Physics-Based Unsupervised Health Assessment and Remaining Life Prediction Methods for Lithium Batteries

Abstract

This invention discloses a physics-based unsupervised health assessment and remaining lifetime prediction method for lithium batteries. The method includes collecting sensor data from lithium battery charge-discharge experiments and performing data preprocessing; constructing a feature extraction network guided by a lithium battery mechanism model to extract unobservable signals and enhance the input space of the health assessment and remaining lifetime prediction algorithm; constructing a PINN-based health assessment and remaining lifetime prediction algorithm based on the lithium battery mechanism model and degradation model; inputting the enhanced feature data into the PINN-based health assessment and remaining lifetime prediction algorithm to optimize the model parameters for constructing health indicators; and constructing health indicators that integrate physics knowledge to achieve remaining lifetime estimation based on these health indicators. This invention can be used for health assessment and remaining lifetime prediction when the dataset is small and only a single sensor signal is available, obtaining relatively accurate health assessment results while ensuring algorithm interpretability.

Description

Technical Field

[0001] This invention relates to the field of health status estimation technology, and in particular to an unsupervised health assessment and remaining life prediction method for lithium batteries based on physical knowledge. Background Technology

[0002] In recent years, lithium batteries have become a key component of energy storage systems in fields including electric vehicles (EVs) and aerospace equipment (AEs) due to their significant advantages in gravimetric energy density, volumetric energy density, and lifespan. According to data from the International Energy Agency, global EV sales in 2024 increased by approximately 25% year-on-year, reaching around 17 million units by the end of the year. Data from the China Association of Automobile Manufacturers (CAAM) shows that the market penetration rate of new energy vehicles in China has shown a steady upward trend in recent years, reaching 39.5% in May 2024. New energy vehicles primarily use lithium batteries as their driving force, with lithium iron phosphate (LFP) batteries accounting for nearly 70% of installed capacity, while ternary lithium batteries, used in high-end models, have a slightly lower share. Since the British STRV-1d satellite first used lithium batteries as its power supply system, lithium batteries have become the main energy storage device in power systems of aerospace equipment, including satellites, space shuttles, and various deep space probes, and are gradually becoming the third-generation power batteries for aerospace applications.

[0003] Under the influence of various factors such as environmental disturbances, material aging, and long-term cycle cumulative losses, lithium battery systems inevitably degrade, leading to a decline in the overall stability, reliability, and economy of the system, and even safety accidents. Therefore, to ensure the long-term reliable operation of lithium batteries and to carry out timely maintenance and component replacement, it is necessary to implement predictive and health management (PHM) for lithium batteries, which specifically includes two tasks: (i) estimating the state of health (SoH) of the lithium battery; and (ii) predicting the remaining useful life (RUL).

[0004] Traditional health assessment algorithms based on physical models or data are often constrained by factors such as the complexity of degradation model construction and the small size of datasets, making it difficult to leverage their advantages. Therefore, researchers have turned their attention to the field of hybrid models, aiming to use physical models to guide the construction of data-driven models, thereby developing machine learning models that integrate physical laws (Physics-informed machine learning, PIML). PIML can be defined as a model that uses prior knowledge of the physical and mathematical understanding of the research object to improve the performance of data-driven algorithms. The paper "Physics-informed machine learning: A comprehensive review on applications in anomaly detection and condition monitoring" reviews the basic applications of different types of PIML. Among these models, the Physics-Informed Neural Network (PINN) has received widespread attention. PINN is an algorithmic framework that uses differential operators to simulate the dynamic equations of the research object, aiming to use prior knowledge to guide and constrain the learning direction of the algorithm. The book "Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations" elaborates on the basic structure and mathematical principles of PINN and proposes a Deep Hidden Physics Model (DeepHPM) based on the PINN framework. This method can still provide prediction results that are relatively consistent with the physical principles even when the dataset is not ideal, and it also demonstrates good generalization ability. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a physical knowledge-based unsupervised health assessment and remaining life prediction method for lithium batteries, which can be used for health assessment and remaining life prediction when the dataset is small and only a single sensor signal is available, and obtains relatively accurate health assessment results while ensuring the interpretability of the algorithm.

[0006] The present invention solves the technical problem by adopting the following technical solution:

[0007] An unsupervised health assessment and remaining life prediction method for lithium batteries based on physical knowledge includes the following steps:

[0008] Step S1, Data Preprocessing:

[0009] Collect relevant sensor data from lithium battery charge and discharge experiments and perform data preprocessing;

[0010] Step S2, Feature extraction network based on physical model:

[0011] The mathematical expression of the lithium battery mechanism model guides the construction of the feature extraction network, extracting unobservable signals containing the system degradation law, and enhancing the input space of health assessment and remaining life prediction algorithms;

[0012] Step S3, construct the network based on PINN's health indicators:

[0013] Based on the dynamic process of the lithium battery mechanism model and the dynamic expression of the degradation model, a PINN-based health assessment and remaining life prediction algorithm is constructed. The enhanced feature data is input into the PINN-based health assessment and remaining life prediction algorithm to optimize the model parameters for constructing health indicators.

[0014] Step S4, Health Assessment and Life Expectancy Prediction:

[0015] Based on the test data, feature signals with physical significance are extracted, and health indicators that integrate physical knowledge are constructed to ultimately achieve remaining life estimation based on health indicators.

[0016] Furthermore, in step S1, the data is preprocessed using the 2-sigma principle, including:

[0017] Step S10: Divide the input sensor data into different groups of data according to a sliding window with a window length of len and a window gap of inter;

[0018] Step S11: Calculate the mean μ and standard deviation σ for each group of data;

[0019] Step S12: According to the 2-sigma principle, data points falling within the interval [μ-2σ, μ+2σ] are considered normal data and are retained; data points falling outside [μ-2σ, μ+2σ] are considered outliers and are removed.

[0020] Furthermore, step S1 also includes: performing Min-Max normalization on the normal data first, and then performing data partitioning.

[0021] Furthermore, in step S2, the specific method for the feature extraction network based on the physical model is as follows:

[0022] Step S21, Equivalent Circuit Model and Mathematical Expression of Lithium Battery

[0023] A second-order equivalent circuit model of a lithium battery is constructed. In the second-order equivalent circuit of a lithium battery, resistor R1-voltage C1 simulates the nonlinear voltage drop; resistor R2-voltage C2 simulates the ohmic drop; and resistor R0 simulates the internal resistance of the battery.

[0024] According to Kirchhoff's laws, the mathematical expression of the second-order equivalent circuit model of a lithium battery is as follows:

[0025]

[0026] U T =U oc (SOC)-U1-U2-R0i(T)

[0027]

[0028] Where T is the sampling time, T0 is the reference time, U1 and U2 are the terminal voltages of R1 and R2, respectively. oc Let Q be the open-circuit voltage, i be the loop current, and Q be the open-circuit voltage. N For rated capacity, U oc There is a functional relationship between the battery's remaining capacity (SOC) and the state of charge (SOC), and the basic formula is as follows:

[0029]

[0030] Where OCV represents the open-circuit voltage, exp(·) represents the exponential function, E is the activation energy, R is the gas constant, and Temp is the open-circuit voltage. ref Here, ω is the approximate polynomial order, where ω is the reference temperature, Temp is the operating temperature, and ω is the reference polynomial order. a k For the coefficients of each order before simplification, a p The coefficients of each order after rearrangement are given, and c0 is the corresponding polynomial coefficient in a single charge-discharge cycle.

[0031] U1, U2, and SOC are selected as unobservable virtual sensor signals that characterize the health status of lithium batteries, i.e., the target parameter signals of the feature extraction network.

[0032] The discrete mathematical expressions for the three signals U1, U2, and SOC are as follows:

[0033]

[0034] Where k represents the sampling time, SOC k The remaining battery power at the sampling time. The voltage of R1 at the sampling time. The voltage of R2 at the sampling time, SOC k-1 The remaining battery power at the previous sampling time. The voltage of R1 at the previous sampling time. The voltage of R2 at the previous sampling time;

[0035] Step S22: Feature extraction network model-RNN based on recurrent neural network

[0036] The core of the feature extraction network model-RNN is the basic RNN network, which is mathematically expressed as:

[0037] h k =g(W hh h k-1 +W hx x k +b h )

[0038] y k =W yh h k +W yx x k

[0039] Among them, h k h is the hidden state at that moment. k-1 x is the hidden state of the previous time step. k Input y for this moment k For the output at this moment, W hh W hx W yh W yx b h All of these are model training parameters, and g(·) is the network model;

[0040] The internal structure of the RNN network is constrained based on the discrete equation of the equivalent circuit, and the unobservable feature signal is extracted using model-RNN.

[0041] Based on the discrete mathematical expression of the equivalent circuit model of a lithium battery, the hidden state of the feature extraction network model-RNN is defined as follows:

[0042]

[0043] According to the discrete equation, W hh Defined as:

[0044]

[0045] Choosing a diagonal matrix constraint to embed the RNN network, the simplified W... hh Defined as:

[0046]

[0047] Where ψ1, ψ2, and ψ3 are the matrix weights to be trained;

[0048] According to U oc The functional relationship between the function and the SOC is modeled using the network model model-Uoc to model the third-order approximate function.

[0049] Furthermore, model-Uoc consists of a power-law computation layer, two fully connected layers, a random deactivation layer, and an activation layer;

[0050] For input samples in Given a set of real numbers, where batch_size is the number of training samples; after passing through the exponentiation layer, its output is:

[0051]

[0052] The first fully connected layer has an input dimension of 9 and an output dimension of 3. Its specific formula is as follows:

[0053]

[0054] Where W1 is the weight of the fully connected layer, b1 is the bias of the fully connected layer, and the output is...

[0055] Next, the data is fed into a random deactivation function, the specific formula of which is:

[0056] y2 = Dropout(y1)

[0057] The data is then fed into a second fully connected layer with an input dimension of 3 and an output dimension of 1, yielding the output. Finally, the data is activated using the following formula:

[0058] y4 = ReLU(y3)

[0059] According to Kirchhoff's second law, the output y of an RNN network unit is calculated using a fully connected layer. u Specifically defined as:

[0060] y u =W u x u +b u

[0061] in, W u b u Here, represents the weights and biases of the fully connected layer, and i represents the input current.

[0062] Furthermore, in step S3, the method for constructing a network based on health indicators of PINN and the degradation model includes:

[0063] Step S31, Degradation dynamic model establishment

[0064] Modeling general degradation processes using multivariate functions:

[0065] u = f(t, x)

[0066] Where t is the number of discharge cycles, x is the vector that constitutes HI, and u is the constructed HI;

[0067] The degradation dynamics equation of the system is expressed as:

[0068]

[0069] Where g(·) is the explicit partial differential equation of the θ-parameterized degradation dynamics, which is a nonlinear function of t, x, and u; based on the explicit partial differential equation, a generalized function approximator G(·) is defined to characterize the nonlinear degradation dynamics equation, and the specific equation is as follows:

[0070] u t ≈G(t,x,u,u t ,u x ,u xx ,…;Θ)

[0071] in, Θ represents the network parameters of G(·);

[0072] The lithium battery kinetic equations are modeled based on the DeepHPM algorithm. A generalized function approximator is defined to characterize the nonlinear degradation kinetic equations, as follows:

[0073] u t -DeepHPM(t,x,u,u t ,u x ,u xx ,…;Θ)=0

[0074] Where Θ represents the trainable model parameters of the DeepHPM network model;

[0075] Step S32: Construct a network based on health indicators of PINN and the degradation model.

[0076] The health indicator construction network based on PINN and degradation model mainly consists of three modules: health indicator HI construction network N(·), degradation dynamics simulation network G(·), and degradation model embedding network E(·).

[0077] Network N(·) has an input dimension of 5 and an output dimension of 1, consisting of two fully connected layers and one sinusoidal nonlinear layer. Network G(·) has an input dimension of 11 and an output dimension of 1, consisting of two fully connected layers and one sinusoidal nonlinear layer.

[0078] Based on the empirical patterns of lithium battery degradation, an exponential degradation model is used to constrain the construction trend of HI. The exponential degradation model is defined as follows:

[0079]

[0080] Where z is the degradation index, φ, θ, α, β are degradation-related parameters, and ε is random noise;

[0081] The corresponding exponential degradation kinetic equation is characterized as follows:

[0082]

[0083] The network E(·) is designed based on the exponential degradation dynamics equation. It uses three training parameters to constrain the dynamic changes of HI and continuously adjusts the direction of the exponential fit as the training process progresses.

[0084] Furthermore, step S3 also includes training a network model based on health indicators constructed from PINN and the degradation model, as follows:

[0085] Step S331: Definition of loss function

[0086] According to step S2, the feature extraction network based on physical knowledge is essentially an RNN model. This network simulates the output voltage of a circuit by using current signals and a network structure embedded with an equivalent model. It is trained using a loss function based on mean square error, and the specific equation of the loss function is as follows:

[0087]

[0088] in, For the output voltage return loss of the lithium battery equivalent circuit, U k For the actual output voltage, The output voltage is predicted by the algorithm, Φ is the network parameters of the model, and N is the total number of training samples. It is the set of non-negative integers;

[0089] According to step S3, the health indicator construction network based on PINN and the degradation model includes three sub-networks, and the corresponding loss function is constructed based on MSE, as specifically expressed below:

[0090]

[0091] in, For the first-order partial differential regression loss function of the dynamics of health indicator degeneration, Let Θ be the regression loss function of the exponential degradation model of health indicator degradation dynamics, Θ be the network parameters of the G(·) model, and Ψ be the network parameters of the E(·) model.

[0092] Step S332: Model Training Scheme

[0093] The training steps of the physics-based unsupervised health assessment and remaining life prediction algorithm for lithium batteries consist of two parts: pre-training of the physics-based feature extraction network and joint training of the feature extraction network and the health indicator construction algorithm.

[0094] In the pre-training of the feature extraction network, the optimization objective is:

[0095]

[0096] In the joint training of the feature extraction network and the health indicator construction algorithm, the optimization objective is:

[0097]

[0098] Where λ1, λ2, λ3, and λ4 are loss functions. The corresponding weighting coefficients, To constrain monotonicity, a lithium battery health assessment model is trained based on the optimization objective. By adjusting the weight coefficients to balance the impact of different loss functions on the HI construction, a stable health indicator that can characterize the degradation characteristics of lithium batteries is finally constructed.

[0099] Furthermore, in step S4, the health assessment and remaining life expectancy prediction specifically include:

[0100] Step S41: Health Status Estimate and Assessment

[0101] The corresponding sensor signals from the test data are input into the physical knowledge-based feature extraction network involved in step S2 to obtain unobservable sensor degradation signals based on the lithium battery equivalent circuit model. Then, the health indicator construction network based on PINN and the degradation model involved in step S3 is used to construct the lithium battery health indicators and perform lithium battery health status assessment. The indicators of health indicators include monotonicity, trend, correlation, robustness, threshold consistency, and remaining lifetime prediction accuracy.

[0102] Step S42: Remaining life prediction and assessment

[0103] Based on historical data from multiple lithium battery lifecycles, corresponding health indicators are constructed. Based on the test time and trend characteristics of multiple health indicators, combined with empirical rules, appropriate failure thresholds are set. For the test set health indicators involved in step S41, the remaining life of the test unit is calculated according to the selected failure threshold, and the accuracy of the remaining life prediction is used to further illustrate the effectiveness of the algorithm.

[0104] The present invention discloses an unsupervised health assessment and remaining life prediction method for lithium batteries based on physical knowledge, which has the following beneficial effects:

[0105] This invention combines the advantages of physical interpretability and model generality. It constructs physically meaningful health indicators through a data-driven model embedding physical units, achieving good predictive performance on small datasets. It enhances the algorithmic space of the HI (High-Intensity Hierarchy Process) network using a physics-based feature extraction algorithm, and achieves targeted degradation feature signal extraction by fusing the main physical features of the lithium battery performance model. A health indicator construction algorithm based on the PINN algorithm framework is used for lithium battery health status assessment. Even in the absence of degradation signal labels, the extracted degradation feature signals are fused with the DeepHPM model to obtain health indicators with system failure dynamics, reducing dataset dependence while improving model interpretability and generalization ability. Attached Figure Description

[0106] Figure 1 This is a flowchart of the method of the present invention;

[0107] Figure 2 This is a schematic diagram of the feature extraction network based on the physical model and the health indicator construction network based on PINN of the present invention;

[0108] Figure 3 This is a schematic diagram of the second-order equivalent circuit of the present invention. Detailed Implementation

[0109] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0110] The algorithm proposed in this invention guides the construction of a feature extraction network based on the lithium battery performance model, and purposefully extracts feature signals with degradation mechanisms. Based on the PINN algorithm framework, a health indicator construction network integrating physical knowledge is constructed. By fusing the exponential degradation model and the DeepHPM model, health indicators with system failure dynamics are obtained, which reduces the dependence on the size of the dataset while improving the interpretability and generalization ability of the model.

[0111] refer to Figure 1 This invention discloses an unsupervised health assessment and remaining life prediction method for lithium batteries based on physical knowledge, comprising the following steps:

[0112] Step S1, Data Preprocessing:

[0113] Collect relevant sensor data from lithium battery charge and discharge experiments and perform data preprocessing;

[0114] Step S2, Feature extraction network based on physical model:

[0115] The mathematical expression of the lithium battery mechanism model guides the construction of the feature extraction network, extracting unobservable signals containing the system degradation law, and enhancing the input space of health assessment and remaining life prediction algorithms;

[0116] Step S3, construct the network based on PINN's health indicators:

[0117] Based on the dynamic process of the lithium battery mechanism model and the dynamic expression of the degradation model, a PINN-based health assessment and remaining life prediction algorithm is constructed. The enhanced feature data is input into the PINN-based health assessment and remaining life prediction algorithm to optimize the model parameters for constructing health indicators.

[0118] Step S4, Health Assessment and Life Expectancy Prediction:

[0119] Based on the test data, feature signals with physical significance are extracted, and health indicators that integrate physical knowledge are constructed to ultimately achieve remaining life estimation based on health indicators.

[0120] To further optimize the technical solution, in step S1, the data is preprocessed using the 2-sigma principle, including:

[0121] Step S10: Divide the input sensor data into different groups of data according to a sliding window with a window length of len and a window gap of inter;

[0122] Step S11: Calculate the mean μ and standard deviation σ for each group of data;

[0123] Step S12: According to the 2-sigma principle, the probability of data distribution in [μ-2σ, μ+2σ] is 95.45%. Data points falling in the interval [μ-2σ, μ+2σ] are normal data and are retained; data points falling outside [μ-2σ, μ+2σ] are outliers and are removed.

[0124] Further optimization of the technical solution includes step S1, which involves first performing Min-Max normalization on the normal data, and then performing data partitioning.

[0125] The specific framework of the algorithm of this invention is as follows: Figure 2 As shown. The algorithm consists of two main parts: a feature extraction network based on a physical model and a health indicator construction network based on PINN and a degradation model. 1) Feature extraction network based on a physical model: Based on the second-order equivalent circuit model of a lithium-ion battery, a discrete mathematical model of the lithium battery is derived. The mathematical model is used to guide the design of node architecture and network weights in a recurrent neural network (RNN), extracting unobservable virtual sensor signals that characterize the health state of the lithium battery. This enhances the input space of the health indicator construction network and improves the physical interpretability of the subsequently constructed health indicators. 2) Health indicator construction network based on PINN and a degradation model: Based on the basic structure of PINN, a health indicator construction algorithm incorporating a degradation model is constructed. Specifically, the relevant dynamic expressions in the lithium battery equivalent model guide the construction of differential operators, the DeepHPM network is used to simulate the degradation dynamics of the lithium battery equivalent model, and the degradation model is used to constrain the health indicator construction method.

[0126] To further optimize the technical solution, in step S2, the specific method for the feature extraction network based on the physical model is as follows:

[0127] Step S21, Equivalent Circuit Model and Mathematical Expression of Lithium Battery

[0128] The second-order equivalent circuit model of a lithium-ion battery is mainly constructed based on empirical knowledge, and its basic components include a variable voltage source, a resistor, and a capacitor. The second-order equivalent circuit of a lithium battery is shown below. Figure 3 As shown, resistor R1-voltage C1 simulates a nonlinear voltage drop; resistor R2-voltage C2 simulates an ohmic drop; and resistor R0 simulates the internal resistance of the battery.

[0129] According to Kirchhoff's laws, the mathematical expression of the second-order equivalent circuit model of a lithium battery is as follows:

[0130]

[0131] U T =U oc (SOC)-U1-U2-R0i(T)

[0132]

[0133] Where T is the sampling time, T0 is the reference time, U1 and U2 are the terminal voltages of R1 and R2, respectively. oc Let Q be the open-circuit voltage, i be the loop current, and Q be the open-circuit voltage. N For rated capacity, U oc There is a functional relationship between the battery's remaining capacity and its state of charge (SOC), and the basic formula is as follows:

[0134]

[0135] Where OCV represents the open-circuit voltage, exp(·) represents the exponential function, E is the activation energy, R is the gas constant, and Temp is the open-circuit voltage. ref Here, ω is the approximate polynomial order, where ω is the reference temperature, Temp is the operating temperature, and ω is the approximate polynomial order. a p For each order of coefficients, a k For the coefficients of each order before simplification, a p The coefficients for each order are represented by c0, which is the polynomial coefficient corresponding to a single charge-discharge cycle. In practical operation, this invention selects a fourth-order polynomial to approximate the open-circuit voltage.

[0136] According to the second-order equivalent circuit model of lithium battery, the three signals U1, U2 and SOC are closely related to the overall operation of the circuit (SOC is related to the open circuit voltage). Therefore, this invention selects U1, U2 and SOC as unobservable virtual sensor signals that characterize the health status of lithium battery, that is, the target parameter signals of the feature extraction network.

[0137] Due to the discrete nature of the collected data, the formulas need to be discretized when analyzing the mathematical model. The discrete mathematical expressions for the three signals U1, U2, and SOC are as follows:

[0138]

[0139] Where k represents the sampling time, SOC k The remaining battery power at the sampling time. The voltage of R1 at the sampling time. The voltage of R2 at the sampling time, SOC k-1 The remaining battery power at the previous sampling time. The voltage of R1 at the previous sampling time. The voltage of R2 at the previous sampling time;

[0140] Step S22: Feature extraction network model-RNN based on recurrent neural network

[0141] The core of the feature extraction network model-RNN is the basic RNN network, which is mathematically expressed as:

[0142] h k =g(W hh h k-1 +W hx x k +b h )

[0143] y k =W yh h k +W yx x k

[0144] Among them, h k h is the hidden state at that moment. k-1 x is the hidden state of the previous time step. k Input y for this moment k For the output at this moment, W hh W hx W yh W yx b h All of these are model training parameters, and g(·) is the network model;

[0145] According to the discrete equation of the second-order equivalent circuit of a lithium battery, its structure is basically consistent with the mathematical expression of an RNN. Based on these characteristics, this invention constrains the internal structure of the RNN network according to the discrete equation of the equivalent circuit, and uses a model-RNN to extract unobservable feature signals.

[0146] Based on the discrete mathematical expression of the equivalent circuit model of a lithium battery, the hidden state of the feature extraction network model-RNN is defined as follows:

[0147]

[0148] According to the discrete equation, W hh Defined as:

[0149]

[0150] To reduce the dependence of network training on model parameter identification and improve the generality of feature extraction networks, the constraints need to be simplified. hh The matrix contains several important physical features, among which the diagonal matrix is ​​an inherent feature. Therefore, the diagonal matrix is ​​chosen to constrain the embedding of the RNN network, resulting in the simplified W. hh Defined as:

[0151]

[0152] Where ψ1, ψ2, and ψ3 are the matrix weights to be trained;

[0153] According to U oc The functional relationship between the function and the SOC is modeled using the network model model-Uoc to model the third-order approximate function.

[0154] The technical solution has been further optimized. The model-Uoc consists of a power-law calculation layer, two fully connected layers (Linear), a random deactivation layer (Dropout), and an activation layer (ReLU).

[0155] For input samples in Given a set of real numbers, where batch_size is the number of training samples; after passing through the exponentiation layer, its output is:

[0156]

[0157] The first fully connected layer has an input dimension of 9 and an output dimension of 3. Its specific formula is as follows:

[0158]

[0159] Where W1 is the weight of the fully connected layer, b1 is the bias of the fully connected layer, and the output is...

[0160] Next, the data is fed into a random deactivation function, the specific formula of which is:

[0161] y2 = Dropout(y1)

[0162] The data is then fed into a second fully connected layer with an input dimension of 3 and an output dimension of 1, yielding the output. Finally, the data is activated using the following formula:

[0163] y4 = ReLU(y3)

[0164] According to Kirchhoff's second law, the output y of an RNN network unit is calculated using a fully connected layer. u Specifically defined as:

[0165] y u =W u x u +b u

[0166] in, W u b uHere, represents the weights and biases of the fully connected layer, and i represents the input current.

[0167] Further optimization of the technical solution: In step S3, the method for constructing a network based on health indicators of PINN and the degradation model includes:

[0168] Step S31, Degradation dynamic model establishment

[0169] In lithium-ion battery systems, the failure trajectory is influenced by various factors, including charging rate, discharging rate, temperature, and time. Therefore, multivariate functions can be used to model the general degradation process.

[0170] u = f(t, x)

[0171] Where t is the number of discharge cycles, x is the vector that constitutes HI, and u is the constructed HI;

[0172] To characterize the common features of the degradation process in different experimental units of similar systems and to avoid the influence of different initial states on the modeling of the degradation process, this invention focuses on the system degradation dynamics. Generally, the degradation dynamics equation of the system is expressed as:

[0173]

[0174] Where g(·) is the explicit partial differential equation of the θ-parameterized degradation dynamics, which is a nonlinear function of t, x, u; further, a generalized function approximator G(·) can be defined based on the explicit partial differential equation to characterize the nonlinear degradation dynamics equation, the specific equation is as follows:

[0175] u t ≈G(t,x,u,u t ,u x ,u xx ,…;Θ)

[0176] in, Θ represents the network parameters of G(·). For the order of the partial differential variables input into the approximate equation G(·), a first-order differential operator is used for calculation based on the accuracy and computational complexity of the lithium battery degradation model.

[0177] Generally, the explicit equation of G(·) in a function approximator is usually unknown and often difficult to obtain through mathematical calculation. To approximate G(·), this invention models the lithium battery kinetic equation based on the DeepHPM algorithm, defining a generalized function approximator to characterize the nonlinear degradation kinetic equation. The specific equation is as follows:

[0178] u t -DeepHPM(t,x,u,u t ,ux ,u xx ,…;Θ)=0

[0179] Where Θ represents the trainable model parameters of the DeepHPM network model;

[0180] Step S32: Construct a network based on health indicators of PINN and the degradation model.

[0181] The health indicator construction network based on PINN and degradation model mainly consists of three modules: health indicator HI construction network N(·), degradation dynamics simulation network G(·), and degradation model embedding network E(·).

[0182] Network N(·) has an input dimension of 5 and an output dimension of 1, consisting of two fully connected layers and one sinusoidal nonlinear layer. Network G(·) has an input dimension of 11 and an output dimension of 1, consisting of two fully connected layers and one sinusoidal nonlinear layer.

[0183] Based on the empirical patterns of lithium battery degradation, this invention uses an exponential degradation model to constrain the construction trend of HI. The exponential degradation model is defined as follows:

[0184]

[0185] Where z is the degradation index, φ, θ, α, β are degradation-related parameters, and ε is random noise;

[0186] The corresponding exponential degradation kinetic equation is characterized as follows:

[0187]

[0188] The network E(·) is designed based on the exponential degradation dynamics equation. It uses three training parameters to constrain the dynamic changes of HI and continuously adjusts the direction of the exponential fit as the training process progresses.

[0189] Furthermore, step S3 also includes training a network model based on health indicators constructed from PINN and the degradation model, as follows:

[0190] Step S331: Definition of loss function

[0191] The physics-based unsupervised health assessment and remaining life prediction algorithm for lithium batteries consists of two algorithm modules: a feature extraction network based on physics knowledge and a health indicator construction network based on PINN and a degradation model.

[0192] According to step S2, the feature extraction network based on physical knowledge is essentially an RNN model. This network simulates the output voltage of the circuit through the current signal and the network structure embedded with the equivalent model. It is trained using a loss function based on Mean Square Error (MSE). The specific equation of the loss function is as follows:

[0193]

[0194] in, For the output voltage return loss of the lithium battery equivalent circuit, U k For the actual output voltage, The output voltage is predicted by the algorithm, Φ is the network parameters of the model, and N is the total number of training samples. It is the set of non-negative integers;

[0195] According to step S3, the health indicator construction network based on PINN and the degradation model includes three sub-networks, where G(·) is used to constrain the degradation kinetic equation in the lithium battery equivalent circuit model, and E(·) is used to constrain the construction rules of the health indicator HI. The corresponding loss function is constructed based on MSE, specifically expressed as follows:

[0196]

[0197] in, For the first-order partial differential regression loss function of the dynamics of health indicator degeneration, Let Θ be the regression loss function of the exponential degradation model of health indicator degradation dynamics, Θ be the network parameters of the G(·) model, and Ψ be the network parameters of the E(·) model.

[0198] Step S332: Model Training Scheme

[0199] The training steps of the physics-based unsupervised health assessment and remaining life prediction algorithm for lithium batteries consist of two parts: pre-training of the physics-based feature extraction network and joint training of the feature extraction network and the health indicator construction algorithm.

[0200] In the pre-training of the feature extraction network, the optimization objective is:

[0201]

[0202] In the joint training of the feature extraction network and the health indicator construction algorithm, the optimization objective is:

[0203]

[0204] Where λ1, λ2, λ3, and λ4 are loss functions. The corresponding weighting coefficients, Monotonicity constraints are imposed to ensure the monotonicity of the HI (High-Intensity Index). A lithium-ion battery health assessment model is trained based on the optimization objective, and the influence of different loss functions on the HI construction is balanced by adjusting the weight coefficients. Finally, a stable health indicator capable of characterizing the degradation properties of lithium-ion batteries is constructed.

[0205] Furthermore, in step S4, the health assessment and remaining life expectancy prediction specifically include:

[0206] Step S41: Health Status Estimate and Assessment

[0207] The corresponding sensor signals from the test data are input into the physical knowledge-based feature extraction network involved in step S2 to obtain unobservable sensor degradation signals based on the lithium battery equivalent circuit model. Then, the health indicator construction network based on PINN and the degradation model involved in step S3 is used to construct the lithium battery health indicators and perform lithium battery health status assessment. The indicators of health indicators include monotonicity, trend, correlation, robustness, threshold consistency, and remaining lifetime prediction accuracy.

[0208] To demonstrate the superiority of the health indicator HI, this invention designs a health indicator evaluation scheme based on the basic characteristics of HI, and uses multiple indicators, including monotonicity, trend, correlation, robustness, threshold consistency, and remaining life prediction accuracy, to comprehensively evaluate the rationality of the health indicator.

[0209] Step S42: Remaining life prediction and assessment

[0210] Based on historical data from multiple lithium battery lifecycles, corresponding health indicators are constructed. Based on the test time and trend characteristics of multiple health indicators, combined with empirical rules, appropriate failure thresholds are set. For the test set health indicators involved in step S41, the remaining life of the test unit is calculated according to the selected failure threshold, and the accuracy of the remaining life prediction is used to further illustrate the effectiveness of the algorithm.

[0211] This invention combines the advantages of physical interpretability and model generality. It constructs physically meaningful health indicators through a data-driven model embedding physical units, achieving good predictive performance on small datasets. It enhances the algorithmic space of the HI (High-Intensity Hierarchy Process) network using a physics-based feature extraction algorithm, and achieves targeted degradation feature signal extraction by fusing the main physical features of the lithium battery performance model. A health indicator construction algorithm based on the PINN algorithm framework is used for lithium battery health status assessment. Even in the absence of degradation signal labels, the extracted degradation feature signals are fused with the DeepHPM model to obtain health indicators with system failure dynamics, reducing dataset dependence while improving model interpretability and generalization ability.

[0212] Example

[0213] The specific effects of this embodiment are demonstrated and verified using an open-source dataset as a case study.

[0214] 1. Open source datasets

[0215] This invention uses the CALCE lithium-ion battery dataset released by the University of Maryland as the validation dataset for the algorithm. The CALCE dataset was established by the University of Maryland for research on algorithms related to assessing the state of health of lithium batteries, including SOC prediction, SOH assessment, and remaining life prediction. The CALCE data was generated based on real constant current-constant voltage (CC-CV) charge-discharge cycle experiments of CS2 batteries. All experiments were conducted using the same standard: charging with a constant current of 0.5C to 4.2V, followed by constant voltage charging at 4.2V until the charging current dropped to 0.05A; after charging, discharging with a constant current of 1C until the terminal voltage dropped to 2.7V.

[0216] 2. Dataset Processing

[0217] To maintain consistency in the training data, the specific implementation plan uses only discharge cycle data for training and result verification. The CS2-33, CS2-34, and CS2-35 battery datasets are used as the training set, denoted as D = {T, I, U, t, OCV, Q}, where T represents the data sampling time, I represents the loop current, U represents the port voltage, t represents the discharge cycle, OCV represents the open-circuit voltage, and Q represents the remaining charge.

[0218] To reduce interference from noisy data and improve dataset quality, outlier cleaning of the original dataset is necessary. The algorithm uses the 2-sigma principle to process the data. The 2-sigma principle is a mathematical concept based on the normal distribution. It assumes that a set of data to be detected contains only random errors and defines an interval based on the normal distribution. Data exceeding this interval are considered outliers and should be removed. The specific steps for outlier cleaning based on the 2-sigma principle are as follows:

[0219] ① Divide the input data into different groups of data according to a sliding window with a window length of len and a window gap of inter.

[0220] ② Calculate the mean μ and standard deviation σ for each group of data;

[0221] ③ According to the 2-sigma principle, the probability of data distribution in [μ-2σ,μ+2σ] is 95.45%. Data points falling in the interval [μ-2σ,μ+2σ] are normal data and are retained; data points falling outside [μ-2σ,μ+2σ] are outliers and are removed.

[0222] Feature data collected by different sensors have different dimensions and units, and their physical meanings vary greatly. Directly using these data for subsequent feature extraction algorithms can lead to biases. To eliminate the influence of different dimensions, feature scaling is needed to bring all indicators to the same order of magnitude, facilitating comprehensive comparison and calculation. The data normalization method used in this section is Min-Max normalization, also known as deviation standardization, which maps data samples to the range [0,1]. The formula for Min-Max normalization is as follows:

[0223]

[0224] Here, we assume the sensor signal to be processed is X, X max X min X represents the maximum and minimum values ​​of the data in X. std This represents the normalized data.

[0225] The training set after outlier removal and data normalization is D. train ={T train ,I train U train ,t train OCV train Q train}

[0226] According to the algorithm requirements, D train Divided into X train ={T train ,I train}, Y train ={U train}, P train ={t train OCV train Q train}, where X train Input data to the network, Y train For the label data of the feature extraction network, P train This is runtime status data.

[0227] Using the CS2-36, CS2-37, and CS2-38 battery datasets as the test set, after outlier cleaning, data normalization, and data partitioning, X was obtained. test ={T test ,I test}, Y test ={U test}, P test ={t test OCV test Q test}

[0228] 3. Model Building and Training

[0229] Based on steps 1 and 2, an unsupervised health assessment and remaining life prediction algorithm for lithium batteries based on physical knowledge is constructed.

[0230] The input signal of the physical model-RNN feature extraction network is X. train Given the hidden state h0, based on the second-order equivalent circuit model of a lithium battery, the hidden dimension of the RNN is set to 3. The network's output signal is hidden, By minimizing With Y train The MSE loss function is used to train the network.

[0231] The input to the health indicator network constructed based on PINN and the degradation model includes X train Hidden state h0 and P train , where X train h0 is used to calculate hidden. Hidden is related to P. train t in train and X train I in train The algorithm consists of 5-dimensional inputs to N(·), and its output is the health indicator HI constructed by the algorithm, denoted as u. train Calculate u train The partial derivative with respect to the N(·) input signal, and its relationship with the input signal and u train Together, they form an 11-dimensional data input network G(·) to simulate the dynamic characteristics of lithium battery degradation. The output of network G(·) is... By minimizing and The MSE loss function constrains the network. The input signals of the network E(·) include t train with u train Its output signal is E, which is obtained by minimizing E and... The MSE loss function implements an exponential trend constraint on health indicators.

[0232] Following the steps above, a model is constructed and trained. First, the model-RNN is pre-trained using only the CS2-33 battery dataset. Pre-training obtains the initial weights for the model-RNN, accelerating the training process and improving efficiency. Based on the pre-training, the model-RNN and model-PINN are jointly trained using the CS2-33, CS2-34, and CS2-35 battery datasets as training sets, resulting in the health assessment and remaining lifespan prediction algorithm model.

[0233] 4. Health Status Assessment

[0234] Based on the training dataset D train The obtained u train Calculate the corresponding failure threshold; here, the 650th charge-discharge cycle of the lithium battery is chosen as the failure threshold. Input test dataset D. test Calculate the corresponding u test .

[0235] 5. Performance Evaluation Indicators

[0236] To demonstrate the superiority of the health indicators constructed by the algorithm proposed in this invention, this invention designs corresponding performance evaluation indicators based on the basic attributes of the health indicator HI.

[0237] The basic attributes of the Health Indicator (HI) include:

[0238] (1) After the degradation process begins, the trend of HI is monotonically decreasing;

[0239] (2) After the degradation process begins, the trend of HI is closely related to the running time;

[0240] (3) Under the same environmental impact and the same degradation mode, the variance of the failure threshold between different units calculated according to HI is the smallest.

[0241] (4) To mitigate the data fluctuations and uncertainties caused by the subtle differences between different units of the same model in HI construction, HI needs to have good versatility;

[0242] (5) The remaining life prediction based on health indicators should be as close as possible to the actual value.

[0243] Based on the above four basic attributes, corresponding performance evaluation indicators are proposed, namely: monotonicity, trend, failure threshold variance, robustness, and accuracy of RUL prediction.

[0244] For the constructed health indicators Where m is the total number of discharge cycles contained in a test unit, and the specific formula for calculating monotonicity is as follows:

[0245]

[0246] The specific formula for calculating the trend is as follows:

[0247]

[0248] The specific formula for calculating the failure threshold variance is as follows:

[0249]

[0250] Where H = [H1, H2, ..., H N [ ] represents the set of health indicator vectors in the training set, and N represents the total number of units in the training set. This represents the failure threshold of the q-th training unit.

[0251] The specific formula for calculating robustness is as follows:

[0252]

[0253] in, The residual between H and its mean trend is generally obtained through methods such as smoothing and fitting.

[0254] The specific formula for calculating the accuracy of RUL predictions is as follows:

[0255]

[0256] Among them, RUL 1:M =[l1,l2,…,l M [ ] represents the set of remaining lifetime prediction vectors for each test set unit. For the predicted lifetime of the r-th unit, l r Let M be the actual lifetime of the r-th unit, and M be the total number of units in the test set.

[0257] To demonstrate the superiority of the proposed unsupervised health indicator construction algorithm based on physical knowledge, and based on the algorithm's characteristics of being unsupervised and having physical meaning, the commonly used health indicator SOC of lithium batteries is selected for comparison. Based on the five indicators proposed above—monotonicity, trend, failure threshold variance, robustness, and RUL prediction accuracy—it is shown that the HI constructed by the algorithm has good performance in terms of stability, versatility, and remaining lifetime prediction.

[0258] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for unsupervised health assessment and remaining life prediction of lithium batteries based on physical knowledge, characterized in that, Includes the following steps: Step S1, Data Preprocessing: Collect relevant sensor data from lithium battery charge and discharge experiments and perform data preprocessing; Step S2, Feature extraction network based on physical model: The mathematical expression of the lithium battery mechanism model guides the construction of the feature extraction network, extracting unobservable signals containing the system degradation law, and enhancing the input space of health assessment and remaining life prediction algorithms; Step S3, construct the network based on PINN's health indicators: Based on the dynamic process of the lithium battery mechanism model and the dynamic expression of the degradation model, a PINN-based health assessment and remaining life prediction algorithm is constructed. The enhanced feature data is input into the PINN-based health assessment and remaining life prediction algorithm to optimize the model parameters for constructing health indicators. Step S4, Health Assessment and Life Expectancy Prediction: Based on the test data, feature signals with physical significance are extracted, and on this basis, health indicators that integrate physical knowledge are constructed to ultimately achieve remaining life estimation based on health indicators. In step S3, the method for constructing a network based on health indicators of PINN and the degradation model includes: Step S31, Degradation dynamic model establishment Modeling general degradation processes using multivariate functions: in, This represents the number of discharge cycles. For the vector that constitutes HI, For the constructed HI; The degradation dynamics equation of the system is expressed as: in, for The explicit partial differential equations of parameterized degradation dynamics are as follows: Nonlinear functions; a generalized function approximator is defined based on explicit partial differential equations. The equation characterizing the nonlinear degradation dynamics is as follows: in, , for Network parameters; The lithium battery kinetic equations are modeled based on the DeepHPM algorithm. A generalized function approximator is defined to characterize the nonlinear degradation kinetic equations, as follows: Among them This represents the trainable model parameters of the DeepHPM network model; Step S32: Construct a network based on health indicators of PINN and the degradation model. The health indicator construction network based on PINN and degradation models mainly includes three modules: the health indicator HI construction network. Degradation dynamics simulation network Degradation model embedded network ; network The network has an input dimension of 5 and an output dimension of 1, and consists of two fully connected layers and one sinusoidal nonlinear layer; It has an input dimension of 11 and an output dimension of 1, and consists of two fully connected layers and one sinusoidal nonlinear layer; Based on the empirical patterns of lithium battery degradation, an exponential degradation model is used to constrain the construction trend of HI. The exponential degradation model is defined as follows: in, As a degradation indicator, , , , For degradation-related parameters, It is random noise; The corresponding exponential degradation kinetic equation is characterized as follows: Design a network based on the exponential degradation kinetic equation. It uses three training parameters to constrain the dynamic changes of HI and continuously adjusts the direction of exponential fitting as the training process progresses. Step S3 also includes training a network model based on health indicators constructed from PINN and the degradation model, as follows: Step S331: Definition of loss function According to step S2, the feature extraction network based on physical knowledge is essentially an RNN model. This network simulates the output voltage of the circuit by using the current signal and the network structure of the embedded equivalent model, and is trained using a loss function based on the mean square error. According to step S3, the health indicator construction network based on PINN and the degradation model includes 3 sub-networks, and the corresponding loss function is constructed based on MSE; Step S332: Model Training Scheme The training steps of the physics-based unsupervised health assessment and remaining life prediction algorithm for lithium batteries consist of two parts: pre-training of the physics-based feature extraction network and joint training of the feature extraction network and the health indicator construction algorithm. In the pre-training of the feature extraction network, the optimization objective is: In the joint training of the feature extraction network and the health indicator construction algorithm, the optimization objective is: in, For the network parameters of the equivalent model, for The network parameters of the model, , , , loss function , , , The corresponding weighting coefficients, This is the regression loss function of the output voltage of the equivalent circuit of a lithium battery. For the first-order partial differential regression loss function of the dynamics of health indicator degeneration, The regression loss function is used for the exponential degradation model of the dynamics of health indicator deterioration. To constrain monotonicity, a lithium battery health assessment model is trained based on the optimization objective. By adjusting the weight coefficients to balance the impact of different loss functions on the HI construction, a stable health indicator that can characterize the degradation characteristics of lithium batteries is finally constructed.

2. The method for unsupervised health assessment and remaining life prediction of lithium batteries based on physical knowledge according to claim 1, characterized in that, In step S1, the data is preprocessed using the 2-sigma principle, including: Step S10: Divide the input sensor data into different groups of data according to a sliding window with a window length of len and a window gap of inter; Step S11: Calculate the mean μ and standard deviation σ for each group of data; Step S12, according to the 2-sigma principle, the data point falls on Data points within the range are considered normal and will be retained; data points falling within the range will be retained. Outliers are excluded.

3. The method for unsupervised health assessment and remaining life prediction of lithium batteries based on physical knowledge according to claim 2, characterized in that, Step S1 also includes: performing Min-Max normalization on the normal data first, and then performing data partitioning.

4. The method for unsupervised health assessment and remaining life prediction of lithium batteries based on physical knowledge according to claim 3, characterized in that, In step S2, the specific method for the feature extraction network based on the physical model is as follows: Step S21, Equivalent Circuit Model and Mathematical Expression of Lithium Battery Construct a second-order equivalent circuit model of a lithium battery. In the second-order equivalent circuit of a lithium battery, the resistance... Simulate nonlinear voltage drop; resistor Simulated ohmic drop; resistance Simulates the internal resistance of a battery; According to Kirchhoff's laws, the mathematical expression of the second-order equivalent circuit model of a lithium battery is as follows: in, Sampling time, As the base time, , for , The terminal voltage, This is the open-circuit voltage of the circuit. For loop current, For rated capacity, There is a functional relationship between the battery's remaining capacity (SOC) and the state of charge (SOC), and the basic formula is as follows: in, OCV Indicates open-circuit voltage. Represents an exponential function. For activation energy, The gas constant is... For reference temperature, For operating temperature, For the order of the approximate polynomial, , These are the polynomial coefficients corresponding to a single charge-discharge cycle; choose , And SOC as an unobservable virtual sensor signal that characterizes the health status of lithium batteries, i.e., the target parameter signal of the feature extraction network; , The discrete mathematical expressions for the three signals of SOC are as follows: in, Indicates the sampling time. The remaining battery power at the sampling time. When sampling time Voltage, At the sampling time Voltage, The remaining battery power at the previous sampling time. For the previous sampling time Voltage, For the previous sampling time Voltage; Step S22: Feature extraction network model-RNN based on recurrent neural network The core of the feature extraction network model-RNN is the basic RNN network, which is mathematically expressed as: in, This is the hidden state at that moment. This is the hidden state from the previous moment. Enter this value at that moment. Output for that moment. , , , , These are all model training parameters. For network models; The internal structure of the RNN network is constrained based on the discrete equation of the equivalent circuit, and the unobservable feature signal is extracted using model-RNN. Based on the discrete mathematical expression of the equivalent circuit model of a lithium battery, the hidden state of the feature extraction network model-RNN is defined as follows: According to the discrete equation Defined as: Choosing a diagonal matrix constraint to embed the RNN network, the simplified version... Defined as: in, , , The weights of the matrix to be trained; according to The functional relationship between the function and the SOC is modeled using the network model model-Uoc to model the third-order approximate function.

5. The method for unsupervised health assessment and remaining life prediction of lithium batteries based on physical knowledge according to claim 4, characterized in that, The model-Uoc consists of a power-law computation layer, two fully connected layers, a random deactivation layer, and an activation layer. For input samples ,in For the set of real numbers, The number of training samples; after passing through the exponential layer, its output is: The first fully connected layer has an input dimension of 9 and an output dimension of 3. Its specific formula is as follows: in, The weights of the fully connected layer, For biasing the fully connected layer, output ; Next, the data is fed into a random deactivation function, the specific formula of which is: The data is then fed into a second fully connected layer with an input dimension of 3 and an output dimension of 1, yielding the output. Finally, the data is activated using the following formula: According to Kirchhoff's second law, the output of an RNN network unit is calculated using a fully connected layer. Specifically defined as: in, , , For the weights and biases of the fully connected layer, This is the input current.

6. The method for unsupervised health assessment and remaining life prediction of lithium batteries based on physical knowledge according to claim 5, characterized in that, Step S4, specifically the health assessment and remaining life expectancy prediction, includes: Step S41: Health Status Estimate and Assessment The corresponding sensor signals from the test data are input into the physical knowledge-based feature extraction network involved in step S2 to obtain unobservable sensor degradation signals based on the lithium battery equivalent circuit model. Then, the health indicator construction network based on PINN and the degradation model involved in step S3 is used to construct the lithium battery health indicators and perform lithium battery health status assessment. The indicators of health indicators include monotonicity, trend, correlation, robustness, threshold consistency, and remaining lifetime prediction accuracy. Step S42: Remaining life prediction and assessment Based on historical data from multiple lithium battery lifecycles, corresponding health indicators are constructed. Based on the test time and trend characteristics of multiple health indicators, combined with empirical rules, appropriate failure thresholds are set. For the test set health indicators involved in step S41, the remaining life of the test unit is calculated according to the selected failure threshold, and the accuracy of the remaining life prediction is used to further illustrate the effectiveness of the algorithm.

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