A Prediction Method for Recycling Prices Based on Bidirectional Denoising Learning of Retired Battery Surface Data

Abstract

Accurately predicting recycling prices at battery recycling sites helps reduce transportation and dismantling costs, ensures economies of scale in the recycling, and supports the sustainable development of the new energy vehicle industry. However, this prediction typically relies on easily accessible surface data, such as battery characteristics and market prices. These data have complex correlations with recycling price, general price prediction methods have low prediction accuracy. To this end, an improved prediction method is proposed to enhance the accuracy of predicting recycling prices through surface data. Firstly, factors influencing recycling prices are selected based on self-factor and market fluctuations, a bidirectional denoising autoencoder and support vector regression model (BDAE-SVR) is established. BDAE is used to adjust the weights of influencing factors to remove noise, extract features related to recycling price. The extracted features are introduced into the SVR model to establish a correspondence between the features and recycling price. Secondly, to have better applications for different batteries, the Grey Wolf algorithm (GWO) is used to adjust the SVR parameters to improve the generalization ability of the prediction model. Finally, taking retired power batteries as an example, the effectiveness of the method is verified. Compared with methods such as random forest (RF), the RMSE predicted by BDAE is decreased from 1.058 to 0.371, indicating better prediction accuracy.

1. Introduction

With the new energy vehicle power batteries stepping into the initial retirement stage, a peak period of power battery retirement is anticipated to arrive within the subsequent between five and eight years [1]. It is estimated that by 2027, the cumulative amount of retired power batteries worldwide will reach 1.14 million tons. At present, how to properly recycle these retired power batteries and ensure the recycling efficiency of recycling and reuse enterprises has become a problem that needs to be solved [2,3]. Currently, effectively recycling retired power batteries and ensuring the efficiency of recycling and reuse enterprises have become critical challenges. Accurately predicting recycling prices before battery disassembly can help evaluate the reuse value of these batteries, avoiding unnecessary transportation and dismantling costs, and ensuring the benefits of large-scale, personalized recycling. This is crucial for promoting the sustainable development of the new energy vehicle industry.

Before disassembling the battery, the recycling price is mainly predicted based on the surface data of retired power batteries, including self-damage factors and market factors. These surface data can reflect the performance of batteries and market changes, avoiding complex disassembly and testing processes. However, there are complex correlations between these surface influencing factor data, which contain a substantial amount of redundant information and noise, making it difficult for the surface influencing factor data to directly reflect the recycling price. The weak correlation between them affects the accuracy of predicting the recycling price of retired power batteries.

To improve the accuracy of surface data-driven prediction of retired power battery recycling prices, it is necessary to extract the characteristics of surface influencing factors. Neural networks are widely used for feature extraction due to their powerful learning ability. However, neural networks suffer from overfitting when dealing with a large number of features. Retired power batteries have a large amount of surface data, resulting in low accuracy in feature extraction using neural networks. In terms of constructing price prediction models, machine learning methods are widely applied. However, these methods require intuitive input data to ensure the accuracy of predictions. Although the surface data of retired power batteries are easy to obtain, there are complex nonlinear relationships between each feature, and the redundant information contained in them makes it difficult for the features to directly reflect the recycling price. In addition, the usage of different power batteries varies greatly, with significant personalized differences, which makes the generalization of the recycling price prediction model insufficient and difficult to apply to different power batteries. Therefore, how to improve the accuracy of predicting the recycling price based on the surface data of retired power batteries has become a difficult problem to be solved.

In summary, this article proposes an improved combination prediction method that enhances the accuracy of predicting the price of retired power battery recycling through surface data. The motivation of this article is to address two issues:

(1)

The surface data of retired power batteries are weakly correlated with recycling prices, and market changes also affect recycling prices, which makes it difficult to ensure the accuracy of predicting recycling prices.

(2)

The usage of different retired power batteries varies and there are significant personalized differences, which poses a challenge to the recycling price prediction model and requires it to be applicable to different retired power batteries.

2. Literature Review

The challenge of predicting the recycling price of retired power batteries shares similarities with predicting product prices, as both are closely linked to their respective influencing factors. While predicting recycling prices based on surface data provides convenience and efficiency, there are complex nonlinear relationships between the features, and the redundant information contained in them makes the correlation between the features and recycling prices weak, resulting in the low accuracy of price prediction. Therefore, the prediction of retired power battery recycling prices proposed in this article mainly focuses on two key points: (1) extracting features of influencing factors affecting recycling prices; and (2) establishing a recycling price prediction model. As of now, there has been extensive research on these two steps.

2.1. Feature Extraction of Influencing Factors

To ensure the accuracy of price forecasting, it is necessary to first process the data and reduce the complexity of influencing factors. The methods can be mainly divided into two types: feature selection and feature extraction [4]. Feature selection is the process of selecting a subset from the original features as the new feature set. However, feature selection methods may not perform well in dealing with nonlinear problems such as the recycling price of retired power batteries, and feature extraction methods are often used in price prediction problems. Feature extraction can reduce the complexity of data by projecting it onto a lower dimensional subspace, while preserving important information and transforming the original dataset into a new simplified dataset. The commonly used feature extraction methods include principal component analysis (PCA), Independent Component Analysis (ICA), Local Linear Embedding (LLE), and Convolutional Neural Networks (CNN) in deep learning [5,6,7].

Many studies are focused on unsupervised feature extraction methods such as principal component analysis. Jia et al. used the kernel principal component analysis (KPCA) dimensionality reduction algorithm to preprocess the ultrasound dataset and accurately extracted effective information [8]; Kritakom et al. combined PCA, empirical mode decomposition, and long short-term memory to predict the closing price of stocks [9]; E et al. preprocessed the ultrasound dataset using KPCA to accurately extract useful information and capture fluctuations in gold prices [10]. PCA and ICA are used to extract the most useful information from the original features. However, these methods are sensitive to datasets, and the surface data of retired power battery recycling prices often contain noise. PCA are easily affected by noise, which affects the accuracy of feature extraction.

Neural networks are widely used for feature extraction due to their powerful learning ability. Li et al. used Convolutional Neural Networks to extract features from macroeconomic variables and other information, improving the accuracy of short-term price predictions for Bitcoin [11]; Tyshchenko et al. used recurrent neural networks to predict the quality of cryptocurrency prices [12]; Zhu et al. proposed a new hybrid neural network prediction model that extracts temporal features of stock prices using a neural network with three convolutional layers and one long short-term memory layer [13]. The market factors for the recycling price of retired power batteries fluctuate greatly, and a more stable feature extraction model is needed. Neural networks have many advantages in feature extraction, but there is an overfitting problem when dealing with a large number of features [14]. Retired power batteries have a large amount of surface data, and the accuracy of feature extraction using neural networks is low.

2.2. The Price Prediction Model

Nowadays, many studies focus on price prediction, and various prediction methods are applied to different prediction problems. Liu et al. proposed an improved pricing model based on parameter updating momentum fuzzy neural network to predict the recycling price of mobile phones [15]; Lu et al. used various machine learning models to predict carbon trading volume and price, and discussed the predictive stability of each model in different application scenarios [16]; Su et al. conducted research on stock price prediction, addressing issues such as the impact of ineffective correlations and dependence on prior expert information [17]. They proposed an adaptive spatiotemporal hypergraph convolutional network prediction method based on attention mechanisms; Nassar et al. used models such as CNN-LSTM to predict the prices of fresh agricultural products [18]. In price prediction, neural networks have high flexibility and can adapt to different prediction problems by adjusting the network structure and number of layers, but they heavily rely on sample data size. For retired power batteries that are still in the early stages of recycling, it is difficult to provide a large amount of sample data, and neural networks have certain limitations in predicting the recycling price of retired power batteries [19].

Machine learning methods can effectively solve this problem. Caliciotti et al. considered the frequent fluctuations in Bitcoin prices and used support vector machine methods for long-term Bitcoin price prediction [20]; Beniwa et al. used forward validation genetic algorithm to optimize SVR and predict daily stock index prices for up to one year [21]. Compared with other machine learning models, SVR has the advantages of high prediction accuracy, fast convergence speed, and good generalization ability [22]. In the problem of predicting the recycling price of retired power batteries, SVR has a certain anti-interference ability and requires a small number of data samples [23]. However, these methods are applicable to a specific type of price prediction problem. There are many models of retired power batteries, and the data of different models of batteries varies greatly. A single-price prediction model shows insufficient generalization and is difficult to apply to predict the recycling prices of different types of power batteries. Bian et al. used the PSO-MLST-LSTM combined method to predict the SOH of lithium-ion batteries in order to alleviate the overfitting problem of a single prediction mode [24]; Zheng et al. improved the prediction accuracy by using the GA-SVR method, considering the volatility of natural gas prices [25]. PSO and GA methods can effectively optimize model parameters, but GA converge slowly on complex problems, while PSO requires the adjustment of many parameters and may fall into local optima when dealing with the complex influencing factors of power batteries.

2.3. Overview Summary

Based on the literature review, it is evident that existing prediction methods still struggle to accurately forecast the recycling price using the surface data of retired power batteries. There is a complex nonlinear relationship between the surface features of retired power batteries. To achieve accurate prediction of recycling prices, current methods still have some limitations, mainly reflected in the following two points:

(1)

For multi-feature retired power battery data, general feature extraction methods tend to lose some information by discarding secondary features. In addition, general feature extraction models are susceptible to noise, resulting in low feature extraction accuracy, which in turn affects the accuracy of recycling price prediction. Therefore, there is a need for methods with stronger anti-interference capabilities, stable and sufficient extraction of data features, and reduction in data complexity.

(2)

Due to the personalized differences in retired power batteries, factors such as usage time fluctuate greatly, making it difficult for a single price prediction model to accurately predict the recycling prices of different types of power batteries. The combination prediction model has high requirements for input data, and redundant information can also affect the accuracy of prediction.

In terms of feature extraction, compared with mainstream linear dimensionality reduction methods such as PCA, BDAE can better capture the deep nonlinear features of retired power batteries, thereby improving the expression ability of the model. Although methods such as CNN have significant advantages in the field of image processing, their application may be limited when dealing with general regression problems, especially complex non-image data, and their training process requires high annotation data. In contrast, BDAE demonstrates greater flexibility and advantages in handling such issues. In terms of parameter optimization in price prediction models, GWO has strong global search capability and can avoid local optima. Therefore, a BDAE-GWO-SVR recycling price prediction model is established with the aim of achieving more accurate pricing for retired power batteries. The primary contributions of this article are as follows:

(1)

BDAE is used to extract the features of factors affecting recycling prices, adjust the weights of these factors to remove redundancy, reduce interference with the price prediction model, and ensure the accuracy of recycling price prediction.

(2)

A BDAE-GWO-SVR-integrated recycling price prediction model is established. After BDAE processing, the complexity of the features is reduced. The hyperparameters of the SVR model are optimized by GWO, the adaptability of the prediction model to different power battery data can be improved, making this method widely applicable for predicting the recycling prices of retired power batteries.

The chapter arrangement of this article is as follows: Section 2 reviews the current research status related to the pricing of retired power battery recycling, Section 3 introduces the overall framework of this article, Section 4 introduces the model method, Section 5 evaluates and compares the results of the method, and Section 6 provides conclusions and suggestions.

3. The Overall Process

This article proposes a method for predicting the recycling price of retired power batteries based on surface data. It is comprised of two main aspects. Firstly, predicting the price of retired power battery recycling through surface data has redundant information. Using BDAE to adjust the weights of various influencing factors to remove noise, extract features related to recycling prices, and avoid the impact of redundant information on price prediction. Secondly, the extracted features are utilized as input for the SVR model to predict the recycling price of retired power batteries. Considering the differences in usage the data of different power batteries, GWO is used to optimize the hyperparameters of the SVR model, improve the generalization of the recycling price prediction model, and enable this method to be widely applied to different power batteries. The overall framework of the proposed method is depicted in Figure 1. The proposed method steps are as follows:

Step 1: Comprehensively consider the self-damage features of retired power batteries and the impact of market fluctuations on recycling prices, and screen the influencing factors of recycling prices. Using Spearman’s correlation analysis, 13 surface influencing factors are ultimately selected.

Step 2: Taking the data of influencing factors of recycling prices as the input, BDAE is used to adjust the weights of the influencing factors to better capture the correlations among the data of retired power batteries and extract the features related to the recycling prices of retired power batteries. BDAE reduces redundant information on the influencing factors of retired power battery recycling prices, reduces data complexity, and improves the accuracy of price prediction.

Step 3: Input the extracted features into the SVR recycling price prediction model. GWO is used to automatically search for the optimal parameter combination of kernel function parameter C and penalty factor σ to improve the generalization ability of prediction models for different power battery data.

4. Methodology

4.1. Selection of Factors Influencing Recycling Prices

To improve the accuracy of predicting the recycling price of power batteries, it is necessary to analyze the main factors that affect their recycling price. By summarizing and analyzing existing research results, the recognized factors that affect the recycling price of power batteries are preliminarily screened from two aspects: self-factors and market factors. Perform correlation analysis on the preliminarily screened influencing factors, using Spearman’s rank correlation coefficient to calculate the correlation between each influencing factor and the recycling price, as shown in Equation (1).

$$r_s=1-{\displaystyle \frac{6{\sum }_{i=1}^n{\left(x_i-y_i\right)}^2}{n\left(n^2-1\right)}}$$

(1)

where $n$ is the number of retired power batteries, $x_i$ is the level value of a certain influencing factor for the retired power battery, and $y_i$ is the level value of the recycling price for the retired power battery.

The closer the absolute value of the correlation coefficient is to 1, the higher the degree of correlation. The closer the absolute value of the correlation coefficient is to 0, the lower the degree of correlation. Based on this, the influencing factors are screened to ultimately determine the 13 factors that affect the price of power battery recycling, as shown in

Table 1. Factors Affecting the Recycling Price of Retired Power Batteries.

Category		Influence Factor
Self-factor	Initial parameters	1. Battery capacity$/kWh$
	Personalized parameters	2. Usage time$/h$ 3. Number of battery cycles (units) 4. Degree of appearance wear and tear (grade) 5. Number of malfunctions/repairs (times) 6. Battery health (%)
Market fluctuations		7. Market recycling prices of major metals in batteries (nickel, 8. cobalt, 9. manganese, 10. lithium) $\left(USD/kg\right)$ 11. Number of retired batteries (units) 12. Price index of new power batteries (percentage change) 13. Price index of used power batteries (percentage change)

The data related to the battery itself in the table are provided by a recycling enterprise. The metal market recycling price data are sourced from the official platform of the Shanghai Futures Exchange (https://www.shfe.cn accessed on 30 June 2025).

.

It can be mainly divided into two aspects: self-factor of batteries and market factors. From the perspective of the battery itself, it can be divided into initial parameters that do not change over time and personalized parameters that change over time. The initial parameters include battery capacity, which directly reflects the storage capacity of retired power batteries. Personalized parameters include usage time, battery cycle times, degree of appearance wear, number of failures/repairs, and battery health. The usage time and number of cycles can reflect the remaining life of the battery. The degree of wear and tear on the appearance reflects the feasibility of secondary utilization of the battery. The number of repairs can evaluate the reliability of the battery, and batteries with more repairs may be more prone to failure during secondary use, resulting in lower recycling prices. The overall health of a battery reflects its performance status, and the higher the health, the higher the recycling price. Market factors include the market recycling prices of major metals in batteries (nickel, cobalt, manganese, lithium), the number of retired batteries, the price index of new power batteries, and the price index of used power batteries. Market factors can reflect the market supply and demand situation and price trends, thereby affecting the recycling price of power batteries.

4.2. The Recycling Price Prediction Model Based on BDAE

It is difficult to guarantee the accuracy of predicting the recycling price of retired power batteries quickly and conveniently based on surface data. It is necessary to perform feature extraction on the relevant features before prediction, capture the intrinsic correlation between the features, and extract the comprehensive features that can better reflect the recycling price. In this paper, a BDAE-SVR model is constructed to accurately predict the recycling price of retired power batteries (as shown in Figure 2). Firstly, the external damage features and market factor data of retired power batteries are input into the BDAE for feature extraction, and then the SVR model is used for recycling price prediction.

This article constructs a bidirectional denoising autoencoder based on the Denoising Autoencoder (DAE), and its principle structure is shown in Figure 3. The surface data of retired power batteries have certain correlations, which cannot be directly used for price prediction models. As a commonly used unsupervised learning model, the BDAE encodes the raw data of retired power batteries to generate a low-dimensional representation of the hidden layer, which is then decoded by the hidden layer to restore the original data using the information from the hidden layer [26,27]. During the encoding process, factors that have a relatively small impact on the recycling price are ignored, while core information closely related to the recycling price is retained in low-dimensional features. The decoder attempts to effectively reconstruct the original data based on these low-dimensional features, thus capturing the most important changes and information among the influencing factors. Specifically, let $X=({\overrightarrow{x}}_{capacity},{\overrightarrow{x}}_{time},\dots ,{\overrightarrow{x}}_{Appearance wear degree})$ be the input data for the original retired power battery, the specific changes in the input layer and hidden layer data of BDAE can be represented as follows.

$$\begin{array}{c}\overrightarrow{H_t}=\sigma ({\overrightarrow{x}}_{capacity},{\overrightarrow{x}}_{time},{\overrightarrow{x}}_{health},\dots )\\ {\overleftarrow{H}}_t=\sigma ({\overleftarrow{x}}_{appearance},{\overleftarrow{x}}_{marketprice},{\overleftarrow{x}}_{priceindex},\dots )\end{array}$$

(2)

where $\overrightarrow{H_t}$ is the hidden layer expression of the forward denoising autoencoder, ${\overleftarrow{H}}_t$ is the hidden layer expression of reverse denoising autoencoder, $\sigma (·)$ is the activation function, $\overrightarrow{x}$ is the input data of retired power batteries in the forward direction, and $\overleftarrow{x}$ is the input data of reverse retirement power battery.

This process takes both positive and negative factors affecting the recycling price of retired power batteries, $\overrightarrow{x}$, $\overleftarrow{x}$ as inputs. It can effectively mine the correlation between retired power battery data using data information in both directions and correct the errors in one-way feature extraction. Due to the fact that the input is the same retired power battery data, there is no increase in the requirement for data volume while enhancing its feature extraction capability.

Data-driven BDAE learns the data features of retired power batteries, and the hidden layer $H_t$ is the retired power battery data after feature extraction, which maximally contains the effective information of the original input data and reduces redundant features. BDAE connects the forward and reverse hidden layers, fuses signals from both sides for decoding, and restores noise-free reconstructed data of retired power batteries. Due to the fusion of information from bidirectional hidden layers with certain weights, BDAE can compensate for the error of unidirectional input. The output retired power battery reconstruction data can be represented as Equation (3).

$${\stackrel{⃡}{Y}}_t=\sigma (w_1{\overrightarrow{H}}_t+w_2{\overleftarrow{H}}_t+b)$$

(3)

where ${\stackrel{⃡}{Y}}_t$ is the reconstructed data of retired power batteries, $w_1$ is forward input weight, $w_2$ is reverse input weight, and $b$ is input bias.

The closer the restored data ${\stackrel{⃡}{Y}}_t$ is to the original data $X$ of the retired power battery, the more data information its hidden layer contains, indicating that the hidden layer is a low-dimensional representation of the original data. During this process, noise data generated by measurement errors or environmental interference will gradually decrease in weight due to not conforming to the normal distribution of the data, achieving denoising effect.

The MSE loss function is used to evaluate the performance of the model, as Equation (4). The closer the MSE value is to 0, the smaller the loss and the better the accuracy of the model.

$$MSE={\displaystyle \frac{1}{n}}\sum _{i=1}^n{(\widehat{y_i}-y_i)}^2$$

(4)

where n is number of retired power battery samples, $\widehat{y_i}$ is the true value of the data, and $y_i$ is predicted data value.

BDAE could analyze the relationships between various features of retired power batteries, automatically discover inherent patterns and structures in the data, and the features contained in the hidden layer can more comprehensively express the raw data of retired power batteries, with less redundant information. The closer the reconstructed data decoded by the hidden layer is to the original input, the more effective features of retired power battery recycling prices contained in the hidden layer, and the better the feature extraction effect, which can be used as input for subsequent recycling price prediction models.

After BDAE feature extraction, the redundant information of the influencing factors on the surface of retired power batteries are reduced, which is more conducive to price prediction models. This article chooses the SVR recycling price prediction model to predict the recycling price of retired power batteries, in order to better fit the nonlinear characteristics of the recycling price of retired power batteries [28]. To predict the recycling price of retired power batteries using SVR, as Equation (5), it is necessary to find a price prediction result $y_i$ that is as close as possible to the actual recycling price $x_j$. The pseudocode for predicting the recycling price of retired power batteries using SVR is shown in Algorithm 1 [29].

$$y_i=\sum _{i,j\in SV}\left(a_i-a_i^{\ast }\right)K\left(x_i,x_j\right)+b$$

(5)

$$K\left(x_i,x_j\right)=\mathrm{e}\mathrm{x}\mathrm{p}(-{\displaystyle \frac{{‖x_i-x_j‖}^2}{2{\sigma }^2}})$$

(6)

where $y_i$ is the predicted price of retired power batteries, $\sigma$ is the parameters of the kernel function to be determined, $K\left(x_i,x_j\right)$ is the kernel function, $a_i,a_i^{\ast }$ are the Lagrange multiplier, $x_i$ is the input data, which is the output of the BDAE hidden layer, and $x_j$ is the actual recycling price of retired power batteries.

Algorithm 1: Prediction of Recycling Prices for Retired Power Batteries

Input: Retired power battery data after BDAE feature extraction Output: Price prediction results 1: Read data from file ‘Price:/7690/gwo-svr.csv’ 2: Extract ‘Price’ column as y and remaining columns as X    $y=df[‘Price’]$    $X=df.drop(\mathrm{‘}\mathrm{P}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{e}\mathrm{’},axis=1)$ 3: Split X and y into training and test sets 4: $svr=SVR(kernel=‘rbf’, C, epsilon)$     $svr.fit(X\_encoded, y\_scaled)$    $return svr$ 5: Create an SVR using parameters and features extracted by BDAE, and fit it to the training data      $X\_encoded=encoder.predict\left(X\right)$      $svr.fit(X, recycling\_prices)$      $return svr$ 6: $y\_pred=svr\_ predict(X\_test)$ Return the price prediction results

To enhance the interpretability of the price prediction model, Shapley Additive explanations (SHAP) are used to quantify the contribution of each feature extracted after feature engineering to the prediction outcome [30]. The SHAP model treats the extracted features as players in a cooperative game, with each feature’s Shapley value representing its average marginal contribution to the model’s prediction, as shown in Equation (7).

$$f_{Shapley}(H_t)=\sum _{S\subseteq N\backslash t}{\displaystyle \frac{k!\left(p-k-1\right)!}{p!}}(f\left(s\cup t\right)-f(S))$$

(7)

where $S$ represents the set of feature subsets; $p$ denotes the number of features; $N\backslash t$ refers to the permutation of all features except for $H_t$; and $f(·)$ represents the model’s prediction outcome.

The selection of kernel function type will directly affect the results of recycling price prediction. Considering the influence of kernel function parameters on the complexity of the prediction model, the radial basis function (RBF) that can achieve nonlinear mapping is selected as the kernel function of SVR in this paper, and its expression is shown in Equation (6). As long as the appropriate $C$ and $\sigma$ are selected, the specific form of SVR can be determined, thereby accurately predicting the recycling price of retired power batteries. However, the hyperparameters of the SVR prediction model are mainly set based on experience, and the surface influencing factors of retired power battery recycling prices, such as battery usage time, fluctuate greatly. Improper selection of hyperparameters for $C$ and $\sigma$ can easily lead to insufficient model generalization, unstable recycling price prediction, and low prediction accuracy. Therefore, this article chooses the Grey Wolf algorithm to optimize the parameters of SVR.

4.3. GWO-Optimized Recycling Price prEdiction Model Parameters

GWO defines the potential solutions of $C$ and σ as a wolf pack, and the recycling price of retired power batteries as prey. The wolf pack continuously searches for prey, which is the process of parameter optimization for the recycling price of retired power batteries [31,32]. Divide $C$ and σ into four levels from high to low based on their adaptability: $\alpha , \beta , \delta$ and $\omega$. Name the three groups of $C$ and σ closest to the prey in descending order as $\alpha$, $\beta$ and $\delta$, corresponding to the optimal solution, suboptimal solution, and third optimal solution for the recycling price of retired power batteries, respectively; Name the remaining potential solutions of $C$ and σ uniformly as $\omega$. $\alpha ,\beta$ and $\delta$ guide $\omega$ to search for prey, while $\omega$ updates its position around $\alpha ,\beta$, and $\delta$.

In the process of optimizing the parameters of the SVR recycling price prediction model by GWO, the retired power battery data extracted through BDAE feature extraction is the input of the SVR model. Then, cross validation is used to evaluate the performance of the SVR model. The results of cross validation are used as the accuracy of the current model, and the positions of $\alpha$, $\mathsf{\beta }$ and $\mathsf{\delta }$ gray wolves in the GWO and the predicted prices of retired power batteries are updated based on the accuracy. The entire process continuously adjusts the position of parameters, ultimately finding the best combination of parameters to achieve the best fitting effect of the support vector machine regression model. The algorithm process is shown in Figure 4. Algorithm 2 is a pseudocode using Python (2021.2.4) to optimize SVR hyperparameters for predicting the price of retired power battery recycling [33].

Algorithm 2: Prediction of Recycling Prices for Retired Power Batteries

Input: Battery features and historical recycling prices Output: Optimized SVR hyperparameters and predicted recycling prices 1: Connect to the data source (parameters) 2: Input data = ‘Battery feature data and corresponding recycling prices’ 3: Initialize the range of SVR hyperparameters (C and gamma) 4: Set the parameters of the Grey Wolf Optimizer (number of wolves, maximum iterations, etc.) 5: Initialize the positions of the wolves randomly within the hyperparameter ranges 6: $t\mathrm{ }<\mathrm{ }T$:     $for\mathrm{ }i\mathrm{ }in\mathrm{ }range$:     $accuracy\mathrm{ }=\mathrm{ }calculate\_accuracy(svr\_model,\mathrm{ }validation\_set)$      $fitness\_value=\mathrm{ }\left(1\mathrm{ }-\mathrm{ }accuracies\right)\ast \mathrm{ }100$     $\alpha \_wolf=wolves\left[0\right]$     $\beta \_wolf=wolves\left[1\right]$     $\delta \_wolf=wolves\left[2\right]$     $wolf.position=update\_position$     $t\mathrm{ }=\mathrm{ }t\mathrm{ }+\mathrm{ }1$ 7: $for\mathrm{ }i\mathrm{ }in\mathrm{ }range$:    $for\mathrm{ }j\mathrm{ }in\mathrm{ }range$ $Positions[i,\mathrm{ }j]\mathrm{ }=\mathrm{ }(X1\mathrm{ }+\mathrm{ }X2\mathrm{ }+\mathrm{ }X3)/3$     $t\mathrm{ }=\mathrm{ }t\mathrm{ }+\mathrm{ }1$     return best_C, best_gamma 8: Use the best hyperparameters to train the final SVR model 9: Make predictions on new battery data

Through the above process, GWO can adaptively search for the optimal C, $\sigma$ parameters of the SVR model for retired power battery data, effectively improving the generalization of the recycling price prediction model, improving the accuracy of retired power battery recycling price prediction, and ensuring the stability and robustness of the model. This article uses the RMSE and the MAPE to evaluate the accuracy of the model [34], as Equations (7) and (8). The closer the values of the RMSE and the MAPE are to 0, the higher the accuracy of the model.

$$RMSE=\sqrt{{\displaystyle \frac{1}{N}}\sum _{i=1}^N{\left|y_i-\widehat{y_i}\right|}^2}$$

(8)

$$MAPE={\displaystyle \frac{100\mathrm{\%}}{n}}\sum _{i=1}^n\left|{\displaystyle \frac{y_i-\widehat{y_i}}{y_i}}\right|$$

(9)

where n is number of retired power battery samples, $\widehat{y_i}$ is the true value of the price, $y_i$ is price forecast value and $\overline{y}$ is real average price.

5. Evaluation of the Performance of the Method

In order to effectively predict the recycling price of retired power batteries, this article takes the retired power battery data as an example, analyzes the influencing factors of the recycling price of retired power batteries, extracts temporal data features in both directions, removes redundant data features, accurately predicts the recycling price of retired power batteries, and verifies the effectiveness of the BDAE-GWO-SVR method.

5.1. Experimental Dataset

The data for this experiment comes from retired power batteries with the same specifications and 5 models. Each model provides 1000 pieces of data, a total of 5000 pieces of data, and is divided into training and testing sets in a 7:3 ratio.

Table 2. Partial dataset.

Number	1	2	3	4	5	6	7	8
Battery capacity$/kWh$	100	85	102	95	70	80	77	65
Usage time$/h$	34,566	45,473	42,387	42,898	38,443	36,283	37,829	42,781
Number of battery cycles	7876	7865	6534	8723	8532	9876	5437	6234
Maintenance frequency	3	2	4	1	5	0	0	3
Battery health	81%	80%	82%	75%	77%	68%	85%	77%
Nickel market recycling price $\left(USD/kg\right)$	36.25	43.75	45.97	37.36	44.72	44.86	45	43.05
Cobalt market recycling price $\left(USD/kg\right)$	36.94	36.8	36.52	37.36	37.22	37.08	38.09	36.67
Manganese market recycling price $\left(USD/kg\right)$	1.83	1.88	1.88	1.79	1.79	1.82	1.78	1.89
Lithium market recycling price $\left(USD/kg\right)$	92.36	91.94	92.91	90.69	91.38	92.98	90.13	90.83
Number of retired batteries	2654	3564	3632	2964	3463	2659	3459	6543
New power battery price index	1.1%	−2.2%	−1.8%	0.3%	0.9%	2.3%	−3.6%	−0.2%
Waste power battery price index	−2.2%	−3.1%	−0.4%	0.9%	3.1%	1.3%	−1.4%	1.2%
Appearance wear degree (1 is poor, 5 is good)	5	1	1	1	5	3	1	2
Price$/USD$	1354.56	898.86	1006.92	907.91	863.89	937.68	1120.21	1243.91

shows the experimental dataset.

The experiment is implemented in Python and run on the Python platform. This experiment is conducted on a laptop equipped with AMD R9-7945HX (2.50 GHz) CPU, 16 GB RAM, and Microsoft Windows 10 enterprise operating system.

Due to the inconsistent order of magnitude between the input feature variables, directly inputting them into the model for training can lead to slow or even non-convergence of the model. In order to eliminate the dimensional influence between different features, data normalization is necessary. The data normalization stage before training adopts the min–max method, which can be expressed as Equation (9).

$$x^{\mathrm{\prime }}={\displaystyle \frac{x-\mathrm{m}\mathrm{i}\mathrm{n}\left(x\right)}{\max \left(x\right)-\mathrm{m}\mathrm{i}\mathrm{n}\left(x\right)}}$$

(10)

where $x^{\mathrm{\prime }}$ is the normalized data of retired power batteries, and $x$ is the original data of retired power batteries.

5.2. Fature Extraction of Influencing Factor Data

The prediction of the recycling price of retired power batteries mainly consists of two steps: (1) feature extraction of influencing factor data; (2) prediction of recycling prices based on influencing factors.

Firstly, the processed retired power battery data are input into BDAE for encoding, and bidirectional feature extraction is performed on the influencing factor data. The activation function of the BDAE is the ELU function. At present, the selection of hyperparameters in neural networks is mostly determined by combining experience with experiments. The hyperparameters used in this article include: input data dimension, number of hidden layers, number of nodes in each hidden layer, and output data dimension. Determine the input dimension as 13 based on the data. Having too many hidden layers in a neural network will reduce the model’s generalization ability, so the number of hidden layers is set to 2 and the number of nodes is 10 and 8, respectively.

For the number of nodes in the output layer, analyze the reconstruction error of feature extraction and the MAPE size of prediction results under different numbers of hidden layer nodes, as shown in Figure 5. From the graph, it can be seen that when the number of nodes is 6, the error of feature extraction is 0.022, indicating that BDAE accurately extracts data features and reduces data complexity. As the number of nodes decreases, the feature extraction error increases and the predicted MAPE also increases. This is because too few nodes may lead to underfitting of the model, resulting in a decrease in the accuracy of feature extraction. Therefore, the number of output layer nodes selected in this article is 6. The parameter settings for the BDAE are shown in the

Table 3. Parameter settings for BDAE.

Parameter Name	Parameter Values
Number of input layer nodes	13
Number of nodes in the first hidden layer	10
Number of nodes in the second hidden layer	8
Number of output layer nodes	6
Batch size	32
Iterations	2000

. The loss of the training and testing sets for the experiment is shown in Figure 5.

5.3. Recycling Price Prediction

Then, the GWO-SVR model is used to predict the recycling price of retired power batteries. Considering the dynamic and nonlinear characteristics of the factors influencing the price of retired power battery recycling, improper parameter selection can easily lead to low prediction accuracy. Using the GWO algorithm to optimize the parameters of SVR prediction model improves its generalization ability and prediction accuracy. The upper and lower bounds on the optimization parameters of the GWO algorithm are ub = 20,000 and lb = 0.01, respectively. As shown in Figure 6 below, the accuracy of the Grey Wolf algorithm reaches its peak after 2 iterations and then tends to stabilize. After two iterations, the optimal parameters have been found, and the accuracy of the GWO for optimization reaches 0.813.

To analyze whether there is a risk of premature convergence in GWO, we conduct 20 independent experiments. The results show that all experiments converge to the optimal solution within the 2nd or 3rd iteration, with an average accuracy of 0.813 ± 0.005 and a very small standard deviation, indicating high stability. Moreover, under the same parameter settings, when the maximum number of iterations is increased to 50 or 100, the algorithm still converges to the optimal solution after the 2nd iteration, with no further improvement in fitness values in subsequent iterations (as shown in Figure 6), indicating that the current solution is close to the global optimum.

The optimal parameters are then input into the subsequent SVR model to obtain the final prediction result. The predicted price of retired power battery recycling is shown in Figure 7. The RMSE is 0.371, the MAPE is 0.060, and the accuracy of the recovery price prediction is good.

From the prediction result of BDAE-GWO-SVR, it can be seen that there is a certain error in the peak value of the prediction result. This is because before the battery is disassembled, the surface data indirectly reflects the recycling price of retired power batteries. It can reflect changes in recycling prices, but there is a certain gap with accurate prediction. In addition, the recycling price of retired power batteries is affected by various factors, including market demand and raw material prices, which exhibit significant volatility. Particularly when the price approaches the peak, fluctuations in these market factors become more pronounced, and the inherent uncertainty of the market affects the accuracy of price predictions. However, most of the predicted values have a high coincidence rate with the true values, indicating that this method can be effectively applied to predict the recycling price of retired power batteries, and can provide reference for evaluating whether retired power batteries have reuse value.

Finally, SHAP value analysis is used to evaluate the contribution of each feature extracted to the prediction outcome, as shown in Figure 8. It can be concluded that Feature 2 has the greatest impact on the recycling price, with a contribution percentage of 28.79%, while Feature 3 has the smallest impact, contributing only 3.38%.

Table 4. Contribution percentage.

Feature	Contribution
Feature 1	16.34%
Feature 2	28.79%
Feature 3	3.38%
Feature 4	11.82%
Feature 5	14.83%
Feature 6	24.85%

shows the contribution percentages of each feature.

Through further analysis of the six potential features, it was found that latent Feature 2, which has the greatest impact on the recycling price, mainly includes original features such as battery capacity, market recycling prices of lithium, nickel, and manganese, and the number of retired batteries. Latent Feature 6, which also has a significant impact on the recycling price, mainly includes original features such as battery capacity, nickel market price, and appearance wear degree. In contrast, factors such as battery repair frequency and battery price index have a weaker influence on the recycling price. The heatmap in Figure 9 and Figure 10 clearly show the contribution of the original features to the potential features.

6. Discussion

6.1. Comparison of the Model Itself

This section uses the same retired power battery data to compare GWO-SVR prediction using SVR without dimensionality reduction, DAE-GWO-SVR prediction, and BDAE-GWO-SVR prediction. In addition, the performance of DAE and BDAE feature extraction was compared, and their reconstruction errors are shown in Figure 11. It can be seen that BDAE has better feature extraction performance than DAE. This is because BDAE can better capture the complex patterns and noise in the surface data of retired power batteries through its bidirectional denoising structure, thereby improving the accuracy of battery performance prediction.

Figure 12 shows the fit of each predicted point, while the scatter plot in Figure 13 provides a more intuitive representation of the overall fit of the model. The closer the scatter plot is to a straight line, the more accurate the price prediction results.

6.2. Comparison with Other Models

In addition, this article also selected random forest models, BP neural networks, CNN, LSTM, and Transformer models for comparison. Figure 14 shows their comparison results.

Table 5. Result comparison.

Method	RMSE	MAPE
SVR	0.453	0.073
GWO-SVR	0.413	0.067
DAE-GWO-SVR	0.396	0.065
BDAE-GWO-SVR	0.371	0.060
RF	1.058	0.084
BP	0.812	0.08
LSTM	0.436	0.071
CNN	1.371	0.106
Transformers	1.314	0.102

compares the RMSE and MAPE results of different models. From the above table, it can be seen that using the BDAE-GWO-SVR method to predict the price of retired power battery recycling is significantly better than other methods. The MAPE of the BDAE-GWO-SVR method is 0.06, while the CNN method has the largest error, with a MAPE of 0.106.

There are two reasons why BDAE-GWO-SVR is superior to other methods: Firstly, BDAE accurately extracts features from retired power battery data, reduces redundant features, and improves the accuracy of the recycling price prediction model. Secondly, GWO is used to optimize the parameters of the SVR prediction model. By searching for the optimal parameter combination in the parameter space to better fit the nonlinear characteristics of retired power batteries, we improve the generalization ability of prediction models for different power battery data.

6.3. Other Cases

Figure 15 shows the fitting situation of using BDAE-GWO-SVR to predict the price of retired power battery recycling under stable market fluctuations. In this stable market environment, the predicted $MAPE$ reaches 0.053, which is lower than the prediction effect considering market fluctuations. This is because the market fluctuates frequently and is difficult to predict, which makes the data unstable and makes it difficult for the model to capture and learn the true trend of price changes. In contrast, in the case of stable market fluctuations, the data presents relatively stable trends and patterns, which makes it easier for the model to identify and fit potential patterns, resulting in higher accuracy in predicting the price of power battery recycling.

To further demonstrate the applicability of the model proposed in this paper, 2000 sets of lithium iron phosphate data provided by a certain enterprise were used for supplementary experiments to calculate the predicted RMSE and MAPE sizes. The predicted results are shown in Figure 16. The predicted RMSE is 0.402 and the MAPE is 0.062. This result indicates that the BDAE-GWO-SVR model also has good applicability in predicting the recycling price of lithium iron phosphate, demonstrating the effectiveness of this method.

7. Conclusions

To address the challenge of effectively exploring the impact mechanisms of predicting recycling prices based on surface influencing factor data, which leads to low prediction accuracy, the BDAE-GWO-SVR method is adopted for predicting the price of retired power batteries. By extracting the data features of factors affecting the price of retired power batteries through BDAE, accurate features related to recycling prices are extracted. The complexity of retired power battery data processed by BDAE is reduced, and the SVR model is used to establish the correspondence between features and recycling price. In addition, considering the fluctuation of data on factors affecting power batteries under different usage scenarios, GWO is used to optimize the hyperparameters of the SVR recycling price prediction model to improve its generalization ability. By comparing with different prediction methods, the proposed method has significantly improved prediction accuracy.

The BDAE-GWO-SVR approach proves to be effective in predicting the recycling price of retired power batteries through surface data. Future steps can involve considering the impact of policy changes on recycling prices to enhance the applicability of the model in dynamic regulatory environments.