CN116401770A - Quick charge strategy design method based on battery digital twin model and machine learning - Google Patents

Quick charge strategy design method based on battery digital twin model and machine learning Download PDF

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CN116401770A
CN116401770A CN202310549532.XA CN202310549532A CN116401770A CN 116401770 A CN116401770 A CN 116401770A CN 202310549532 A CN202310549532 A CN 202310549532A CN 116401770 A CN116401770 A CN 116401770A
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张永志
韩斗
罗国庆
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Abstract

The invention relates to a battery digital twin model and machine learning-based fast charge strategy design method, which belongs to the field of battery fast charge optimization and comprises the following steps: when the electric automobile is connected into the charging pile for charging, detecting battery state data of the automobile; inputting the battery state data into a Bayesian optimizer based on a battery digital twin model, and predicting the aging condition of the battery in the current charging under an initial protocol according to the current battery state; transmitting the current charging protocol and the battery aging corresponding to the current charging protocol to a Bayesian optimizer, and recommending a quick charging protocol for next round of extraction; updating the next round of fast charge protocol to the digital twin model of the battery, and predicting the battery state again to obtain the aging condition of the updated battery in the current charge; and adding the updated charging protocol and the battery aging corresponding to the updated charging protocol into the existing data set, transmitting the updated charging protocol to the Bayesian optimizer again for quick charging protocol recommendation, and repeating the steps to obtain the finally recommended charging protocol.

Description

Quick charge strategy design method based on battery digital twin model and machine learning
Technical Field
The invention belongs to the field of battery fast charge optimization, and relates to a fast charge strategy design method based on a battery digital twin model and machine learning.
Background
With the increasing trend of traffic electrification, automobile manufacturers have made significant advances in the field of electric vehicles for pure electric vehicles (BEVs). The number of BEV models available on the market increases substantially, as well as the performance. At the same time, some challenges have hindered widespread use of electric vehicles, such as long charging times and mileage anxiety problems.
Lithium ion batteries are used as BEVs core components, and have the advantages of high energy density and long service life, occupy the main market of vehicle-mounted batteries, and are paid attention to. The demand of electric vehicles for lithium ion (Li-ion) batteries is increasing, and the demand for new optimal charging methods is accelerated, so as to improve the speed and reliability of the charging process without reducing the performance of the batteries. In addition to developing new materials and new batteries, optimizing charging strategies is also critical to solving the charging time problem. The method of increasing the charging current only to achieve reduced charging time causes temperature rise and deleterious side effects, and the tradeoff between fast charging and battery health should be considered simultaneously.
Generally, existing lithium ion battery charging strategies can be divided into three categories according to internal mathematical models:
the first is a model-free method, including Constant Current (CC), constant Current and Constant Voltage (CCCV), multi-stage constant current and constant voltage, and pulse charging techniques. These methods preset a charging curve without considering the dynamic response of the battery.
The second type of charging strategy utilizes empirical models, such as equivalent circuit based models and neural network models. These models predict battery status and calculate electrical components using past experimental data. The battery state is estimated by different circuit models using a kalman filter, a recursive least square method, a sliding mode observer, and a moving field of view estimation. Meanwhile, methods such as frequency optimization, multi-objective optimization, fuzzy control, linear secondary control and model predictive control are also used for optimizing the charging strategy. However, the empirical model cannot reflect internal changes of the battery, such as internal parameters of the battery and aging states of the battery.
The third class is complex electrochemical model-based charging algorithms. Formulation of closed loop optimization problems can minimize charging time and compensate for model uncertainty and disturbances. The electrochemical model may be coupled to a temperature model, an aging model, to reflect more internal cell characteristics, and the model is more closely related to a real cell. However, the computational complexity of the full-order nonlinear Partial Differential Equations (PDEs) that are difficult to handle limits their further application on real-time charge controllers. More electrochemical models of degradation, such as Single Particle Models (SPM), are used in practice.
The charging curve of the model-free charging algorithm is preset and cannot adapt to the dynamic change of the battery; the charging algorithm based on the empirical model cannot capture the internal state of the battery, such as temperature, lithium plating, SEI film, and change of active materials; the electrochemical model-based charging algorithm has complex model and excessive calculated amount, and cannot be used for real-time charging control. The data-driven optimization algorithm requires a large amount of data for training and can only be applied to the same type of battery as the battery used for training data, and has poor universality. The invention combines the battery twin model with the data driving, adopts the enhanced single particle model as the battery digital twin model, reduces the calculation cost of the model on the premise of ensuring certain precision, and explores the charging protocol space by using a Bayesian optimization method to obtain the optimal charging protocol.
Disclosure of Invention
In view of the above, the present invention aims to provide a fast charge strategy design method based on a battery digital twin model and machine learning, which solves the problem that the existing charge optimization algorithm cannot fully consider the initial state of the battery during charging, and reduces the calculation amount and calculation cost of an electrochemical model by a data driving method. The invention establishes a digital twin model of the battery, fully considers the initial state of the battery, and dynamically determines the optimal charging protocol of the battery in the current state according to different initial states of the battery. And the process of searching the most available protocol is accelerated by using a machine learning method, so that the calculation cost and time are reduced to realize online optimization.
In order to achieve the above purpose, the present invention provides the following technical solutions:
a fast charge strategy design method based on a battery digital twin model and machine learning comprises the following steps:
s1: when an electric automobile is connected into a charging pile for charging, battery state data of the automobile are detected, wherein the battery state data comprise battery temperature, state of charge (SOC), state of health (SOH), ampere-hour throughput, current lithium inventory loss, electrochemical Impedance Spectrum (EIS) detection and the like;
s2: inputting the battery state data into a Bayesian optimizer based on a battery digital twin model, and predicting aging of the battery in the current charging under an initial protocol according to the current battery state through the battery digital twin model; the initial protocol can be any number of protocols, and the corresponding data is used for initializing a Bayesian optimization model;
s3: transmitting an initial charging protocol and battery aging of a battery single cycle under the initial charging protocol as a data set to a Bayesian optimizer, wherein the initial charging protocol is used as input of a Bayesian optimization model, and the battery aging condition of the battery single cycle under the initial charging protocol is used as output; predicting battery aging corresponding to all protocols in a charging protocol space by utilizing Gaussian process regression GPR, and recommending a charging protocol for next round of extraction by utilizing an acquisition function;
s4: based on the battery state in the step S2, the digital twin model of the battery carries out simulation prediction on the aging of the battery under the charging protocol extracted in the next round, so as to obtain the aging of the battery under the charging protocol extracted in the next round;
s5: and adding the new charging protocol and the corresponding battery aging into the existing data set, transmitting the new charging protocol to the Bayesian optimizer again to recommend the next round of extracted quick charging protocol, and repeating the steps S4-S5 until the final recommended charging protocol is obtained, and charging the vehicle battery by the charging protocol.
Further, the initial protocol and the protocol recommended by the bayesian optimizer are both protocols in a charging protocol space; the charging protocol in the charging protocol space aims to charge the battery state of charge (SOC) from 0% to 80% through constant current charging of a plurality of stages within 10 minutes, and in the process, the battery is charged by stages by using j kinds of currents with different magnitudes;
the charging protocol is a multi-stage constant-current constant-voltage charging MSCC, which consists of a plurality of constant-current charging stages and a constant-voltage charging stage which follows the constant-current charging stages;
when j=3, the charging protocol charges the battery state of charge SOC from 0% to 80% in 3 steps within 10 minutes, and parameters of the charging protocol have CC1', CC2', which are also two-dimensional inputs of the black box optimization model; the method comprises the following steps: the charging rate of the 0-26.67% SOC interval is CC1', the charging rate of the 26.67% -53.34% SOC interval is CC2', the charging rate of the 53.34% -80% SOC interval is CC3', the size of the CC3' is determined by CC1', CC2', and the charging rate is expressed as:
Figure BDA0004230847900000031
when j=4, the charging protocol charges the battery state of charge SOC from 0% to 80% in 10 minutes in 4 steps, and parameters of the charging protocol are CC1, CC2, and CC3, which are also three-dimensional inputs of the black box optimization model; the method comprises the following steps: the charging rate of the 0-20% SOC interval is CC1, the charging rate of the 21-40% SOC interval is CC2, the charging rate of the 41-60% SOC interval is CC3, and the charging rate of the 61-80% SOC interval is CC4, wherein the size of the CC4 is determined by CC1, CC2 and CC3, and the formula is as follows:
Figure BDA0004230847900000032
when j=5, the charging protocol charges the battery state of charge SOC from 0% to 80% in 5 steps within 10 minutes, with parameters of the charging protocol being CC1 ", CC 2", CC3 ", CC 4", which is also a four-dimensional input of the black box optimization model; the method comprises the following steps: the charging rate of the 0-16% SOC interval is CC1 ", the charging rate of the 16-32% SOC interval is CC 2", the charging rate of the 32-48% SOC interval is CC3 ", the charging rate of the 48-64% SOC interval is CC 4", the charging rate of the 64-80% SOC interval is CC5 ", wherein the size of CC 5" is CC1 ", CC 2", CC3 ", and the formula is as follows:
Figure BDA0004230847900000033
further, the battery digital twin model is a battery electrochemical model that considers battery aging mechanisms including SEI film growth, lithium plating, particle cracking, and active material loss, integrated into a DFN model (Doyle-Fuller-Newman) to characterize the aging behavior of the battery.
Further, the SEI film growth specifically includes:
the growth of the SEI film is divided into two processes: firstly, polarization of a battery cathode, reduction decomposition of an organic solvent in electrolyte to generate a new compound, and secondly, precipitation of a new chemical substance on the surface of the anode to form a new SEI film; the growth of the SEI film is captured using a diffusion limited model, whose reaction rate is limited by the rate of transport of solvent through the SEI outer layer, assuming that the flux of solvent molecules follows the Phake law:
Figure BDA0004230847900000041
the boundary conditions are:
Figure BDA0004230847900000042
wherein c sol Is the concentration of the solvent, c sol,e Is the concentration of the solvent in the electrolyte, D sol (T) is the solvent diffusion coefficient, L is the position of the SEI film, L SEI Is SEI film thickness;
the flux density at the SEI film interface is:
Figure BDA0004230847900000043
rate of increase of SEI film thickness:
Figure BDA0004230847900000044
wherein L is SEI Is the SEI film thickness,
Figure BDA0004230847900000045
is the average partial molar volume of the SEI; the growth of the SEI film is affected by temperature and solvent diffusion coefficient, which follows the Arrhenius equation:
Figure BDA0004230847900000046
wherein T is ref ＝25℃,E sol Is the activation energy of solvent diffusion;
the growth of the SEI film will result in the following effects:
(1) the porosity of the negative electrode is reduced:
Figure BDA0004230847900000047
(2) SEI film overpotential increases due to increases in SEI film internal resistance:
Figure BDA0004230847900000048
wherein ε is n Is the porosity of the cathode, a n Is the specific surface area, a for spherical particles n ＝3ε n /R n ,R n Is the radius eta of the spherical particles of the negative electrode SEI Is the overpotential of SEI film, j tot Is the total current density in conservation of negative charge, σ SEI Is the conductivity of the SEI film.
Further, the lithium plating specifically includes:
when lithium ions are not intercalated into an electrode but lithium metal is formed on the surface of the electrode, lithium plating occurs, which is partially or completely recovered in a subsequent discharge reaction by lithium stripping; lithium electroplating also chemically reacts with the electrolyte solution to form an SEI film, and the metal lithium separated by the SEI film cannot be peeled off, and the part of lithium is called dead lithium; thus, a partially reversible lithium plating model was constructed, according to the butler-furat equation, with the lithium plating/stripping flux at the anode/electrolyte interface in the overpotential correction form being:
Figure BDA0004230847900000051
wherein k is Li Is the lithium plating/stripping constant, c Li Is the concentration of lithium plating, F is Faraday constant, c e Is Li in electrolyte + Concentration, transfer coefficient alpha a,Li And alpha c,Li Are all set to 0.5; η (eta) Li Is the lithium deposition potential LDP, defined as eta Li ＝φ s -φ e -η SEI Wherein phi is s And phi e Respectively relative to Li/Li + Electrode potential and electrolyte potential of (a);
by coupling three models of lithium electroplating, lithium stripping and SEI growth, the electroplated lithium will decay over time into SEI film and dead lithium, c Li Is expressed as:
Figure BDA0004230847900000052
wherein a is - Is the ratio of the surface area to the volume of the cathode, c dl Is the concentration of dead lithium, defined as:
Figure BDA0004230847900000053
it is assumed that the dead lithium decay rate γ is inversely proportional to the thickness of the SEI film:
Figure BDA0004230847900000054
wherein gamma is 0 Is a fitting parameter, L SEI,0 Is the initial SEI thickness, L SEI,t Is the SEI thickness at time t.
Further, the particle cracking specifically includes:
radial stress sigma using fatigue crack model based on spherical electrode particles r (r) tangential stress sigma t The expressions of (r) and displacement u are as follows:
Figure BDA0004230847900000055
Figure BDA0004230847900000056
Figure BDA0004230847900000057
where Ω is the partial molar volume, E is the Young's modulus, v is the Poisson's ratio, c avg (R) is a function of average lithium ion concentration and radius, R is particle radius,
Figure BDA0004230847900000058
is the concentration c of lithium ion and the reference concentration c under no stress ref Deviation of (2);
the fatigue crack propagation model follows Paris's law, assuming that all electrode particle surfaces have the same crack length l cr Crack width w cr And crack density ρ cr ：
Figure BDA0004230847900000059
Wherein t is 0 Time of single period, b cr Is a stress intensity correction factor, k cr And m cr Is a constant obtained from the experiment;
the growth model of the SEI film on the new crack is defined as follows:
Figure BDA0004230847900000061
wherein L is SEI,cr Is the average thickness of SEI film on new crack, L SEI,cr0 ＝L SEI,0 And/10000 is the thickness of the initial SEI film on the new crack.
Further, the active material loss specifically includes:
loss of active substance epsilon a Simulation by decreasing the volume fraction of active material:
Figure BDA0004230847900000062
wherein beta, m 2 Sum sigma c Is the coefficient obtained from the experiment, the hydrostatic stress sigma h ＝(σ r +2σ t )/3，σ h The subscripts max and min of (c) represent the maximum and minimum values, respectively.
Further, the Bayesian optimizer consists of a Gaussian process regression model GPR and an acquisition function, and the optimization target is that the aging of the battery is minimum, wherein the aging of the battery comprises capacity loss, lithium inventory loss, coulombic efficiency, active substance loss and the like;
the GPR model is used for outputting logarithmic variance characteristics of all three-dimensional charging protocols; the acquisition function is used to decide which protocols to test in the next round;
when GPR is applied, the actual output y after taking noise into account is expressed as:
y i ＝f(x i )+ε i
wherein (x) i ,y i ) Represents the i-th data point, f represents the feature map, f (x i ) Representing the output of the gaussian model; epsilon i Represents observation noise, and
Figure BDA0004230847900000063
optionally haveSet x= { X of limited input composition 1 ,x 2 ,…,x n } d*n D x n represents n samples, each sample having d features as input, { x 1 ,x 2 ,…,x n } d*n Obeys a joint gaussian probability distribution p (f (x) 1 ),f(x 2 ),…,f(x n ) The mean function and covariance function of f (x) are:
m(x)＝E[f(x)]
k(x,x′)＝E[(f(x)-m(x))(f(x′)-m(x′))]
since there is no a priori information of the distribution of f (x), m (x) is set to 0, and the distribution of y is written as:
Figure BDA0004230847900000064
wherein K is ff Is an n-by-n dimensional matrix, and [ K ] ff ] i,j ＝k(x i ,x j )；
For a new input
Figure BDA0004230847900000065
d x n represents that the new data set has m samples, each sample having d features input thereto; the joint distribution of this and the known observed target values is written as:
Figure BDA0004230847900000066
wherein the method comprises the steps of
Figure BDA0004230847900000071
[K ff ] i,j ＝k(x i ,x j )；
Conditional distribution p (f) * |X,y,X * ) Obeys normal distribution:
Figure BDA0004230847900000072
wherein,,
Figure BDA0004230847900000073
represents the mean of posterior distribution, cov (f * ) The variance of the posterior distribution is expressed as follows:
Figure BDA0004230847900000074
Figure BDA0004230847900000075
kernel functions that can be used in the GPR model include the following:
the first kernel function is a gaussian kernel RBF, given by:
Figure BDA0004230847900000076
wherein II x-x' II 2 Representing the square of the Euclidean distance of the vectors x and x', and sigma represents the standard deviation;
the second kernel function is a Matern kernel, given by:
Figure BDA0004230847900000077
it has positive parameters v and l, where f (v) is a f function, k v Is a second type of bessel function, d (x, x') represents the euclidean distance.
Further, the acquisition function is a confidence interval upper bound function UCB, an improvement probability function PI, or an expected delta function EI, wherein:
the UCB acquisition function is as follows:
UCB(x)＝μ(x)+βσ(x)
wherein μ (x) and σ (x) are the mean and standard deviation of the posterior distribution, respectively, β is a hyper-parameter to be optimized for balanced exploration and development, said exploration being to explore untested parameter spaces with high uncertainty, said development being to test promising areas according to completed experimental results; as the number of steps increases, the focus is changed from exploration to development, and beta is gradually reduced, so that the following steps are obtained:
UCB(x)＝μ(x)+β 0 ε k σ(x)
wherein beta is 0 ,ε k Are super parameters, k represents the optimized times, epsilon is (0, 1) in the value range, epsilon k Characterization reduces the weight of σ (x) to turn emphasis towards development;
the PI acquisition function is as follows:
the PI utilizes posterior model to estimate that the function value is larger than the maximum value mu in the actual observed value at present + To find the next round of sampling points, PI (x) represents the probability, and the formula is as follows:
Figure BDA0004230847900000081
wherein phi represents a normal cumulative distribution function, mu (x) and sigma (x) respectively represent a Gaussian average value and a standard deviation of posterior prediction, and xi is more than or equal to 0 and is an adjustable parameter, wherein the aim is to find the sum mu + The point at which the probability of a comparative boost ζ is greatest;
the EI acquisition function is as follows:
Figure BDA0004230847900000082
Figure BDA0004230847900000083
the weight Φ (Z) is a normal cumulative distribution function, and ζ represents the sum μ + The degree of improvement in the phase ratio, phi (Z), represents the normal probability distribution function, and the objective of EI is to find the point (μ (x) - μ) with the greatest improvement expectations + ζ) Φ (Z) and σ (x) Φ (Z) are used for development and exploration, respectively.
The invention has the beneficial effects that: model-based bayesian optimization can greatly save time: the states of the battery are different when the vehicle is charged each time, the combination of the states such as temperature, SOC, SOH and the like is changed, the charging protocol space of the battery is large, each protocol in the current battery state is simulated by using a battery model, and the calculation amount is huge. The diversity of battery states during charging also makes it difficult to determine battery protocols using look-up tables. The battery digital twin model is combined with Bayesian optimization, so that the running time and cost of the model can be greatly reduced, and quick optimization is realized.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objects and other advantages of the invention may be realized and obtained by means of the instrumentalities and combinations particularly pointed out in the specification.
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For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in the following preferred detail with reference to the accompanying drawings, in which:
fig. 1 is a flowchart of a method for designing a fast charge strategy based on a battery digital twin model and machine learning according to the present invention.
FIG. 2 is a graph comparing the effect of a method according to the invention with a charging method without optimized constant current;
FIG. 3 is a graph showing the results of Bayesian parallel optimization, wherein (a) - (d) are graphs showing the results of optimization for the 1 st to 4 th charges, respectively.
Detailed Description
Other advantages and effects of the present invention will become apparent to those skilled in the art from the following disclosure, which describes the embodiments of the present invention with reference to specific examples. The invention may be practiced or carried out in other embodiments that depart from the specific details, and the details of the present description may be modified or varied from the spirit and scope of the present invention. It should be noted that the illustrations provided in the following embodiments merely illustrate the basic idea of the present invention by way of illustration, and the following embodiments and features in the embodiments may be combined with each other without conflict.
Wherein the drawings are for illustrative purposes only and are shown in schematic, non-physical, and not intended to limit the invention; for the purpose of better illustrating embodiments of the invention, certain elements of the drawings may be omitted, enlarged or reduced and do not represent the size of the actual product; it will be appreciated by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The same or similar reference numbers in the drawings of embodiments of the invention correspond to the same or similar components; in the description of the present invention, it should be understood that, if there are terms such as "upper", "lower", "left", "right", "front", "rear", etc., that indicate an azimuth or a positional relationship based on the azimuth or the positional relationship shown in the drawings, it is only for convenience of describing the present invention and simplifying the description, but not for indicating or suggesting that the referred device or element must have a specific azimuth, be constructed and operated in a specific azimuth, so that the terms describing the positional relationship in the drawings are merely for exemplary illustration and should not be construed as limiting the present invention, and that the specific meaning of the above terms may be understood by those of ordinary skill in the art according to the specific circumstances.
Referring to fig. 1, a fast charge strategy design method based on a battery digital twin model and machine learning includes the following steps:
s1: when an electric automobile is connected into a charging pile for charging, battery state data of the automobile are detected, including battery temperature, state of charge (SOC), state of health (SOH), ampere-hour throughput, current lithium inventory loss, electrochemical Impedance Spectrum (EIS) detection and the like;
s2: inputting the battery state data into a Bayesian optimizer based on a battery digital twin model, and predicting the aging condition of the battery in the current charging under an initial protocol according to the current battery state through the battery digital twin model; in this embodiment, the initial protocol is to randomly select 10 charging protocols from the charging protocol space; the charging protocol in the charging protocol space aims to charge the state of charge (SOC) of the battery from 0% to 80% by constant current charging of a plurality of stages within 10 minutes, and in the process, the battery is charged by stages by using j kinds of currents with different magnitudes;
the charging protocol is a multi-stage constant-current constant-voltage charging MSCC, which consists of a plurality of constant-current charging stages and a constant-voltage charging stage which follows the constant-current charging stages;
when j=3, the charging protocol charges the battery state of charge SOC from 0% to 80% in 3 steps within 10 minutes, and parameters of the charging protocol have CC1', CC2', which are also two-dimensional inputs of the black box optimization model; the method comprises the following steps: the charging rate of the 0-26.67% SOC interval is CC1', the charging rate of the 26.67% -53.34% SOC interval is CC2', the charging rate of the 53.34% -80% SOC interval is CC3', the size of the CC3' is determined by CC1', CC2', and the charging rate is expressed as:
Figure BDA0004230847900000091
when j=4, the charging protocol charges the battery state of charge SOC from 0% to 80% in 10 minutes in 4 steps, and parameters of the charging protocol are CC1, CC2, and CC3, which are also three-dimensional inputs of the black box optimization model; the method comprises the following steps: the charging rate of the 0-20% SOC interval is CC1, the charging rate of the 21-40% SOC interval is CC2, the charging rate of the 41-60% SOC interval is CC3, and the charging rate of the 61-80% SOC interval is CC4, wherein the size of the CC4 is determined by CC1, CC2 and CC3, and the formula is as follows:
Figure BDA0004230847900000101
when j=5, the charging protocol charges the battery state of charge SOC from 0% to 80% in 5 steps within 10 minutes, with parameters of the charging protocol being CC1 ", CC 2", CC3 ", CC 4", which is also a four-dimensional input of the black box optimization model; the method comprises the following steps: the charging rate of the 0-16% SOC interval is CC1 ", the charging rate of the 16-32% SOC interval is CC 2", the charging rate of the 32-48% SOC interval is CC3 ", the charging rate of the 48-64% SOC interval is CC 4", the charging rate of the 64-80% SOC interval is CC5 ", wherein the size of CC 5" is CC1 ", CC 2", CC3 ", and the formula is as follows:
Figure BDA0004230847900000102
the battery digital twin model is a battery electrochemical model that considers battery aging mechanisms including SEI film growth, lithium plating, particle cracking, and active material loss, integrated into a DFN model (Doyle-Fuller-Newman) to characterize the aging behavior of the battery.
SEI film growth, specifically including:
the growth of the SEI film is divided into two processes: firstly, polarization of a battery cathode, reduction decomposition of an organic solvent in electrolyte to generate a new compound, and secondly, precipitation of a new chemical substance on the surface of the anode to form a new SEI film; the growth of the SEI film is captured using a diffusion limited model, whose reaction rate is limited by the rate of transport of solvent through the SEI outer layer, assuming that the flux of solvent molecules follows the Phake law:
Figure BDA0004230847900000103
the boundary conditions are:
Figure BDA0004230847900000104
wherein c sol Is the concentration of the solvent, c sol,e Is the concentration of the solvent in the electrolyte, D sol (T) is the solvent diffusion coefficient, L is the position of the SEI film, L SEI Is SEI film thickness;
the flux density at the SEI film interface is:
Figure BDA0004230847900000105
rate of increase of SEI film thickness:
Figure BDA0004230847900000111
wherein L is SEI Is the SEI film thickness,
Figure BDA0004230847900000112
is the average partial molar volume of the SEI; the growth of the SEI film is affected by temperature and solvent diffusion coefficient, which follows the Arrhenius equation:
Figure BDA0004230847900000113
wherein T is ref ＝25℃,E sol Is the activation energy of solvent diffusion;
the growth of the SEI film will result in the following effects:
(1) the porosity of the negative electrode is reduced:
Figure BDA0004230847900000114
(2) SEI film overpotential increases due to increases in SEI film internal resistance:
Figure BDA0004230847900000115
wherein ε is n Is the porosity of the cathode, a n Is the specific surface area, a for spherical particles n ＝3ε n /R n ,R n Is the radius eta of the spherical particles of the negative electrode SEI Is the overpotential of SEI film, j tot Is the total current density in conservation of negative charge, σ SEI Is the conductivity of the SEI film.
The lithium plating specifically includes:
when lithium ions are not inserted into an electrode but lithium metal is formed on the surface of the electrode, lithium plating occurs, which is partially or completely recovered in a subsequent discharge reaction by stripping, the lithium plating chemically reacts with an electrolyte solution to form an SEI film, and the metal lithium separated by the SEI film cannot be stripped, which is called "dead lithium"; thus, a partially reversible lithium plating model was constructed, according to the butler-furat equation, with the lithium plating/stripping flux at the anode/electrolyte interface in the overpotential correction form being:
Figure BDA0004230847900000116
wherein k is Li Is the lithium plating/stripping constant, c Li Is the concentration of lithium plating, F is Faraday constant, c e Is Li in electrolyte + Concentration, transfer coefficient alpha a,Li And alpha c,Li Are all set to 0.5; η (eta) Li Is the lithium deposition potential LDP, defined as eta Li ＝φ s -φ e -η SEI Wherein phi is s And φ e is respectively relative to Li/Li + Electrode potential and electrolyte potential of (a); the electrode potential in the anode is close to 0, and the internal resistance of the SEI film is small at 25 ℃. Thus, LDP is primarily affected by electrolyte potential.
By coupling three models of lithium electroplating, lithium stripping and SEI growth, the electroplated lithium will decay over time into SEI film and dead lithium, c Li Is expressed as:
Figure BDA0004230847900000117
wherein a is - Is the ratio of the surface area to the volume of the cathode, c dl Is the concentration of dead lithium, defined as:
Figure BDA0004230847900000118
since dead lithium is formed by the reaction of lithium electroplating with an electrolyte solution, the reaction rate is affected by the solvent diffusion rate, as is SEI film formation. It is assumed that the dead lithium decay rate γ is inversely proportional to the thickness of the SEI film:
Figure BDA0004230847900000121
wherein gamma is 0 Is a fitting parameter, L SEI,0 Is the initial SEI thickness, L SEI,t Is the SEI thickness at time t.
The granule cracking specifically includes:
the electrode material expands and contracts greatly as lithium ions intercalate and deintercalate on the electrode. Alternating deformation of the electrode volume can lead to alternating stresses, resulting in fracture propagation on the active particles and the creation of new surfaces, which in turn affect side reactions such as SEI and lithium plating. Radial stress sigma using fatigue crack model based on spherical electrode particles r (r) tangential stress sigma t The expressions of (r) and displacement u are as follows:
Figure BDA0004230847900000122
Figure BDA0004230847900000123
Figure BDA0004230847900000124
wherein Ω is the partial molar volume, E is the Young's modulus, v is the Poisson's ratio, c avg (R) is a function of average lithium ion concentration and radius, R is particle radius,
Figure BDA0004230847900000125
is the concentration c of lithium ion and the reference concentration c under no stress ref Deviation of (2);
the fatigue crack propagation model follows Paris's law, assuming that all electrode particle surfaces have the same crack length l cr Crack width w cr And crack density ρ cr ：
Figure BDA0004230847900000126
Wherein t is 0 Time of single period, b cr Is a stress intensity correction factor, k cr And m cr Is a constant obtained from the experiment;
the growth model of the SEI film on the new crack is defined as follows:
Figure BDA0004230847900000127
wherein L is SEI,cr Is the average thickness of SEI film on new crack, L SEI,cr0 ＝L SEI,0 And/10000 is the thickness of the initial SEI film on the new crack.
Particle cracking also results in Loss of Active Material (LAM). The basic principle of the physical phenomenon is the same, so the above-described mechanism-based model can also be used to calculate the active substance loss. Loss of active substance epsilon a Simulation by decreasing the volume fraction of active material:
Figure BDA0004230847900000128
wherein beta, m 2 Sum sigma c Is the coefficient obtained from the experiment, the hydrostatic stress sigma h ＝(σ r +2σ t )/3，σ h The subscripts max and min of (c) represent the maximum and minimum values, respectively.
S3: transmitting an initial charging protocol and battery aging of a battery single cycle under the initial charging protocol as a data set to a Bayesian optimizer, wherein the initial charging protocol is used as input of a Bayesian optimization model, and the battery aging condition of the battery single cycle under the initial charging protocol is used as output; predicting battery aging corresponding to all protocols in a charging protocol space by utilizing Gaussian process regression GPR, and recommending a charging protocol for next round of extraction by utilizing an acquisition function; the Bayesian optimizer consists of a Gaussian process regression model GPR and an acquisition function; the optimization targets are that the battery has minimum aging, including but not limited to capacity loss, lithium inventory loss, coulombic efficiency, active material loss, etc.; the GPR model is used for outputting the logarithmic variance characteristics of all three-dimensional charging protocols; the acquisition function is used to decide which protocols to test in the next round;
when GPR is applied, the actual output y after taking noise into account is expressed as:
y i ＝f(x i )+ε i
wherein (x) i ,y i ) Represents the i-th data point, f represents the feature map, f (x i ) Representing the output of the gaussian model; epsilon i Represents observation noise, and
Figure BDA0004230847900000131
set x= { X of arbitrary finite input composition 1 ,x 2 ,…,x n } d*n D x n represents n samples, each sample having d features as input, { x 1 ,x 2 ,…,x n } d*n Are all subject to a joint gaussian probability distribution p (f (x) 1 ),f(x 2 ),…,f(x n ) The mean function and covariance function of f (x) are:
m(x)＝E[f(x)]
k(x,x′)＝E[(f(x)-m(x))(f(x′)-m(x′))]
since there is no a priori information of the distribution of f (x), m (x) is set to 0, and the distribution of y is written as:
Figure BDA0004230847900000132
wherein K is ff Is an n-by-n dimensional matrix, and [ K ] ff ] i,j ＝k(x i ,x j )；
For a new input
Figure BDA0004230847900000133
d x n represents that the new data set has m samples, each sample having d features input thereto; the joint distribution of this and the known observed target values is written as:
Figure BDA0004230847900000134
/>
wherein the method comprises the steps of
Figure BDA0004230847900000135
[K ff ] i,j ＝k(x i ,x j )；
Conditional distribution p (f) * |X,y,X * ) Obeys normal distribution:
Figure BDA0004230847900000136
wherein,,
Figure BDA0004230847900000137
represents the mean of posterior distribution, cov (f * ) The variance of the posterior distribution is expressed as follows:
Figure BDA0004230847900000141
Figure BDA0004230847900000142
kernel functions that can be used in the GPR model include the following:
the first kernel function is a gaussian kernel RBF, given by:
Figure BDA0004230847900000143
wherein II x-x' II 2 Representing the square of the Euclidean distance of the vectors x and x', and sigma represents the standard deviation;
the second kernel function is a Matern kernel, given by:
Figure BDA0004230847900000144
it has positive parameters v and l, where f (v) is a f function, K v Is a second type of bessel function, d (x, x') represents the euclidean distance.
The acquisition function is a confidence interval upper bound function UCB, an improved probability function PI or an expected delta function EI, wherein:
the UCB acquisition function is as follows:
UCB(x)＝μ(x)+βσ(x)
wherein μ (x) and σ (x) are the mean and standard deviation of the posterior distribution, respectively, β is a hyper-parameter to be optimized for balanced exploration and development, said exploration being to explore untested parameter spaces with high uncertainty, said development being to test promising areas according to completed experimental results; as the number of steps increases, the focus is changed from exploration to development, and beta is gradually reduced, so that the following steps are obtained:
UCB(x)＝μ(x)+β 0 ε k σ(x)
wherein beta is 0 ,ε k Are super parameters, k represents the optimized times, epsilon is (0, 1) in the value range, epsilon k Characterization reduces the weight of σ (x) to turn emphasis towards development;
the PI acquisition function is as follows:
the PI utilizes posterior model to estimate that the function value is larger than the maximum value mu in the actual observed value at present + To find the next round of sampling points, PI (x) represents the probability, and the formula is as follows:
Figure BDA0004230847900000145
wherein phi represents a normal cumulative distribution function, mu (x) and sigma (x) respectively represent a Gaussian average value and a standard deviation of posterior prediction, and xi is more than or equal to 0 and is an adjustable parameter, wherein the aim is to find the sum mu + The point at which the probability of a comparative boost ζ is greatest;
the EI acquisition function is as follows:
Figure BDA0004230847900000146
Figure BDA0004230847900000151
the weight Φ (Z) is a normal cumulative distribution function, and ζ represents the sum μ + The degree of improvement in the phase ratio, phi (Z), represents the normal probability distribution function, and the objective of EI is to find the point (μ (x) - μ) with the greatest improvement expectations + ζ) Φ (Z) and σ (x) Φ (Z) are used for development and exploration, respectively.
S4: based on the battery state in the step S2, the digital twin model of the battery carries out simulation prediction on the aging of the battery under the charging protocol extracted in the next round, so as to obtain the aging of the battery under the charging protocol extracted in the next round;
s5: and adding the new charging protocol and the corresponding battery aging into the existing data set, transmitting the new charging protocol to the Bayesian optimizer again to recommend the next round of extracted quick charging protocol, and repeating the steps S4-S5 until the final recommended charging protocol is obtained, and charging the vehicle battery by the charging protocol.
Taking the single cycle lithium inventory loss as an example of an optimization objective, as shown in fig. 2, the SPMe model as a digital twin model of the battery, and the DFN model as an actual vehicle, the cumulative lithium inventory loss is shown in fig. 2. When 100 loops are continuously optimized, an optimal charging protocol is obtained for each loop, 100 loops correspond to 100 charging protocols, 100 loops are continuously simulated by an SPMe model and a DFN model, and the results are respectively shown as a simulation result-SPMe curve and an experimental result-DFN curve. To verify the optimized performance, 100 cycles were simulated in a DFN model with constant current charging, as shown by the "constant current experimental results-DFN". By comparison, the method provided by the invention is used for optimizing, so that the loss of lithium inventory can be effectively reduced. In this experiment, a charging protocol from 0 to 80% SOC for 30 minutes was used, and the "constant current experiment result-DFN" corresponds to a charging rate of 2.4C.
The bayesian optimization can adopt a parallel optimization method, the idea is that a plurality of charging protocols are recommended for each time by an acquisition function, namely, suboptimal protocols are recommended in addition to optimal protocols, then the recommended protocols are simulated in parallel by a battery digital twin model, the recommended protocols and corresponding battery aging are added into a dataset to obtain a new dataset, gaussian process regression is performed based on the new dataset, the charging protocols are recommended by the acquisition function, and the processes are repeated until the optimal charging protocols are obtained. As shown in (a) - (d) in fig. 3, the optimization results of the 10 th, 30 th, 50 th and 80 th charging of the vehicle are selected and displayed, the initial 3+parallel 3 represents that the initial data set contains three samples, and the acquisition function recommends three charging protocols each time during parallel optimization. It can be seen that the greater the number of protocols for initializing the data set and for parallel optimization, the better the result of the optimization and the faster the convergence rate of the optimization.
Finally, it is noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the present invention, which is intended to be covered by the claims of the present invention.

Claims (9)

1. A fast charge strategy design method based on a battery digital twin model and machine learning is characterized in that: the method comprises the following steps:
s1: when an electric automobile is connected into a charging pile for charging, battery state data of the automobile are detected, wherein the battery state data comprise battery temperature, state of charge (SOC), state of health (SOH), ampere-hour throughput, current lithium inventory loss and Electrochemical Impedance Spectroscopy (EIS) detection;
s2: inputting the battery state data into a Bayesian optimizer based on a battery digital twin model, and predicting the aging condition of the battery in the current charging under an initial protocol according to the current battery state through the battery digital twin model; the initial protocol is any number of protocols, and corresponding data are used for initializing a Bayesian optimization model;
s3: transmitting an initial charging protocol and battery aging of a battery single cycle under the initial charging protocol as a data set to a Bayesian optimizer, wherein the initial charging protocol is used as an input of a Bayesian optimization model, and the battery aging of the battery single cycle under the initial charging protocol is used as an output; predicting battery aging corresponding to all protocols in a charging protocol space by utilizing Gaussian process regression GPR, and recommending a charging protocol for next round of extraction by utilizing an acquisition function;
s4: based on the battery state in the step S2, the digital twin model of the battery carries out simulation prediction on the aging of the battery under the charging protocol extracted in the next round, and the aging condition of the battery under the charging protocol extracted in the next round is obtained;
s5: and adding the new charging protocol and the corresponding battery aging into the existing data set, transmitting the new charging protocol to the Bayesian optimizer again to recommend the next round of extracted quick charging protocol, and repeating the steps S4-S5 until the final recommended charging protocol is obtained, and charging the vehicle battery by the charging protocol.
2. The battery digital twin model and machine learning based fast charge strategy design method of claim 1, wherein the method comprises the following steps: the initial protocol and the protocol recommended by the Bayesian optimizer are both protocols in a charging protocol space; the charging protocol in the charging protocol space aims to charge the battery state of charge (SOC) from 0% to 80% through constant current charging of a plurality of stages within 10 minutes, and in the process, the battery is charged by stages by using j kinds of currents with different magnitudes;
the charging protocol is a multi-stage constant-current constant-voltage charging MSCC, which consists of a plurality of constant-current charging stages and a constant-voltage charging stage which follows the constant-current charging stages;
when j=3, the charging protocol charges the battery state of charge SOC from 0% to 80% in 3 steps within 10 minutes, and parameters of the charging protocol have CC1', CC2', which are also two-dimensional inputs of the black box optimization model; the method comprises the following steps: the charging rate of the 0-26.67% SOC interval is CC1', the charging rate of the 26.67% -53.34% SOC interval is CC2', the charging rate of the 53.34% -80% SOC interval is CC3', the size of the CC3' is determined by CC1', CC2', and the charging rate is expressed as:
Figure FDA0004230847880000011
when j=4, the charging protocol charges the battery state of charge SOC from 0% to 80% in 10 minutes in 4 steps, and parameters of the charging protocol are CC1, CC2, and CC3, which are also three-dimensional inputs of the black box optimization model; the method comprises the following steps: the charging rate of the 0-20% SOC interval is CC1, the charging rate of the 21-40% SOC interval is CC2, the charging rate of the 41-60% SOC interval is CC3, and the charging rate of the 61-80% SOC interval is CC4, wherein the size of the CC4 is determined by CC1, CC2 and CC3, and the formula is as follows:
Figure FDA0004230847880000021
when j=5, the charging protocol charges the battery state of charge SOC from 0% to 80% in 5 steps within 10 minutes, with parameters of the charging protocol being CC1 ", CC 2", CC3 ", CC 4", which is also a four-dimensional input of the black box optimization model; the method comprises the following steps: the charging rate of the 0-16% SOC interval is CC1 ", the charging rate of the 16-32% SOC interval is CC 2", the charging rate of the 32-48% SOC interval is CC3 ", the charging rate of the 48-64% SOC interval is CC 4", the charging rate of the 64-80% SOC interval is CC5 ", wherein the size of CC 5" is CC1 ", CC 2", CC3 ", and the formula is as follows:
Figure FDA0004230847880000022
3. the battery digital twin model and machine learning based fast charge strategy design method of claim 1, wherein the method comprises the following steps: the battery digital twin model is a battery electrochemical model that considers battery aging mechanisms including SEI film growth, lithium plating, particle cracking, and active material loss, integrated into a DFN model (Doyle-Fuller-Newman) to characterize the aging behavior of the battery.
4. The battery digital twin model and machine learning based fast charge strategy design method according to claim 3, wherein: the SEI film growth specifically comprises:
the growth of the SEI film is divided into two processes: firstly, polarization of a battery cathode, reduction decomposition of an organic solvent in electrolyte to generate a new compound, and secondly, precipitation of a new chemical substance on the surface of the anode to form a new SEI film; the growth of the SEI film is captured using a diffusion limited model, whose reaction rate is limited by the rate of transport of solvent through the SEI outer layer, assuming that the flux of solvent molecules follows the Phake law:
Figure FDA0004230847880000023
the boundary conditions are:
Figure FDA0004230847880000024
wherein c sol Is the concentration of the solvent, c sol,e Is the concentration of the solvent in the electrolyte, D sol (T) is the solvent diffusion coefficient, L is the position of the SEI film, L SEI Is SEI film thickness;
the flux density at the SEI film interface is:
Figure FDA0004230847880000025
rate of increase of SEI film thickness:
Figure FDA0004230847880000031
wherein L is SEI Is SThe thickness of the EI film is set,
Figure FDA0004230847880000032
is the average partial molar volume of the SEI; the growth of the SEI film is affected by temperature and solvent diffusion coefficient, which follows the Arrhenius equation:
Figure FDA0004230847880000033
wherein T is ref ＝25℃,E sol Is the activation energy of solvent diffusion;
the growth of the SEI film will result in the following effects:
(1) the porosity of the negative electrode is reduced:
Figure FDA0004230847880000034
(2) SEI film overpotential increases due to increases in SEI film internal resistance:
Figure FDA0004230847880000035
wherein ε is n Is the porosity of the cathode, a n Is the specific surface area, a for spherical particles n ＝3ε n /R n ,R n Is the radius eta of the spherical particles of the negative electrode SEI Is the overpotential of SEI film, j tot Is the total current density in conservation of negative charge, σ SEI Is the conductivity of the SEI film.
5. The battery digital twin model and machine learning based fast charge strategy design method according to claim 3, wherein: the lithium plating specifically includes:
when lithium ions are not intercalated into an electrode but lithium metal is formed on the surface of the electrode, lithium plating occurs, which is partially or completely recovered in a subsequent discharge reaction by lithium stripping; lithium electroplating also chemically reacts with the electrolyte solution to form an SEI film, and the metal lithium separated by the SEI film cannot be peeled off, and the part of lithium is called dead lithium; thus, a partially reversible lithium plating model was constructed, according to the butler-furat equation, with the lithium plating/stripping flux at the anode/electrolyte interface in the overpotential correction form being:
Figure FDA0004230847880000036
wherein k is Li Is the lithium plating/stripping constant, c Li Is the concentration of lithium plating, F is Faraday constant, c e Is Li in electrolyte + Concentration, transfer coefficient alpha a,Li And alpha c,Li Are all set to 0.5; η (eta) Li Is the lithium deposition potential LDP, defined as eta Li ＝φ s -φ e -η SEI Wherein phi is s And phi e Respectively relative to Li/Li + Electrode potential and electrolyte potential of (a);
by coupling three models of lithium electroplating, lithium stripping and SEI growth, the electroplated lithium will decay over time into SEI film and dead lithium, c Li Is expressed as:
Figure FDA0004230847880000037
wherein a is - Is the ratio of the surface area to the volume of the cathode, c dl Is the concentration of dead lithium, defined as:
Figure FDA0004230847880000038
it is assumed that the dead lithium decay rate γ is inversely proportional to the thickness of the SEI film:
Figure FDA0004230847880000041
wherein gamma is 0 Is a fitting parameter, L SEI,0 Is the initial SEI thickness, L SEI,t Is the SEI thickness at time t.
6. The battery digital twin model and machine learning based fast charge strategy design method according to claim 3, wherein: the particle cracking specifically includes:
radial stress sigma using fatigue crack model based on spherical electrode particles r (r) tangential stress sigma t The expressions of (r) and displacement u are as follows:
Figure FDA0004230847880000042
Figure FDA0004230847880000043
Figure FDA0004230847880000044
where Ω is the partial molar volume, E is the Young's modulus, v is the Poisson's ratio, c avg (R) is a function of average lithium ion concentration and radius, R is particle radius,
Figure FDA0004230847880000045
is the concentration c of lithium ion and the reference concentration c under no stress ref Deviation of (2);
the fatigue crack propagation model follows Paris's law, assuming that all electrode particle surfaces have the same crack length l cr Crack width w cr And crack density ρ cr ：
Figure FDA0004230847880000046
Wherein t is 0 Time of single period, b cr Is a stress intensity correction factor, k cr And m cr Is a constant obtained from the experiment;
the growth model of the SEI film on the new crack is defined as follows:
Figure FDA0004230847880000047
wherein L is SEI,cr Is the average thickness of SEI film on new crack, L SEI,cr0 ＝L SEI,0 And/10000 is the thickness of the initial SEI film on the new crack.
7. The battery digital twin model and machine learning based fast charge strategy design method according to claim 3, wherein: the active material loss specifically includes:
loss of active substance epsilon a Simulation by decreasing the volume fraction of active material:
Figure FDA0004230847880000048
wherein beta, m 2 Sum sigma c Is the coefficient obtained from the experiment, the hydrostatic stress sigma h ＝(σ r +2σ t )/3，σ h The subscripts max and min of (c) represent the maximum and minimum values, respectively.
8. The battery digital twin model and machine learning based fast charge strategy design method of claim 1, wherein the method comprises the following steps: the Bayesian optimizer consists of a Gaussian process regression model GPR and an acquisition function, and the optimization target is that the aging of the battery is minimum, wherein the aging of the battery comprises capacity loss, lithium inventory loss, coulomb efficiency and active substance loss;
the GPR model is used for outputting logarithmic variance characteristics of all three-dimensional charging protocols; the acquisition function is used to decide which protocols to test in the next round;
when GPR is applied, the actual output y after taking noise into account is expressed as:
y i ＝f(x i )+ε i
wherein (x) i ,y i ) Represents the i-th data point, f represents the feature map, f (x i ) Representing the output of the gaussian model; epsilon i Represents observation noise, and
Figure FDA0004230847880000051
set x= { X of arbitrary finite input composition 1 ,x 2 ,...,x n } d*n D x n represents n samples, each sample having d features as input, { x 1 ,x 2 ,...,x n } d*n Obeys a joint gaussian probability distribution p (f (x) 1 ),f(x 2 ),...,f(x n ) The mean function and covariance function of f (x) are:
m(x)＝E[f(x)]
k(x，x′)＝E[(f(x)-m(x))(f(x′)-m(x′))]
since there is no a priori information of the distribution of f (x), m (x) is set to 0, and the distribution of y is written as:
Figure FDA0004230847880000052
wherein K is ff Is an n-by-n dimensional matrix, and [ K ] ff ] i,j ＝k(x i ,x j )；
For a new input
Figure FDA0004230847880000053
d x n represents that the new data set has m samples, each sample having d features input thereto; the joint distribution of this and the known observed target values is written as:
Figure FDA0004230847880000054
wherein the method comprises the steps of
Figure FDA0004230847880000055
[K ff ] i，j ＝k(x i ，x j )；
Conditional distribution p (f) * |X,y,X * ) Obeys normal distribution:
Figure FDA0004230847880000056
wherein,,
Figure FDA0004230847880000057
represents the mean of posterior distribution, cov (f * ) The variance of the posterior distribution is expressed as follows:
Figure FDA0004230847880000058
Figure FDA0004230847880000059
kernel functions that can be used in the GPR model include the following:
the first kernel function is a gaussian kernel RBF, given by:
Figure FDA0004230847880000061
wherein II x-x' II 2 Representing the square of the Euclidean distance of the vectors x and x', and sigma represents the standard deviation;
the second kernel function is a Matern kernel, given by:
Figure FDA0004230847880000062
having positive parameters v and l, wherein v is a f functionNumber, K ν Is a second type of bessel function, d (x, x') represents the euclidean distance.
9. The battery digital twin model and machine learning based fast charge strategy design method of claim 8, wherein the method comprises the following steps: the acquisition function is a confidence interval upper bound function UCB, an improved probability function PI or an expected increment function EI, wherein:
the UCB acquisition function is as follows:
UCB(x)＝μ(x)+βσ(x)
wherein μ (x) and σ (x) are the mean and standard deviation of the posterior distribution, respectively, β is a hyper-parameter to be optimized for balanced exploration and development, said exploration being to explore untested parameter spaces with high uncertainty, said development being to test promising areas according to completed experimental results; as the number of steps increases, the focus is changed from exploration to development, and beta is gradually reduced, so that the following steps are obtained:
UCB(x)＝μ(x)+β 0 ε k σ(x)
wherein beta is 0 ,ε k Are super parameters, k represents the optimized times, epsilon is (0, 1) in the value range, epsilon k Characterization reduces the weight of σ (x) to turn emphasis towards development;
the PI acquisition function is as follows:
the PI utilizes posterior model to estimate that the function value is larger than the maximum value mu in the actual observed value at present + To find the next round of sampling points, PI (x) represents the probability, and the formula is as follows:
Figure FDA0004230847880000063
wherein phi represents a normal cumulative distribution function, mu (x) and sigma (x) respectively represent a Gaussian average value and a standard deviation of posterior prediction, and xi is more than or equal to 0 and is an adjustable parameter, wherein the aim is to find the sum mu + The point at which the probability of a comparative boost ζ is greatest;
the EI acquisition function is as follows:
Figure FDA0004230847880000064
Figure FDA0004230847880000065
the weight Φ (Z) is a normal cumulative distribution function, and ζ represents the sum μ + The degree of improvement in the phase ratio, σ (Z), represents a normal probability distribution function, and the objective of EI is to find the point (μ (x) - μ) with the greatest improvement expectations + ζ) Φ (Z) and σ (x) Φ (Z) are used for development and exploration, respectively.
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CN116577680A (en) * 2023-07-13 2023-08-11 无锡大派电子有限公司 Lithium battery lithium precipitation detection method and device
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