CN117110923A - Lithium battery remaining life prediction method for electric forklift - Google Patents
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- WHXSMMKQMYFTQS-UHFFFAOYSA-N Lithium Chemical compound [Li] WHXSMMKQMYFTQS-UHFFFAOYSA-N 0.000 title claims abstract description 175
- 229910052744 lithium Inorganic materials 0.000 title claims abstract description 175
- 238000000034 method Methods 0.000 title claims abstract description 95
- 238000009826 distribution Methods 0.000 claims abstract description 76
- 238000006731 degradation reaction Methods 0.000 claims abstract description 67
- 230000036541 health Effects 0.000 claims abstract description 62
- 230000015556 catabolic process Effects 0.000 claims abstract description 51
- 230000008929 regeneration Effects 0.000 claims abstract description 45
- 238000011069 regeneration method Methods 0.000 claims abstract description 45
- 230000008569 process Effects 0.000 claims abstract description 36
- 230000015654 memory Effects 0.000 claims abstract description 34
- 238000013528 artificial neural network Methods 0.000 claims abstract description 24
- 230000007774 longterm Effects 0.000 claims abstract description 17
- 238000000354 decomposition reaction Methods 0.000 claims abstract description 14
- 230000006870 function Effects 0.000 claims description 38
- 230000014509 gene expression Effects 0.000 claims description 16
- 230000001537 neural effect Effects 0.000 claims description 15
- 230000003862 health status Effects 0.000 claims description 14
- 238000012360 testing method Methods 0.000 claims description 12
- 238000004422 calculation algorithm Methods 0.000 claims description 11
- 230000032683 aging Effects 0.000 claims description 10
- 230000010287 polarization Effects 0.000 claims description 10
- 238000012549 training Methods 0.000 claims description 8
- 238000004088 simulation Methods 0.000 claims description 7
- 239000007784 solid electrolyte Substances 0.000 claims description 7
- 238000000342 Monte Carlo simulation Methods 0.000 claims description 6
- 230000007787 long-term memory Effects 0.000 claims description 6
- 238000005070 sampling Methods 0.000 claims description 6
- 230000006403 short-term memory Effects 0.000 claims description 6
- 238000007476 Maximum Likelihood Methods 0.000 claims description 5
- 238000007600 charging Methods 0.000 claims description 5
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- 238000007599 discharging Methods 0.000 claims description 3
- 239000011159 matrix material Substances 0.000 claims description 3
- 210000005036 nerve Anatomy 0.000 claims description 3
- 238000012795 verification Methods 0.000 claims description 3
- OKTJSMMVPCPJKN-UHFFFAOYSA-N Carbon Chemical compound [C] OKTJSMMVPCPJKN-UHFFFAOYSA-N 0.000 claims description 2
- KMTRUDSVKNLOMY-UHFFFAOYSA-N Ethylene carbonate Chemical compound O=C1OCCO1 KMTRUDSVKNLOMY-UHFFFAOYSA-N 0.000 claims description 2
- 229910012851 LiCoO 2 Inorganic materials 0.000 claims description 2
- 229910013870 LiPF 6 Inorganic materials 0.000 claims description 2
- HBBGRARXTFLTSG-UHFFFAOYSA-N Lithium ion Chemical compound [Li+] HBBGRARXTFLTSG-UHFFFAOYSA-N 0.000 claims description 2
- 239000002033 PVDF binder Substances 0.000 claims description 2
- 238000004458 analytical method Methods 0.000 claims description 2
- IEJIGPNLZYLLBP-UHFFFAOYSA-N dimethyl carbonate Chemical compound COC(=O)OC IEJIGPNLZYLLBP-UHFFFAOYSA-N 0.000 claims description 2
- 239000010439 graphite Substances 0.000 claims description 2
- 229910002804 graphite Inorganic materials 0.000 claims description 2
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- 230000037427 ion transport Effects 0.000 claims description 2
- 238000012804 iterative process Methods 0.000 claims description 2
- 239000007791 liquid phase Substances 0.000 claims description 2
- 229910000625 lithium cobalt oxide Inorganic materials 0.000 claims description 2
- 229910001416 lithium ion Inorganic materials 0.000 claims description 2
- 229910003002 lithium salt Inorganic materials 0.000 claims description 2
- 159000000002 lithium salts Chemical class 0.000 claims description 2
- BFZPBUKRYWOWDV-UHFFFAOYSA-N lithium;oxido(oxo)cobalt Chemical compound [Li+].[O-][Co]=O BFZPBUKRYWOWDV-UHFFFAOYSA-N 0.000 claims description 2
- 238000002156 mixing Methods 0.000 claims description 2
- 230000005501 phase interface Effects 0.000 claims description 2
- 229920002981 polyvinylidene fluoride Polymers 0.000 claims description 2
- 238000012216 screening Methods 0.000 claims description 2
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- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
- G01R31/392—Determining battery ageing or deterioration, e.g. state of health
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Abstract
The invention discloses a method for predicting the residual life of a lithium battery for an electric forklift, which divides a lithium battery health state degradation curve into a normal degradation trend part, a capacity regeneration part and a random fluctuation part. And (3) carrying out empirical mode decomposition on the capacity degradation curve of the lithium battery to obtain a known long-term degradation trend part of the lithium battery. The long-short-term memory neural network is utilized to predict future normal degradation on the basis of known long-term degradation trend data of the lithium battery, the state of health, the initial state of charge and the rest time of the lithium battery are used as input values of Gaussian process regression, the capacity regeneration part of the lithium battery is predicted to set a capacity degradation rate failure threshold value of the lithium battery, the Stable distribution is adopted to obtain a random fluctuation part, the influence of the regeneration capacity and the random fluctuation on the degradation process of the lithium battery is accurately considered, and the accuracy of the residual life prediction of the lithium battery is improved.
Description
Technical Field
The invention relates to the field of electric forklifts, in particular to a method for predicting the residual life of a lithium battery for an electric forklift.
Background
As the users of class 4 and class 5 truck powered by diesel or propane continue to convert to class 1 electric trucks, more than half of today's trucks are battery powered. The strong market competition enables manufacturers to provide more environment-friendly vehicle types for the masses by adopting new energy technology, and the types which can be selected by users are increased explosively. Due to the improvement of manufacturing technology, it is widely recognized that excellent battery technology is a necessity for improving competitiveness. The market demand of lithium battery forklifts is rapidly exceeding that of lead-acid battery forklifts, and the use of lithium batteries by forklifts is a technical trend of industry development.
Even so, the development of lithium battery forklifts still has a series of bottlenecks that need to be broken through. However, in a long-term charge and discharge state, the available capacity of the lithium battery is reduced, the performance is reduced, and even potential safety hazards are generated. Therefore, the prediction of the remaining life of a lithium battery is of great importance.
In recent years, lithium battery remaining life prediction has been largely classified into a model-based method and a data driving method. Model-based methods are typically a combination of mathematical functions and filtering techniques. Various studies in the literature report that particle filters, kalman filtering, wiener process regression, box-Cox transformation, and other model-based methods predict the remaining service life of lithium batteries and obtain relatively accurate prediction results. However, in the aging process of the lithium battery, the aging mechanism is complex, and an accurate aging model is difficult to establish.
The existing patent basically does not describe or deal with the capacity regeneration of a lithium battery, which is a phenomenon that the effective capacity of the lithium battery suddenly increases after full charge and discharge and long-time storage. Capacity regeneration will have a significant impact on the available capacity, and it is a current difficulty to consider and accurately predict the remaining useful life of the battery.
The existing patent 'a lithium battery life prediction method (CN 202110778444.8) based on LSTM', wherein the patent predicts the life of a lithium battery by adopting LSTM, and the method adopts two LSTM layers, two Dropout layers and a top prediction output layer as a neural network structure to construct a lithium battery residual life prediction model; the patent 'lithium battery residual life prediction method (CN 202110206262.3) based on the MFF multi-core GPR algorithm' utilizes a combined kernel function to calculate the residual predicted life of the lithium battery according to the time reaching the failure threshold value. In the field of lithium battery life prediction, there are several patents or documents for prediction, and then, the patents only take some data of the lithium battery as input of a data driving method such as a neural network, and do not study the mechanism of internal action of the lithium battery, so that the prediction accuracy is to be improved.
Disclosure of Invention
The invention mainly solves the technical problem of providing the method for predicting the residual life of the lithium battery for the electric forklift, which can predict the residual life of the lithium battery by utilizing priori data and limited process parameters in the operation process, pre-warn the faults of the lithium battery and improve the reliability of an energy storage system.
In order to solve the technical problems, the technical scheme provided by the invention is as follows:
the method for predicting the residual life of the lithium battery for the electric forklift comprises the following steps of:
step one: dividing the useful capacity in the degradation process of the lithium battery into three parts of normal degradation trend capacity, regeneration capacity and random fluctuation capacity;
step two: performing empirical mode decomposition on a lithium battery health state degradation curve and predicting a long-term degradation trend by using a long-term and short-term memory neural network;
step three: constructing an internal equivalent circuit model of the lithium battery, and establishing a relation between a circuit state and terminal voltage;
step four: predicting a regeneration part of lithium battery capacity by adopting lithium battery health State (SOH), initial state of charge (SOC) and rest time as input quantity of GPR;
step five: selecting Stable distribution parameters, and generating random numbers obeying Stable distribution as random fluctuation of the lithium battery;
step six: the superiority of the method of the invention is verified by adopting a Monte Carlo simulation method.
Step one, due to different useful capacities of lithium batteries of different models, standardized treatment is needed to obtain a general lithium battery health state with a cycle period health state, useful capacity and initial capacity. The method for obtaining the normal degradation trend capacity, the regeneration capacity and the random fluctuation capacity of the lithium battery in the degradation process by adopting the standardized treatment comprises the following steps of taking the battery health state as a ratio not exceeding 100%, and defining the battery health state SOH as follows:
in SOH i Indicating the health status of the ith cycle of the lithium battery, cap i Useful capacity, cap, representing the ith cycle period ini Representing the initial capacity. And establishing the health state of the lithium battery in the degradation process by using the obtained health state of the lithium battery.
In the second step, empirical mode decomposition is mainly performed by performing iterative screening on the signals, and non-stationary signal data is decomposed into a residual sequence (RES) and a series of Intrinsic Mode Functions (IMFs). The present invention provides that the effective IMF sequence should satisfy two conditions: 1. the number of extreme points and zero crossing points should be equal or differ by at most one; 2. the mean of the upper and lower envelopes of the local maxima and local minima is zero. The method for predicting the health state of the normal degradation trend by adopting empirical mode decomposition comprises the following steps: 1. finding out the local maximum value and local minimum value points of the original signal x (t); 2. and respectively interpolating the local maximum value points and the local minimum value points by using a cubic spline function to obtain an upper envelope u (t) and a lower envelope l (t) of x (t). Averaging the upper envelope curve and the lower envelope curve to obtain3. Letting h (t) -x (t) -m (t), judging whether h (t) meets the IMF condition, if not, continuing the iterative process until h (t) meets the IMF condition; 4. if h (t) meets IMF conditions, an effective subsequence is obtained, which may be denoted as IMF i (t) mixing imf i Filtering from the original signal x (t) to obtain a new original signal x i (t) repeating the above steps to obtain all imf i (t), (i-1, 2,3 …, n) and a residual error r 0 (t) the final lithium battery degradation curve can be expressed as:
the long-short time neural memory network is adopted to predict the future normal degradation trend on the basis of the known long-term degradation trend data of the lithium battery. The long-short-term memory neural network unit consists of a long-term state c <t> And a short term state a <t> Composition is prepared. Furthermore, it relies on three control gates: forgetting door gamma f Input gate Γ u And an output gate Γ o . The hidden layer node calculates an activation value that depends on the input of the current layer and the node at the previous time. The expression is as follows:
Γ u ＝σ(W u [a <t-1 >,x <t> ]+b u ) (3b)
Γ f ＝σ(W f [a <t-1> ,x <t> ]+b f ) (3c)
Γ o ＝σ(W o [a <t-1> ,x <t> ]+b o ) (3d)
a <t> ＝Γ o *tanh(c <t> ) (3f)
wherein W is a weight matrix, b is a bias, σ () is a sigmoid function, x <t> For input at time t, a <t> And a <t-1> Output of short-time memory nerve unit with time duration of t and t-1 respectively, c <t> And c <t-1> The cell states at times t and t-1 respectively,a unit that is the current input state.
The method for predicting the regenerated health state of the lithium battery comprises the following steps: 1. establishing an equivalent circuit model by using a state of charge and terminal voltage fitting equation and establishing an equivalent circuit model of the lithium ion battery; 2. calculating an initial state of charge through an initial terminal voltage, and judging whether the rest time exceeds capacity regeneration time or not according to the acquired rest time, the initial state of charge and the current health state; 3. if the rest time exceeds the capacity regeneration time threshold, carrying out Gaussian process regression, and if not, returning to the step of calculating the initial state of charge; 4. and predicting the regenerated health state of the lithium battery through Gaussian process regression.
In the degradation process of the lithium battery, the electrode material and the electrolyte react on the solid-liquid phase interface to form a layer of solid electrolyte interface film covering the surface of the electrode material, so that the internal resistance of the lithium battery can change along with the change of the solid electrolyte interface film. And the lithium battery can generate polarization phenomenon in the charge and discharge process, so that the actual electrode potential deviates from the balance electrode potential. In order to show the influence of the solid electrolyte interface film and the polarization phenomenon in the charge and discharge process of the lithium battery, the invention is based on a second-order RC circuit equivalent model.
The circuit equivalent equation can be expressed as:
wherein U is oc Is an Open Circuit Voltage (OCV), is influenced by the state of charge (SOC) of the current lithium battery, I L R is the charge-discharge current 0 Is resistance, determined by SEI film, R 1 ，C 1 Resistance and capacitance, respectively, affected by electrochemical polarization, R 2 ，C 2 The resistance and capacitance, respectively, are affected by concentration polarization.
State of charge-open circuit voltage fitting equation:
the SOC is the current battery state of charge, and a, b, c, d, e and f are electric quantity parameters.
Because some position parameters exist in the equation, the invention adopts a least square method to carry out parameter estimation on the equivalent circuit equation and the circuit state-terminal voltage fitting equation. And calculating according to the open-circuit voltage of the lithium battery to obtain an initial electric quantity state. And then, predicting the regenerated health state of the lithium battery by adopting a Gaussian process according to the initial electric quantity state, the rest time and the current health state.
And step four, the specific flow of predicting the capacity regeneration part of the lithium battery by adopting Gaussian regression is as follows:
1) Establishing a Gaussian process expression according to a lithium battery simulation equivalent circuit electric quantity state-open circuit voltage fitting equation:
f(x)～GP(m(x),κ(x,x')) (5a)
where m (x) represents the mean value, κ (x, x ') represents the covariance function, and E [ (m (x) -f (x')) (m (x) -f (x)) ] represents the desired value. In practical applications, m (x) is generally set to 0. Kappa (x, x') is also called a kernel function, explaining the degree of correlation of similarity between two samples.
2) The Gaussian process predictions of the square index kernel, the 5/2Matern kernel and the secondary rational kernel are compared, and the optimal kernel function is selected and is subjected to predictive analysis by outputting the prior probability density of Y:
f(x)～N(m(x),κ(,x')) (5d)
ε～N(0,σ 2 I) (5e)
Y＝(f(x)+ε)～N(m(x),κ(x,x')+σ 2 I) (5f)
wherein sigma f L is a superparameter, k f Representative of the invention adoptsIs a square-index kernel, N () represents a normal distribution, epsilon represents a noise component, sigma represents a noise variance, Y represents an a priori probability density distribution of the output,to be in training set x and test set x * And under the condition of independent same distribution, predicting the joint distribution obeyed by the output capacity regeneration. The present invention defines the capacity regeneration time threshold as 18H.
3) Super parameter sigma using maximum likelihood estimation method f And l, optimizing.
Wherein L (sigma) f L) is a maximum likelihood function, P (f (x) * )|Y,X,X * ) For f (x) in scheme 2) * ) Is determined by the a-priori estimates of (c),for the mean expression, cov (f (x * ) Is a covariance expression.
Step five, the advantage of predicting the capacity regeneration of the lithium battery by using the Gaussian process regression is that: firstly, the Gaussian process is a random process consisting of infinite high-dimensional random variables in a continuous domain, and has good adaptability to processing complex problems such as small samples, linearity, high dimensionality and the like; secondly, by a simple mode of maximizing edge likelihood, gaussian process regression can give a better regularization effect under the condition of no need of cross verification; thirdly, the residual service life of the lithium battery belongs to small sample data, and the lithium battery has a stepwise attenuation characteristic, and the Gaussian process has better performance.
The specific flow for predicting the random fluctuation health status distribution by adopting Stable distribution is as follows:
1) Considering that the health state of the random fluctuation of the lithium battery is near 0 and is unimodal, the invention adopts Stable distribution to approximate the actual health state distribution of the random fluctuation, and the characteristic function is as follows;
where j represents a complex unit and sign () represents a sign function. The distribution needs to be described by 4 parameters: characteristic parameter alpha epsilon (0, 2)]It can control the thickness of the tail of the probability density function; skew parameter beta epsilon [ -1,1]It determines the degree of symmetry of the distribution, β=0 then the distribution is symmetrical; position parametersIt describes the central location of the Stable distribution; scale parameter->It describes how far the distribution sample deviates from its mean. 2) Setting upper and lower limits of a prediction result based on the low probability time standard;
the invention adopts the roulette algorithm to predict the health status of random fluctuation, but because the Stable distribution is infinitely separable, the upper limit and the lower limit of the predicted result are set based on the low probability time standard.
Upper and lower limit expressions of Stable distribution:
wherein X-S α (γ,β,δ)，Z α For the upper limit of sampling, Z β Is the lower limit of the sampling.
3) And defining the degradation rate failure threshold value of the lithium battery as 76%, calculating to obtain the random fluctuation health state of the training set according to the formula, and then obtaining distribution parameters gamma, beta and delta to obtain the fitted Stable distribution.
ΔSOH～S α (γ,β,δ) (9)
Wherein delta SOH is a randomly fluctuating health state which is subject to Stable distribution S α (gamma, beta, delta), alpha is a characteristic parameter, beta is a deflection parameter, delta is a position parameter, and gamma is a scale parameter.
Step six, selecting the data in the test lithium battery data sets CS2_33, CS2_34, CS2_35, CS2_36 and CS 2_38. The data set was derived from a cell with a nominal capacity of 1.1Ah, the cathode consisting of lithium cobalt oxide LiCoO 2 The anode consists of lamellar graphite and polyvinylidene fluoride. Electrolyte consisting of equal amounts of ethylene carbonate and dimethyl carbonate, in LiPF 6 As lithium salts, a medium is provided for ion transport between the two electrodes. In this dataset, five groups of lithium batteries were operated in three different modes of operation (charge, discharge, impedance measurement) at room temperature, obtaining the results of the aging test. In the process, the lithium battery is charged in a constant current mode of 0.55A until the voltage reaches 4.2V, and then is charged in a constant voltage mode, and the voltage is maintained at 4.2V until the charging current is reduced to below 50 mA. Thereafter, the cs2_33, cs2_34 cells were discharged in the 0.55A constant current mode, and the cs2_35, cs2_36, and cs2_38 cells were discharged in the 1.1A constant current mode until the cell voltage was reduced to 2.7V. When the lithium battery reaches the cut-off life, the test is ended.
The invention has the advantages that:
1) The lithium battery health state degradation curve is divided into a normal degradation trend part, a capacity regeneration part and a random fluctuation part.
2) And (3) carrying out empirical mode decomposition on the capacity degradation curve of the lithium battery to obtain a known long-term degradation trend part of the lithium battery.
3) And predicting the future normal degradation trend based on the known long-term degradation trend data of the lithium battery by using the long-term and short-term memory neural network.
4) And taking the health state, the initial electric quantity state and the rest time of the lithium battery as input quantities of Gaussian process regression, and predicting a capacity regeneration part of the lithium battery.
5) And setting a capacity degradation rate failure threshold of the lithium battery, and obtaining a random fluctuation part by adopting Stable distribution.
Drawings
FIG. 1 is a general flow chart of the EMD-LSTM-GPR-Stable lithium battery life prediction algorithm of the invention.
Fig. 2 is a schematic diagram showing three phenomena of the degradation process of the lithium battery of the present invention.
FIG. 3 is a graph comparing the original degradation curve of the present invention with the empirical mode decomposition residual curve.
Fig. 4 is a graph comparing long-short-term memory neural network prediction data with original residual data of lithium batteries with different numbers of hidden layers.
Fig. 5 is a schematic diagram of an internal equivalent circuit of the lithium battery of the present invention.
Fig. 6 is a schematic diagram of the state of charge and terminal voltage established during the charge and discharge process of the lithium battery according to the present invention.
Fig. 7 is a flow chart of the present invention for predicting the state of health of a lithium battery regeneration.
Fig. 8 is a schematic diagram of the state of health of a lithium battery according to the present invention randomly fluctuating.
Fig. 9 is a graph showing the comparison of random fluctuation data and stable distribution of a lithium battery of the invention.
Fig. 10 is a simulation result of predicting remaining life of a lithium battery at 321 cycles.
Fig. 11 is a simulation result of predicting the remaining life of the lithium battery in 361 cycles.
Fig. 12 is a simulation result of predicting the remaining life of the lithium battery at 401 cycles.
Fig. 13 is a simulation result of predicting remaining life of a lithium battery at 441 cycles.
Fig. 14 is a simulation result of predicting the remaining life of the lithium battery at 481 cycles.
Detailed Description
The invention is further described in detail below with reference to the accompanying drawings.
The invention provides a lithium battery residual life prediction estimation method based on EMD-LSTM-GPR-Stable. Firstly, dividing a lithium battery health state degradation curve into a normal degradation trend part, a capacity regeneration part and a random fluctuation part; secondly, carrying out empirical mode decomposition on a capacity degradation curve of the lithium battery to obtain a known long-term degradation trend part of the lithium battery, and predicting a future normal degradation trend part on the basis of the known long-term degradation trend data of the lithium battery by utilizing a long-short memory neural network; then, taking the health state, the initial electric quantity state and the rest time of the lithium battery as the input quantity of Gaussian process regression, and predicting the capacity regeneration part of the lithium battery; then, generating random numbers obeying stable distribution as random fluctuation parts of the lithium battery; and finally, adopting Monte Carlo simulation to predict a probability density function of the residual service life of the lithium battery. The result shows that the method for predicting the residual service life of the lithium battery by adopting the EMD-LSTM-GPR-Stable prediction can effectively predict the residual service life of the lithium battery by comprehensively considering the attenuation characteristic and the capacity regeneration characteristic of the residual service life of the lithium battery and the influence of random partial interference characteristic, and has the advantages of early warning on the faults of the lithium battery, good accuracy and good reliability.
As shown in FIG. 1, the lithium battery residual service life prediction estimation method based on EMD-LSTM-GPR-Stable specifically comprises the following steps:
step one: dividing useful capacity in the degradation process of the lithium battery into three parts, namely normal degradation trend capacity, regeneration capacity and random fluctuation capacity by adopting a mode of defining the health state of the lithium battery through standardized treatment;
as shown in fig. 2, the aging of the lithium battery is generally caused by the growth of the solid electrolyte interface film, which causes the total decrease of the useful capacity of the lithium battery, and the lithium battery has other complicated aging mechanisms, which cause the local capacity regeneration phenomenon and random fluctuation phenomenon of the useful capacity of the lithium battery.
Because the lithium batteries of different models have different useful capacities, the lithium batteries need to be standardized. The lithium battery state of health is defined as follows:
wherein SOH i Indicating the health status of the ith cycle of the lithium battery, cap i Useful capacity, cap, representing the ith cycle period ini Representing the initial capacity.
According to the above, the present invention divides the useful capacity of the degradation process of a lithium battery into three parts, and the health state expression of the degradation process is as follows:
SOH i ＝NSOH i +λGSOH i +(1-λ)ΔSOH (1b)
GSOH i ＝GPR(t i ,ISOC i ,SOH i ) (1d)
ΔSOH～S α (γ,β,δ) (1e)
wherein NSOH i Is in a healthy state with normal degradation trend, lambda is a capacity regeneration parameter, t G,th For capacity regeneration time threshold, t i GSOH for rest time of lithium battery i For regenerated health status, ISOC i SOH for the initial state of charge of the ith cycle period i For the health status of the ith cycle period, ΔSOH is a randomly fluctuating health status that follows the Stable distribution S α (γ,β,δ)。
Step two: an empirical mode decomposition mode and a long-short-time neural memory network are adopted to obtain the health degradation state trend of the lithium battery;
in the degradation process of the lithium battery, a random fluctuation phenomenon and a capacity regeneration phenomenon generated due to a complex aging mechanism jointly cause short-term fluctuation of the health state, and the short-term fluctuation is used as a high-frequency part of a health state degradation curve; while lithium batteries exhibit an overall decreasing trend in state of health throughout the degradation process, which will be the low frequency portion of the state of health degradation curve.
The empirical mode decomposition algorithm of the present invention can be expressed as shown in table 1 below:
TABLE 1
As shown in fig. 3, after empirical mode decomposition of the original sequence data, a residual sequence is extracted. It can be obviously seen that the empirical mode decomposition removes local fluctuation, the obtained residual error shows overall monotonous long-term degradation trend, and the health state of the current normal degradation trend is successfully obtained.
The long-short time neural memory network is adopted to predict the future normal degradation trend on the basis of the known long-term degradation trend data of the lithium battery. The long-short-term memory neural network unit consists of a long-term state c <t> And a short term state a <t> Composition is prepared. Furthermore, it relies on three control gates: forgetting door gamma f Input gate Γ u And an output gate Γ o . The hidden layer node calculates an activation value that depends on the input of the current layer and the node at the previous time. The expression is as follows:
Γ u ＝σ(W u [a <t-1> ,x <t> ]+b u ) (2b)
Γ f ＝σ(W f [a <t-1> ,x <t> ]+b f ) (2c)
Γ o ＝σ(W o [a <t-1> ,x <t> ]+b o ) (2d)
a <t> ＝Γ o *tanh(c <t> ) (2f)
wherein W is a weight matrix, b is a bias, σ () is a sigmoid function, x <t> For input at time t, a <t> And a <t-1> Output of short-time memory nerve unit with time duration of t and t-1 respectively, c <t> And c <t-1〉 The cell states at times t and t-1 respectively,a unit that is the current input state.
For the long-short time memory neural network algorithm, the selection of proper hidden layer mathematical is critical, so that the prediction performance of the long-short time memory neural network with 5 different hidden layer numbers is compared, and the prediction result is shown in fig. 4.
The long-short-term memory neural network with different numbers of hidden layers can better predict residual error data. When the hidden layers are only 10 layers, the number of the hidden layers is too small, so that the long-and-short-term memory neural network is not fit, and the prediction error is increased. However, it can be seen from table 2 that the number of hidden layers is not as high as possible, and when the number of hidden layers is greater than 30, too many hidden layers may overfit the long-short-term memory neural network, and may increase the prediction error. Therefore, the number of hidden layers of the long-short-term memory neural network selected by the invention is 20.
| Number of hidden layers | 10 | 20 | 30 | 40 | 50 |
| Root mean square error | 0.0147 | 0.0018 | 0.0139 | 0.0096 | 0.0120 |
TABLE 2
Step three: constructing an internal equivalent circuit model of the lithium battery, and acquiring the relation between the circuit state and terminal voltage;
as shown in fig. 5, U in the lithium battery internal equivalent circuit model oc Is an Open Circuit Voltage (OCV), is influenced by the state of charge (SOC) of the current lithium battery, I L R is the charge-discharge current 0 Is resistance, determined by SEI film, R 1 ,C 1 Resistance and capacitance, respectively, affected by electrochemical polarization, R 2 ,C 2 The resistance and capacitance, respectively, are affected by concentration polarization.
The equivalent circuit equation is as follows:
wherein U is oc 、I L 、R 0 、R 1 、R 2 、C 1 、C 2 、U L The method is characterized by comprising open-circuit voltage, charge-discharge current, resistance and capacitance in an equivalent circuit model in the lithium battery.
Fig. 6 is a graph of terminal voltage corresponding to the state of charge during charging and discharging of a lithium battery, respectively. Obviously, the terminal voltage can be increased along with the increase of the state of charge, and the process is nonlinear, but the terminal voltage is different in the charging and discharging process of the lithium battery due to the existence of the internal resistance of the lithium battery. The invention establishes a fitting equation of the electric quantity state and the open circuit voltage:
U oc (SOC)＝a*ln(SOC+0.01)+b*SOC 4 +c*SOC 3 +d*SOC 2 +e*SOC+f (2b)
the SOC is the current state of charge of the battery, and a, b, c, d, e, and f are electrical parameters. And carrying out parameter estimation on the equivalent circuit and the electric quantity state-terminal voltage fitting equation by adopting a least square method.
Step four: taking the health state, the initial electric quantity state and the rest time of the lithium battery as the input quantity of Gaussian process regression, and predicting the regeneration part of the capacity of the lithium battery;
the capacity regeneration phenomenon is a phenomenon in which the useful capacity of a lithium battery increases suddenly after long-term storage with complete charge and discharge. Aiming at the phenomenon, the invention predicts the regenerated health state by adopting a Gaussian regression algorithm, takes the rest time, the initial electric quantity state and the current health state of the lithium battery as the input quantity of Gaussian regression. A flow chart of the health status of gaussian regression prediction regeneration is shown in fig. 7.
The Gaussian process is a random process formed by infinite high-dimensional random variables in a continuous domain, and has good adaptability to processing complex problems of small samples, linearity, high dimensionality and the like. The gaussian process expression is as follows:
f(x)～GP(m(x),κ(x,x')) (3a)
where m (x) represents the mean value. Kappa (X, X') represents the covariance function. The concrete expression is as follows:
where E () represents an expected value, m (x) is generally set to 0 in practical applications. Kappa (X, X') is also known as a kernel function, explaining the degree of correlation of similarity between two samples.
The kernel function adopted by the invention is a square index kernel function, and is specifically expressed as follows:
wherein sigma f L is a superparameter.
In the regression calculation, the prior probability density of the output Y obeys the following distribution:
f(x)～N(m(x),κ(x,x')) (3d)
ε～N(0,σ 2 I) (3e)
Y＝(f(x)+ε)～N(m(x),κ(x,x')+σ 2 I) (3f)
where N () represents a normal distribution, epsilon represents a noise component, and sigma represents a noise variance.
Suppose training set x and test set x * Independent of the same distribution, then the predicted output y * Will obey the following joint distribution:
to ensure performance of gaussian regression, the hyper-parameters σ present in the covariance function need to be matched during training f And l, optimizing. The invention adopts a maximum likelihood estimation method to optimize parameters, and likelihood functions are as follows:
through super parameter sigma f After optimization, f (x) * ) Is a posterior estimate of (2):
its average valueAnd covariance cov (f (x) * ) The expression of) is as follows:
the present invention defines the capacity regeneration time threshold as 18H. Since the lithium battery aging test is mostly an uninterrupted test, the lithium battery data set has less capacity regeneration data. However, the capacity regeneration phenomenon occurs after a long rest period in the aging test process of the lithium battery, so the capacity regeneration phenomenon is a non-negligible common phenomenon.
For the Gaussian regression model, a proper kernel function is selected to more accurately predict the regenerated health state, and in order to verify the advantages of the square index kernel, a secondary rational kernel and a Matern kernel with parameters of 5/2 are additionally introduced. As can be seen from table 3, the prediction results of the three kernel functions all have more significant errors, which is caused by less capacity regeneration data. It is still evident that the secondary rational kernel computes a smaller root mean square error than other kernel functions, meaning that the gaussian regression of the secondary rational kernel can more accurately predict the regenerated health.
| Kernel function | Capacity regeneration point 1 | Capacity regeneration point 2 | Capacity regeneration point 3 | Root mean square error |
| Square index kernel | 0.0301 | 0.0237 | 0.0214 | 0.0096 |
| 5/2Matern kernel | 0.0281 | 0.0198 | 0.0177 | 0.0064 |
| Secondary rational kernel | 0.0232 | 0.0160 | 0.0135 | 0.0021 |
| Actual regeneration value | 0.0315 | 0.0132 | 0.0017 | / |
TABLE 3 Table 3
Step five: selecting Stable distribution parameters, and generating random numbers obeying Stable distribution as random fluctuation of the lithium battery;
the health status of lithium batteries may locally fluctuate during degradation due to the complex degradation mechanism. The probability density distribution of the state of health of the lithium battery randomly fluctuates is shown in fig. 8. In fig. 8, the abscissa is the health status of random fluctuation, and the ordinate is the probability density. It can be seen that most of the random fluctuations are in the vicinity of 0 and are a unimodal distribution. In order to more accurately predict the random fluctuation health state of the lithium battery, the invention adopts Stable distribution to approximate the actual random fluctuation health state distribution.
Stable distributions are a class of infinitely separable distributions, the definition of which is generally given by its characteristic function.
Where j represents a complex unit and sign () represents a sign function. The distribution needs to be described by 4 parameters: characteristic parameter alpha epsilon (0, 2)]It can control the thickness of the tail of the probability density function; skew parameter beta epsilon [ -1,1]It determines the degree of symmetry of the distribution, β=0 distribution symmetry; position parametersIt describes the central location of the Stable distribution; dimensional parametersIt describes how far the distribution sample deviates from its mean.
The present invention will then employ a roulette algorithm to predict the health of the random fluctuations. However, since Stable distribution is infinite distribution, the invention sets the upper and lower limits of the prediction result based on the small probability event standard, and the specific expression is as follows:
/>
in the above, X-S α (γ,β,δ)，Z α For the upper limit of sampling, Z β Is the lower limit of sampling
The invention defines the capacity degradation rate failure threshold of the lithium battery as 76%. The health status data of random fluctuation of the training set can be calculated according to the above formula, and the result is shown in the following table 4.
Stable distribution parameter
| Distribution parameters | α | β | δ | γ |
| Data | 0.9989 | -0.1127 | 0.0010 | 9.6556e-05 |
TABLE 4 Table 4
In table 4, α is a characteristic parameter, β is a skew parameter, δ is a position parameter, and γ is a scale parameter. From the parameters of the Stable distribution estimation, a fitted Stable distribution can be obtained, as shown in fig. 9. In fig. 9, the Stable distribution is closer to the actual random fluctuation data distribution.
In order to verify the feasibility of the EMD-LSTM-GPR-Stable algorithm, and to embody the uncertainty of random fluctuation health state data on the prediction process, the invention adopts a Monte Carlo simulation method to carry out multiple tests. In order to verify the superiority of the method provided by the invention, the long-short-time memory neural network, the empirical mode decomposition-long-time memory neural network and the empirical mode decomposition-long-time memory neural network-Gaussian regression are compared with the method provided by the invention.
The verification is performed using a lithium battery common data set,
the invention predicts the residual service life of the CS 2-36 battery by using the data estimation algorithm parameters of the CS 2-33, CS 2-34, CS 2-35 and CS 2-38 batteries.
As shown in fig. 10, 11, 12, 13, 14, the remaining life of the lithium battery is predicted at 321, 361, 401, 441, 481 cycles, respectively. Each graph shows four prediction curves, wherein a dotted line is a long and short time memory neural network, a straight line is an empirical mode decomposition-long and short time memory neural network method, a dotted line is an empirical mode decomposition-long and short time memory neural network-Gaussian regression method, and a dot-dashed line is the empirical mode decomposition-long and short time memory neural network-Gaussian regression-stable distribution method. As can be seen from fig. 10, 11, 12, 13, 14, the narrower the PDF predicted based on empirical mode decomposition-long and short term memory neural network-gaussian regression-stable distribution, the higher the confidence of the prediction, when more data is used for training. In the periods 321 and 361, the life errors predicted by the long-short-time memory neural network, the empirical mode decomposition-long-time memory neural network and the empirical mode decomposition-long-time memory neural network-Gaussian regression method are obviously larger. At periods 401, 441, 481, the accuracy of each method improves as the lithium battery reaches its final life. Compared with other methods, the method provided by the invention can always accurately predict the residual service life of the lithium battery, which proves the superiority of the prediction method provided by the invention.
To compare the performance of the proposed method with other methods, the detailed prediction error results for the different algorithms at 321, 361, 401, 441 and 481 cycles are shown in FIG. 5. The prediction error is an error between the median and the actual life of a plurality of prediction results obtained by Monte Carlo simulation in one method, and the 95% confidence interval is calculated by taking a prediction result sample as a large sample.
TABLE 5
As can be seen from table 5, when the predicted remaining service life is 321 cycles, the residual service life prediction error based on empirical mode decomposition-long-short-term memory neural network-gaussian regression-stable distribution is only 6 cycles, which is an accurate life prediction. The prediction error of the long-short time memory neural network, the empirical mode decomposition-the long-short time memory neural network and the empirical mode decomposition-the long-short time memory neural network-the Gaussian regression method is not less than 60 cycles. And the root mean square error of the neural network-Gaussian regression-stable distribution is far smaller than that of other comparison methods in empirical mode decomposition-long and short time memory, so that the method provided by the invention can be used for more accurately predicting the track of the real curve. Although the root mean square error of the proposed method is significantly smaller than the prediction error of empirical mode decomposition-long and short term memory neural network-gaussian regression method at 441 cycles. In addition, the prediction error of the method proposed herein is always less than + -10 cycles in the whole degradation process of the lithium battery, which again demonstrates the superiority of the neural network-gaussian regression-stable distribution method based on empirical mode decomposition-long and short term memory proposed by the present invention.
Claims (2)
1. The method for predicting the residual life of the lithium battery for the electric forklift is characterized by comprising the following steps of:
step one: dividing the useful capacity in the degradation process of the lithium battery into three parts of normal degradation trend capacity, regeneration capacity and random fluctuation capacity;
step two: performing empirical mode decomposition on a lithium battery health state degradation curve and predicting a long-term degradation trend by using a long-term and short-term memory neural network;
step three: constructing an internal equivalent circuit model of the lithium battery, and establishing a relation between a circuit state and terminal voltage;
step four: predicting a regeneration part of lithium battery capacity by adopting lithium battery health State (SOH), initial state of charge (SOC) and rest time as input quantity of GPR;
step five: selecting Stable distribution parameters, and generating random numbers obeying Stable distribution as random fluctuation of the lithium battery;
step six: verifying by adopting a Monte Carlo simulation method;
in the first step, the method for obtaining the normal degradation trend capacity, the regeneration capacity and the random fluctuation capacity of the lithium battery in the degradation process is to take the battery health state as a ratio not exceeding 100%, and define the battery health state SOH as follows:
in SOH i Indicating the health status of the ith cycle of the lithium battery, cap i Useful capacity, cap, representing the ith cycle period ini Representing initial capacity, and establishing a health state in the degradation process of the lithium battery by using the obtained health state of the lithium battery;
in the second step, the empirical mode decomposition mainly decomposes the nonstationary signal data into a residual sequence (RES) and a series of Intrinsic Mode Functions (IMFs) by performing iterative screening on the signal, and the effective IMF sequence is specified to satisfy the following two conditions: 1. the number of extreme points and zero crossing points should be equal or differ by at most one; 2. the average value of the upper envelope line and the lower envelope line of the local maximum value and the local minimum value is zero, and the method for predicting the health state of the normal degradation trend by adopting empirical mode decomposition is as follows: 1. finding out the local maximum value and local minimum value points of the original signal x (t); 2. interpolation is respectively carried out on the local maximum value points and the local minimum value points by utilizing a cubic spline function to obtain an upper envelope u (t) and a lower envelope l (t) of x (t), and the upper envelope and the lower envelope are averaged to obtain3. Letting h (t) -x (t) -m (t), judging whether h (t) meets the IMF condition, if not, continuing the iterative process until h (t) meets the IMF condition; 4. if h (t) meets IMF conditions, an effective subsequence is obtained, which may be denoted as IMF i (t) mixing imf i Filtering from the original signal x (t) to obtain a new original signal x i (t) repeating the above steps to obtain all imf i (t), (i-1, 2,3 …, n) and a residual error r 0 (t) the final lithium battery degradation curve is expressed as:
and then predicting the future normal degradation trend by adopting a long-short time neural memory network on the basis of the known long-term degradation trend data of the lithium battery, wherein the unit of the long-short time neural memory network is in a long-term state c <t> And a short term state a <t> Composition, in addition, it relies on three control gates: forgetting door gamma f Input gate Γ u And an output gate Γ o The hidden layer node calculates an activation value depending on the input of the current layer and the node at the previous time, the expression of which is as follows:
Γ u ＝σ(W u [a <t-1> ,x <t> ]+b u ) (3b)
Γ f ＝σ(W f [a <t-1> ,x <t> ]+b f ) (3c)
Γ o ＝σ(W o [a <t-1> ,x <t> ]+b o ) (3d)
a <t> ＝Γ o *tanh(c <t> ) (3f)
wherein W is a weight matrix, b is a bias, σ () is a sigmoid function, x <t> For input at time t, a <t> And a <t-1〉 Output of short-time memory nerve unit with time duration of t and t-1 respectively, c <t> And c <t-1> The cell states at times t and t-1 respectively,a unit that is a current input state;
the method for predicting the health state of lithium battery regeneration is as follows: 1. establishing an equivalent circuit model by using a state of charge and terminal voltage fitting equation and establishing an equivalent circuit model of the lithium ion battery; 2. calculating an initial state of charge through an initial terminal voltage, and judging whether the rest time exceeds capacity regeneration time or not according to the acquired rest time, the initial state of charge and the current health state; 3. if the rest time exceeds the capacity regeneration time threshold, carrying out Gaussian process regression, and if not, returning to the step of calculating the initial state of charge; 4. predicting the regenerated health state of the lithium battery through Gaussian process regression;
in the third step, in the degradation process of the lithium battery, the electrode material and the electrolyte react on the solid-liquid phase interface to form a layer of solid electrolyte interface film covering the surface of the electrode material, so that the internal resistance of the lithium battery can change along with the change of the solid electrolyte interface film, and the lithium battery can generate polarization phenomenon in the charge and discharge process, so that the actual electrode potential deviates from the balance electrode potential, and in order to express the influence of the solid electrolyte interface film and the polarization phenomenon in the charge and discharge process of the lithium battery, the research is established on the basis of a second-order RC circuit equivalent model;
the circuit equivalent equation is expressed as:
wherein U is oc Is an Open Circuit Voltage (OCV), is influenced by the state of charge (SOC) of the current lithium battery, I L R is the charge-discharge current 0 Is resistance, determined by SEI film, R 1 ，C 1 Resistance and capacitance, respectively, affected by electrochemical polarization, R 2 ，C 2 Resistance and capacitance affected by concentration polarization, respectively;
state of charge-open circuit voltage fitting equation:
U oc (SOC)＝a*ln(SOC+0.01)+b*SOC 4 +c*SOC 3 +d*SOC 2 +e*SOC+f (4b)
the SOC is the current battery state of charge, and a, b, c, d, e and f are electric quantity parameters;
because some position parameters exist in the equation, a least square method is adopted to carry out parameter estimation on an equivalent circuit equation and a circuit state-terminal voltage fitting equation; calculating to obtain an initial electric quantity state according to the open circuit voltage of the lithium battery; then, predicting the regenerated health state of the lithium battery by adopting a Gaussian process according to the initial electric quantity state, the rest time and the current health state;
in the fourth step, the specific flow of the lithium battery capacity regeneration part predicted by Gaussian regression is as follows:
1) Establishing a Gaussian process expression according to a lithium battery simulation equivalent circuit electric quantity state-open circuit voltage fitting equation:
f(x)～GP(m(x),κ(x,x')) (5a)
where m (x) represents the mean value, κ (x, x ') represents the covariance function, E [ (m (x) -f (x ')) (m (x) -f (x)) ] represents the expected value, in practical application, m (x) is generally set to 0, κ (x, x ') is also called the kernel function, explaining the degree of association of the similarity between two samples;
2) The Gaussian process predictions of the square index kernel, the 5/2Matern kernel and the secondary rational kernel are compared, and the optimal kernel function is selected and is subjected to predictive analysis by outputting the prior probability density of Y:
f(x)～N(m(x),κ(x,x')) (5d)
ε～N(0,σ 2 I) (5e)
Y＝(f(x)+ε)～N(m(x),κ(x,x')+σ 2 I) (5f)
wherein sigma f L is a superparameter, k f The kernel function used in the present invention is represented as a square index kernel function, N () represents a normal distribution, epsilon represents a noise component, sigma represents a noise variance, Y represents an a priori probability density distribution of the output,to be in training set x and test set x * Predicting the joint distribution obeyed by the output capacity regeneration under the condition of independent same distribution;
3) Super parameter sigma using maximum likelihood estimation method f L is optimized and the method is carried out,
wherein L (sigma) f L) is a maximum likelihood function, P (f (x) * )|Y,X,X * ) For f (x) in scheme 2) * ) Is determined by the a-priori estimates of (c),for the mean expression, cov (f (x * ) Is a covariance expression;
in the fifth step, the first step is to carry out the process,
the specific flow for predicting the random fluctuation health status distribution by adopting Stable distribution is as follows:
1) Considering that the health state of the random fluctuation of the lithium battery is near 0 and is unimodal, for more accurately predicting the health state of the random fluctuation of the lithium battery, the Stable distribution is adopted to approximate the actual health state distribution of the random fluctuation, and the characteristic function is as follows;
where j represents complex units and sign () represents a sign function, the distribution needs to be described by 4 parameters: characteristic parameter alpha epsilon (0, 2)]It can control the thickness of the tail of the probability density function; skew parameter beta epsilon [ -1,1]It determines the degree of symmetry of the distribution, β=0 then the distribution is symmetrical; position parametersIt describes the central location of the Stable distribution; scale parameter->It describes how far the distribution sample deviates from its mean,
2) Setting upper and lower limits of a prediction result based on the low probability time standard;
the roulette algorithm is used to predict the health status of random fluctuations, but because the Stable distribution is an infinitely separable distribution, the upper and lower limits of the predicted outcome are set based on a low probability time standard,
upper and lower limit expressions of Stable distribution:
wherein X-S α (γ,β,δ)，Z α For the upper limit of sampling, Z β As a lower limit of the sampling to be performed,
3) Defining the degradation rate failure threshold value of the lithium battery as 76%, calculating to obtain the random fluctuation health state of the training set according to the formula, then obtaining distribution parameters gamma, beta and delta to obtain fitted Stable distribution,
ΔSOH～S α (γ,β,δ) (9)
wherein delta SOH is a randomly fluctuating health state which is subject to Stable distribution S α (gamma, beta, delta), alpha being characteristic parameter and beta being biasOblique parameters, delta is a position parameter, and gamma is a scale parameter.
2. The method for predicting the remaining life of a lithium battery for an electric forklift according to claim 1, wherein,
step six: the Monte Carlo simulation method is adopted for verification, data of CS2_33, CS2_34, CS2_35, CS2_36 and CS2_38 in a lithium battery data set are selected, the data set is derived from a battery with a calibrated capacity of 1.1Ah, and a cathode is formed by lithium cobalt oxide LiCoO 2 The anode consists of lamellar graphite and polyvinylidene fluoride, and electrolyte consisting of equal amounts of ethylene carbonate and dimethyl carbonate, and is prepared by LiPF 6 As lithium salts, a medium is provided for ion transport between the two electrodes, and in this dataset five groups of lithium cells are operated in three different modes at room temperature: and (3) charging, discharging and impedance measurement work to obtain an aging test result, wherein in the process, the lithium battery is charged in a 0.55A constant current mode until the voltage reaches 4.2V, then is charged in a constant voltage mode, the voltage is maintained at 4.2V until the charging current is reduced to below 50mA, then the CS 2-33 and CS 2-34 batteries are discharged in a 0.55A constant current mode, and CS 2-35, CS 2-36 and CS 2-38 are discharged in a 1.1A constant current mode until the voltage of the battery is reduced to 2.7V, and when the lithium battery reaches the cut-off life, the test is ended.
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