A lithium battery service life prediction method based on a physical neural network

Abstract

This invention provides a method for predicting the lifespan of lithium batteries based on physical neural networks, comprising: constructing a coupled ordinary differential equation of lithium battery charge state and thermodynamic evolution, and establishing a continuous-time dynamic model of lithium battery charge change; constructing a PI-LSTM hybrid analysis framework based on physical information neural networks, and incorporating the coupled ordinary differential equation as a physical constraint term into the loss function of the PI-LSTM hybrid analysis framework; collecting time-series sensing data of lithium battery operation, training the PI-LSTM hybrid analysis framework, and completing the inversion identification of lithium battery physical parameters; based on the trained PI-LSTM hybrid analysis framework, outputting the state of charge and time to depletion of the lithium battery under the target operating condition, and completing the prediction of lithium battery lifespan; this invention aims to achieve accurate and interpretable prediction of lithium battery SOC and TTE in multiple devices, providing support for battery management of electrical equipment such as drones.

Description

Technical Field

[0001] This invention relates to the field of battery state monitoring technology, and in particular to a method for predicting the lifespan of lithium batteries based on physical neural networks. Background Technology

[0002] Lithium-ion batteries, due to their high energy density and long cycle life, have become the core energy carrier for portable smart devices. Battery life prediction has also become a core research direction for battery management systems. Its development has gone through three generations of technological iterations. The first generation is the traditional physical model method, such as the ampere-hour integral method and equivalent circuit model. It relies on electrochemical and thermodynamic laws to build mathematical models, which have strong interpretability, but are difficult to adapt to multi-parameter coupling scenarios under complex working conditions. The second generation is the pure data-driven machine learning method, with neural networks such as LSTM and CNN as the core. It can extract the feature patterns of complex working conditions, but has the limitation of being a "black box". The prediction results lack physical consistency and are highly dependent on the amount of data. The third generation is the exploration of the integration of physical information and deep learning. Although it attempts to incorporate simple physical constraints into the model, it has not yet formed a systematic electrothermal coupling dynamics framework, nor can it achieve cross-device generalization and adaptation. Current technologies still face several key challenges. First, traditional physical models struggle to accurately depict the nonlinear discharge characteristics of lithium batteries under extreme temperatures and dynamic loads, resulting in poor adaptability to complex operating conditions such as strong wind resistance in drones and weak signals in smartphones. Second, purely data-driven models experience a significant drop in prediction accuracy in scenarios with missing data or noise interference, and they cannot explain the intrinsic physical relationship between parameters and battery life. Third, existing prediction methods can only output single numerical results, lacking the quantification of prediction uncertainties and failing to provide risk assessments for device operation. Fourth, most models are designed for single devices, lacking a modular architecture, leading to high migration costs across devices and difficulty in simultaneously adapting to different types of portable devices such as drones and smartphones. These issues make it difficult for existing lithium battery life prediction methods to meet the practical application needs of portable smart devices in terms of accuracy, robustness, interpretability, and generalization. Therefore, there is an urgent need in this field for a lithium battery life prediction method based on physical neural networks to solve the above problems. Summary of the Invention

[0003] This invention provides a lithium battery life prediction method based on physical neural networks, aiming to solve the problems of poor physical interpretability, low adaptability to complex operating conditions, insufficient robustness in sparse data scenarios, lack of prediction uncertainty quantification, and weak generalization across devices in existing lithium battery life prediction methods. It achieves accurate and interpretable prediction of SOC and TTE of lithium batteries in multiple devices, providing support for battery management of portable smart devices.

[0004] This invention provides a method for predicting the lifespan of lithium batteries based on physical neural networks, comprising the following steps: S1. Construct a coupled ordinary differential equation for the charge state and thermodynamic evolution of the lithium battery, and establish a continuous-time dynamic model for the change in the charge of the lithium battery. S2, Construct a PI-LSTM hybrid analysis framework based on physical information neural network, and incorporate the coupled ordinary differential equations described in step S1 as physical constraint terms into the loss function of the PI-LSTM hybrid analysis framework; S3, Collect time-series sensing data of lithium battery operation, train the PI-LSTM hybrid analysis framework, and complete the inversion and identification of lithium battery physical parameters. S4, based on the trained PI-LSTM hybrid analysis framework, outputs the state of charge (SOC) and time to depletion (TTE) of the lithium battery under the target operating conditions, thus completing the prediction of the lithium battery's lifespan.

[0005] Compared with the prior art, the beneficial effects of this application are as follows: 1. This application combines physical interpretability with data-driven adaptability. It integrates electrothermal coupling ordinary differential equations as physical constraints into the PI-LSTM framework, ensuring that the prediction results strictly follow the laws of electrochemistry and thermodynamics. This breaks through the "black box" limitation of pure data-driven models, while retaining the feature extraction capability of deep learning for complex working conditions.

[0006] 2. This application significantly improves robustness under complex working conditions and data sparse scenarios. Through physical parameter inversion identification, it extracts physical parameters that are difficult to measure directly from limited time series data. Even under extreme conditions with high data missing rate, it can still reduce prediction error and can accurately adapt to complex working conditions such as strong winds for drones and weak signals for smartphones.

[0007] 3. This application realizes the quantification of the uncertainty of the prediction results. By combining heteroscedastic negative log-likelihood loss and Monte Carlo Dropout method, it quantifies random and cognitive uncertainty respectively and outputs a 95% confidence interval, providing a scientific risk assessment for drone flight path planning and low battery use of smartphones, and avoiding sudden power outage problems.

[0008] 4. This application has excellent cross-device generalization and migration capabilities. It adopts a modular architecture design, which only requires replacing the underlying physical constraint equations to quickly migrate from drones to smartphones without reconstructing the neural network, thus greatly reducing the cost of cross-device adaptation.

[0009] 5. This application identifies the core driving factors of battery life under different operating conditions through SHAP feature attribution and Sobol global sensitivity analysis, providing targeted guidance for drone hardware design, smartphone algorithm optimization and low-power usage by users.

[0010] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0011] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention, but do not constitute a limitation thereof; in the drawings: Figure 1 This is a flowchart illustrating a lithium battery life prediction method based on a physical neural network provided by the present invention. Figure 2 This is a schematic diagram of the prediction method applied in the drone scenario; Figure 3 This is a schematic diagram of the prediction method applied in smartphone scenarios; Figure 4 This is a schematic diagram illustrating the estimated performance of battery state of charge (SOC) in drone scenarios. Detailed Implementation

[0012] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention. Example 1:

[0013] This invention provides a method for predicting the lifespan of lithium batteries based on physical neural networks. Please refer to [link to relevant documentation]. Figure 1 This includes the following steps: S1. Construct a coupled ordinary differential equation for the charge state and thermodynamic evolution of the lithium battery, and establish a continuous-time dynamic model for the change in the charge of the lithium battery. S2, Construct a PI-LSTM hybrid analysis framework based on physical information neural network, and incorporate the ordinary differential equation coupled in step S1 as a physical constraint term into the loss function of the PI-LSTM hybrid analysis framework; S3 collects time-series sensing data of lithium battery operation, trains the PI-LSTM hybrid analysis framework, and completes the inversion and identification of lithium battery physical parameters. S4, based on the trained PI-LSTM hybrid analysis framework, outputs the state of charge (SOC) and time to depletion (TTE) of the lithium battery under the target operating conditions, thus completing the prediction of the lithium battery's lifespan.

[0014] Specifically, this embodiment is based on the Physical Information Neural Network (PINN), which integrates the underlying physical mechanisms of lithium battery electrochemistry and thermodynamics with the temporal feature extraction capabilities of the Long Short-Term Memory (LSTM) network. First, a coupled ordinary differential equation that can accurately characterize the state of charge (SOC) and temperature evolution of the lithium battery is constructed to form a continuous-time dynamic model that reflects the dynamic changes in the lithium battery charge. Then, this coupled ordinary differential equation is embedded as a physical constraint term into the loss function of the PI-LSTM hybrid analysis framework to avoid the "black box" limitations of purely data-driven models. Subsequently, time-series sensor data of lithium batteries during actual operation are collected, including data on hardware load, environmental parameters, and battery status of drones / smartphones. This data is used to train the PI-LSTM hybrid analysis framework, and the inversion and identification of physical parameters in lithium batteries that are difficult to measure directly are completed simultaneously during the training process. Finally, the relevant parameters of the target operating condition are input into the trained PI-LSTM hybrid analysis framework, which outputs the state of charge (SOC) time-series change curve of the lithium battery under the operating condition and the time to depletion (TTE), thus achieving accurate prediction of the lithium battery's lifespan. The method in this embodiment can be mainly adapted to drone equipment, and is also compatible with various devices equipped with lithium batteries, such as smartphones.

[0015] In one implementation, in step S1, the coupled ordinary differential equations include the lithium battery state of charge (SOC) evolution equation, the battery temperature thermodynamic evolution equation, and the battery effective capacity correction equation, which constitute a continuous-time dynamic model of electrothermal coupling. The equation for the evolution of the state of charge (SOC) is: in, Let t represent the state of charge of the lithium battery. Let be the instantaneous total power consumption of the lithium battery at time t. Let be the terminal voltage of the lithium battery at time t. The effective capacity of a lithium battery; The thermodynamic evolution equation for battery temperature is based on Newton's law of cooling, and its expression is: in, Let t be the temperature of the lithium battery at time t. The heat generation coefficient, For heat dissipation coefficient, Ambient temperature; The corrected equation for the effective capacity of a battery is: in, Let N be the health state decay function based on the number of charge-discharge cycles. For temperature sensitivity coefficient, This is the reference temperature.

[0016] Specifically, the coupled ordinary differential equations constructed in step S1 are in the form of electrothermal coupling. The three core equations respectively characterize the dynamic changes of the charge, temperature and effective capacity of the lithium battery, realizing a multi-dimensional physical characterization of the changes in the lithium battery capacity. Among them, the State of Charge (SOC) evolution equation reflects the rate of change of the lithium battery's state of charge at time t. Its change is negatively correlated with the instantaneous total power consumption and positively correlated with the product of the terminal voltage and the effective capacity. Its physical essence is the embodiment of the law of conservation of charge. The instantaneous total power consumption of a drone is the sum of the power consumption of components such as the motor and ESC, while the instantaneous total power consumption of a smartphone is the sum of the power consumption of components such as the processor and the screen. The thermodynamic evolution equation for battery temperature is based on Newton's law of cooling, characterizing the rate of temperature change of the lithium battery at time t, which is determined by both heat generation and heat dissipation processes. This is the heat generation term for lithium batteries, reflecting the rate at which the total power consumption of the device is converted into heat energy. Drones experience forced convection due to the downwash airflow from their propellers. This is a heat dissipation item, reflecting the heat exchange rate between the lithium battery and the environment; The battery effective capacity correction equation is used to correct the effective capacity of lithium batteries. This capacity is affected by both the battery's health and the ambient temperature. The function is a health state decay function based on the number of charge-discharge cycles N. This function is used to reflect the impact of battery aging on the effective capacity. The function is considered constant in a single charge-discharge cycle. The specific function form is not limited in this embodiment. Those skilled in the art can set it according to the actual situation. For temperature correction, the reference temperature. Take 25℃, temperature sensitivity coefficient Temperature sensitivity coefficient is used to reflect the sensitivity of battery capacity to temperature changes. The value is set based on experience. If applied to drone scenarios, the effect of this temperature correction term is more significant under conditions such as high altitude and low temperature and high speed flight generating heat.

[0017] In one implementation, such as Figure 2 As shown, in the application scenario of drones, the instantaneous total power consumption Basic power consumption Wind resistance overcomes power consumption and system static power consumption The algebraic sum of is expressed as: The basic power consumption is: ,in, The motor's energy efficiency coefficient. Let be the dynamic characterization parameters at time t; The power consumption to overcome wind resistance is: ,in, This is the overall drag coefficient. Let be the relative wind speed at time t.

[0018] Specifically, in drone application scenarios, the instantaneous total power consumption of lithium batteries... It consists of the algebraic sum of three parts: basic power consumption, wind resistance overcoming power consumption, and system static power consumption, comprehensively covering the main energy consumption sources during UAV flight; Among them, basic power consumption The core power consumption and power performance parameters that provide flight propulsion for drones It is proportional to the cube of the power. In specific implementations... The normalized throttle value at time t directly reflects the rotational speed of the drone's propellers. The motor efficiency coefficient is determined by the hardware characteristics of the drone motor and is a physical parameter that needs to be identified through model inversion. Wind resistance overcomes power consumption The power consumption of the drone to overcome environmental wind resistance, and relative wind speed It is proportional to the square of the power. The drag coefficient is determined by factors such as the drone's fuselage shape and payload. The relative wind speed of the drone at time t is the core environmental interference source in the drone scenario; System static power consumption This represents the standby power consumption of basic components such as the drone's onboard computer and flight control system, while the other represents the constant power consumption during the drone's flight.

[0019] In one implementation, such as Figure 3 As shown, in the application scenario of a smartphone, the instantaneous total power consumption processor instantaneous power The screen displays instantaneous power. Instantaneous power of communication With basic standby power The algebraic sum of is expressed as: The processor's instantaneous power is: ,in, This refers to the processor's dynamic energy efficiency coefficient. Let be the processor utilization at time t. Let t be the processor's clock frequency at time t; The instantaneous power displayed on the screen is: ,in, This is a comprehensive ratio coefficient between screen area and luminous efficiency. Let be the screen brightness level at time t. Gamma correction factor; The instantaneous power of communication is: ,in, The energy efficiency coefficient of the network communication module. For the target reference signal strength, Let be the environmental signal strength at time t.

[0020] Specifically, in smartphone applications, the instantaneous total power consumption of lithium batteries... It consists of the algebraic sum of four parts: the instantaneous power of the processor, the screen, the communication module, and the basic standby power; Among them, processor instantaneous power Processor utilization and clock frequency Decision, and It is proportional to the square of the power. The dynamic energy efficiency coefficient of the processor is determined by the hardware characteristics of the mobile phone processor. The screen displays instantaneous power. With screen brightness level of Proportional to the power, gamma correction factor The preferred value is 1.5, which is suitable for the non-linear perception of brightness by the human eye. It is a comprehensive ratio coefficient between screen area and luminous efficiency, determined by the hardware parameters of the mobile phone screen; instantaneous power of communication The power consumption of the mobile communication module is related to the ambient signal strength. Negative correlation, when Below the target reference signal strength At this time, the communication module will increase the transmission power to compensate for path loss. The energy efficiency coefficient of the network communication module; Basic standby power This refers to the standby power consumption of basic components such as the mobile phone baseband and sensors, while the other refers to the constant power consumption during the use of a smartphone.

[0021] It should be noted that the parameters not mentioned above are all parameters that can be obtained by existing means. This embodiment does not limit the source, but only limits the function of the parameters.

[0022] In one embodiment, step S1 further includes constructing a terminal voltage response model based on the nonlinear discharge characteristics of the lithium battery. The terminal voltage response model includes the Shepherd nonlinear voltage model and the Rint internal resistance model. The Shepherd nonlinear voltage model is as follows: ,in, Let be the open-circuit voltage of the lithium battery at time t. This is the constant voltage of the lithium battery. It is the polarization constant. It is an exponential amplitude constant. It is the exponential decay constant; The Rint internal resistance model is: ,in, Let be the instantaneous load current at time t. The internal resistance of the lithium battery is ohmic. By combining the Shepherd nonlinear voltage model and the Rint internal resistance model described above, the lithium battery terminal voltage can be obtained. The explicit solution is used to solve coupled ordinary differential equations.

[0023] Specifically, this embodiment also constructs a terminal voltage response model to characterize the nonlinear discharge characteristics of lithium batteries and solve the problem of nonlinear voltage drop in lithium batteries under low SOC conditions. This model is suitable for calculating the terminal voltage of lithium batteries in drones and smartphones, and its nonlinear characterization is more prominent in drones under high load and extreme temperature conditions. Among them, the Shepherd nonlinear voltage model is used to calculate the open-circuit voltage of the lithium battery at time t. , This is the constant voltage of the lithium battery. The term is used to characterize the nonlinear polarization effect at the end of battery discharge. The term is used to simulate the exponentially decreasing region at the beginning of the discharge curve. The polarization constant K, exponential amplitude constant A, and exponential decay constant B are all determined by the electrochemical characteristics of the lithium battery and are physical parameters that need to be identified through inversion. The Rint internal resistance model is used to calculate the terminal voltage of a lithium battery in conjunction with its open-circuit voltage. This reflects the ohmic internal resistance of the battery. Voltage loss, Let be the instantaneous load current at time t. The ohmic internal resistance of lithium batteries is affected by battery temperature and aging conditions. High-load operating conditions of drones can cause this. Because the heat generation changes rapidly, the model needs to be corrected in real time; By combining the Shepherd nonlinear voltage model and the Rint internal resistance model, and using the root-finding formula to obtain the physically correct positive root, the lithium battery terminal voltage can be obtained. The explicit solution is obtained, and this explicit solution is substituted into the coupled ordinary differential equations such as the SOC evolution equation to complete the exact solution of the coupled ordinary differential equations.

[0024] In one implementation, in step S2, the PI-LSTM hybrid analysis framework is a multi-layer recursive architecture. The input layer takes in the time-series hardware load sequence and the environmental parameter sequence, the hidden layer uses an LSTM structure to extract time-series features, and the output layer outputs the state of charge (SOC), time to depletion (TTE), and prediction uncertainty variance parameters of the lithium battery. The input layer includes processor utilization, screen brightness, ambient signal strength, ambient temperature, and initial battery SOC. The output layer includes the predicted SOC timing curve, TTE value, and variance parameter used to quantify prediction uncertainty.

[0025] Specifically, the PI-LSTM hybrid analysis framework constructed in this embodiment is a multi-layer recursive physical information neural network architecture that integrates the temporal feature extraction capability of LSTM with the interpretability of physical constraints. The framework is also adaptable to drone and smartphone scenarios. The framework's input layer is used to input timing hardware load sequences and environmental parameter sequences. For drone scenarios, input parameters include normalized throttle size, relative wind speed, ambient temperature, and initial battery SOC. For smartphone scenarios, input parameters include processor utilization, screen brightness, ambient signal strength, ambient temperature, and initial battery SOC. All input parameters are input in the form of timing sequences to match the dynamic operating characteristics of the device. The hidden layer of the framework adopts an LSTM structure and utilizes the gating mechanism of LSTM to extract deep dynamic features of the input time series, solve the long-term dependency problem of time series data, and adapt to the continuous time characteristics of lithium battery power changes. The framework's output layer is a multi-output structure that can simultaneously output the lithium battery's State of Charge (SOC), Time to Depletion (TTE), and prediction uncertainty variance parameter. The predicted SOC is in the form of a time-series curve, reflecting the dynamic changes of SOC over time. The TTE is a specific numerical result, characterizing the time from the current moment to the depletion of the lithium battery's charge. The prediction uncertainty variance parameter is used to quantify the error of the model's prediction results, providing data support for subsequent uncertainty analysis.

[0026] It should be noted that the temporal feature extraction capability and gating mechanism of LSTM are existing methods, and their principles will not be elaborated in this embodiment.

[0027] In one implementation, the total loss function of the PI-LSTM hybrid analysis framework Data-driven loss terms With physical constraint loss term The composition, expressed as: ,in These are the weighting coefficients for the physical constraint terms; The data-driven loss term uses heteroscedasticity negative log-likelihood loss, expressed as follows: ,in, For the sample size, This is the measured SOC value. The SOC prediction value is the output of the continuous-time dynamic model. For heteroscedasticity parameters; The physical constraint loss term is: ,in The predicted state of charge, The time derivative of the predicted SOC. This represents the terminal voltage of the lithium battery at the current moment. For the predicted temperature, This is the time derivative for predicting temperature.

[0028] Specifically, the total loss function of the PI-LSTM hybrid analysis framework It integrates data-driven loss and physical constraint loss, through weighting coefficients. Balancing the effects of both ensures that the model closely matches the measured data; Data-driven loss term The heteroscedasticity negative log-likelihood loss method, unlike the traditional mean squared error loss, is adopted. This method is suitable for the heteroscedasticity characteristics of lithium batteries under complex operating conditions, meaning the model can dynamically adjust its tolerance to noise based on the input. Here, N is the number of training samples. Let SOC be the measured value of the i-th sample. Let i be the predicted SOC value for the i-th sample. for and The heteroscedasticity parameter is used to quantify the random uncertainty of the prediction result of the i-th sample. This loss term allows the model to automatically reduce the strictness of data fitting under noisy conditions. Physical constraint loss term The error is expressed in squared form. The time derivatives of the predicted State of Charge (SOC) and predicted temperature are calculated automatically using differentiation. This forces the model's predictions to satisfy the SOC evolution equation and the battery temperature thermodynamic evolution equation constructed in step S1. The state of charge predicted by the model. Its time derivative, The temperature predicted by the model, Its time derivative is used to avoid numerical illusions in the model and ensure the physical consistency of the prediction results; Weighting coefficient These are hyperparameters and can be adjusted according to the actual training scenario. In extreme operating conditions of the drone (such as strong winds or low temperatures), they can be appropriately increased. This strengthens the role of physical constraints, and under normal operating conditions of smartphones, the impact can be appropriately reduced. This improves the model's fit to the measured data.

[0029] In one implementation, step S3, the physical parameter inversion and identification process includes: During the training process of the PI-LSTM hybrid analysis framework, the weight parameters of the neural network and the parameters to be identified with clear physical meaning are optimized simultaneously. The parameters to be identified include the heat generation coefficient. Heat dissipation coefficient Motor energy efficiency coefficient Comprehensive wind resistance coefficient Processor dynamic energy efficiency coefficient Screen overall ratio coefficient Energy efficiency coefficient of communication module polarization constant Ohmic internal resistance ; By minimizing the total loss function, the optimal value of the parameter to be identified is obtained by inversely solving from the time-series sensing data, thus completing the parameter inversion identification.

[0030] Specifically, the physical parameter inversion identification in this embodiment differs from the traditional model that only optimizes network weights. In the training process of the PI-LSTM hybrid analysis framework, this method simultaneously optimizes the weight parameters of the neural network and the parameters to be identified that have clear physical meanings, so as to extract physical parameters that are difficult to measure directly from time-series sensing data. The parameters to be identified are divided into general physical parameters and scene-specific physical parameters. General physical parameters include the heat generation coefficient. Heat dissipation coefficient polarization constant Ohmic internal resistance It is suitable for all devices equipped with lithium batteries, such as drones and smartphones; drone-specific physical parameters include motor energy efficiency coefficient. Comprehensive wind resistance coefficient These are core parameters for calculating drone energy consumption; specific physical parameters for smartphone scenarios include the processor's dynamic energy efficiency coefficient. Screen overall ratio coefficient Energy efficiency coefficient of communication module , is a core parameter for calculating smartphone power consumption; The core logic of inversion identification is to minimize the total loss function. The parameters to be identified are used as the optimizable parameters of the model and are trained together with the weight parameters of the neural network. Through optimization algorithms such as gradient descent, the values ​​of the parameters to be identified and the weight parameters are continuously adjusted until the total loss function reaches the minimum value. At this time, the value of the parameters to be identified is the optimal value. For drone scenarios, the motor energy efficiency coefficient can be obtained through this inversion identification process. Comprehensive wind resistance coefficient Parameters that are difficult to measure through hardware can be adapted to different models and payloads of drones; for smartphone scenarios, the energy efficiency coefficients of processors, screens and communication modules can be obtained to adapt to smartphones of different brands and configurations, thus achieving generalized adaptation of the model.

[0031] In one implementation, step S4 includes a step of quantifying the uncertainty of the prediction results while outputting the SOC and TTE of the lithium battery. Uncertainty quantification includes the quantification of accidental uncertainty and the quantification of cognitive uncertainty, and the total uncertainty is the superposition of the two. Random uncertainty is expressed by the heteroscedasticity parameter in the model output. Quantification is performed to characterize the prediction error caused by sensor noise and random fluctuations in user behavior; Cognitive uncertainty is quantified using the Monte Carlo Dropout method. During the inference phase, the Dropout layer remains active, and a predicted trajectory is generated through N random samplings. The expected value and variance of the predicted value are calculated, expressed as follows: in, Represents the final predicted trajectory. For the first The SOC prediction value at time t obtained from the second sampling is based on variance. Calculate the 95% confidence interval for SOC prediction to quantify the cognitive uncertainty of the prediction results.

[0032] Specifically, this embodiment, while outputting SOC and TTE, also needs to quantify the uncertainty of the prediction results to avoid the limitations of a single prediction value and provide risk assessment for equipment use decisions. This uncertainty quantification method is corely adapted to the complex operating conditions of UAVs (such as wind speed fluctuations and high-altitude low temperatures), under which the uncertainty of prediction is more significant. The total uncertainty is composed of the superposition of random uncertainty and cognitive uncertainty, comprehensively covering the sources of prediction error. Random uncertainty is the error at the data level, while cognitive uncertainty is the error at the model level. The combination of the two can accurately characterize the reliability of the prediction results; random uncertainty is expressed through the heteroscedasticity parameter of the model output. Quantization primarily characterizes the prediction error caused by inherent sensor noise and random fluctuations during equipment operation (such as sudden wind speed changes in drones or sudden background task startups on smartphones). The larger the value, the higher the random uncertainty of the sample, and the greater the noise in the prediction results; Cognitive uncertainty is quantified using the Monte Carlo Dropout method. During the model inference phase, the Dropout layer is kept on, and multiple SOC prediction trajectories are generated through N random samplings (typically 100), and then the expected value of the prediction is calculated. and variance ,in For the final SOC predicted trajectory, The SOC prediction value at time t is obtained from the m-th sampling; based on variance. Calculate the 95% confidence interval of the SOC prediction. This confidence interval can characterize the cognitive blind spot of the model under the current operating conditions, such as the extreme weak / strong wind of the drone, the nonlinear region at the end of the lithium battery discharge. Under such operating conditions, the confidence interval will widen, indicating that the cognitive uncertainty of the prediction results is high. For drone flight decisions, the quantification of uncertainty can provide a reference for drone route planning and endurance assessment. If the confidence interval is too wide, it can prompt the drone to return to base in time. For smartphone use, it can provide users with a warning of the risk of shutdown when the battery is low.

[0033] In one implementation, step S4 further includes: performing sensitivity analysis on parameters affecting the lifespan of lithium batteries based on the trained PI-LSTM hybrid analysis framework; the sensitivity analysis includes feature attribution analysis based on SHAP values ​​and global sensitivity analysis based on the Sobol method; Feature attribution analysis based on SHAP values ​​is used to quantify the contribution of each input variable to the prediction results of SOC and TTE, and to identify the core driving factors affecting lithium battery power consumption. Global sensitivity analysis based on the Sobol method is used to cover the entire parameter space, quantify the influence weight of each physical parameter on TTE, and identify nonlinear coupling effects between parameters.

[0034] Specifically, this embodiment also includes a step of conducting sensitivity analysis based on the trained PI-LSTM hybrid analysis framework to identify the core parameters affecting the lifespan of lithium batteries, providing a theoretical basis for energy consumption optimization and usage strategy formulation for drones / smartphones, providing guidance for hardware design and flight control optimization for drones, and providing auxiliary guidance for smartphone users and manufacturers. Among them, the feature attribution analysis based on SHAP value is a global feature importance analysis method. By calculating the SHAP value of each input variable, it quantifies its contribution to the prediction results of SOC and TTE, and clarifies the driving or inhibiting effect of each variable on lithium battery power consumption. For drone scenarios, it can identify core driving factors such as relative wind speed, normalized throttle, and ambient temperature. For smartphone scenarios, it can identify core driving factors such as signal strength, ambient temperature, and processor utilization. Moreover, this analysis can reveal the nonlinear influence law of variables, such as the "threshold effect" of temperature on battery power consumption. Global sensitivity analysis based on the Sobol method differs from traditional univariate local analysis. It can cover the entire parameter space, quantify the influence weight of each physical parameter on TTE, and identify nonlinear coupling effects between parameters. For drone scenarios, ambient temperature, normalized throttle, and payload are used as core analysis parameters, and analyses are conducted under different wind speed scenarios to obtain the dominant influencing factors under different operating conditions. For example, wind speed is the core dominant factor in strong wind scenarios, while normalized throttle is the core dominant factor in windless scenarios. For smartphone scenarios, ambient temperature, processor utilization, and screen brightness are used as core analysis parameters, and analyses are conducted under strong and weak signal scenarios. It can be found that processor utilization is the core dominant factor in strong signal scenarios, while temperature is the core dominant factor in weak signal scenarios. The results of sensitivity analysis can directly guide energy consumption optimization. For drones, motor design, wind resistance structure, and flight control algorithms can be optimized based on core driving factors. For smartphones, it can provide users with low-power usage suggestions and provide manufacturers with directions for hardware design and algorithm optimization. Moreover, the analysis results can make the model's prediction logic more interpretable, further breaking through the "black box" limitations of purely data-driven models.

[0035] In one implementation, this embodiment uses the above model to predict the SOC curve of the UAV in a complex environment with drastic wind speed fluctuations, and compares it with observation data; the simulation results are as follows. Figure 4 As shown, Figure 4 The horizontal axis represents time in minutes; the vertical axis represents the battery state of charge (SOC), ranging from 0 to 1; the blue solid line represents the pure data-driven LSTM model, which does not rely on the battery's electrochemical equations or equivalent circuit parameters, but directly learns the mapping relationship from input data (such as voltage, current, and temperature) to the output SOC; the black dashed line represents the true SOC; the purple solid line represents the SOC estimated by the PI-LSTM model; the purple shaded area represents the confidence interval, reflecting the range of uncertainty in the estimation. Depend on Figure 4It is evident that even in complex environments with drastic wind fluctuations, the model maintains strict physical smoothness and accuracy in predicting the SOC curve. Furthermore, the model successfully transfers its ability to perceive "signal fluctuations" to "wind speed disturbances." In gusty wind conditions, the model's output confidence interval automatically widens, demonstrating strong cross-domain environmental adaptability.

[0036] 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 predicting the lifespan of lithium batteries based on physical neural networks, characterized in that, Includes the following steps: S1. Construct a coupled ordinary differential equation for the charge state and thermodynamic evolution of the lithium battery, and establish a continuous-time dynamic model for the change in the charge of the lithium battery. S2, Construct a PI-LSTM hybrid analysis framework based on physical information neural network, and incorporate the coupled ordinary differential equations described in step S1 as physical constraint terms into the loss function of the PI-LSTM hybrid analysis framework; S3, Collect time-series sensing data of lithium battery operation, train the PI-LSTM hybrid analysis framework, and complete the inversion and identification of lithium battery physical parameters. S4, based on the trained PI-LSTM hybrid analysis framework, outputs the state of charge (SOC) and time to depletion (TTE) of the lithium battery under the target operating conditions, thus completing the prediction of the lithium battery's lifespan.

2. The lithium battery life prediction method based on physical neural networks according to claim 1, characterized in that, In step S1, the coupled ordinary differential equations include the lithium battery state of charge (SOC) evolution equation, the battery temperature thermodynamic evolution equation, and the battery effective capacity correction equation, which constitute a continuous-time dynamic model of electrothermal coupling. The equation for the evolution of the state of charge (SOC) is as follows: in, Let t represent the state of charge of the lithium battery. Let be the instantaneous total power consumption of the lithium battery at time t. Let be the terminal voltage of the lithium battery at time t. The effective capacity of a lithium battery; The thermodynamic evolution equation for the battery temperature is constructed based on Newton's law of cooling, and its expression is: in, Let t be the temperature of the lithium battery at time t. The heat generation coefficient, For heat dissipation coefficient, Ambient temperature; The battery effective capacity correction equation is as follows: in, Let N be the health state decay function based on the number of charge-discharge cycles. For temperature sensitivity coefficient, This is the reference temperature.

3. The lithium battery life prediction method based on physical neural networks according to claim 2, characterized in that, In the application scenario of drones, the instantaneous total power consumption Basic power consumption Wind resistance overcomes power consumption and system static power consumption The algebraic sum of is expressed as: The basic power consumption is: ,in, The motor's energy efficiency coefficient. Let be the dynamic characterization parameters at time t; The power consumption to overcome wind resistance is: ,in, This is the overall drag coefficient. Let be the relative wind speed at time t.

4. The lithium battery life prediction method based on physical neural networks according to claim 2, characterized in that, In smartphone application scenarios, the instantaneous total power consumption processor instantaneous power The screen displays instantaneous power. Instantaneous power of communication With basic standby power The algebraic sum of is expressed as: The instantaneous power of the processor is: ,in, This refers to the processor's dynamic energy efficiency coefficient. Let be the processor utilization at time t. Let t be the processor's clock frequency at time t; The instantaneous power displayed on the screen is: ,in, This is a comprehensive ratio coefficient between screen area and luminous efficiency. Let be the screen brightness level at time t. Gamma correction factor; The instantaneous power of the communication is: ,in, The energy efficiency coefficient of the network communication module. For the target reference signal strength, Let be the environmental signal strength at time t.

5. The lithium battery life prediction method based on physical neural networks according to claim 2, characterized in that, In step S1, a terminal voltage response model is constructed based on the nonlinear discharge characteristics of the lithium battery. The terminal voltage response model includes the Shepherd nonlinear voltage model and the Rint internal resistance model. The Shepherd nonlinear voltage model is as follows: ,in, Let be the open-circuit voltage of the lithium battery at time t. This is the constant voltage of the lithium battery. It is the polarization constant. It is an exponential amplitude constant. It is the exponential decay constant; The Rint internal resistance model is as follows: ,in, Let be the instantaneous load current at time t. The internal resistance of the lithium battery is ohmic. By combining the Shepherd nonlinear voltage model and the Rint internal resistance model, the lithium battery terminal voltage can be obtained. The explicit solution is used to solve the coupled ordinary differential equation.

6. The lithium battery life prediction method based on physical neural networks according to claim 1, characterized in that, In step S2, the PI-LSTM hybrid analysis framework is a multi-layer recursive architecture. The input layer takes in the time-series hardware load sequence and the environmental parameter sequence, the hidden layer uses an LSTM structure to extract time-series features, and the output layer outputs the state of charge (SOC), time to depletion (TTE), and prediction uncertainty variance parameters of the lithium battery. The inputs to the input layer include processor utilization, screen brightness, ambient signal strength, ambient temperature, and initial battery state of charge (SOC). The outputs of the output layer include the predicted SOC timing curve, TTE value, and variance parameter used to quantify prediction uncertainty.

7. The lithium battery life prediction method based on physical neural networks according to claim 6, characterized in that, The total loss function of the PI-LSTM hybrid analysis framework Data-driven loss terms With physical constraint loss term The composition, expressed as: ,in These are the weighting coefficients for the physical constraint terms; The data-driven loss term uses heteroscedastic negative log-likelihood loss, expressed as follows: ,in, For the sample size, This is the measured SOC value. The SOC prediction value output by the continuous-time dynamics model. For heteroscedasticity parameters; The physical constraint loss term is: ,in The predicted state of charge, The time derivative of the predicted SOC. This represents the terminal voltage of the lithium battery at the current moment. For the predicted temperature, This is the time derivative for predicting temperature.

8. The method for predicting the lifespan of a lithium battery based on a physical neural network according to claim 1, characterized in that, In step S3, the inversion and identification process of the physical parameters includes: During the training process of the PI-LSTM hybrid analysis framework, the weight parameters of the neural network and the parameters to be identified with clear physical meaning are optimized simultaneously. The parameters to be identified include the heat generation coefficient. Heat dissipation coefficient Motor energy efficiency coefficient Comprehensive wind resistance coefficient Processor dynamic energy efficiency coefficient Screen overall ratio coefficient Energy efficiency coefficient of communication module polarization constant Ohmic internal resistance ; By minimizing the total loss function, the optimal value of the parameter to be identified is obtained by inversely solving from the time-series sensing data, thus completing the parameter inversion identification.

9. The method for predicting the lifespan of a lithium battery based on a physical neural network according to claim 1, characterized in that, In step S4, while outputting the SOC and TTE of the lithium battery, the step of quantifying the uncertainty of the prediction results is also included. The uncertainty quantification includes the quantification of accidental uncertainty and the quantification of cognitive uncertainty, and the total uncertainty is the superposition of the two. The random uncertainty is expressed by the heteroscedasticity parameter output by the model. Quantification is performed to characterize the prediction error caused by sensor noise and random fluctuations in user behavior; The cognitive uncertainty is quantified using the Monte Carlo Dropout method. During the inference phase, the Dropout layer remains active, and a predicted trajectory is generated through N random samplings. The expected value and variance of the predicted value are calculated, expressed as follows: in, Represents the final predicted trajectory. For the first The SOC prediction value at time t obtained from the second sampling is based on variance. Calculate the 95% confidence interval for SOC prediction to quantify the cognitive uncertainty of the prediction results.

10. The method for predicting the lifespan of a lithium battery based on a physical neural network according to claim 1, characterized in that, Step S4 further includes: performing sensitivity analysis on parameters affecting the lifespan of lithium batteries based on the trained PI-LSTM hybrid analysis framework; the sensitivity analysis includes feature attribution analysis based on SHAP values ​​and global sensitivity analysis based on the Sobol method; The SHAP-based feature attribution analysis is used to quantify the contribution of each input variable to the SOC and TTE prediction results, and to identify the core driving factors affecting lithium battery power consumption. The global sensitivity analysis based on the Sobol method is used to cover the entire parameter space, quantify the influence weight of each physical parameter on TTE, and identify the nonlinear coupling effect between parameters.

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