A new energy vehicle sales prediction method based on a virtual variable containing power model
By introducing a grey multivariate power model with dummy variables and time exponents, the problem of neglecting factors in the prediction of new energy vehicle sales is solved, and higher prediction accuracy is achieved, especially in the application in the Chinese market.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NANTONG UNIV
- Filing Date
- 2026-03-19
- Publication Date
- 2026-06-09
AI Technical Summary
Existing methods for predicting new energy vehicle sales mostly rely on univariate models, which ignore relevant factors related to the development and changes of the system and are difficult to effectively characterize qualitative influencing factors, resulting in insufficient prediction accuracy.
We adopted a grey multivariate power model, introduced dummy variables and time power terms, estimated structural parameters by innovation-first accumulation and least squares method, and constructed a VVIGPM model to deeply explore the dynamic change characteristics and quantitative and qualitative factors of the system.
It improved the accuracy of new energy vehicle sales forecasts, especially in the Chinese market where it significantly outperformed other models, with significant improvements in both MAPE and RMSE.
Smart Images
Figure CN122175631A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of new energy vehicle industry analysis and planning technology, specifically a new energy vehicle sales forecasting method based on a power model with dummy variables. Background Technology
[0002] With the advancement of global energy transition and dual-carbon goals, the new energy vehicle industry has become a focal point of strategic competition among nations. Sales forecasts are crucial for government policy-making and infrastructure planning, as well as for companies optimizing resource allocation. However, the development of the new energy vehicle industry is driven by multiple factors, including policy, technology, cost, infrastructure, and market environment, which presents challenges to accurate sales forecasting.
[0003] In recent years, the main methods for predicting new energy vehicle sales have included mathematical statistical models, machine learning models, and grey prediction models. Mathematical statistical models require data to meet specific distribution conditions, while machine learning models rely on large data samples. However, my country's new energy vehicle industry is still in its nascent stage of development, with limited historical data accumulation, making it difficult to meet the data scale and distribution requirements of these two methods. In contrast, grey prediction models are particularly suitable for scenarios with small samples and limited information; therefore, many studies have adopted grey models to predict new energy vehicle sales. However, most existing research is based on univariate time series modeling and fails to fully incorporate systemic influencing factors, resulting in several problems: First, existing research on new energy vehicle sales prediction based on grey prediction models mainly uses univariate models, thus ignoring relevant factors related to systemic development and changes; second, existing grey multivariate methods focus primarily on quantitative factors, lacking effective representation of the numerous qualitative influencing factors present in the real world; third, new energy vehicle sales data exhibits complex changing characteristics, and the data structures described by different models have limitations, making it difficult for existing models to accurately capture their actual evolution trends. Summary of the Invention
[0004] To address the aforementioned problems, this invention proposes a new energy vehicle sales forecasting method based on a power model with dummy variables. The model is based on a grey multivariate power model, employing an innovation-first accumulation approach for data preprocessing. Dummy variables and a time power term are introduced into the structure. The grey multivariate power model uses the power exponent to describe the system's nonlinear characteristics; dummy variables are used to describe the quantitative and qualitative influencing factors; and the time power term is used to deeply explore the system's dynamic change characteristics. These improvements effectively enhance the model's forecasting accuracy in new energy vehicle sales applications.
[0005] The aforementioned algorithm for predicting new energy vehicle sales based on a power model with dummy variables includes the following steps in its construction and application:
[0006] Step 1) Collect new energy vehicle sales data and related influencing factor sequences. The influencing factor sequences are divided into quantitative influencing factor sequences and dummy variable sequences, resulting in the sequence. , Initialize the power exponent. and cumulative generation order ;
[0007] Step 2) Calculate the new information priority accumulation sequence , and adjacent mean series , ;
[0008] Step 3) Establish VVIGPM(1,N, The model estimates the structural parameters using the least squares method. ;
[0009] Step 4) Solve for the model's time response and use an intelligent optimization algorithm to find the optimal parameters. and ;
[0010] Step 5) Input the estimated parameters into the model time response equation to obtain the estimated values, and then obtain the model prediction results through cumulative subtraction and restoration, and evaluate the model prediction accuracy based on the prediction results;
[0011] Step 6) Input the historical sales data of new energy vehicles into the trained model to obtain the predicted future sales value of new energy vehicles.
[0012] Furthermore, in step 1), among the collected N data sequences, the new energy vehicle sales data sequence is used as the system's main behavior sequence, for... Of the remaining N-1 data sequences, the 2nd to Mth sequences are quantitative influencing factor sequences. The (M+1)th to Nth factors are a sequence of qualitative influencing factors, represented by dummy variables. Power exponent and cumulative generation order All initial values are set to 1.
[0013] Furthermore, in step 2), the collected data sequence , The new-first-accumulation generation sequence is obtained by performing new-first-accumulation. , The nearest mean sequence is further calculated based on the information-first accumulation generation sequence. , The specific calculation steps are as follows:
[0014] Step 2-1): Let For the new-first-accumulation generation order, the new-first-accumulation generation sequence is... , The calculation formula is as follows:
[0015]
[0016]
[0017] Step 2-2): Based on the information-first accumulation sequence obtained in Step 2-1), the nearest neighbor mean sequence is further calculated as follows:
[0018]
[0019]
[0020] Furthermore, in step 3), an improved grey multivariate power model (VVIGPM(1,N,)) with dummy variables is constructed. The model structure parameters are estimated using the least squares method. The model construction and structure parameter calculation methods are as follows:
[0021] Step 3-1): VVIGPM(1,N, The model structure is as follows:
[0022]
[0023] in, The power exponent, These are the model structure parameters.
[0024] Step 3-2): The model structure parameter vector is Will , and Substituting the model structure from step 3-1), we obtain the following system of linear equations:
[0025]
[0026] in:
[0027]
[0028]
[0029] The estimation of structural parameters can be divided into the following three cases:
[0030] 1) When hour, , ;
[0031] 2) When hour, , ;
[0032] 3) When hour, , .
[0033] Furthermore, in step 4), VVIGPM(1,N, The time response of the model is then used to solve for the optimal power exponent and the cumulative order of the model by establishing a constrained nonlinear optimization problem. The calculation steps are as follows:
[0034] Step 4-1): In Under the given conditions, VVIGPM(1,N,) is obtained by mathematical induction. The time response of the model is:
[0035]
[0036] in, Next, regarding The predicted value is obtained by performing cumulative subtraction and restoration. The calculation formula is as follows:
[0037]
[0038] Step 4-2): Using minimizing the Mean Absolute Percentage Error (MAPE) as the objective criterion, construct a constrained nonlinear optimization problem and solve for the optimal power exponent and accumulation order of the model. Since excessively high power exponents can easily lead to overfitting, the range of the power exponent is set to (-10, 10). The constrained nonlinear optimization problem is as follows:
[0039]
[0040] in, Estimate the predicted values for the model. The values represent the true values. The aforementioned nonlinear optimization problems are solved using intelligent algorithms, such as the particle swarm optimization algorithm.
[0041] Furthermore, in step 5), the collected data sequence of new energy vehicle sales and related factors is used to solve for VVIGPM(1,N, )Model parameters, evaluate the model's prediction accuracy. The specific steps are as follows:
[0042] Step 5-1): Collect the necessary data on new energy vehicle sales and related factors, and initialize the power exponent and cumulative order in the model;
[0043] Step 5-2): Divide the data into training and testing sets, and calculate the model structure parameters, power exponent, and cumulative order. Test the model's prediction accuracy using the testing set.
[0044] The beneficial effects of this invention are:
[0045] This invention addresses the issue that most existing methods neglect the multiple factors influencing new energy vehicle sales during modeling. Based on the characteristics of the data itself, it proposes an improved grey multivariate power model with dummy variables. This method describes the nonlinear characteristics of the system using a grey power model; it quantifies qualitative factors in the system's development process through dummy variables to comprehensively consider all relevant factors affecting system development; it introduces a priority accumulation of new information to reflect the importance of new information; and it introduces a time power term to deeply explore the dynamic changes of the system. Validation was conducted on Chinese new energy vehicle sales data. Experimental results show that the prediction accuracy of this method is superior to existing new energy vehicle sales prediction methods. Attached Figure Description
[0046] Figure 1 This is a schematic diagram illustrating the steps of a new energy vehicle sales prediction algorithm based on a power model with dummy variables according to the present invention.
[0047] Figure 2 This invention presents a new energy vehicle sales forecasting algorithm based on a power model with dummy variables, and a comparison chart of the predicted and actual values of various comparative models on Chinese new energy vehicle sales data. Detailed Implementation
[0048] The technical method of the present invention will now be described in further detail with reference to the accompanying drawings.
[0049] Step 1) Collect new energy vehicle sales data and related influencing factor sequences. The influencing factor sequences are divided into quantitative influencing factor sequences and dummy variable sequences, resulting in the sequence. , Initialize the power exponent. and cumulative generation order ;
[0050] In step 1), among the collected N data sequences, the new energy vehicle sales data sequence is selected as the system's main behavior sequence. Of the remaining N-1 data sequences, the 2nd to Mth sequences are quantitative influencing factor sequences. The (M+1)th to Nth factors are a sequence of qualitative influencing factors, represented by dummy variables. Power exponent and cumulative generation order All initial values are set to 1.
[0051] Step 2): Collect the data sequence , The new-first-accumulation generation sequence is obtained by performing new-first-accumulation. , The nearest mean sequence is further calculated based on the information-first accumulation generation sequence. , The specific calculation steps are as follows:
[0052] Step 2-1): Let For the new-first-accumulation generation order, the new-first-accumulation generation sequence is... , The calculation formula is as follows:
[0053]
[0054]
[0055] Step 2-2): Based on the information-first accumulation sequence obtained in Step 2-1), the nearest neighbor mean sequence is further calculated as follows:
[0056]
[0057]
[0058] Step 3): Construct an improved grey multivariate power model with dummy variables (VVIGPM(1,N, The model structure parameters are estimated using the least squares method. The model construction and structure parameters are calculated as follows:
[0059] Step 3-1): VVIGPM(1,N, The model structure is as follows:
[0060]
[0061] in, The power exponent, These are the model structure parameters.
[0062] Step 3-2): The model structure parameter vector is ,Will , and Substituting the model structure from step 3-1), we obtain the following system of linear equations:
[0063]
[0064] in:
[0065]
[0066]
[0067] The estimation of structural parameters can be divided into the following three cases:
[0068] 1) When hour, , ;
[0069] 2) When hour, , ;
[0070] 3) When hour, , .
[0071] Step 4): First solve VVIGPM(1,N, The time response of the model is then used to solve for the optimal power exponent and the cumulative order of the model by establishing a constrained nonlinear optimization problem. The calculation steps are as follows:
[0072] Step 4-1): In Under the given conditions, VVIGPM(1,N,) is obtained by mathematical induction. The time response of the model is:
[0073]
[0074] in, Next, regarding The predicted value is obtained by performing cumulative subtraction and restoration. The calculation formula is as follows:
[0075]
[0076] Step 4-2): Using minimizing the Mean Absolute Percentage Error (MAPE) as the objective criterion, construct a constrained nonlinear optimization problem and solve for the optimal power exponent and accumulation order of the model. Since excessively high power exponents can easily lead to overfitting, the range of the power exponent is set to (-10, 10). The constrained nonlinear optimization problem is as follows:
[0077]
[0078] in, Estimate the predicted values for the model. The values represent the true values. The aforementioned nonlinear optimization problems are solved using intelligent algorithms, such as the particle swarm optimization algorithm.
[0079] Step 5): Using the collected data sequence of new energy vehicle sales and related factors, solve for VVIGPM(1,N, )Model parameters, evaluate the model's prediction accuracy. The specific steps are as follows:
[0080] Step 5-1): Collect the necessary data on new energy vehicle sales and related factors, and initialize the power exponent and cumulative order in the model;
[0081] Step 5-2): Divide the data into training and testing sets, and calculate the model structure parameters, power exponent, and cumulative order. Test the model's prediction accuracy using the test set.
[0082] Step 6): Input historical sales data of new energy vehicles into the trained model to obtain the predicted future sales value of new energy vehicles.
[0083] To verify the predictive performance of the improved grey multivariate power model with dummy variables described in this invention, historical data on new energy vehicle sales in China, using data from 2012 to 2020 as the test set, was used to predict data for 2022-2023. Since the development of China's new energy vehicle industry has a relatively short history and has been affected by various factors, the original data was preprocessed using an average weakening buffer operator before the experiment. The calculation method is as follows:
[0084] Let the original sequence be Its first-order weakened buffer sequence is ,in .
[0085] Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE) were used as evaluation metrics, and the following models were selected as comparison models:
[0086] (1) DVCGM(1,N): Grey multivariate model with dummy variables
[0087] (2) GPM(1,N): Grey multivariate power model
[0088] (3) FNDGM(1,N,γ,t) α Flexible nonlinear discrete grey multivariable model
[0089] (4) DTGPM(1,1): Discrete-time grey power model
[0090] (5) TVBGM(1,1): Time-varying gray Bernoulli model
[0091] (6) OFDGPM(1,1): Optimization of fractional discrete grey power model
[0092] Among them, models (1)-(3) are models with improvement methods similar to those described in this invention, and models (4)-(6) are all grey prediction models applied to the field of new energy vehicle sales forecasting. The experimental results of the above models on historical data of new energy vehicle sales in China are shown in Table 1:
[0093] Table 1. Experimental results of each model on historical sales data of new energy vehicles in China.
[0094]
[0095] The experimental results show that, in the historical data of new energy vehicle sales in China, the error index of the method described in this invention is better than that of the comparison model. Compared with the DTGPM(1,1) model with the highest accuracy, the MAPE and RMSE are improved by 15.51% and 29.09%, respectively.
[0096] The above description is merely a preferred embodiment of the present invention based on historical sales data of new energy vehicles in China. The scope of protection of the present invention is not limited to the above embodiments. Any equivalent modifications and other alterations made by those skilled in the art based on the content disclosed in the present invention should be included in the scope of protection set forth in the claims.
Claims
1. A method for predicting new energy vehicle sales based on a power model with dummy variables, characterized in that, Includes the following steps: Obtain the sales data sequence of new energy vehicles and the historical data sequence of multiple related influencing variables, including quantitative and qualitative influencing factors, and divide the data sequence into a training set and a test set; The data sequence is preprocessed using a new-first accumulation strategy to generate a new-first accumulation sequence; Based on the aforementioned information-priority cumulative sequence, an improved grey multivariate power model with dummy variables is established. This model uses new energy vehicle sales as the main system behavior sequence and the multiple influencing variables as related factor sequences. The model introduces dummy variables and a time power term on top of the grey multivariate power model. The grey multivariate power model describes the nonlinear characteristics of the system through power exponents. The dummy variables are used to quantitatively characterize the qualitative influencing factors. The time power term is used to explore the dynamic evolution characteristics of the system. The parameters in the improved grey multivariate power model containing dummy variables are solved using the least squares method and intelligent optimization algorithm to obtain the estimated values of the model parameters, including structural parameters, power exponents and cumulative order. Substitute the data of the influencing variables for the period to be predicted into the solved model to output the predicted value of new energy vehicle sales.
2. The method for predicting new energy vehicle sales based on a power model with dummy variables as described in claim 1, characterized in that, The information-first accumulation sequence is generated by the following formula: ； ； in, The order of priority accumulation is given to new information. This provides the raw data for quantitative influencing factors. The original data for qualitative influencing factors The number of observations contained in each sequence is N, where N is the total number of variables in the system. The number of quantitative influencing factors is M-1, and the number of qualitative influencing factors is NM.
3. The method for predicting new energy vehicle sales based on a power model with dummy variables as described in claim 2, characterized in that, The basic form of the improved grey multivariate power model containing dummy variables is as follows: ; in, and These are sequences generated from the nearest neighbor means of the information-first cumulative sequences of quantitative and qualitative influencing factors, respectively. For time exponentiation; These are the model structure parameters; The exponent is t; t = 1, 2, ..., n.
4. The method for predicting new energy vehicle sales based on a power model with dummy variables according to claim 3, characterized in that, The calculation method for the nearest neighbor mean generation sequence is as follows: ， 。 5. The method for predicting new energy vehicle sales based on a power model with dummy variables according to claim 3, characterized in that, The qualitative influencing factors include policies related to the new energy vehicle industry. These policies include at least one of the new energy vehicle purchase subsidy policy and the purchase tax exemption policy. The implementation status of these policies is quantitatively represented by setting dummy variables.
6. The method for predicting new energy vehicle sales based on a power model with dummy variables according to claim 3, characterized in that, The model time response solution and predicted value estimation include: under initial conditions The time response of the model is then obtained by solving for: ； in, ; Time response estimate After performing cumulative reduction and restoration, the sales forecast value is obtained. : Among them, when hour, .
7. The method for predicting new energy vehicle sales based on a power model with dummy variables according to claim 6, characterized in that, The model parameters are solved using a nested optimization approach combining the least squares method and intelligent optimization algorithms: for structural parameters... Construct a system of linear equations The least squares method is used to estimate where: when the sample size The number of parameters satisfies hour, , ;when hour, , ;when hour, , For a given power exponent and cumulative order To minimize the mean absolute percentage error, a constrained nonlinear optimization problem is constructed to solve for the optimal value: The constraints are: ； The nonlinear optimization problem is solved using an intelligent optimization algorithm, which includes either a genetic algorithm or a particle swarm optimization algorithm.