori CDF and standard normal CDF of The inverse normal transformation operator between represents a standard normal random vector, and They represent the grid points of SGNI and their corresponding weights in the standard normal space.

[0087] Furthermore, step S5 includes the following steps:

[0088] S5.4, the first three raw moments of the posterior reliability index are obtained After that, the statistical characteristics of the posterior RUL distribution are further calculated:

[0089] ;

[0090] ;

[0091] ;

[0092] in, is the mean, is the standard deviation, is the skewness.

[0093] S5.5, Location ,Proportion , shape parameters The statistical characteristics satisfy the following relationship:

[0094] ;

[0095] ;

[0096] .

[0097] S5.6, according to the SLN distribution characteristics, when the RUL threshold Corresponding to the preset safety life, the expected failure probability can be directly calculated by the cumulative distribution function:

[0098] ;

[0099] in, , is the probability density function, is the cumulative distribution function, is the CDF of the standard normal distribution.

[0100] Accordingly, the confidence level is The lower limit of the RUL under can be calculated by the inverse transformation of the SLN distribution:

[0101] ;

[0102] So we get the confidence level The failure probability under .

[0103] S5.7, the probability density function PDF of the failure probability is expressed as :

[0104] ;

[0105] in, is the independent variable.

[0106] The present invention has the following beneficial effects:

[0107] This paper proposes a deep-sea energy system life prediction method for predicting the remaining useful life (RUL) of lithium-ion batteries in deep-sea environments. The lightweight data branch network operates as an independent deep learning model. The physical branch network embeds a degradation modeling formula based on physical principles to model the mechanics of battery degradation. Physical consistency constraints enhance the feature expression capabilities of the data-driven branch, thereby improving the model's prediction accuracy and interpretability. The final prediction results combine the adaptability of data-driven learning with the reliability of physical modeling. BRIEF DESCRIPTION OF THE DRAWINGS

[0108] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the specific embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work. In the drawings:

[0109] Figure 1 A flow chart of a deep-sea energy system life prediction method of the present invention is shown.

[0110] Figure 2 The figure shows the RUL prediction results of the deep-sea energy system. DETAILED DESCRIPTION

[0111] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0112] like Figure 1 A deep-sea energy system life prediction method shown in FIG. 1 includes the following steps:

[0113] S1, Multimodal Data Input: Collect and standardize battery electrical characteristics and deep-sea environmental stresses. Battery electrical characteristics include voltage and current; deep-sea environmental stresses include temperature and pressure. After standardization, high-pressure and low-temperature characteristics are combined.

[0114] S2, based on the Arrhenius equation, Weibull distribution and Wiener process, constructs a deep-sea environmental degradation model, and constrains physical characteristics based on the deep-sea environmental model.

[0115] Compared to degradation models under constant temperature conditions, lithium-ion battery degradation in deep-sea, high-pressure, and low-temperature environments exhibits more complex characteristics. The coupled effects of temperature fluctuations and hydrostatic pressure alter electrolyte ion mobility, electrode material phase transition dynamics, and solid electrolyte interface (SEI) film growth mechanisms, leading to random fluctuations in degradation rate and discharge capacity exhibiting multi-scale spatiotemporal correlations. Therefore, constructing a degradation model in this environment requires addressing two core issues: first, how to accurately establish the mathematical relationship between degradation rate and changes in deep-sea temperature and pressure; and second, how to map battery capacity degradation under random environmental variables to equivalent capacity loss under a reference environment (i.e., normal temperature and pressure). To this end, this paper constructs a lithium-ion battery degradation model suitable for deep-sea environments by coupling the pressure-temperature factor based on the Arrhenius equation and combining it with the time-dependent Weibull distribution and the Wiener process.

[0116] S3, input the data processed in step S1 into the physical branch network to extract the consistency constraint features and physical initial priors.

[0117] S4, inputs the standardized data, physical enhancement features and consistency constraint features processed by 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 by the lightweight data branch network after pre-training is passed to the physical branch network; the lightweight data branch network uses the iSparC-Former network for feature extraction and time series modeling.

[0118] S5, the RUL prior estimate output by the physical branch network and the data correction term output by the data branch constitute the final prediction input into the Bayesian framework to derive the posterior distribution and perform uncertainty quantification.

[0119] Specifically, S3 is as follows: the data processed by 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 the physical enhancement feature , the fully connected layer outputs consistency constraint features and physical initial priors .

[0120] Specifically, step S2 includes the following steps:

[0121] S2.1, deep-sea environmental degradation model is :

[0122] ;

[0123] ;

[0124] ;

[0125] ;

[0126] in, is the initial battery capacity, is the degradation rate model, is the temperature, For pressure, For time, is the basic amplitude factor of the degradation rate, which obeys Gaussian distribution , is the activation energy at room temperature and pressure, is the pressure sensitivity coefficient, is the probability density function of the Weibull distribution, is the Weibull scaling parameter, is the Weibull shape parameter (reflecting the degenerate mode), is the capacity fluctuation caused by Brownian noise, It is the capacity benchmark offset and obeys Gaussian distribution. It is used to correct the capacity measurement deviation caused by environmental changes, making the model comparable in different environments. is the temperature compensation coefficient, is the temperature nonlinear index, is the pressure compensation coefficient, is the pressure nonlinear index; Reflects degradation mode: Indicates early rapid degeneration, corresponds to a constant degradation rate, while This distribution can well describe the degradation trajectory of lithium batteries throughout their life cycle, from the initial stage (SEI film formation), slow degradation in the middle stage, to accelerated degradation of the material structure in the late stage.

[0127] S2.2, define the first arrival time of standard Brownian motion for:

[0128] ;

[0129] in, is the infimum of the set, is the battery failure threshold.

[0130] S2.3, transform the degradation process into the first arrival time problem of standard Brownian motion and define the normalization threshold :

[0131] ;

[0132] in, .

[0133] Get the approximate probability density of RUL :

[0134] ;

[0135] in, is a natural exponential function. The first term Characterizes the impact of threshold distance on failure probability, the second term The contribution of the degradation rate at a specific time is characterized. This result provides a closed-form solution for RUL assessment in deep-sea environments.

[0136] At the data flow 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 physical enhancement features 𝑝 at the hidden layer level. This feature is extracted through the 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 lightweight data-branch networks to make them consistent with physical prior knowledge.

[0137] Specifically, the main network and auxiliary network in step S4 include the following connected in sequence: input layer, linear layer, multi-head sparse self-attention module, feature splicing layer, linear fusion layer, DRC&CLN layer, gated feedforward network, DRC&Norm layer and linear prediction layer. Step S4 specifically includes the following steps:

[0138] S4.1, after linear transformation of the linear layer, we get query, key and value vectors:

[0139] ;

[0140] in, 、 and is the projection parameter matrix.

[0141] S4.2. To address the long sequence nature of deep-sea sensor data, this paper introduces a sparse multi-head self-attention (SMHA) module into the data branch network. This module aims to filter dominant attention pairs based on a sparsity metric, thereby filtering out redundant computations and highlighting key relationships. This key feature screening strategy prunes redundant computations while retaining the ability to focus on information-sensitive regions. This reduces computational complexity while ensuring the model's predictive accuracy and generalization capabilities.

[0142] In the multi-head sparse self-attention module, for the query vector , the sparsity measure is defined as follows:

[0143] ;

[0144] in, is the total length of the key sequence, is the normalization factor when scaling the dot product attention, For the keys, To get the maximum, the first term in the formula represents the query On all keys The maximum dot product value calculated on , and 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 it is large, it means that the attention distribution deviates significantly from the uniform distribution and relies on a few key vectors, which can be sparsely processed.

[0145] S4.3, therefore, construct a sparse query matrix , only keep each query vector and the previous The dot product between the key vectors with the largest sparsity and the rest are set to zero to define a multi-head sparse self-attention layer:

[0146] ;

[0147] in, For the The feature representation obtained by the sparse attention calculation of the attention heads is is a row-wise SoftMax function used to normalize the sparse attention scores into a probability distribution.

[0148] The selection basis of sparsity 𝑢 is:

[0149] ;

[0150] in, Indicates the total length of the query sequence, To take the logarithm.

[0151] In most practical application scenarios, the key sequence and the query sequence are of equal length, i.e. 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 , achieving sparse expression and enhancement of different subspace features.

[0152] In order to further improve the adaptability of iSparC-Former to the dynamic and non-stationary data distribution of deep-sea environments, 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.

[0153] Specifically, step S4 further includes the following steps:

[0154] S4.4, then enters the DRC&CLN layer through the feature concatenation layer and the linear fusion layer, and the scaling factor of the normalized parameters in the DRC&CLN layer and offset By time step feature generate:

[0155] ;

[0156] in, 、 Represent the linear transformation weight matrices that generate scaling factors and offsets, respectively. and represent the corresponding bias vectors respectively.

[0157] The normalization operation is expressed as:

[0158] ;

[0159] in, and are the mean and standard deviation of the current time step, is the matrix dot product, Represents the characteristics of the current time step. This design enables the model to adaptively adjust the normalization strategy. For example, when changes in deep-sea pressure or temperature cause sensor measurement baseline drift, CLN can effectively correct the distribution offset and improve model stability.

[0160] S4.5, in addition, to enhance the feature transfer capability of deep networks, iSparC-Former uses cross-layer dense residual connections (DRCs) to alleviate the gradient vanishing problem and preserve fine-grained information in shallow layers. Specifically, in the output calculation of each layer, in addition to multi-head sparse self-attention, the outputs of all previous layers are also spliced ​​together:

[0161] ;

[0162] in, Representation layer normalization, represents multi-head sparse self-attention, Indicates splicing, Represents the features extracted by the DRC&CLN layer.

[0163] This design ensures information sharing across different layers, allowing shallow-layer features to directly influence deep-layer feature extraction, thereby improving the ability to perceive weak degradation signals. Weak signals during long-term operation can carry critical degradation information for deep-sea energy system lifespan prediction, and dense residual connections ensure this information is not forgotten in deep networks.

[0164] S4.6, adaptive control of feature flow is achieved through the gated feedforward network GLU:

[0165] ;

[0166] in, is the projection matrix, is the Sigmoid function, is element-wise multiplication, and are the bias terms corresponding to the projection matrix, respectively. This design allows the model to assign feature-level weights to input features, for example, assigning greater transmission weight to sensors with high signal-to-noise ratios while suppressing signals contaminated by environmental noise. In the early stages of energy system degradation, abnormal features in sensor signals are often weak and easily drowned out by noise. Through this mechanism, the GLU dynamically controls the flow of information, making the network more selective for different input features and improving the sensitivity of early degradation warnings.

[0167] Specifically, step S4 further includes the following steps:

[0168] During the long-term operation of deep-sea energy systems, sensor data is subject to environmental changes, equipment aging, and fluctuations in operating conditions, leading to drift in data distribution. If a statically trained model is used directly for prediction, the model may not adapt to the new data distribution, resulting in decreased prediction accuracy. Therefore, to enhance the model's generalization and adaptability, an online incremental learning mechanism is introduced. This allows the data branch to dynamically update parameters as it continuously receives new data, thereby reducing the impact of error accumulation and improving the accuracy of predictions of long-term degradation trends.

[0169] 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. 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 the prediction. After the DRC&Norm layer and the linear prediction layer, the incremental data is passed through the main network feature extractor. Extract training data The latent feature representation :

[0170] ;

[0171] in, is the main network training data at time step The extracted latent features, is the total length of the time series of the current training sample, is the number of time steps into the future, The dimension of the latent features extracted for each time step, is the historical window length of the input sequence; incremental data refers to the data samples newly introduced relative to the existing training data, which are used to improve the generalization ability of the model or adapt to new tasks / states. S4.8, the output of the main network As input, it is fed into the prediction network of the residual MLP , used to predict future potential representations:

[0172] ;

[0173] in, is the time step The prediction results of the latent features, is the predicted end time point of the current test sequence.

[0174] In order to provide supervision signals, an auxiliary network is introduced , the network structure is the same as the main network, but its parameters are frozen and do not participate in gradient updates. The auxiliary network is responsible for extracting real future samples Potential characteristics of , and participate in the optimization as a comparison target. In order to ensure that the model learning only comes from the current training data, the gradient truncation (stopgradient) is set. This operation is applied to the potential feature encoding path of future test data, that is, the auxiliary network The output result is It is statically encoded, the gradient cannot be returned, and it only participates in supervision as a target vector. For test data.

[0175] S4.9, since the potential representation of future time series is learned from historical series, the future features predicted by the model Should be consistent with real future characteristics There is a high similarity in the representation space. To this end, the cosine similarity is used to calculate the feature similarity. The similarity between the predicted features and the actual features in the incremental learning IL:

[0176] ;

[0177] in, It is The average cosine similarity of incremental learning, express Norm. The larger the value, the better the potential representation predicted by the model. and the true potential representation The closer the relationship is, the more successfully the model captures the future structural evolution trends hidden in the historical features. By minimizing the differences between the potential representations, it guides the main network to optimize the modeling ability of future degradation states without relying on future labels, thereby enhancing the model's adaptability and robustness to distribution drift and unknown data.

[0178] Specifically, step S4 further includes the following steps:

[0179] S4.10, due to test data Cannot be used for The network is updated during the IL process, so the loss is compared Defined as:

[0180] .

[0181] Based on this, the test loss function in the 𝑘th incremental learning training process is The definition is as follows:

[0182] ;

[0183] in, is the prediction time step The system health status, is the adjustment coefficient.

[0184] 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 of the deep-sea energy system.

[0185] In order to construct training data, the RMS feature sequence is window-sliding sampled to form the input sequence , each window length is , the prediction target is the future The model outputs the predicted value , add it to the sequence for prediction at the next moment.

[0186] S4.11, when predicting health status First time below the failure threshold When the system is considered to be about to fail, the remaining useful life RUL is defined as:

[0187] ;

[0188] Among them, m is the length of historical data, 𝑟 represents the prediction step from the current moment to the time when the health state is lower than the failure threshold; when When , the system is still in a healthy state; when When , the system is judged to have degraded failure, and the RUL prediction ends; is the failure threshold.

[0189] Specifically, step S5 includes the following steps:

[0190] S5.1, in the remaining useful life (RUL) prediction of deep-sea energy systems, facing the challenges of high dimensionality, complex degradation mechanisms and environmental uncertainty, this paper proposes a physics-data fusion method based on a Bayesian probabilistic framework to achieve dynamic and interpretable RUL prediction and uncertainty quantification. The method is based on a dual parallel architecture, in which the physical branch network calculates the initial RUL estimate based on the pressure-corrected Arrhenius model-Weibull distribution-nonlinear Wiener process hybrid mechanism. , while the deep temporal model iSparC-Former learns the sensor data features to form the residual correction term , which together constitute the final prediction output To achieve a reasonable fusion of these two parts of information, this paper proposes a Bayesian reasoning fusion framework, which regards data branches as statistical corrections to the prediction errors of the physical branch network and assumes that the prediction residuals obey the Gaussian noise model, thereby constructing the Bayesian likelihood function form:

[0191] ;

[0192] in, is the uncertainty of the prediction error of the data-driven model, is proportional to , which can usually be obtained by estimating the variance of the historical residuals. At the same time, the uncertainty of the physical branch network parameters is obtained by the prior distribution Description, such prior information usually comes from laboratory data calibration or domain expert experience.

[0193] After combining the likelihood function, we can get the Bayesian posterior fusion distribution:

[0194] ;

[0195] in, is the RUL value to be estimated, is the prior information from the physical branch network, is the likelihood function from the light data branch network.

[0196] However, the high-dimensional nature of the deep-sea energy system model makes the above integral difficult to analyze. Therefore, the present invention adopts the sparse grid integral (SGNI) method to efficiently approximate the statistical moment of the posterior reliability index through the Smolyak formula.

[0197] S5.2, let the reliability index be , the posterior The original moments are expressed as:

[0198] ;

[0199] in is the update factor, For the prior PDF, Bayesian evidence As a normalization constant, it needs to be calculated by integration on the prior space. is the l-order raw moment estimate in the Bayesian framework.

[0200] S5.3, under the SGNI framework, the sparse expression of multiple integrals is constructed using orthogonal polynomials and nested sampling points. The above formula can be further rewritten as:

[0201] ;

[0202] in, , Represents the sum of multiple indices, a non-negative integer Indicates the level of precision, set is the multidimensional grid point set under the SGNI rule, is the parameter space dimension, is the likelihood function, Represents the distribution parameters The a priori CDF and standard normal CDF of The inverse normal transformation operator between represents a standard normal random vector, and denote the grid points of SGNI and their corresponding weights in the standard normal space, is the hth dimension, The coordinates of the sampling points in the standard normal distribution space of nested sampling points, is the Gauss-Hermite quadrature point, The weighting coefficients corresponding to the sampling points are used to approximate the linear combination of multidimensional integrals. are the weights of the Gauss-Hermitian quadrature points, which can be used with the weights The relevant Gauss-Hermite formula is used to determine this.

[0203] Specifically, step S5 includes the following steps:

[0204] S5.4, the first three raw moments of the posterior reliability index are obtained After that, the statistical characteristics of the posterior RUL distribution are further calculated:

[0205] ;

[0206] ;

[0207] ;

[0208] in, is the mean, is the standard deviation, is the skewness.

[0209] S5.5, in order to achieve a closed-form expression of the posterior RUL distribution, the present invention adopts the shifted-lognormal distribution (SLN) for fitting, and its probability density function achieves a flexible description of the non-zero lower limit degradation process by adding a displacement parameter 𝜆, and its position ,Proportion , shape parameters The statistical characteristics satisfy the following relationship:

[0210] ;

[0211] ;

[0212] .

[0213] A step-by-step optimization strategy is used to solve the problem: first, the displacement parameters are set based on experience. Initial value (such as the intercept of the degradation curve fitting), and then updated by the Newton-Raphson iteration method and To minimize the moment error and ensure the consistency of statistical moments.

[0214] S5.6, according to the SLN distribution characteristics, when the RUL threshold Corresponding to the preset safety life, the expected failure probability can be directly calculated by the cumulative distribution function:

[0215] ;

[0216] in, , is the probability density function, is the cumulative distribution function, is the CDF of the standard normal distribution.

[0217] Accordingly, the confidence level is The lower limit of the RUL under can be calculated by the inverse transformation of the SLN distribution:

[0218] .

[0219] So we get the confidence level The failure probability under .

[0220] S5.7, the probability density function PDF of the failure probability is expressed as :

[0221] ;

[0222] in, is the independent variable.

[0223] This Bayesian fusion scheme combines a physical branching network with a data-driven model, using the SGNI method to calculate posterior distribution moments and fitting them with a shifted lognormal distribution to efficiently calculate posterior failure probabilities. This method not only improves prediction accuracy but also provides uncertainty quantification, providing theoretical support for reliability analysis of deep-sea energy systems.

[0224] During the prediction phase, the Bayesian fusion module uses the RUL predictions from the physical branch as priors and the prediction residuals from the data branch as observations to jointly construct a posterior RUL distribution. To overcome the difficulties of high-dimensional integration, this method employs a sparse grid integral (SGNI) to efficiently approximate the posterior moments. The prediction results are then fitted with a shifted lognormal (SLN) distribution to further derive failure probabilities and confidence life indicators, providing a health assessment method that can interpret and quantify uncertainty for deep-sea energy systems.

[0225] Figure 2 The solid blue line in the middle represents the actual measured capacity curve, the solid red line represents the model's predicted capacity trend, the dashed black line represents the capacity failure threshold (2.1Ah), and the blue shaded area on the left represents the initial training data window (the first 200 days). In terms of predictive performance, the overall error between the red line and the true blue line remains within ±0.03Ah, and the fluctuation period remains consistent, indicating that the model has strong long-term trend modeling capabilities. Its mean absolute error (MAE) is approximately 0.015Ah, and the loss rate is less than 2%. This demonstrates that the model not only has high accuracy in health status assessment but also has a certain degree of noise immunity, enabling reliable inference of the remaining useful life (RUL) of deep-sea battery systems.

[0226] The proposed method for lithium-ion battery remaining useful life (RUL) prediction, based on a dual parallel framework of a physical branch network and a lightweight data branch network, is particularly suitable for battery management and RUL prediction in deep-sea, high-pressure, and low-temperature environments. In deep-sea environments, batteries face the coupled stresses of high pressure and low temperature. By constructing a deep-sea-corrected Arrhenius-Weibull-Wiener hybrid model and an incremental sparse contrastive learning network (iSparC-Former), this method accurately captures the multi-scale spatiotemporal correlations between environmental factors (such as temperature and pressure) and battery degradation, effectively addressing the shortcomings of traditional methods in modeling battery degradation under extreme operating conditions. Furthermore, the introduction of a physical branch network enhances the model's physical consistency, ensuring the reliability and interpretability of RUL prediction results, thereby improving prediction accuracy in high-pressure, low-temperature environments such as the deep sea. Furthermore, by dynamically quantifying prediction uncertainty through Bayesian fusion, this method provides more comprehensive and reliable health status assessment and decision support for deep-sea battery management systems.

[0227] Of course, 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 technicians in this technical field within the essential scope of the present invention should also fall within the scope of protection of the present invention.

Claims

1. A method for predicting the life of a deep-sea energy system, characterized in that: The specific steps include: S1, collects battery electrical characteristics and deep-sea environmental stress and performs standardization processing; S2, based on the Arrhenius equation, Weibull distribution and Wiener process, constructs a deep-sea environmental degradation model and constrains the physical characteristics based on the deep-sea environmental model; S3, inputting the data processed in step S1 into the physical branch network to extract consistency constraint features and physical initial priors; S4, inputting the normalized data, physical enhancement features, and consistency constraint features processed in step S1 into a lightweight data branch network, the lightweight data branch network comprising: a main network and an auxiliary network, and transmitting the deep residual information formed by the lightweight data branch network after pre-training to the physical branch network; S5, the RUL prior estimate output by the physical branch network and the data correction term output by the data branch constitute the final prediction input into the Bayesian framework to derive the posterior distribution and quantify uncertainty; Step S3 is specifically as follows: the data processed by 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 the physical enhancement feature , the fully connected layer outputs consistency constraint features and physical initial priors .

2. A deep-sea energy system life prediction method according to claim 1, characterized in that: Step S2 specifically includes the following steps: S2.1, deep-sea environmental degradation model is : ； ； ； ； in, is the initial battery capacity, is the degradation rate model, is the temperature, For pressure, For time, is the basic amplitude factor of the degradation rate, is the activation energy at room temperature and pressure, is the pressure sensitivity coefficient, is the probability density function of the Weibull distribution, is the Weibull scaling parameter, is the Weibull shape parameter, is the capacity fluctuation caused by Brownian noise, is the capacity reference offset, is the temperature compensation coefficient, is the temperature nonlinear index, is the pressure compensation coefficient, is the pressure nonlinear index; S2.2, define the first arrival time of standard Brownian motion for: ； in, is the infimum of the set, is the battery failure threshold; S2.3, transform the degradation process into the first arrival time problem of standard Brownian motion and define the normalization threshold : ； in, ; Get the approximate probability density of RUL : ； in, is the natural exponential function.

3. A deep-sea energy system life prediction method according to claim 1, characterized in that: The main network and auxiliary network in step S4 both include the following connected in sequence: input layer, linear layer, multi-head sparse self-attention module, feature splicing layer, linear fusion layer, DRC&CLN layer, gated feedforward network, DRC&Norm layer and linear prediction layer. Step S4 specifically includes the following steps: S4.1, after linear transformation of the linear layer, we get query, key and value vectors: ； in, 、 and is the projection parameter matrix; S4.2, in the multi-head sparse self-attention module, for the query vector , the sparsity measure is defined as follows: ； in, is the total length of the key sequence, is the normalization factor when scaling the dot product attention, For the keys, To take the maximum; S4.3, constructing a sparse query matrix , only keep each query vector and the previous The dot product between the key vectors with the largest sparsity and the rest are set to zero to define a multi-head sparse self-attention layer: ； in, For the The feature representation obtained by the sparse attention calculation of the attention heads is It is the SoftMax function performed row by row; The selection basis of sparsity 𝑢 is: ； in, Indicates the total length of the query sequence, To take the logarithm.

4. A deep-sea energy system life prediction method according to claim 3, characterized in that: Step S4 also includes the following steps: S4.4, then passes through the feature concatenation layer and the linear fusion layer and enters the DRC&CLN layer, where the scaling factor of the normalized parameters is and offset By time step feature generate: ； in, 、 Represent the linear transformation weight matrices that generate scaling factors and offsets, respectively. and Respectively represent the corresponding bias vectors; The normalization operation is expressed as: ； in, and are the mean and standard deviation of the current time step, is the matrix dot product, Represents the characteristics of the current time step; S4.5 uses cross-layer dense residual connections (DRC). In the output calculation of each layer, in addition to multi-head sparse self-attention, the outputs of all previous layers are also spliced ​​together: ； in, Representation layer normalization, represents multi-head sparse self-attention, Indicates splicing, Represents the features extracted by the DRC&CLN layer; 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 respectively.

5. A deep-sea energy system life prediction method according to claim 4, characterized in that: Step S4 also includes the following steps: S4.7, then passes through the DRC&Norm layer and the linear prediction layer to obtain the incremental data and pass it through the main network feature extractor Extract training data The latent feature representation : ； in, is the main network training data at time step The extracted latent features, is the total length of the time series of the current training sample, is the number of time steps into the future, The dimension of the latent features extracted for each time step, is the history window length of the input sequence; S4.8, the main network output As input, it is fed into the prediction network of the residual MLP , used to predict future potential representations: ； in, is the time step The prediction results of the latent features, is the predicted end time point of the current test sequence; Auxiliary Network The output result is ,in, For test data; S4.9, use cosine similarity to calculate feature similarity, calculate the The similarity between the predicted features and the actual features in the incremental learning IL: ； in, It is The average cosine similarity of incremental learning, express norm.

6. A deep-sea energy system life prediction method according to claim 5, characterized in that: Step S4 also includes the following steps: S4.10, the contrast loss Defined as: ； Test loss function during the 𝑘th incremental learning training process The definition is as follows: ； in, is the prediction time step The health status of the system, is the adjustment coefficient; S4.11, when predicting health status First time below the failure threshold When the system is considered to be about to fail, the remaining useful life RUL is defined as: ； Among them, m is the length of historical data, 𝑟 represents the prediction step from the current moment to the time when the health state is lower than the failure threshold; when When , the system is still in a healthy state; when When , the system is judged to have degraded failure, and the RUL prediction ends; is the failure threshold.

7. A deep-sea energy system life prediction method according to claim 1, characterized in that: Step S5 includes the following steps: S5.1, final prediction output , construct the Bayesian likelihood function form: ； in, 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 obtained through the prior distribution Description, combined with the likelihood function, we can get the Bayesian posterior fusion distribution: ； in, 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 , the posterior The original moments are expressed as: ； in is the update factor, is the prior PDF, is the l-order raw moment estimate under the Bayesian framework; S5.3, in the SGNI framework, using orthogonal polynomials and nested sampling points to construct sparse expressions for multiple integrals, Further rewritten as: ； in, Represents the sum of multiple indices, a non-negative integer Indicates the level of precision, set is the multidimensional grid point set under the SGNI rule, is the parameter space dimension, is the likelihood function, Represents the distribution parameters The a priori CDF and standard normal CDF of The inverse normal transformation operator between represents a standard normal random vector, and They represent the grid points of SGNI and their corresponding weights in the standard normal space.

8. A deep-sea energy system life prediction method according to claim 7, characterized in that: Step S5 includes the following steps: S5.4, the first three raw moments of the posterior reliability index are obtained After that, the statistical characteristics of the posterior RUL distribution are further calculated: ； ； ； in, is the mean, is the standard deviation, is the skewness; S5.5, Location ,Proportion , shape parameters The statistical characteristics satisfy the following relationship: ； ； ； S5.6, according to the SLN distribution characteristics, when the RUL threshold Corresponding to the preset safety life, the expected failure probability can be directly calculated by the cumulative distribution function: ； in, , is the probability density function, is the cumulative distribution function, is the CDF of the standard normal distribution; Accordingly, the confidence level is The lower limit of the RUL under can be calculated by the inverse transformation of the SLN distribution: ； So we get the confidence level The failure probability under ; S5.7, the probability density function PDF of the failure probability is expressed as : ； in, is the independent variable.

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