Robust Savitzky-Golay Filtering Method for Battery State Estimation

Abstract

The present invention discloses a robust Savitzky-Golay filtering method for battery state estimation, comprising the following steps: step 1, collecting real-time operation data c containing unknown distribution noise of lithium-ion batteries through a battery management system; step 2, judging the sequence length of the real-time operation data c collected in step 1, and determining the filter window length and the fitting polynomial order; step 3, using the robust fitting criterion MGC, combined with the filter window length and the fitting polynomial order determined in step 2, to generate an MGCSG filtering algorithm; step 4, using the MGCSG filtering algorithm obtained in step 3 to perform smooth filtering on the real-time operation data c collected in step 1. The filtering method of the present invention solves the problem in the prior art that the unknown distribution noise in the BMS collected data has a great influence on the filtering effect of the filtering algorithm.

Description

Technical Field

[0001] The invention belongs to the technical field of digital signal noise processing, and in particular relates to a robust Savitzky-Golay filtering method for battery state estimation. Background Art

[0002] Since the advent of industrialization, the massive consumption of traditional fossil energy by humans has caused serious global environmental problems. In order to deal with this problem, a variety of new clean energy sources have been developed. However, new energy sources have extremely high uncertainty, which has caused serious obstacles to their use. Energy storage devices that output energy steadily can solve this problem, making it quickly become a research hotspot.

[0003] Among many types of energy storage devices, lithium-ion batteries (LIB) have become one of the mainstream energy storage units due to their high energy density, low self-discharge rate, long life, and light weight. Its main application scenarios include power system energy storage, electric vehicles, and various small electronic devices. In consideration of the requirements for LIB operation safety and user interactivity, the battery management system (BMS) was developed. BMS can comprehensively analyze and calculate a variety of measurement data to obtain the current and future state parameters of LIB, such as state of charge (SOC), state of health (SOH), state of power (SOP), etc. However, the working environment of the sensors that measure and collect data in BMS is usually very complex, such as changing temperature, humidity, vibration, etc. This series of uncertain factors will cause the data measured by the sensor to contain unknown distribution noise. If these noisy data are not preprocessed, all subsequent operation calculations of BMS will produce huge errors, which is very unfavorable for accurately reflecting the true state of LIB.

[0004] In summary, as the basic and important state estimation function of BMS, it is necessary to effectively process the unknown distributed noise in the measurement data transmitted by the sensor to the system, which is crucial for the accuracy of the subsequent calculation of multiple states by BMS. The Savitzky-Golay (SG) digital filtering algorithm has the advantages of low computational complexity and high filtering smoothness. Based on it, a filtering algorithm for measurement data with unknown distributed noise can be constructed. However, the SG filtering algorithm uses high-order polynomials to fit the original data within a fixed window length. The fitting criterion is to minimize the fitting error. The fitting criterion of traditional SG filtering is based on least squares (LS). LS is very effective when the noise in the measurement data is Gaussian distributed. However, affected by multiple factors such as the environment, the noise in the measurement data is not necessarily Gaussian distributed, but more likely to be unknown distributed noise containing outliers. When faced with unknown distributed noise, the traditional SG filtering algorithm based on LS cannot show satisfactory filtering effect. Summary of the invention

[0005] The purpose of the present invention is to provide a robust Savitzky-Golay filtering method for battery state estimation, which solves the problem in the prior art that unknown distributed noise in BMS collected data has a significant impact on the filtering effect of the filtering algorithm.

[0006] The technical solution adopted by the present invention is a robust Savitzky-Golay filtering method for battery state estimation, comprising the following steps:

[0007] Step 1: collecting real-time operating data c of the lithium-ion battery containing unknown distributed noise through a battery management system;

[0008] Step 2: judging the sequence length of the operation data c collected in step 1, and determining the filter window length and the fitting polynomial order;

[0009] Step 3, using the robust fitting criterion MGC, combined with the filter window length and fitting polynomial order determined in step 2, to generate the MGCSG filtering algorithm;

[0010] Step 4: Use the MGCSG filtering algorithm generated in step 3 to perform smoothing filtering on the real-time operation data c collected in step 1.

[0011] The present invention is also characterized in that:

[0012] The real-time operation data c containing unknown distributed noise in step 1 includes current data and voltage data.

[0013] The real-time running data c containing unknown distribution noise in step 1 is:

[0014]

[0015] In the formula, is the true value of the operating data which is theoretically unavailable, and ν is the measurement noise of unknown distribution.

[0016] The specific process of step 2 is: judging the sequence length of the collected real-time operation data c, the filter window length is smaller than the sequence length of the real-time operation data c, and the fitting polynomial order is smaller than the filter window length.

[0017] The specific process of step 3 is:

[0018] Using the MGC fitting criterion, the expression of the MGC fitting criterion is as follows:

[0019]

[0020] Where ζ∈[0,1], α1,α2>0 are shape parameters, and β1,β2>0 are scale parameters;

[0021] The MGCSG robust filtering algorithm can be generated from (7), and the fixed point iteration method is used in the solution process.

[0022] The beneficial effects of the present invention are:

[0023] The robust Savitzky-Golay filtering method for battery state estimation provided by the present invention adopts the Mixture Generalized Correntropy (MGC) criterion to replace the Least Square (LS) criterion in the traditional SG filtering algorithm, and derives the robust MGCSG filtering algorithm based on the gradient method and the fixed point iteration method, so that the MGCSG filtering algorithm can achieve higher robustness and stronger generalization ability under various unknown distribution noises. Under the influence of different distribution noises, the MGCSG filtering result can still have a better true value, improve the authenticity of LIB collected data, and provide more accurate raw data for subsequent state estimation and other operations of BMS, thereby ensuring the effectiveness and reliability of subsequent state estimation to a certain extent. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 It is a flow chart of a robust Savitzky-Golay filtering method for battery state estimation according to the present invention;

[0025] Figure 2 is a comparison diagram of the MGCSG and SG filtering results in the current measurement data of Example 1;

[0026] Figure 3 is a comparison diagram of the absolute errors of MGCSG and SG filtering in the current measurement data of Example 1;

[0027] Figure 4 is a comparison diagram of the filtering results of MGCSG and SG in the voltage measurement data of Example 1;

[0028] Figure 5 is a comparison diagram of the absolute errors of MGCSG and SG filtering in the voltage measurement data of Example 1;

[0029] Figure 6 is a comparison diagram of the MGCSG and SG filtering results in the current measurement data of Example 2;

[0030] Figure 7 is a comparison diagram of the absolute errors of MGCSG and SG filtering in the current measurement data of Example 2;

[0031] Figure 8 is a comparison diagram of the filtering results of MGCSG and SG in the voltage measurement data of Example 2;

[0032] Fig. 9 is a comparison diagram of the absolute errors of MGCSG and SG filtering in the voltage measurement data of Example 2;

[0033] Fig.10 is a comparison diagram of the MGCSG and SG filtering results in the current measurement data of Example 3;

[0034] Fig.11 is a comparison diagram of the absolute errors of MGCSG and SG filtering in the current measurement data of Example 3;

[0035] Fig.12 is a comparison diagram of the filtering results of MGCSG and SG in the voltage measurement data of Example 3;

[0036] Fig.13 It is a comparison diagram of the absolute errors of MGCSG and SG filtering in the voltage measurement data of Example 3. DETAILED DESCRIPTION

[0037] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0038] The present invention provides a robust Savitzky-Golay filtering method for battery state estimation, such as Figure 1 As shown, the following steps are included:

[0039] Step 1: collecting real-time operating data c of the lithium-ion battery containing unknown distributed noise through a battery management system;

[0040] In step 1, the real-time operation data c includes current data and voltage data;

[0041] The real-time running data c in step 1 is:

[0042]

[0043] In the formula, is the true value of the operating data that is theoretically unavailable, ν is the measurement noise of unknown distribution;

[0044] Step 2: judging the sequence length of the real-time operation data c collected in step 1, and determining the filter window length and the fitting polynomial order;

[0045] The specific process of step 2 is: judging the sequence length of the collected real-time operation data c, the filter window length is smaller than the sequence length of the real-time operation data c, and the fitting polynomial order is smaller than the filter window length.

[0046] Step 3: Replace the fitting criterion LS of the traditional SG filtering algorithm with the robust fitting criterion MGC, and generate the MGCSG filtering algorithm by combining the filter window length and the fitting polynomial order determined in step 2;

[0047] The specific process of step 3 is:

[0048] The length of the sequence data window c = [c -m ,c -m+1 ,...,c0,...,c m-1 ,c m ], an n-order polynomial is used to fit the data in the window. The fitting criterion of the traditional SG filtering algorithm is to minimize the loss function based on LS:

[0049]

[0050] In the formula Indicates the lth fitting result of the polynomial in the current window, a k Represents the coefficient of the k-th order in the polynomial;

[0051] In order to obtain the coefficient a k The coefficient matrix a is composed of (2), and the derivative of the coefficients is obtained based on the gradient method:

[0052]

[0053] Matrixing (3) yields:

[0054] (l T l)a=l T c (4);

[0055] Where a=[a1,a2,...,a n ] T is the coefficient matrix, c=[c -m ,c-m+1 ...,c0,...,c m ] T is the sample matrix in the window, and l is:

[0056]

[0057] Therefore, the coefficient matrix can be calculated as:

[0058] a=(l T l) -1 l T c (6);

[0059] The LS fitting criterion in (2) of the SG filter is replaced by the MGC fitting criterion. The expression of the MGC fitting criterion is as follows:

[0060]

[0061] Where ζ∈[0,1], α1,α2>0 are shape parameters, and β1,β2>0 are scale parameters;

[0062] Derivative (7) with respect to coefficient a can be derived based on the gradient method:

[0063]

[0064] Where p = 0, 1, ..., n, Λ is a diagonal matrix whose diagonal elements are:

[0065]

[0066] From (8), we can get the MGCSG robust filtering algorithm;

[0067] Step 4: Use the MGCSG filtering algorithm generated in step 3 to perform smoothing filtering on the real-time operation data c collected in step 1.

[0068] Example 1

[0069] When the real data is interfered by Gaussian noise, this embodiment proposes a robust Savitzky-Golay filtering method for battery state estimation, including the following steps:

[0070] Step 1, collecting real-time operating data c of the lithium-ion battery containing unknown distributed noise when the real data is interfered by Gaussian noise through the battery management system;

[0071] The real-time operation data c in step 1 includes current data and voltage data;

[0072] The real-time running data c in step 1 is:

[0073]

[0074] In the formula, is the true value of the operating data that is theoretically unavailable, ν is the measurement noise of unknown distribution;

[0075] Step 2: judging the sequence length of the real-time operation data c collected in step 1, and determining the filter window length and the fitting polynomial order;

[0076] The specific process of step 2 is: judging the sequence length of the collected real-time operation data c, the filter window length is smaller than the sequence length of the real-time operation data c, and the fitting polynomial order is smaller than the filter window length.

[0077] Step 3: Replace the fitting criterion LS of the traditional SG filtering algorithm with the robust fitting criterion MGC, and generate the MGCSG filtering algorithm by combining the filter window length and the fitting polynomial order determined in step 2;

[0078] The specific process of step 3 is:

[0079] The length of the sequence data window c = [c -m ,c -m+1 ,...,c0,…,c m-1 ,c m ], an n-order polynomial is used to fit the data in the window. The fitting criterion of the traditional SG filtering algorithm is to minimize the loss function based on LS.

[0080]

[0081] In the formula Indicates the lth fitting result of the polynomial in the current window, a k Represents the coefficient of the k-th order in the polynomial;

[0082] In order to obtain the coefficient a k The coefficient matrix a is composed of (2), and the derivative of the coefficients is obtained based on the gradient method:

[0083]

[0084] Matrixing (3) yields:

[0085] (l T l)a=l T c (4);

[0086] Where a=[a1,a2,…,a n ] T is the coefficient matrix, c=[c -m ,c -m+1 …,c0,…,c m ] Tis the sample matrix in the window, and l is:

[0087]

[0088] Therefore, the coefficient matrix can be calculated as:

[0089] a=(l T l) -1 l T c (6);

[0090] The LS fitting criterion in (2) of the SG filter is replaced by the MGC fitting criterion. The expression of the MGC fitting criterion is as follows:

[0091]

[0092] Where ζ∈[0,1], α1,α2>0 are shape parameters, and β1,β2>0 are scale parameters;

[0093] Derivative (7) with respect to coefficient a can be derived based on the gradient method:

[0094]

[0095] Where p = 0, 1, ..., n, Λ is a diagonal matrix whose diagonal elements are:

[0096]

[0097] The traditional SG filter algorithm fitting criterion in (2) is replaced by the fitting criterion shown in (8) to generate a MGCSG filter algorithm with stronger robustness and generalization;

[0098] Step 4: Use the MGCSG filtering algorithm obtained in step 3 to smooth the real-time operation data c collected in step 1 to obtain more realistic filtered operation data, such as Figure 2 , Figure 3 , Figure 4 and Figure 5 shown.

[0099] It can be seen from the figure that when the collected real-time operation data contains Gaussian noise, there is almost no difference in filtering accuracy between the MGCSG filtering algorithm and the traditional SG filtering algorithm. This not only verifies the good performance of the SG filtering algorithm under Gaussian noise conditions, but also proves that the MGCSG filtering algorithm still retains this good performance.

[0100] Example 2

[0101] When the real data is interfered by double Gaussian mixed noise with Gaussian noise as background noise, this embodiment proposes a robust Savitzky-Golay filtering method for battery state estimation, including the following steps:

[0102] Step 1, collecting, through a battery management system, real-time operating data c of a lithium-ion battery containing unknown distributed noise when the real data is interfered by a double Gaussian mixed noise with Gaussian noise as background noise;

[0103] The real-time operation data c in step 1 includes current data and voltage data;

[0104] The real-time running data c in step 1 is:

[0105]

[0106] In the formula, is the true value of the operating data that is theoretically unavailable, ν is the measurement noise of unknown distribution;

[0107] Step 2: judging the sequence length of the real-time operation data c collected in step 1, and determining the filter window length and the fitting polynomial order;

[0108] The specific process of step 2 is: judging the sequence length of the collected real-time operation data c, the filter window length is smaller than the sequence length of the real-time operation data c, and the fitting polynomial order is smaller than the filter window length.

[0109] Step 3: Replace the fitting criterion LS of the traditional SG filtering algorithm with the robust fitting criterion MGC, and generate the MGCSG filtering algorithm by combining the filter window length and the fitting polynomial order determined in step 2;

[0110] The specific process of step 3 is:

[0111] The length of the sequence data window c = [c -m ,c -m+1 ,…,c0,...,c m-1 ,c m ], an n-order polynomial is used to fit the data in the window. The fitting criterion of the traditional SG filtering algorithm is to minimize the loss function based on LS:

[0112]

[0113] In the formula Indicates the lth fitting result of the polynomial in the current window, a k Represents the coefficient of the k-th order in the polynomial;

[0114] In order to obtain the coefficient a kThe coefficient matrix a is composed of (2), and the derivative of the coefficients is obtained based on the gradient method:

[0115]

[0116] Matrixing (3) yields:

[0117] (l T l)a=l T c (4);

[0118] Where a=[a1,a2,...,a n ] T is the coefficient matrix, c=[c -m ,c -m+1 ...,c0,...,c m ] T is the sample matrix in the window, and l is:

[0119]

[0120] Therefore, the coefficient matrix can be calculated as:

[0121] a=(l T l) -1 l T c (6);

[0122] The LS fitting criterion in (2) of the SG filter is replaced by the MGC fitting criterion. The expression of the MGC fitting criterion is as follows:

[0123]

[0124] Where ζ∈[0,1], α1,α2>0 are shape parameters, and β1,β2>0 are scale parameters;

[0125] Derivative (7) with respect to coefficient a can be derived based on the gradient method:

[0126]

[0127] Where p = 0, 1, ..., n, Λ is a diagonal matrix whose diagonal elements are:

[0128]

[0129] From (8), we can get the MGCSG robust filtering algorithm;

[0130] Step 4: Use the MGCSG filtering algorithm obtained in step 3 to smooth the real-time operation data c collected in step 1 to obtain more realistic filtered operation data, such as Figure 6 , Figure 7 , Figure 8and Fig. 9 shown.

[0131] It can be seen from the figure that the filtering effect of the MGCSG filtering algorithm is significantly better than that of the SG filtering algorithm. The overall volatility of the MGCSG filtering result is smaller, smoother, and more robust to outliers.

[0132] Example 3

[0133] When real data is interfered by Gaussian and Laplace mixed noise with Laplace noise as background noise, this embodiment proposes a robust Savitzky-Golay filtering method for battery state estimation, including the following steps:

[0134] Step 1, collecting, through a battery management system, real-time operating data c of a lithium-ion battery containing unknown distributed noise when the real data is interfered by a mixed noise of Gaussian and Laplace with Laplace noise as background noise;

[0135] The real-time operation data c in step 1 includes current data and voltage data;

[0136] The real-time running data c in step 1 is:

[0137]

[0138] In the formula, is the true value of the operating data that is theoretically unavailable, ν is the measurement noise of unknown distribution;

[0139] Step 2: judging the sequence length of the real-time operation data c collected in step 1, and determining the filter window length and the fitting polynomial order;

[0140] The specific process of step 2 is: judging the sequence length of the collected real-time operation data c, the filter window length is smaller than the sequence length of the real-time operation data c, and the fitting polynomial order is smaller than the filter window length.

[0141] Step 3: Replace the fitting criterion LS of the traditional SG filtering algorithm with the robust fitting criterion MGC, and generate the MGCSG filtering algorithm by combining the filter window length and the fitting polynomial order determined in step 2;

[0142] The specific process of step 3 is:

[0143] The length of the sequence data window c = [c -m ,c -m+1 ,...,c0,...,c m-1 ,c m ], an n-order polynomial is used to fit the data in the window. The fitting criterion of the traditional SG filtering algorithm is to minimize the loss function based on LS:

[0144]

[0145] In the formula Indicates the lth fitting result of the polynomial in the current window, a k Represents the coefficient of the k-th order in the polynomial;

[0146] In order to obtain the coefficient a k The coefficient matrix a is composed of (2), and the derivative of the coefficients is obtained based on the gradient method:

[0147]

[0148] Matrixing (3) yields:

[0149] (l T l)a=l T c (4);

[0150] Where a=[a1,a2,...,a n ] T is the coefficient matrix, c=[c -m ,c -m+1 ...,c0,...,c m ] T is the sample matrix in the window, and l is:

[0151]

[0152] Therefore, the coefficient matrix can be calculated as:

[0153] a=(l T l) -1 l T c (6);

[0154] The LS fitting criterion in (2) of the SG filter is replaced by the MGC fitting criterion. The expression of the MGC fitting criterion is as follows:

[0155]

[0156] Where ζ∈[0,1], α1,α2>0 are shape parameters, and β1,β2>0 are scale parameters;

[0157] Derivative (7) with respect to coefficient a can be derived based on the gradient method:

[0158]

[0159] Where p = 0, 1, ..., n, Λ is a diagonal matrix whose diagonal elements are:

[0160]

[0161] From (8), we can get the MGCSG robust filtering algorithm;

[0162] Step 4: Use the MGCSG filtering algorithm obtained in step 3 to smooth the real-time operation data c collected in step 1 to obtain more realistic filtered operation data, such as Fig.10 , Fig.11 , Fig.12 and Fig.13 shown.

[0163] It can be seen from the figure that under the same filtering parameters, MGCSG filtering can still show satisfactory results, reflecting the excellent generalization of MGCSG to noises with different distributions. At the same time, compared with the SG filtering algorithm, MGCSG still shows better performance and higher smoothness.

[0164] In summary, the above conclusions can also be obtained in the following table. The evaluation index MSE in the table represents mean square error, and MAPE represents mean absolute percentage error:

[0165]

[0166] It can be seen that, in response to the problem of unknown distributed noise collected in BMS, the proposed MGCSG filtering algorithm can better adapt to unknown noise of different types of distribution, showing higher generalization; it can effectively reduce the interference of unknown distributed noise in the real-time operation data collected by BMS, showing better robustness, improving the accuracy of measurement data, and providing more reliable reference data for subsequent operations of BMS.

Claims

1. A robust Savitzky-Golay filtering method for battery state estimation, characterized in that: The steps include: Step 1: collecting real-time operating data c of the lithium-ion battery containing unknown distributed noise through a battery management system; Step 2: judging the sequence length of the operation data c collected in step 1, and determining the filter window length and the fitting polynomial order; Step 3, using the robust fitting criterion MGC, combined with the filter window length and the fitting polynomial order determined in step 2, to generate the MGCSG filtering algorithm; The specific process is: Using the MGC fitting criterion, the expression of the MGC fitting criterion is as follows Where ζ∈[0,1], α1, α2>0 are shape parameters, and β1, β2>0 are scale parameters; The MGCSG robust filtering algorithm can be generated from (7), and the fixed point iteration method is used in the solution process; Step 4: Use the MGCSG filtering algorithm obtained in step 3 to perform smoothing filtering on the operating data c collected in step 1.

2. The robust Savitzky-Golay filtering method for battery state estimation according to claim 1, characterized in that: The real-time operation data c in step 1 includes current data and voltage data.

3. The robust Savitzky-Golay filtering method for battery state estimation according to claim 1, characterized in that: The real-time running data c in step 1 is: In the formula, is the true value of the operating data that is theoretically unavailable, and v is the measurement noise of unknown distribution.

4. The robust Savitzky-Golay filtering method for battery state estimation according to claim 1, characterized in that: The specific process of step 2 is: judging the sequence length of the collected real-time operation data c, the filter window length is smaller than the sequence length of the real-time operation data c, and the fitting polynomial order is smaller than the filter window length.

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