CN103018673B - Method for predicating life of aerospace Ni-Cd storage battery based on improved dynamic wavelet neural network - Google Patents

Abstract

An aerospace Ni-Cd storage battery life prediction method based on an improved dynamic wavelet neural network, implemented as follows: collect all relevant data of aerospace Ni-Cd storage battery life prediction; preprocess data related to life prediction; analyze data correlation; Equivalent data value of discharge end voltage of Ni-Cd battery; improvement of DWNN network; establishment, training and prediction of primary M-DWNN (1M-DWNN) network; adaptive iteration based on secondary M-DWNN (2M-DWNN) network Prediction model establishment, training and prediction; dynamic time window adjustment; the present invention dynamically adjusts the entire DWNN network during the life prediction process to ensure that the prediction accuracy is continuously improved with the extension of time and the increase of data volume throughout the life prediction process.

Description

A Life Prediction Method of Aerospace Ni-Cd Battery Based on Improved Dynamic Wavelet Neural Network

technical field

The invention belongs to the technical field of life prediction of aerospace Ni-Cd accumulators, in particular to a method for predicting the life of aerospace Ni-Cd accumulators based on an improved dynamic wavelet neural network.

Background technique

Life prediction technology involves a wide range of fields and fields, from the fatigue life of raw materials to the life of complex molded products, from the civil field to the national defense field. At present, the main life prediction technologies for aerospace Ni-Cd batteries can be summarized as follows:

a, Life prediction based on physical model: This method analyzes the physical and chemical process inside the Ni-Cd battery, so as to establish a physical model reflecting the evolution process of the object, adjust the model parameters through relevant data, and finally obtain the required life prediction model;

b. Life prediction based on statistical model assumptions: This method first assumes that the life of Ni-Cd batteries obeys a certain statistical distribution, and uses a large number of existing life data to determine the parameters of the model, thereby establishing a life prediction model for Ni-Cd batteries ;

c, Life prediction based on life-influencing factor analysis training: This method mainly studies and determines the various life-influencing factors that affect Ni-Cd batteries, and establishes the correlation between the influencing factors and life with the help of a large number of life test data. Life prediction model for Ni-Cd batteries.

For the above three methods, life prediction based on physical models requires in-depth study of the internal mechanism of Ni-Cd batteries, which has a huge workload and relatively poor portability. For different types of Ni-Cd batteries, life prediction models need to be established separately; Life prediction based on statistical model assumptions and life-influencing factor analysis training requires a large amount of Ni-Cd battery life data to establish a life prediction model. Considering that in practical engineering applications, aerospace Ni-Cd batteries are often limited by various objective conditions, and it is impossible to have a large amount of life data for life prediction. Therefore, it is of great significance to study a life prediction method for Ni-Cd batteries with very little life data.

Artificial Neural Network (ANN) is an artificial network that simulates the structure and function of the nervous system of the brain and is composed of a large number of simple processing units, namely neurons, which are widely connected. It can automatically induce rules from known data, obtain the internal laws of these data, and has a strong nonlinear mapping ability. Artificial neural network has the following outstanding advantages: 1. High degree of parallelism; 2. High degree of non-linear global effect; 3. Good fault tolerance and associative memory function; 4. Very strong self-adaptive and self-learning function.

The applicant previously applied for a patent, application number 20101022095.1, titled: A life prediction method for small sample data objects based on dynamic bipolar MPNN, by collecting all available data of life prediction objects and performing life prediction related data preprocessing on them and data correlation analysis; obtain the functional relationship between these life-influencing factors and the life-span characterization parameters of the predicted object. Then the data is mapped and the equivalent data value of the predicted object is obtained; the training and prediction of the MPNN network and the training and prediction of the MPNN network for the second time are performed through the improved MPNN network; finally, the predicted object is determined according to the end-of-life criterion of the life characteristic parameter of the predicted object lifetime value. This patent realizes battery life prediction based on small sample data through a bipolar MPNN network, and provides a solution to a class of problems with small sample data characteristics, which has strong versatility. Since the core of this patent lies in the prediction accuracy of the primary and secondary MPNN, and the MPNN network is improved from the PNN network with statistical characteristics, the MPNN network retains the advantages of the PNN network and also introduces a problem that cannot be well reflected. Insufficient prediction of battery cell characteristics; in addition, in this patent, the iterative prediction used by the secondary MPNN network is a single-step iterative prediction without repeated training, which makes the battery life prediction accuracy low, and only when the battery is in serious condition The accuracy of life prediction can only be guaranteed during the recession period, which limits the engineering application of battery life prediction to a large extent.

Dynamic wavelet neural network (Dynamic Wavelet Neural Networks, DWNN) is a kind of artificial neural network, which consists of four parts: input, WNN, output, and output feedback, as shown in Figure 2.

Among them, U is the external input, N is the dimension of external input; Y is the output; M is the number of output feedback nodes; WNN is the standard static wavelet neural network. The expression of DWNN is:

Y(t+1)=WNN(Y(t),…,Y(t-M+1),U(t),…,U(t-N))

Since the DWNN network builds network recursion from multiple angles, enhances the memory capacity of historical information, and presents process dynamic characteristics during the calculation process, it has stronger dynamic behavior and calculation capabilities than feedforward neural networks and existing recursive wavelet neural networks, and At the same time, it has the advantages of the ability to distinguish and analyze the overall and individual characteristics of the predicted object, and is widely used in actual engineering projects. On the basis of inheriting patent application 20101022095.1 to solve the idea of life prediction for small sample data objects, the present invention firstly improves DWNN, so that the improved DWNN model can track the decline process of the storage battery more precisely, and at the same time, uses the self-adaptive iterative prediction method to improve The secondary prediction accuracy, and then, greatly improve the battery life prediction accuracy to meet the life prediction requirements of Ni-Cd objects and their data characteristics.

Contents of the invention

The technical problem of the present invention is to overcome the deficiencies of the prior art, and provide a method for predicting the life of an aerospace Ni-Cd storage battery based on an improved dynamic wavelet neural network. On the basis of retaining the advantages of the application number 20101022095.1, on the one hand, through The improvement of the DWNN network with strong resolution and analysis ability for the overall and individual information enables the present invention to have the resolution ability for single prediction objects, and enables the improved DWNN model to track the decline process of the storage battery more precisely; on the other hand , the 2M-DWNN model was constructed by using the adaptive iterative process, so that the accuracy of battery life prediction is well guaranteed; furthermore, on the basis of the integrated M-DWNN model and adaptive iterative model, the accuracy of life prediction is greatly improved, and further overcome The problem of low precision in the application 20101022095.1 was solved.

The overall flow of the aerospace Ni-Cd storage battery life prediction method provided by the present invention is shown in Figure 1, and is specifically realized through the following steps:

Step 1, collect relevant data of life prediction of all Ni-Cd accumulators;

Collect all relevant data available for life prediction by analyzing Ni-Cd batteries and similar products.

Step 2, data preprocessing related to life prediction;

The life prediction data obtained in step 1 is analyzed and screened, and the discharge end voltage parameter data required by the present invention (Ni-Cd storage battery life end criterion in the present invention) and life influencing factor data are extracted, including: discharge current data , charging current data, charge and discharge cycle times and discharge depth data, etc. At the same time, preprocessing work such as singular value elimination and data noise reduction is performed on the screened relevant data.

Step three, data correlation analysis;

Considering the factors affecting the discharge depth and life of similar products and Ni-Cd batteries, it is necessary to perform correlation analysis on the parameters after pretreatment of similar products and Ni-Cd batteries through function approximation or SPSS methods, so as to obtain similar products and Ni-Cd batteries. Correlation between batteries on discharge terminal voltage.

The correlation analysis refers to realizing the correlation analysis of different parameter data through function approximation or using SPSS (Statistical Product and Service Solutions), so as to obtain the mapping relationship between parameter data.

Step 4, data mapping and obtaining the equivalent data value of the final discharge voltage of the Ni-Cd storage battery;

Using the relationship between the similar products obtained in step 3 and the end-of-discharge voltage of Ni-Cd batteries under the influence of various life-influencing factors, based on the data of the end-of-discharge voltage of the referenced similar products, map and obtain the Ni-Cd The equivalent data value of the final discharge voltage of the battery is shown in Figure 4 as the "equivalent-EoDV" curve, where the dotted curve indicates that the Ni-Cd battery has on-orbit end-of-discharge voltage (EoDV) data; the solid curve is the same as the on-orbit EoDV curve The equivalent discharge end voltage (ED-EoDV) curve under the condition of some of the same influencing factors.

Step 5. Improvement of DWNN network (M-DWNN);

According to the requirements of aerospace Ni-Cd storage battery life prediction accuracy, DWNN is improved, and the improvement plan is as follows: use the DWNN output data sequence {Yi} to build an AR model (in this invention: {Yi} is {EoDV_orbi}), including determining the AR model The order p and the coefficient a _i , i=0,1,2,...,p-1, furthermore, the order of the AR model is taken as the number of feedback nodes of the DWNN model, that is, M=p, and the coefficient of the AR model is taken as each feedback node The weight coefficient is used as the input of the WNN model, and then the improvement of the DWNN network model is completed. Wherein, the corresponding relationship between AR model coefficients and nodes is: a _i ·Y(ti), i=0, 1, 2, . . . , p-1, as shown in FIG. 5 .

Step 6. Establishment, training and prediction of an M-DWNN (1M-DWNN) network;

According to the analysis of influencing factors and the results of correlation analysis, the number of input nodes of 1M-DWNN is determined, and the output is the final discharge voltage of the treated Ni-Cd battery (single output). Use the Ni-Cd battery on-rail EoDV and the ED-EoDV obtained from step 4 to do differential proportional processing, as shown in Figure 4, to construct the training samples and test samples of 1M-DWNN. In order to eliminate the singular values in the training samples and speed up the convergence speed of the network, the input vector and target vector constructed above are normalized, and then input into the 1M-DWNN network for training, so as to determine the parameters of the 1M-DWNN network, and The trained 1M-DWNN network is used for prediction, and the predicted value of the final discharge voltage of the Ni-Cd battery is obtained through the process of inverse normalization and inverse difference, and then the data segment a-e of the final discharge voltage prediction result is obtained using the O-c segment curve as a reference.

Step 7. Establishment, training and prediction of an adaptive iterative prediction model based on the secondary M-DWNN (2M-DWNN) network;

Determine the number of 2M-DWNN input nodes and output nodes (single output). Using the preprocessed Ni-Cd battery discharge end voltage data and the discharge end voltage prediction results of 1M-DWNN, the training and test samples of 2M-DWNN are constructed, that is, adaptive iterative prediction. The process is shown in Figure 6. Then carry out prediction work, and finally determine the life value of Ni-Cd battery according to the end of life criterion of Ni-Cd battery.

Among them, the adaptive iterative prediction model is described as follows:

(1) Data preparation for adaptive iterative forecasting (mean-slope time series construction)

The iterative prediction model in the present invention performs segmental mean value processing on the final discharge voltage value of the o-e segment, and on this basis, calculates the slope of the mean value, and the second M-DWNN prediction is the self-adaptive iteration of the mean value-slope time series Forecasting, Figure 7 shows the mean-slope sequence generation plot.

$\mathrm{the\; s}\left(k\right)=\frac{\mathrm{Avr}(k+1)-\mathrm{Avr}\left(k\right)}{\mathrm{Avr}\left(k\right)}$ (k=1,2,…,n-1)

$\mathrm{<span\; class="notranslate">\; Avr</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; interval</span>}}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; interval</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; interval</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>$

(j=1,2,…,n;n=fix(N/interval)) Equ.1

Among them, { _xi } represents the EoDV value sequence, the length is N, interval is the mean interval, {Avr(j)} is the mean value sequence, the length is n, {s(k)} is the mean-slope sequence, the length is n- 1,

The follow-up content starting from step (2) takes the {s(k)} mean-slope sequence as the object, and describes the core content of the adaptive iterative forecasting method.

(2) Adaptive iterative process

After the mean-slope time series is constructed by step (1), the core content of adaptive iterative prediction is started, and the specific method is as follows:

(2.1) Adaptive time series data resampling

For a given time series {A ⁱ _j } of length n, where i, j respectively represent the number of iterative predictions of the original time series and the resampling interval of the time series, then A ⁰ ₁ :={s(k)}=s ₁ ,s ₂ ,s ₃ ,…,s _k ,…,s _n-1 ,s _n represent the original data, the number of iterated predictions is 0, and the time series sampling interval is defined as 1, where ':=' means the definition is'; and A ¹ ₂ represents the time series data with a resampling interval of 2 after an iterative forecast. According to the requirement of 2M-DWNN network training sample size, resample from A ⁰ ₁ at equal intervals to obtain a new time series:

A ⁰ _j : S _n-(jn-3),*j '...,S _n-(i+1)*j ,S _ni*j ,...,S _n-2*j ,S _nj ,S _n

[j=1,2,3,...,jmax,n-(j _n -1)*j≥1, j _n ≥Sample_size_min]

Among them: n is the length of the original time series A ⁰ ₁ ; A ⁰ _j means that the time series is obtained with a resampling interval of j, and the sampling starts from the last data (s _n ) of the original data; j _n means the time series A ⁰ _j and satisfy: n-(j _n -1)*j≥1, and j _n decreases with the increase of j. Assuming that the minimum required sample size for 2M-DWNN network training is Sample_size_min, then j _n should satisfy j _n ≥ Sample_size_min. Let j _max =fix(n/(Sample_size_min)) be the maximum value of j, where fix means rounding down. This completes the adaptive resampling process.

(2.2) Single-step forecasting of adaptively resampled time series data

Using the idea of single-step forecasting, the 2M-DWNN model is constructed respectively (the construction idea is the same as that of 1M-DWNN, and both adopt the fixed order and coefficient weight method based on the AR model), and perform single-step forecasting on the time series data obtained by resampling. The one-step forecast value of A ⁰ _j can be obtained, and then the new time series A ⁰ _j ′ can be expressed as:

…,S _n-(i+1)*j ,S _ni*j ,…,S _n-2*j ,S _nj ,S _n ,S′ _n+j

(j=1,2,3,...jmax)

The same process completes all A ⁰ _j time series, where j=1,2,3,...,j _max . In this way, an iterative process is completed, and j _max predicted values are obtained, and the new time series formed can be expressed as:

A ₁ ¹ :S ₁ ,S ₂ ,…,S _n-1 ,S _n ,S′ _n+1 ,S′ _n+2 ,…,S′ _n+jmax

The first two steps realize the new time series A ¹ ₁ after obtaining j _max predicted values from any time series A ⁰ ₁ , and then complete an iterative forecasting process. When A ¹ ₁ is used to replace the original data A ⁰ ₁ and the above process is repeated, A ² ₁ , A ³ ₁ ,…,A ^k ₁ ,… can be obtained through such iterations.

(3) Inverse transformation of adaptive prediction iterative data results and judgment of Ni-Cd life value

Through the iterative process, an infinite number of mean-slope sequences A ^k ₁ can be obtained. In order to finally determine the life of the battery, it is necessary to inversely transform the predicted mean-slope sequence A ^k ₁ and obtain the end-of-discharge voltage of the Ni-Cd battery Sequence {x′ _i }, which contains the existing on-orbit discharge final voltage data, 1M-DWNN prediction result data and 2M-DWNN iterative prediction result data. Based on {x' _i } sequence, the predicted value of remaining life of Ni-Cd battery is determined by battery life criterion.

Step 8, dynamic time window adjustment;

In the process of using M-DWNN to predict Ni-Cd battery, due to the passage of time, new data will be continuously obtained. At this time, it is necessary to dynamically (every N days is an adjustment period, and N is determined according to actual needs) repeat the above steps 2 to 7 to rebuild and train the M-DWNN network (including 1M-DWNN and 2M-DWNN models) to update Network parameters are re-predicted to ensure that the prediction accuracy will continue to improve as the on-orbit operation time increases.

Explanation: In the early stage of life prediction, the performance of the system is stable, so the final discharge voltage changes slowly in a long period of time. During this period, the 'dynamic adjustment time window' for network training can be appropriately relaxed, such as half a month or one month. As the prediction progresses, the performance of the system begins to decline gradually, and the time window width of life prediction should be appropriately reduced (eg: one week), so as to obtain the remaining life value of the battery in a more timely and accurate manner.

The advantage of the present invention compared with prior art is:

(1) DWNN has the ability to distinguish and analyze the overall and individual characteristics of the predicted object, so that the present invention can effectively combine the information of the battery cell and the overall information, and provide accurate battery life prediction results;

(2) Improve the DWNN, so that the improved DWNN model can track the decline process of the battery more precisely, so as to ensure the accuracy of the prediction in terms of model establishment;

(3) The adaptive iterative technology adopted has the ability to perform iterative prediction adaptively based on the actual data, which improves the accuracy of the secondary prediction;

(4) The comprehensive prediction model including 1M-DWNN and 2M-DWNN proposed by the present invention greatly improves the life prediction accuracy on the whole, especially when the battery is not in a severe recession, the battery life prediction accuracy can be improved by about One order of magnitude.

Description of drawings

Figure 1 is a flow chart of aerospace Ni-Cd battery life prediction;

Fig. 2 is existing classical dynamic wavelet neural network model diagram;

Figure 3 is the logic diagram of life prediction control of aerospace Ni-Cd battery based on improved DWNN;

Fig. 4 is the schematic diagram of the establishment process of the aerospace Ni-Cd storage battery life prediction model in the present invention;

Fig. 5 is an improved dynamic wavelet neural network model diagram;

Fig. 6 is the flowchart of adaptive iterative prediction in the present invention;

Fig. 7 is mean value-slope sequence generation figure;

Figure 8 is a graph of the original data of the final discharge voltage;

Figure 9 is a data diagram of the end-of-discharge voltage after abnormal value processing and noise reduction;

Figure 10 is a structural diagram of the 1M-DWNN model;

Figure 11 is a curve diagram of 1M-DWNN prediction test accuracy;

Fig. 12 is a Ni-Cd accumulator battery discharge end-voltage decay prediction curve based on the 1M-DWNN model;

Figure 13 is a graph of the comprehensive M-DWNN prediction results including the prediction results of the 2M-DWNN model.

Detailed ways

The present invention will be described in detail below in conjunction with the accompanying drawings and embodiments.

The present invention is a life prediction method for aerospace Ni-Cd storage battery based on improved dynamic wavelet neural network. The life prediction method is a non-parametric method, and the method improves the existing DWNN network to obtain M-DWNN Network, after the analysis and preprocessing of the Ni-Cd battery data, use the processed data to form the training set and test set of the 1M-DWNN network, after training and learning, use the 1M-DWNN network to predict and supplement historical data samples; After completing these tasks, the 2M-DWNN network can be used to carry out iterative life prediction work, and finally the Ni-Cd accumulator life value is determined according to the end-of-life criterion. Fig. 1 shows the overall flow chart of the life prediction method of the present invention, and Fig. 3 It is the logic diagram of life prediction control, and the specific implementation steps are as follows:

Step 1, collecting all available life prediction related data for Ni-Cd storage battery life prediction;

Through the analysis of aerospace Ni-Cd battery and its similar products, all available life prediction related data are collected. Including: temperature, charging current, discharging current, discharging power, load current data, charging power, remaining power, voltage, charge-discharge ratio and other parameter data; for solar cell arrays, the available data are: temperature, square array current data, load Current data, power, bus voltage, booster output voltage and other parameter data.

The similar product refers to a product that is similar or identical to Ni-Cd storage battery in terms of physical structure, logical structure and functional structure.

Step 2, data preprocessing related to life prediction;

The data related to life prediction obtained in step 1 are analyzed and screened, the end-of-discharge data of Ni-Cd batteries and life-influencing factors are extracted, and the life-influencing factors are classified.

The end-of-discharge voltage (EoDV) and parameter data of the Ni-Cd storage battery are as follows:

(1) The full-life data of the end-of-discharge voltage (EoDV_sim) of similar products, that is, the historical time series data from the beginning of use of similar products to the end of the life of similar products, and the time series data can be expressed as: {EoDV_simi};

(2) The incomplete life data of the end-of-discharge voltage (EoDV_orb) of the Ni-Cd battery on orbit, that is, all the time-series data from the Ni-Cd battery to the present. The time-series data can be expressed as: {EoDV_orbi} .

The life-influencing factors and life-influencing factor data can be divided into the following two categories:

(1) Time-series life-influencing factor data: In the present invention, the data of life-influencing factors having the same time scale as the final discharge voltage of Ni-Cd battery, these influencing factor data include: charging current data (Charge Current: CC), discharging current ( Discharge Current: DC), the number of charge-discharge cycles, the data of life-influencing factors include the full-life data of similar product life-influencing factors and the existing time series data of on-orbit Ni-Cd battery life-influencing factors, and the data of similar product data The composition and expression are similar to those of the on-orbit Ni-Cd battery discharge terminal voltage and life-span influencing factors, which can be divided into: similar product charging current, similar product discharge current, similar product charge-discharge cycle data, and on-orbit Ni-Cd battery charging Current, on-rail Ni-Cd battery discharge current, on-rail Ni-Cd battery charge and discharge cycle times;

(2) Data adjustment of life-influencing factor data: different from time-series life-influencing factor data, this type of influencing factor data is a limited number of data pairs, these data pairs are historical data of similar products, and reflect the corresponding life-influencing factor parameters with the same Correspondence between life spans. It is used to locally adjust Ni-Cd battery discharge terminal voltage (EoDV_sim, EoDV_orb), charge current data (Charge Current: CC), discharge current (Discharge Current: DC) and other timing data. For Ni-Cd batteries, the depth of discharge is such a life-influencing factor. When the depth of discharge (Depth of Discharge: DOD) is 17%, the corresponding life value is 20,000 charge-discharge cycles, thus forming a Data pairs (17%-20000).

After completing the classification of life-influencing factors, the discharge end voltage data (EoDVi: including similar products (EoDV_simi) and on-orbit Ni-Cd battery discharge end voltage data (EoDV_orbi)), charging current data, and discharge current data of the above-mentioned Ni-Cd batteries , depth of discharge (including similar products and on-orbit data) for singular value elimination, data noise reduction preprocessing, and then get preprocessed data {EoDV_p_simi}, {EoDV_p_orbi}, {CC_p_simi}, {CC_p_orbi}, {DC_p_simi} , {DC_p_orbi}, {C_simi}, {C_orbi}, {DOD_simi}, {DOD_orbi}. In the process of life prediction, the life-influencing factor data of Ni-Cd battery and the operation of these data in the prediction process must correspond to the life-influencing factor data and operation of similar products.

Step three, data correlation analysis;

Use SPSS to conduct correlation analysis on the data of factors affecting the life of discharge depth screened in step 2, so as to obtain the functional relationship f between these factors affecting life and the end-of-discharge data of the Ni-Cd battery.

Step 4, data mapping and obtaining the equivalent time series data value of the forecast object;

Using the correlation f between similar products and Ni-Cd batteries obtained in step 3 on the end-of-discharge voltage, based on the end-of-discharge data of similar products, map and obtain the equivalent end-of-discharge data of the end-of-discharge voltage of Ni-Cd batteries {EDEoDVi}, as shown in the solid line 'Equivalent-EoDV' in Figure 4.

Step 5. Improvement of DWNN network (M-DWNN);

Taking the time-series data {EoDV_p_orbi} of the final discharge voltage of the on-orbit battery as the data object, construct the AR model, determine the AR model order p and the coefficient a _i , i=0,1,2,...,p-1, that is, set M=p, The coefficients of the AR model are used as the weight coefficients of each feedback node and input as the WNN model, and then the improvement of the DWNN network model is completed. The corresponding relationship between the coefficients of the AR model and the nodes is: a _i Y(ti), i=0 ,1,2,…,p-1, as shown in Figure 5. Both 1M-DWNN and 2M-DWNN need to build AR models separately to improve DWNN. Among them, 1M-DWNN needs to build an AR model, and 2M-DWNN needs to build j _max AR models in each iteration process, and the establishment process is based on the available on-orbit discharge final voltage data (for iterative prediction, its Time series data are existing and predicted mean-slope series). The meaning of j _max is defined by step seven (2.1) of the summary of the invention.

Step 6. Establishment, training and prediction of an M-DWNN (1M-DWNN) network;

The final discharge point voltage {EoDV_p_orbi} of the Ni-Cd battery obtained in step 2 and the equivalent data value {ED-EoDVi} of the Ni-Cd battery obtained in step 4 are differentially processed and output as a 1M-DWNN network. Perform differential proportional processing on the time-series life-influencing factor data (including charging current, discharge point current, and number of charge-discharge cycles of similar products and on-rail Ni-Cd batteries) obtained from step 2, and use it as the input parameter of the 1M-DWNN network, so far , to construct the input vector and target vector of the 1M-DWNN network.

In order to eliminate the singular values in the training samples and speed up the convergence of the network, the input vector and target vector constructed above are normalized; then input into the 1M-DWNN network for training; finally, use the trained 1M- DWNN neural network predicts life index parameters. After denormalization and reverse difference, the predicted value sequence {EoDV_pre_i} of 1M-DWNN is obtained. The specific process is described as follows:

(1) AR model establishment

The final discharge point voltage {EoDV_p_orbi} of the Ni-Cd battery obtained in step 2 and the equivalent data value {ED-EoDVi} of the Ni-Cd battery obtained in step 4 are subjected to differential proportional processing, and used to establish an AR model, and then, to obtain AR model order p and coefficient {a _i }, the basic expression of AR model is as follows:

AR: Y(t+1)＝a ₀ Y(t)+a ₁ Y(t-1)+…+a _p Y(tp)+e(t)

Among them, e(t) is a white noise signal with a mean value of 0.

(2) 1M-DWNN differential proportional input/output

As shown in Figure 3, after the analysis of the above steps, the 1M-DWNN of the present invention is a three-input single-output network (the external is three-input, and the number of internal inputs is determined by the order p of the AR model. In the case of no special instructions in this patent, All inputs refer to external inputs), whose inputs can be described as:

1) Differential CC (the difference between the charging current {CC_p_orbi} corresponding to the on-rail EoDV and the charging current {CC_p_simi} corresponding to the EDEoDV curve) (linear normalization);

2) Differential DC (the difference between the discharge current {DC_p_orbi} corresponding to the on-rail EoDV and the discharge current {DC_p_simi} corresponding to the ED-EoDV curve) (linear normalization);

3) Number of cycles (the number of charge and discharge cycles {C_orbi} corresponding to the ED-EoDV curve) (arctangent normalized);

The output is: differential EoDV (difference between on-track {EoDV_p_orbi} and {EoDV_p_simi}) (linear normalization), the specific expression after normalization is:

$<span\; class="notranslate">\; \&DoubleRightArrow;</span>\mathrm{<span\; class="notranslate">\; \&Delta;EoD</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; EoDV</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; orbi</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; ED</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; EoDV</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; EoDV</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; orbi</span>}$

Among them: CC_p_orbi and CC_p_simi represent the discharge current values corresponding to the on-orbit EoDV curve and ED-EoDV curve in the i-th cycle respectively; DC_p_orbi and DC_p_simi represent the on-orbit EoDV curve and ED-EoDV curve in the i-th cycle respectively Corresponding discharge current value; C_orbi is the number of charge and discharge cycles, EoDV_p_orbi and ED_EoDVi are the final discharge voltage values on the rail EoDV curve and ED-EoDV curve respectively. As shown in Figure 3, there is a corresponding ΔEoDV _i for any point C_orbi, and the existence of this difference is the result of the joint action of the charging current, discharging current and the number of charging and discharging cycles. Thus, it can be considered that ΔEoDV _i is a function of the input vector, and this functional relationship can be expressed by Equ.2.

(3) 1M-DWNN training, testing and prediction

Using the existing on-track EoDV data (from O-a segment) and its corresponding ED-EoDV data (from O point to b point segment) in Figure 4, discharge current, charge current and charge-discharge cycle times to construct the 1M-DWNN network Input vector and target vector, train/test and build 1M-DWNN network. Based on the prediction input of 1M-DWNN, and based on the b-c segment data, the a-e segment data curve is predicted.

Step 7. Establishment, training and prediction of an adaptive iterative prediction model based on the secondary M-DWNN (2M-DWNN) network;

Based on the end-of-discharge data {EoDV_p_i} of the Ni-Cd battery pretreated in step 2 (corresponding oa segment data in Figure 4) and the end-of-discharge data {EoDV_pre_i} predicted by the 1M-DWNN network in step 6 (Figure 4 Based on the corresponding ae section data in ), after determining the Sample_size_min and interval, the mean-slope time series A _j ⁰ is generated according to the construction method of the mean-slope time series.

From the description of the 2M-DWNN prediction process, it can be seen that a large number of prediction values under single-step prediction can be realized through adaptive iterative prediction. In the whole process of building the 2M-DWNN model, since the data prediction after resampling and iterative prediction are essentially the same, here only the A _j ⁱ sequence is taken as an example to describe the implementation process of 2M-DWNN.

(1) AR model establishment

Taking the generated A _j ⁱ (under the condition of given iteration number i and resampling interval j, the sequence obtained, as shown in Figure 6) mean-slope time series as the data basis, carry out the single-step time series as the data basis, establish Classical AR model, and obtain the order p and coefficient {a _i } in the AR model, the basic expression of the AR model is as follows:

AR: X(t+1)＝a ₀ X(t)+a ₁ X(t-1)+…+a _p X(tp)+e(t)

Among them, e(t) is a white noise signal with a mean value of 0. Therefore, the number of feedback link nodes and weight coefficients of the 2M-DWNN model are determined, so as to construct the 2M-DWNN model under the condition of A _j ⁱ data.

(2) Data input/output of 2M-DWNN

The single-step time series prediction is carried out based on the generated A _j ⁱ mean-slope time series data, as shown in Figure 3, the number of input nodes of the 2M-DWNN network is determined according to the experience of Ni-Cd battery life prediction or through experimental testing, Its output node number is 1.

(3) 2M-DWNN training, testing and prediction

Taking 4-input and single-output as an example, at this time, the logical relationship of the single-step function of the 2M-DWNN network can be expressed as follows:

k=EoDV_end, (EoDV_end-j), (EoDV_end-2 j), ..., (EoDV_end-(Len_j-5) j)

Among them, EoDV_end and Len_j are respectively the last value of the EoDV sequence formed after iterative prediction for i times, and the time sequence length of the new sequence obtained by sampling at interval j on the basis of EoDV. In this way, the adaptive iterative prediction process is completed gradually based on the established mean-slope time series A ₁ ⁱ , and finally the mean-slope inverse transformation is performed on the obtained predicted value to obtain the end-of-discharge voltage sequence {x(i)}, and the graph The on-orbit EoDV data curve of the ed segment shown in 4 and the coordinate value d(C_end1, EoDV_threshold) of the position d point marking the end of life (life criterion), where C_end1 is the predicted life of the Ni-Cd battery.

Step 8, dynamic time window adjustment;

In actual engineering, with the passage of time, the amount of data on the above parameters of Ni-Cd batteries gradually increases, and new data can effectively improve the accuracy of life prediction. According to the characteristics and usage requirements of Ni-Cd battery, set the corresponding dynamic time window value, such as: one month, two weeks, one week, etc. Then, according to the set time window value, repeat the above steps 2 to 7, retrain and predict the 1M-DWNN and 2M-DWNN networks, and re-determine the life value of the Ni-Cd battery.

Based on the improved dynamic wavelet neural network (DWNN network), the present invention constructs the first improved dynamic wavelet neural network (1M-DWNN) and the second improved The dynamic wavelet neural network (2M-DWNN) is used to predict and obtain the life value of the Ni-Cd storage battery by using the two improved neural networks constructed. In addition, the present invention can update the data for life prediction under the premise of a given time window, and retrain the neural network, and then obtain the life value of the Ni-Cd storage battery under the new data. Users can know the remaining service life of the predicted object through life prediction, so that they can control the life of Ni-Cd battery by configuring the use environment and provide a basis for decision-making in logistics management, so that the most important task of ensuring Ni-Cd battery can be implemented Under the premise of the maximum, reliable use and use of Ni-Cd batteries, so as to give full play to the performance of Ni-Cd batteries.

The following takes the 30AhNi-Cd storage battery of my country Aerospace HY-1B small satellite as the object, and the similar product is the ground test 45AhNi-Cd storage battery as an example to further explain. Since the life-related data of the power system of the small satellite is very little, it meets the problem of life prediction of small sample data that needs to be solved in the present invention. Through the detailed elaboration of this embodiment, the implementation process and engineering application process of the present invention are further described.

For HY-1B small satellite Ni-Cd batteries, the data that can be used for life prediction are: on-orbit battery discharge voltage data (incomplete data), on-orbit battery discharge current data (incomplete data), on-orbit battery charging current data (incomplete data), on-orbit battery discharge depth data (incomplete data), ground battery test discharge final voltage data (complete data), ground battery test discharge current data (constant), ground battery test charging current data (constant), Ground battery test discharge depth data (constant) and historical discharge depth and corresponding life value 5 pairs.

The "incomplete data" means that the on-orbit battery is still able to work normally, and it is only the time series data of the first part of the full life data.

On the basis of utilizing the above-mentioned data for life prediction, apply the life prediction method proposed by the present invention to predict the life of the small satellite storage battery, the steps and methods of its application are as follows:

Step 1, collecting all available life prediction related data for Ni-Cd storage battery life prediction;

Through the analysis of small satellite batteries, all relevant data that can be collected are as follows:

Prediction object data - Ni-Cd storage battery for small satellites in orbit:

(1) On-orbit battery discharge voltage data (incomplete data);

(2) On-orbit battery charging voltage data (incomplete data);

(3) On-orbit battery discharge current data (incomplete data);

(4) On-orbit battery charging current data (incomplete data);

(5) On-orbit battery discharge data (incomplete data);

(6) On-orbit battery charge data (incomplete data);

(7) On-orbit battery temperature data (incomplete data);

(8) On-orbit battery charge-discharge ratio (incomplete data);

Similar product data - ground test Ni-Cd battery:

(1) Ground test Ni-Cd battery discharge final voltage data (complete data);

(2) Ground test Ni-Cd battery discharge current data (constant);

(3) Ground test Ni-Cd battery charging current data (constant);

(4) The discharge depth data of the Ni-Cd battery in the ground test (constant);

(5) 5 pairs of historical discharge depth and corresponding life value;

Step 2, data preprocessing related to life prediction;

Reasonably analyze all relevant data obtained in step 1, and in conjunction with the above description of the present invention, extract the data that can be used for the end-of-discharge voltage and life-span influencing factors as follows:

(1) Life characterization parameters:

On-orbit battery discharge final voltage data {EoDV_orbi}——can be extracted from the 'on-orbit small satellite battery discharge voltage';

Ground test Ni-Cd battery discharge final voltage data {EoDV_simi};

(2) Factors affecting life expectancy:

Ground test Ni-Cd battery charging current (CC_sim);

Ground test Ni-Cd battery discharge current (DC_sim);

Ground test Ni-Cd battery charge and discharge cycle data (C_sim);

On-orbit Ni-Cd battery charging current (CC_orb);

On-orbit Ni-Cd battery discharge current (DC_orb);

On-orbit Ni-Cd battery charge and discharge cycle times (C_orb);

On-orbit battery discharge depth data (DOD_orb) - can be extracted from the 'on-orbit battery discharge power data';

Ground test Ni-Cd battery depth of discharge data (DOD_sim);

5 pairs of historical discharge depth and corresponding life value;

Perform singular value elimination and data noise reduction preprocessing on the above data. Fig. 8 and Fig. 9 are data diagrams of the final discharge voltage data of the ground battery test before and after singular value removal processing and noise reduction. From the comparison in the figure, it can be seen that the data after value removal and noise reduction are more regular and less volatile. In addition, it is necessary to obtain the discharge end voltage data of the on-rail battery from the discharge voltage of the on-rail battery to characterize the performance and life of the on-rail battery.

Step three, data correlation analysis;

Through function approximation or SPSS, the correlation analysis is carried out on the parameters after pretreatment corresponding to the ground test Ni-Cd battery and the in-orbit Ni-Cd battery. According to the actual 17% discharge depth of the Ni-Cd battery on the track and the 30% discharge depth of the ground test Ni-Cd battery, the correlation between the Ni-Cd battery life and the reference ground test Ni-Cd battery life is established f: 1: 1.7.

Step 4, data mapping and obtaining the equivalent time series data value of the forecast object;

Using the correlation f: 1:1.7 obtained in step 3, based on the discharge end voltage data of the Ni-Cd battery in the ground test, map and obtain the equivalent discharge end voltage data {EDEoDVi} of the discharge end voltage of the Ni-Cd battery, as shown in Figure 4 The solid line 'Equivalent EoDV' is shown.

Step 5. Improvement of DWNN network (M-DWNN);

For the specific improvements and parameter settings in this part, please refer to the establishment of the AR model in steps 6 and 7.

Step 6. Establishment, training and prediction of an M-DWNN (1M-DWNN) network;

Taking the differential data results of {EoDV_p_orbi} and {ED-EoDVi} as the object, the constructed AR model parameters are as follows: p=4,a _i ={-0.632,0.545,-0.021,0.162}, and then, 1M-DWNN The number of feedback nodes is M=4, and the weighting coefficient is known. Since the number of input nodes of the 1M-DWNN network is three, based on Equ.2, the established 1M-DWNN model is shown in Figure 10.

According to the input and output data requirements of the 1M-DWNN network, use the normalized on-rail Ni-Cd battery charging current (CC_p_orb), on-rail Ni-Cd battery discharge current (DC_p_orb), and on-rail discharge final voltage data {EoDV_p_orbi}, ground test Ni-Cd battery charging current (CC_p_sim), ground test Ni-Cd battery discharge current (DC_p_sim) charge and discharge cycle times and equivalent discharge end voltage data {ED_EoDVi} obtained from step 4 to construct 1M-DWNN network The input vector and target vector, train/test and establish 1M-DWNN network, the specific parameters related to training and prediction are as follows:

Training time: 2.3153s

Prediction accuracy: mean square error MSE=0.0143

Figure 11 shows the 1M-DWNN prediction test accuracy curve. It can be seen from the figure that 1M-DWNN can track the battery performance degradation process very well.

The output of the 1M-DWNN network is the corresponding normalized value of the difference under the corresponding number of charge and discharge cycles. After denormalization and reverse difference, the final voltage value of the on-rail discharge can be obtained. Figure 12 shows the Ni-Cd based on the 1M-DWNN model The battery discharge end-voltage decline prediction curve generally follows the trend of the existing on-orbit discharge end-voltage data well.

Step 7. Establishment, training and prediction of adaptive iterative prediction based on the secondary M-DWNN (2M-DWNN) network;

Set Sample_size_min=100, interval=8, use the end-of-discharge data {EoDV_p_i} of the Ni-Cd battery pretreated in step 2 (corresponding oa section data in Figure 4) and the discharge predicted by the 1M-DWNN network in step 6 Based on the final pressure data {EoDV_pre_i} (corresponding data in section ae in Figure 4), the mean-slope time series A _j ⁰ is generated according to the construction method of the mean-slope time series.

For 2M-DWNN, j _max AR models need to be constructed in each iteration process, and the establishment process is based on A _j ⁰ (for data with iteration times greater than 0, the data basis for AR model construction is A _j ⁱ , where i>0) is the data basis, and j _max is limited to a fixed value for any A _j ⁱ resampling sequence, so as to ensure that the amount of the constructed AR model is the same in each iteration process. Based on the constructed AR model, a 4-input/single-output 2M-DWNN model is established according to Equ.3, and the adaptive iterative prediction process is completed. Finally, the average slope inverse transformation is performed on the obtained predicted value to obtain the final discharge voltage sequence {x(i )}, the on-orbit EoDV data curve of the ed segment shown in Figure 4 and the coordinate value d(C_end1, EoDV_threshold) of the position d point marking the end of life (life criterion) can be obtained, where C_end1 is the prediction of the Ni-Cd battery life.

Figure 13 shows the comprehensive M-DWNN prediction results including the 2M-DWNN model prediction results, where the thick line on the right shows the second iteration prediction results. According to the life criterion of the HY-1B small satellite storage battery, the predicted life value of the embodiment of the present invention is 5.21 years, that is, 5 years, 2 months, 15 days, 14 hours and 24 minutes.

Step 8, dynamic time window adjustment;

The time window of the embodiment of the present invention is 1 week. When the set one week time arrives, use the new in-orbit small satellite battery data that has been collected and repeat the above steps 2 to 7 to obtain a new life prediction value.

The parts not described in detail in the description of the present invention belong to the well-known technology in the art.

The above is only a preferred embodiment of the present invention, it should be pointed out that, for those of ordinary skill in the art, without departing from the principle of the present invention, some improvements and modifications can also be made, and these improvements and modifications can also be made. It should be regarded as the protection scope of the present invention.

Claims (1)

1. A method for predicting the life of an aerospace Ni-Cd accumulator based on the improved dynamic wavelet neural network, is characterized in that the realization steps are as follows: Step 1. Collect all relevant data of aerospace Ni-Cd battery life prediction; Through the analysis of aerospace Ni-Cd batteries and similar products, collect all available life prediction related data, including: temperature, charging current, discharging current, discharging power, load current data, charging power, remaining power, voltage, charging and discharging Ratio and other parameter data; for solar cell arrays, the available data are: temperature, square array current data, load current data, power, bus voltage, booster output voltage and other parameter data; The similar products refer to products that are similar or identical to Ni-Cd storage batteries in terms of physical structure, logical structure and functional structure; Step 2, data preprocessing related to life prediction; All aerospace Ni-Cd storage battery life prediction data obtained in step 1 are analyzed and screened, and the required aerospace Ni-Cd storage battery discharge terminal voltage parameter data and life-influencing factor data are extracted. The factor data includes: discharge current data, Charge current data, number of charge and discharge cycles, and discharge depth data; at the same time, carry out singular value elimination and data noise reduction preprocessing for the screened relevant factor data; Step three, data correlation analysis; Through function approximation or SPSS (Statistical Product and Service Solutions, Statistical Product and Service Solutions) method, correlation analysis is carried out on similar products and the corresponding preprocessed data of aerospace Ni-Cd batteries, and the relationship between similar products and Ni-Cd batteries is obtained. Correlation on discharge terminal voltage; Described correlation analysis refers to by function approximation or utilizes SPSS method, realizes the correlation analysis to different parameter data, obtains the mapping relation between parameter data; Step 4, data mapping and obtaining the equivalent data value of the final discharge voltage of the Ni-Cd storage battery; Based on the correlation between the similar product obtained in step 3 and the end-of-discharge voltage of the Ni-Cd battery, based on the end-of-discharge data of the referenced similar product, map and obtain the equivalent data value of the end-of-discharge voltage of the Ni-Cd battery; Step five, improvement of DWNN network (M-DWNN); According to the requirements of aerospace Ni-Cd battery life prediction accuracy, DWNN is improved, and the improvement scheme is as follows: use the DWNN output data sequence {Yi} to construct an AR model, including determining the AR model order p and coefficient sequence a _i , i=0,1 ,2,...,p-1, and then take the order of the AR model as the number of feedback nodes of the DWNN model, that is, let M=p, where M represents the number of feedback nodes of the DWNN network, and the coefficient sequence a _i of the AR model is used as each feedback node The corresponding weight coefficients are input as the WNN model, and then the improvement of the DWNN network model is completed; the corresponding relationship between the AR model coefficients and the nodes is: a _i Y(ti), i=0,1,2,...,p -1; Step 6. Establishment, training and prediction of an M-DWNN (1M-DWNN) network; According to the analysis of influencing factors and the results of correlation analysis, the number of input nodes of 1M-DWNN is determined, and the output is the final discharge voltage of the Ni-Cd battery after treatment, that is, single output; -EoDV performs differential proportional processing to construct 1M-DWNN training samples and test samples; in order to eliminate the singular values in the training samples and speed up the convergence of the network, normalize the input vector and target vector constructed above, and then Input the 1M-DWNN network to train it, determine the parameters of the 1M-DWNN network, and use the trained 1M-DWNN network to predict, and obtain the predicted value of the final discharge voltage of the Ni-Cd battery through the process of inverse normalization and inverse difference, and then Realize that the ground test data segment is used as a reference to obtain the on-orbit discharge final pressure prediction result data segment; Step 7, establishment, training and prediction of an adaptive iterative prediction model based on the secondary M-DWNN (2M-DWNN) network, the implementation steps are as follows: (1) Data preparation for adaptive iterative prediction, that is, mean-slope time series construction Segmented mean value processing is performed on the data sequence composed of the on-rail discharge end voltage and the discharge end voltage value predicted by 1M-DWNN, and on this basis, the slope of the mean value is calculated, and the second M-DWNN prediction is the mean value -Slope time series for adaptive iterative prediction, the mean-slope time series construction formula is as follows: $\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; Avr</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; Avr</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; Avr</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; )</span>$ $\mathrm{<span\; class="notranslate">\; Avr</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; interval</span>}}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; interval</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; interval</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>$ (j=1,2,...,n; n=fix(N/interval)) Among them, { _xi } represents the EoDV value sequence, the length is N, interval is the mean interval, {Avr(j)} is the mean value sequence, the length is n, {s(k)} is the mean-slope sequence, the length is n- 1; The follow-up content from step (2) takes the {s(k)} mean-slope sequence as the object, and describes the core content of the adaptive iterative prediction method; (2) Adaptive iterative process After the mean-slope time series is constructed by step (1), the core content of adaptive iterative prediction is started, and the specific method is as follows: (2.1) Adaptive time series data resampling For a given time series {A ⁱ _j } of length n, where i, j respectively represent the number of iterative predictions of the original time series and the resampling interval of the time series, then A ⁰ ₁ :={s(k)}=s ₁ ,s ₂ ,s ₃ ,…,s _k ,…,s _n-1 ,s _n , where s(k) is s(k) in Equ.1, which represents the constructed mean-slope sequence, s _k is the kth data of the sequence, representing the original data, the number of iterative predictions is 0, and the time series sampling interval is defined as 1, where ':=' means 'defined as'; and A ¹ ₂ means that after one iteration After prediction, the time series data with a resampling interval of 2 is resampled from A ⁰ ₁ at equal intervals according to the needs of the 2M-DWNN network training sample size, and then a new time series is obtained: $\begin{array}{c}{{\mathrm{<span\; class="notranslate">\; A</span>}}^{\mathrm{<span\; class="notranslate">\; 0</span>}}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; :</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; j</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; j</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; jm</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}\\ <span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2,3</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; j</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; j</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; Sample</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; suze</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; ]</span>\end{array}$ Among them: n is the length of the original time series A ⁰ ₁ ; A ⁰ _j means that the time series is obtained with a resampling interval of j, and the sampling starts from the last data (s _n ) of the original data; j _n means the time series A ⁰ _j , and satisfy: n-(j _n -1)*j≥1, and j _n decreases with the increase of j, assuming that the minimum requirement of 2M-DWNN network training sample size is Sample_size_min, then j _n j _n ≥ Sample_size_min should be satisfied, so that j _max =fix(n/(Sample_size_min)) is the maximum value of j, where fix means rounding down, so as to complete the adaptive re-sampling process; (2.2) Single-step forecasting of adaptively resampled time series data Using the idea of single-step forecasting, the 2M-DWNN model is constructed respectively, and the time series data obtained by re-sampling is used for single-step forecasting, and the one-step forecast value of A ⁰ _j is obtained, and then the new time series A ⁰ ' _j is expressed as: $\begin{array}{c}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; :</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; j</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; j</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; j</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ,</span>{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; k</span>}}\\ <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2,3</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; )</span>\end{array}$ The same process completes all A ⁰ _j time series, where j=1,2,3,...,j _max , so as to complete an iterative process and obtain j _max predicted values. The new time series formed can be expressed as: A ₁ ¹ :s ₁ ,s ₂ ,…,s _n-1 ,s _n ,s’ _n+1 ,s’ _n+2 ,…,s’ _n+jmax The first two steps realize the new time series A ¹ ₁ after obtaining j _max predicted values from any time series A ⁰ ₁ , and then complete an iterative forecasting process; when replacing the original data A ⁰ ₁ with A ¹ ₁ and repeating In the above process, A ² ₁ , A ³ ₁ ,…,A ^k ₁ ,… are obtained through such iterations; (3) Inverse transformation of adaptive prediction iterative data results and judgment of Ni-Cd life value Through the iterative process, an infinite number of mean-slope sequences A ^k ₁ are obtained. In order to finally determine the life of the battery, it is necessary to inversely transform the predicted mean-slope sequence A ^k ₁ and obtain the end-of-discharge voltage of the Ni-Cd battery Sequence {x′ _i }, which contains the existing on-orbit discharge final pressure data, 1M-DWNN prediction result data and 2M-DWNN iterative prediction result data; finally, based on the {x′ _i } sequence, determine Ni by battery life criterion -Cd battery remaining life prediction value; Step 8. Dynamic time window adjustment In the process of using M-DWNN to predict Ni-Cd batteries, due to the passage of time, new data will be continuously obtained. At this time, it is necessary to dynamically repeat the above steps 2 to 7 to rebuild and train the M-DWNN network. The M-DWNN network includes 1M-DWNN and 2M-DWNN models to update network parameters and re-predict, ensuring that the prediction accuracy will continue to improve with the extension of the on-orbit operation time.