CN115508729A - Lithium battery broadband impedance spectrum testing method based on maximum length binary sequence - Google Patents

Abstract

The invention discloses a method for testing a broadband impedance spectrum of a lithium battery based on a maximum length binary sequence, which comprises the following steps of: designing a maximum length binary sequence for broadband impedance measurement; injecting a maximum length binary sequence into the lithium battery through a battery management system, collecting the terminal voltage and current of the lithium battery in the injection process, and calculating the measurement impedance of the lithium battery under different frequencies; establishing a three-dimensional data cloud in a frequency domain by using the power spectral density characteristic of the excitation signal and the real part and the imaginary part of the measured impedance; and filtering data points in the three-dimensional data cloud by establishing a data cleaning automatic selection mechanism based on statistics to obtain a broadband impedance spectrum curve of the lithium battery. According to the invention, the maximum length binary sequence is injected into the lithium battery, and the three-dimensional data cloud is filtered by using a data cleaning automatic selection mechanism, so that the noise interference is reduced, and the accuracy and stability of the broadband impedance measurement of the power lithium battery are improved.

Description

Broadband Impedance Spectroscopy Test Method for Lithium Batteries Based on Maximum Length Binary Sequence

technical field

The invention belongs to the technical field of power lithium battery applications, and in particular relates to a lithium battery broadband impedance spectrum testing method based on a maximum-length binary sequence.

Background technique

In the field of electric vehicles, power batteries are mainly responsible for providing vehicle power. With the continuous innovation of power battery technology, there are more and more types of power batteries. Among them, lithium-ion batteries are widely used because of their excellent performance. Lithium batteries convert chemical energy into electrical energy by using the electrochemical potential of its internal two poles. Due to the existence of the aging mechanism, the performance of lithium batteries will gradually decline after repeated use, and the outstanding performance is the decrease in capacity and the increase in resistance. The operating status of the system needs to be diagnosed and predicted. Electrochemical impedance spectroscopy technology is a safe perturbation technology used to detect the internal change process of the electrochemical system. This technology measures the impedance of the battery within a certain frequency range, which can provide rich electrode kinetic information, and is used in the estimation and degradation of lithium battery SOX. Pattern recognition, internal temperature estimation, and safety detection have great application potential.

The measurement methods of electrochemical impedance spectroscopy mainly include frequency-domain measurement methods and time-domain measurement methods. The frequency-domain measurement method is easy to implement and is characterized in that the frequency range of the excitation signal is selected and different frequency points are determined, and the excitation signals of different frequency points are used sequentially. Perform frequency sweep measurement, analyze the amplitude and phase of the excitation and response signals at the same frequency to obtain the frequency response characteristics of the system, and finally obtain the electrochemical impedance spectrum. This method is a single frequency point excitation frequency sweep measurement, and the measured data is accurate, but the test time is long. By superimposing sinusoidal signals, the impedance spectrum test time can be greatly shortened, but the wave generation of sinusoidal superposition signals requires complex hardware design, which greatly limits the practical use of this method. Using square wave signal to measure impedance spectrum is relatively easy to implement, but the frequency domain information contained in square wave signal is extremely insufficient, so it is difficult to obtain complete impedance spectrum information. In contrast, the pseudo-random binary sequence has a simple structure, low complexity, short measurement time, and high accuracy. The autocorrelation characteristics are similar to white noise, and the spectrum is distributed in a wide frequency range. It only needs to be injected once to obtain Impedance in a wide frequency range, the time required for testing is greatly reduced, and the results are accurate.

The pseudo-random sequence can inject broadband signals into the battery in a very short time, but the power content of the frequency-domain signal of the pseudo-random sequence is low, and it is easily interfered by measurement noise when measuring impedance. The impedance filter can filter out the interference of noise to the signal to a certain extent, and can be used to smooth the measurement and improve the signal-to-noise ratio. The moving average filter is a good choice, mainly used to suppress the interference of noise to the signal, but the moving average The ability of linear filters is limited, and the filtering effect in the frequency domain is relatively poor. As the signal power and signal-to-noise ratio decrease, the impedance filtering results are very prone to deviations. At present, there are still multi-frequency synthesis signals that cannot be received in all broadband bands. Problems with high signal-to-noise ratio responses.

Contents of the invention

Aiming at the deficiencies of the prior art, the present invention provides a lithium battery broadband impedance spectrum testing method based on the maximum length binary sequence, by injecting the maximum length binary sequence into the lithium battery, and using the data cleaning automatic selection mechanism to filter the three-dimensional data cloud , reduce noise interference, thereby improving the accuracy and stability of power lithium battery broadband impedance measurement.

In order to achieve the above object, the present invention adopts the following technical solution: a lithium battery broadband impedance spectrum testing method based on a maximum length binary sequence, specifically comprising the following steps:

Step 1. Design a maximum length binary sequence for broadband impedance measurement;

Step 2. Inject the maximum length binary sequence into the lithium battery through the battery management system, collect the terminal voltage and current of the lithium battery during the injection process, and calculate the measured impedance of the lithium battery at different frequencies;

Step 3, using the power spectral density characteristics of the excitation signal and the real and imaginary parts of the measured impedance in the frequency domain to establish a three-dimensional data cloud;

Step 4. Filtering the data points in the three-dimensional data cloud by establishing an automatic selection mechanism for data cleaning based on statistics to obtain a lithium battery broadband impedance spectrum curve.

Further, the maximum length binary sequence is generated by a multi-stage linear feedback shift register, and the sequence is determined by the length N _L and the resolution f _r , wherein, the length N _L of the maximum length binary sequence is: N _L =2 ^w − 1. w is the order of the shift register, and the resolution f _r satisfies: f _r = f _c /N _L , f _c is the clock frequency of the maximum length binary sequence.

Further, the calculation process of the measured impedance is:

为第k个频率下的阻抗，V(k)为锂电池端电压v(t)的傅里叶变化，I(k)为锂电池端电流i(t)的傅里叶变化：

n为变换点数，j代表复平面上的虚数。in,

is the impedance at the kth frequency, V(k) is the Fourier change of the lithium battery terminal voltage v(t), and I(k) is the Fourier change of the lithium battery terminal current i(t):

n is the number of transformation points, and j represents the imaginary number on the complex plane.

Further, the kth frequency is kf _k , f _k =f _s /N _s , where f _s is the sampling frequency, and N _s is the number of sampled data.

Further, the calculation process of the power spectral density P _{MLBS_k} (f _n ) is:

a为加权系数，N_L为最大长度二进制序列的长度，n为变换点数，P_MLBS(f₁)为傅里叶变换后最大长度二进制序列在频率f₁处的幅值。Among them, I _MLBS (f _n ) is the amplitude of the maximum length binary sequence at frequency f _n after Fourier transform,

a is the weighting coefficient, N _L is the length of the maximum length binary sequence, n is the number of transformation points, P _MLBS (f ₁ ) is the amplitude of the maximum length binary sequence at frequency f ₁ after Fourier transform.

Further, step 4 includes the following sub-steps:

Step 401. Divide all three-dimensional data clouds into three groups according to the high, middle and low frequency ranges. Each group of data points forms a field, traverse all data points in each field, and calculate the average Euclidean value between the remaining data points in each field and this data point. distance

的均值

和方差Δ[d_k]，根据正态分布概率密度曲线，利用均值和方差组成公式

计算阀值，将每个领域内平均欧氏距离大于阀值的数据点滤除，得到锂电池宽频阻抗谱曲线，其中，N_g为三维数据云的分组数。Step 402, calculating the average Euclidean distance in each field in step 401

mean of

and variance Δ[d _k ], according to the normal distribution probability density curve, using the mean and variance to form the formula

Calculate the threshold value, filter out the data points whose average Euclidean distance in each field is greater than the threshold value, and obtain the lithium battery broadband impedance spectrum curve, where N _g is the grouping number of the three-dimensional data cloud.

Further, the rule for dividing the three-dimensional data cloud into three groups in step S401 is: the low frequency range is [0.21Hz, 10Hz], the middle frequency range is [10Hz, 1kHz], and the high frequency range is [1kHz, 3.5kHz].

的计算过程为：Further, the average Euclidean distance between the other data points in each field and the data point

The calculation process is:

Among them, m is the number of points in the field, u is the index of m, (x _k , y _k , z _k ) is a data point in the field, x _k represents the real part of the measured impedance at the kth frequency, y _k represents the imaginary part of the measured impedance at the kth frequency, z _k represents the power spectral density of the measured impedance at the kth frequency; (x _u , y _u , z _u ) are the remaining data points in the field, x _u represents the The real part of the measured impedance at the u frequency, y _u represents the imaginary part of the measured impedance at the uth frequency, z _u represents the power spectral density of the measured impedance at the uth frequency.

的均值

计算过程为：

所述每个领域内平均欧氏距离

的方差Δ[d_k]计算过程为：

其中，m为领域中的点数，k为m的索引。Further, the average Euclidean distance in each field

mean of

The calculation process is:

The average Euclidean distance within each field

The calculation process of the variance Δ[d _k ] is:

where m is the number of points in the domain and k is the index of m.

Compared with the prior art, the present invention has the following beneficial effects: the present invention is based on the maximum-length binary sequence lithium battery broadband impedance spectrum testing method, by injecting the maximum-length binary sequence, and adopting a three-dimensional cloud data cleaning method to filter the measurement results, Therefore, the rapid measurement of the broadband impedance of the lithium battery can be realized. The power spectral density reflects the power of the signal at different frequencies. A large power spectral signal indicates that more power is injected into the battery, which can resist noise interference, while a signal with a lower power spectral density contains less information and becomes an effective signal. The probability of the value is low, combining the power spectral density with the battery impedance, removing the impedance with a lower power spectral density, can obtain an accurate and effective battery impedance spectrum curve. In addition, the maximum length binary sequence proposed by the present invention is a deterministic periodic signal, which can weaken noise interference by increasing the number of cycles. Compared with pulse signals, the maximum length sequence has a lower excitation amplitude intensity, and the lithium battery has a lower impact on the disturbance. The amplitude is more sensitive, the smaller the amplitude of the excitation signal, the higher the test accuracy, and the application of the maximum length binary sequence can better exert its characteristics and advantages.

Description of drawings

The accompanying drawings are used to provide a further understanding of the present invention, and constitute a part of the description, and are used together with the specific implementation to explain the present invention, but do not constitute a limitation to the present invention.

Fig. 1 is the flow chart of the present invention based on the lithium battery broadband impedance spectrum test method based on the maximum length binary sequence;

Fig. 2 is the original impedance spectrum Nyquist figure of the lithium battery injected into the maximum length binary sequence of the embodiment;

Fig. 3 is the power spectral density diagram of the lithium battery injected into the maximum length binary sequence of the embodiment;

Fig. 4 is the three-dimensional data nephogram of lithium battery impedance in the embodiment;

Fig. 5 is a schematic diagram of a three-dimensional data cloud cleaning with _Ng = 1 in the automatic selection mechanism of data cleaning based on statistics;

Fig. 6 is a schematic diagram of secondary three-dimensional data cloud cleaning with _Ng =3 in the automatic selection mechanism of data cleaning based on statistics;

FIG. 7 is a comparison chart of broadband impedance tests of the embodiment and the comparative example at an ambient temperature of 25° C. and a lithium battery with a 50% state of charge.

detailed description

The technical solutions of the present invention will be described in detail below in conjunction with the drawings and embodiments. It should be understood that the specific embodiments mentioned here are only used to illustrate and explain the technical solutions of the present invention, and do not constitute limitations of the present invention.

Figure 1 is a flow chart of the lithium battery broadband impedance spectrum testing method based on the maximum length binary sequence of the present invention, the lithium battery broadband impedance spectrum testing method specifically includes the following steps:

Step 1. Design a maximum-length binary sequence for broadband impedance measurement. The maximum-length binary sequence is a deterministic periodic signal, and noise interference can be weakened by increasing the number of cycles. Compared with pulse signals, the maximum-length sequence excitation amplitude The value intensity is lower, the lithium battery is more sensitive to the disturbance amplitude, the smaller the excitation signal amplitude, the higher the test accuracy;

Among the present invention, the maximum length binary sequence is produced by a multi-stage linear feedback shift register, and the sequence is determined by the length N _L and the resolution f _r , wherein, the length N _L of the maximum length binary sequence is: N _L = ^2w -1, w is the order of the shift register, and the resolution f _r satisfies: f _r =f _c /N _L , f _c is the clock frequency of the maximum length binary sequence.

Step 2. Inject the maximum length binary sequence into the lithium battery through the battery management system, collect the terminal voltage and current of the lithium battery during the injection process, and calculate the measured impedance of the lithium battery at different frequencies;

The calculation process of measuring impedance among the present invention is:

为第k个频率下的阻抗，V(k)为锂电池端电压v(t)的傅里叶变化，I(k)为锂电池端电流i(t)的傅里叶变化：

n为变换点数，j代表复平面上的虚数；本发明中第k个频率为kf_k，f_k＝f_s/N_s，其中，f_s为采样频率，N_s为采样数据个数。in,

is the impedance at the kth frequency, V(k) is the Fourier change of the lithium battery terminal voltage v(t), and I(k) is the Fourier change of the lithium battery terminal current i(t):

n is the number of transformation points, j represents the imaginary number on the complex plane; in the present invention, the kth frequency is kf _k , f _k =f _s /N _s , where f _s is the sampling frequency, and N _s is the number of sampled data.

Step 3. In the frequency domain, use the power spectral density characteristics of the excitation signal and the real and imaginary parts of the measured impedance to establish a three-dimensional data cloud; the power spectral density reflects the power of the signal at different frequencies, and a large power spectral signal represents a more More power is injected into the battery, which can resist noise interference, and the signal with lower power spectral density contains less information, and the possibility of becoming an effective value is lower. The power spectral density is combined with the battery impedance to remove the power spectral density. With lower impedance, accurate and effective battery impedance spectrum curve can be obtained.

The calculation process of power spectral density P _{MLBS_k} (f _n ) in the present invention is:

a为加权系数，N_L为最大长度二进制序列的长度，n为变换点数，P_MLBS(f₁)为傅里叶变换后最大长度二进制序列在频率f₁处的幅值。Among them, I _MLBS (f _n ) is the amplitude of the maximum length binary sequence at frequency f _n after Fourier transform,

a is the weighting coefficient, N _L is the length of the maximum length binary sequence, n is the number of transformation points, P _MLBS (f ₁ ) is the amplitude of the maximum length binary sequence at frequency f ₁ after Fourier transform.

Step 4. Filter the data points in the three-dimensional data cloud by establishing an automatic selection mechanism for data cleaning based on statistics to obtain a lithium battery broadband impedance spectrum curve, which can reduce noise interference and improve the accuracy and stability of power lithium battery broadband impedance measurement Specifically, it includes the following sub-steps:

其中，m为领域中的点数，u为m的索引，(x_k，y_k，z_k)为领域中某一数据点，x_k表示第k个频率下量测阻抗的实部，y_k表示第k个频率下量测阻抗的虚部，z_k表示第k个频率下量测阻抗的功率谱密度；(x_u，y_u，z_u)为领域中剩余数据点，x_u表示第u个频率下量测阻抗的实部，y_u表示第u个频率下量测阻抗的虚部，z_u表示第u个频率下量测阻抗的功率谱密度。本发明中将三维数据云分成三组的规则是：低频率范围为[0.21Hz,10Hz],中频范围为[10Hz,1kHz],高频范围为[1kHz,3.5kHz]；Step 401. Divide all three-dimensional data clouds into three groups according to the high, middle and low frequency ranges. Each group of data points forms a field, traverse all data points in each field, and calculate the average Euclidean value between the remaining data points in each field and this data point. distance

Among them, m is the number of points in the field, u is the index of m, (x _k , y _k , z _k ) is a data point in the field, x _k represents the real part of the measured impedance at the kth frequency, y _k represents the imaginary part of the measured impedance at the kth frequency, z _k represents the power spectral density of the measured impedance at the kth frequency; (x _u , y _u , z _u ) are the remaining data points in the field, x _u represents the The real part of the measured impedance at the u frequency, y _u represents the imaginary part of the measured impedance at the uth frequency, z _u represents the power spectral density of the measured impedance at the uth frequency. The rules for dividing the three-dimensional data cloud into three groups in the present invention are: the low frequency range is [0.21Hz, 10Hz], the middle frequency range is [10Hz, 1kHz], and the high frequency range is [1kHz, 3.5kHz];

的均值

和方差Δ[d_k]，根据正态分布概率密度曲线，利用均值和方差组成公式

计算阀值，将每个领域内平均欧氏距离大于阀值的数据点滤除，得到锂电池宽频阻抗谱曲线，其中，N_g为三维数据云的分组数；本发明中每个领域内平均欧氏距离

的均值

计算过程为：

所述每个领域内平均欧氏距离

的方差Δ[d_k]计算过程为：

其中，m为领域中的点数，k为m的索引。Step 402, calculating the average Euclidean distance in each field in step 401

mean of

and variance Δ[d _k ], according to the normal distribution probability density curve, using the mean and variance to form the formula

Calculate the threshold value, filter out the data points whose average Euclidean distance is greater than the threshold value in each field, and obtain the lithium battery broadband impedance spectrum curve, wherein, N _g is the grouping number of three-dimensional data cloud; Average in each field in the present invention Euclidean distance

mean of

The calculation process is:

The average Euclidean distance within each field

The calculation process of the variance Δ[d _k ] is:

where m is the number of points in the domain and k is the index of m.

Example

In this embodiment, taking a 18650NMC-based lithium battery with a rated capacity of 3Ah and a voltage range of 2.0V-4.25V, and a signal sampling frequency of 70kHz as an example, the lithium battery broadband impedance spectrum test based on the maximum length binary sequence of the present invention is used. method to obtain the broadband impedance spectrum curve.

Figure 2 is the Nyquist diagram of the original impedance spectrum of the lithium battery injected with the maximum length binary sequence in this embodiment. As shown in Figure 2, the high frequency region of the impedance spectrum of the lithium battery is polluted by noise, and the shape of the normal impedance is only visible in the low frequency range , it is difficult to directly obtain the effective impedance spectrum. Figure 3 is the power spectral density diagram of the lithium battery injected with the maximum length binary sequence in this embodiment, as shown in Figure 3, the power spectral density of the maximum length binary sequence gradually decays with the increase of frequency, and the power spectral density is between similar frequencies A large power spectral density signal indicates that more power is injected into the battery. The power spectral density information and the real and imaginary parts of the measured impedance are used to build a three-dimensional data cloud for further data cleaning. Fig. 4 is the three-dimensional data cloud diagram of the lithium battery impedance in this embodiment, the sparseness of the three-dimensional cloud diagram shows the power spectrum intensity of each measured impedance, and the impedance calculation result is processed by using the power spectral density of the data points in the three-dimensional data cloud, As shown in Figure 4, the bright spots in the grayscale image have higher power than the dark spots, and most of the dark spots deviate from the main data set, and are more likely to be outliers measured by EIS, while those with high power spectral intensity The bright spots are concentrated in the middle of the dataset, consistent with the basic shape of the impedance spectrum. Figure 5 is a schematic diagram of a three-dimensional cloud data cleaning with N _g = 1 in the automatic selection mechanism of data cleaning based on statistics. It can be seen from Figure 5 that the result of cleaning all the data points in the three-dimensional data cloud is not ideal. The reference value is a smooth curve. In contrast, the curve after cleaning the 3D cloud data still has a lot of useless impedance information. In order to clean up the data more efficiently, the data points in the 3D data cloud are divided into three groups according to the frequency range characteristics, as shown in Figure 6, which is a schematic diagram of the secondary 3D cloud data cleaning with N _g = 3 in the automatic selection mechanism for data cleaning based on statistics. As shown in Figure 6, after all the data points in the 3D data cloud are divided into 3 groups for cleaning, only 102 useful points remain, indicating that the noise data and the measurement of low power spectral density have been effectively removed after the 3D cloud cleaning. value.

comparative example

In this embodiment, an 18650NMC-based lithium battery with a rated capacity of 3Ah and a voltage range of 2.0V-4.25V is taken as an example, and the signal sampling frequency is 70kHz.

Step 1: Design a maximum length binary sequence for broadband impedance measurement;

Step 2: Inject the maximum length binary sequence designed in step 1 into the 18650NMC-based lithium battery through the battery management system, collect the terminal voltage and current at both ends of the battery during the signal injection, and calculate the measured impedance of the lithium battery at different frequencies;

Step 3: In the frequency domain, the measured impedance is filtered by a sliding average window filtering method to obtain a broadband impedance spectrum curve.

Figure 7 is a comparison chart of the broadband impedance test of the embodiment and the comparative example at an ambient temperature of 25°C and a battery with a 50% state of charge. Compared with the sliding average window filtering method, the filtering method proposed by the present invention is significantly closer to the reference value. Although the method of the present invention has some offsets in the low-frequency region, no outliers are found in the impedance spectrum shown in Figure 7. In contrast, the sliding average window filtering method has a large error, and there are multiple anomalies in the middle and high frequencies value.

The above are only preferred implementations of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions under the idea of the present invention belong to the protection scope of the present invention. It should be pointed out that for those skilled in the art, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims (9)

1. A lithium battery broadband impedance spectrum testing method based on maximum length binary sequence, is characterized in that, specifically comprises the steps: Step 1. Design a maximum length binary sequence for broadband impedance measurement; Step 2. Inject the maximum length binary sequence into the lithium battery through the battery management system, collect the terminal voltage and current of the lithium battery during the injection process, and calculate the measured impedance of the lithium battery at different frequencies; Step 3, using the power spectral density characteristics of the excitation signal and the real and imaginary parts of the measured impedance in the frequency domain to establish a three-dimensional data cloud; Step 4. Filtering the data points in the three-dimensional data cloud by establishing an automatic selection mechanism for data cleaning based on statistics to obtain a lithium battery broadband impedance spectrum curve. 2. a kind of lithium battery broadband impedance spectrum test method based on the maximum length binary sequence according to claim 1, is characterized in that, described maximum length binary sequence is produced by multistage linear feedback shift register, and this sequence is by length N _L and the resolution f _r are determined, wherein the length N _L of the maximum length binary sequence is: N _L =2 ^w -1, w is the order of the shift register, and the resolution f _r satisfies: f _r =f _c /N _L , f _c is the clock frequency of the maximum length binary sequence. 3. a kind of lithium battery broadband impedance spectrum testing method based on the maximum length binary sequence according to claim 1, is characterized in that, the calculation process of described measurement impedance is:

in,

is the impedance at the kth frequency, V(k) is the Fourier change of the lithium battery terminal voltage v(t), and I(k) is the Fourier change of the lithium battery terminal current i(t):

n is the number of transformation points, and j represents the imaginary number on the complex plane. 4. A lithium battery broadband impedance spectrum testing method based on a maximum length binary sequence according to claim 3, wherein the kth frequency is kf _k , f _k =f _s /N _s , wherein, f _s is the sampling frequency, and N _s is the number of sampled data. 5. a kind of lithium battery broadband impedance spectrum testing method based on maximum length binary sequence according to claim 1, is characterized in that, the calculation process of described power spectral density P _{MLBS_k} (f _n ) is:

Among them, I _MLBS (f _n ) is the amplitude of the maximum length binary sequence at frequency f _n after Fourier transform,

a is the weighting coefficient, N _L is the length of the maximum length binary sequence, n is the number of transformation points, P _MLBS (f ₁ ) is the amplitude of the maximum length binary sequence at frequency f ₁ after Fourier transform. 6. A kind of lithium battery broadband impedance spectrum testing method based on maximum length binary sequence according to claim 1, is characterized in that, step 4 comprises following sub-steps: Step 401. Divide all three-dimensional data clouds into three groups according to the high, middle and low frequency ranges. Each group of data points forms a field, traverse all data points in each field, and calculate the average Euclidean value between the remaining data points in each field and this data point. distance

Step 402, calculating the average Euclidean distance in each field in step 401

mean of

and variance Δ[d _k ], according to the normal distribution probability density curve, using the mean and variance to form the formula

Calculate the threshold value, filter out the data points whose average Euclidean distance in each field is greater than the threshold value, and obtain the lithium battery broadband impedance spectrum curve, where N _g is the grouping number of the three-dimensional data cloud. 7. A lithium battery broadband impedance spectrum testing method based on a maximum length binary sequence according to claim 6, wherein the rule for dividing the three-dimensional data cloud into three groups in step S401 is: the low frequency range is [0.21Hz ,10Hz], the middle frequency range is [10Hz, 1kHz], and the high frequency range is [1kHz, 3.5kHz]. 8. A lithium battery broadband impedance spectrum testing method based on a maximum length binary sequence according to claim 6, wherein the average Euclidean distance between the remaining data points and the data point in each field

The calculation process is:

Among them, m is the number of points in the field, u is the index of m, (x _k , y _k , z _k ) is a data point in the field, x _k represents the real part of the measured impedance at the kth frequency, y _k represents the imaginary part of the measured impedance at the kth frequency, z _k represents the power spectral density of the measured impedance at the kth frequency; (x _u , y _u , z _u ) are the remaining data points in the field, x _u represents the The real part of the measured impedance at the u frequency, y _u represents the imaginary part of the measured impedance at the uth frequency, z _u represents the power spectral density of the measured impedance at the uth frequency. 9. A lithium battery broadband impedance spectrum testing method based on a maximum length binary sequence according to claim 6, wherein the average Euclidean distance in each field is

mean of

The calculation process is:

The average Euclidean distance within each field

The calculation process of the variance Δ[d _k ] is:

where m is the number of points in the domain and k is the index of m.

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