Electric passenger car ownership prediction method based on dynamic parameter Bass model
By using the dynamic parameter Bass model and employing nonlinear least squares and principal component analysis to calibrate the parameters of the electric passenger vehicle ownership model, the problem that existing models cannot reflect dynamic factors is solved, and high-precision prediction of electric passenger vehicle ownership is achieved, supporting policy and infrastructure planning.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-15
- Publication Date
- 2026-03-27
AI Technical Summary
Existing Bass models suffer from problems such as static parameters, coarse estimation, fixed weights, and outdated updates in predicting electric vehicle ownership. They cannot effectively reflect the dynamic impact of policy, economic, and technological factors, resulting in large errors in the prediction results.
A dynamic parameter Bass model was adopted, and the innovation coefficient and imitation coefficient were calibrated by nonlinear least squares method and principal component analysis. The relationship between dynamic parameters and influencing factors was established by combining multiple regression, and a prediction model for the number of electric passenger vehicles was constructed.
This improves the model's prediction accuracy and interpretability, enabling it to better reflect changes in the market environment, achieve high-precision medium- and long-term electric passenger vehicle ownership forecasts, and support policy formulation and infrastructure planning.
Smart Images
Figure CN121745367A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of electric vehicle ownership prediction technology, and in particular to a method for predicting the ownership of electric passenger vehicles based on the dynamic parameter Bass model. Background Technology
[0002] Electric vehicles, represented by pure electric and plug-in hybrid electric vehicles, differ significantly from traditional gasoline-powered vehicles in terms of powertrain, chassis, and electrical systems. In particular, various promotional incentive policies, the rapid iteration of the three key technologies (electric drive, battery, and motor), and the development of charging infrastructure all have a significant impact on electric vehicle sales. Research on the forecasting of electric passenger vehicle ownership can provide important reference data for the future development of the passenger vehicle industry, charging infrastructure planning, and prediction of vehicle carbon emissions.
[0003] In existing research on methods for predicting electric vehicle ownership, there are many different methods and models, including the Gompertz model, the Logistic model, the LSTM-SD combined prediction model, and the grey prediction model. Among them, prediction methods based on the Bass model are gradually becoming mainstream. The Bass diffusion model is widely used for new product market penetration prediction due to its simple form and clear physical meaning of parameters.
[0004] However, current research on Bass model prediction still has the following shortcomings:
[0005] 1. Static parameters: Treating the innovation coefficient p and the imitation coefficient q as constants fails to reflect the time-varying characteristics brought about by technological iteration and subsidy reduction.
[0006] 2. Coarse estimation: The use of genetic algorithms or analogy methods to calibrate p and q lacks systematic dimensionality reduction for multivariate collinear data, leading to regional...
[0007] Migration deviation amplification;
[0008] 3. Weight solidification: The entropy weight method is used to allocate model weights ex-post, which does not reveal the intrinsic driving mechanism of "economy-policy-technology" on diffusion rate, and does not solve the problem of urban heterogeneous adaptability;
[0009] 4. Lagging updates: The multi-factor framework requires manual recalibration and is difficult to automatically update with the release of data. In a rapidly changing market environment, the reliability of predictions drops rapidly.
[0010] In summary, existing Bass models lack consideration of multiple factors, including policy, economic, social, and technological factors. They fail to reflect the dynamic impact of exogenous variables such as policy subsidies, infrastructure, and technological progress on diffusion speed, leading to significant medium- and long-term prediction errors. Continuing to use the Bass equation with fixed p and q will fail to reflect the level of economic development and electric vehicle technology, thus not aligning with the actual development of electric passenger vehicles and resulting in substantial biases in the predictions. Summary of the Invention
[0011] In view of this, the purpose of this invention is to provide a method for predicting the number of electric passenger vehicles based on the dynamic parameter Bass model, so as to improve the prediction accuracy and interpretability of the model and better predict the number of electric passenger vehicles in China over the next ten years.
[0012] To achieve the above objectives, the present invention adopts the following technical solution: a method for predicting the number of electric passenger vehicles based on a dynamic parameter Bass model, comprising the following steps:
[0013] S1: Obtain time series data on the number of electric passenger vehicles and multi-source influencing factors in the target area over the years through publicly available data;
[0014] S2: The initial innovation coefficient p and imitation coefficient q of the Bass model are calibrated based on the nonlinear least squares method. Taking the annual electric passenger vehicle ownership as input, the optimization objective is to minimize the error. Through iterative solution, the initial static parameter values that best fit the historical diffusion curve are obtained.
[0015] S3: Principal component analysis is used to extract three types of principal components—economic, policy, and technological—from the influencing factors. A multiple regression equation is established between the dynamic parameter p(t) of the innovation coefficient, the dynamic parameter q(t) of the imitation coefficient, and the principal components and time to achieve parameter dynamization.
[0016] S4: Substitute the dynamic parameters p(t) of the innovation coefficient and q(t) of the imitation coefficient into the Bass diffusion differential equation to obtain the future electric passenger vehicle ownership prediction curve and the prediction results for each year;
[0017] S5: Backtest the prediction curve using the actual holdings in historical years. When the mean absolute error (MAPE) is less than or equal to 5%, output the final prediction result.
[0018] In a preferred embodiment, the influencing factors include: GDP per capita, the number of charging facilities, the intensity of government subsidies, the average driving range of electric passenger vehicles, and the energy density of battery mass.
[0019] In a preferred embodiment, the cumulative variance contribution rate of principal component analysis is ≥98%, and the Kaiser-Meyer-Olkin test value is >0.9.
[0020] In a preferred embodiment, the initial values of the innovation coefficient p and the imitation coefficient q are fitted using the least squares method, and the estimation is optimized based on minimizing the sum of squared errors between the predicted values and the actual data. Furthermore, there are significant differences between the years, and they are not stable.
[0021] In a preferred embodiment, the multiple regression equation describes the relationship between the innovation coefficient dynamic parameter p(t), the imitation coefficient dynamic parameter q(t), and the influencing factors X(t) and Y(t), specifically:
[0022] Principal component analysis (PCA) was used to study the relationship between various influencing factors and the number of electric passenger vehicles in operation, thereby extracting the main influencing factors. The external and internal influencing factors were denoted as vectors X(t) = [X1(t), X2(t), ..., X...]. n (t)] and Y(t)=[Y1(t),Y2(t),…,Y n [(t)], where X j (t) and Y j (t) represents the value of the j-th influencing factor at time t;
[0023] Combining the future development patterns of internal and external influencing factors X(t) and Y(t), expressions for p(t) and q(t) are established based on multiple linear regression:
[0024]
[0025]
[0026] Where, α j and β j The parameters to be estimated, j=0...n, are obtained through Stata regression estimation.
[0027] In a preferred embodiment, the basic expression of the Bass diffusion differential equation is:
[0028]
[0029] Where f(t) is the adoption rate of the new product at time t, and F(t) is the cumulative adoption rate of the new product;
[0030] The cumulative number of new products adopted before time t is expressed as:
[0031]
[0032] Where N(t) is the cumulative holdings in year t, and m is the maximum market potential, i.e., the maximum value used in the diffusion process.
[0033] In a preferred embodiment, the dynamic parameter Bass diffusion model is:
[0034] .
[0035] In a preferred embodiment, the backtesting step in S5 includes:
[0036] Calculate MAPE based on the actual holdings over the past five years. If MAPE > 5%, return to S3 to readjust the principal component weights or increase the number of sample years until MAPE ≤ 5%. Specifically:
[0037] .
[0038] Among them, a i represents the actual data, and a*i represents the model's predicted data.
[0039] In a preferred embodiment, the diffusion solution module uses MATLAB to numerically solve the Bass differential equation to obtain the diffusion trend of electric passenger vehicles in China, and outputs data and curves on the number of electric passenger vehicles in China for the next 10 years.
[0040] In a preferred embodiment, after the parameter dynamization step, an economic rationality test is performed on p(t) and q(t) to ensure that p(t)∈[0,1] and q(t)∈[0,1] and conform to the actual diffusion law.
[0041] Compared with the prior art, the present invention has the following beneficial effects:
[0042] 1) Introducing dynamic innovation and imitation coefficients to enhance the Bass model's adaptability to the diffusion process of electric passenger vehicles. Traditional Bass models use fixed parameters, making it difficult to reflect the dynamic impact of internal and external factors such as policies, technologies, and markets. This study constructs time-varying innovation coefficients p(t) and imitation coefficients q(t), enabling the model parameters to respond to changes in the market environment, significantly improving the model's ability to capture and predict the evolution trend of electric passenger vehicle ownership.
[0043] 2) By integrating principal component analysis and multiple regression, dynamic coupling modeling of model parameters and key influencing factors is achieved. Principal component analysis (PCA) is used to screen out the five key factors that have the greatest impact on the number of electric passenger vehicles (such as GDP per capita, charging infrastructure, government subsidies, driving range, and battery energy density), and establish multiple linear regression relationships between them and p(t) and q(t). This enhances the dynamic prediction and explanatory power of the model parameters and overcomes the "black box" problem of traditional models.
[0044] 3) Construct a parameter fitting mechanism based on nonlinear least squares to improve the fitting accuracy of historical data. Nonlinear least squares is used to perform parameter inversion on historical stock data, combined with linear regression to predict the future trends of p(t) and q(t). This effectively reduces the model's sensitivity to initial parameter settings and improves the consistency and stability of the model in historical fitting and future prediction.
[0045] 4) Achieve high-precision medium- and long-term forecasts of electric passenger vehicle ownership, supporting policy formulation and infrastructure planning. In actual data verification, the MAPE (Mean Absolute Percentage Error) of the model is significantly better than that of traditional fixed-parameter models. It can provide a scientific basis for the government to formulate new energy vehicle promotion policies and for enterprises to plan production capacity and charging infrastructure layout, and has strong engineering application value. Attached Figure Description
[0046] Figure 1 This is a flowchart illustrating a method for predicting the number of electric passenger vehicles in China based on a dynamically parameter-improved Bass model, according to the present invention.
[0047] Figure 2 This is a graph showing the predicted number of electric passenger vehicles in use according to the present invention.
[0048] Figure 3 A comparison chart showing the predicted number of electric passenger vehicles using two Bass models. Detailed Implementation
[0049] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0050] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.
[0051] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations according to this application; as used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise; furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.
[0052] This invention proposes a method for predicting the number of electric passenger vehicles in China based on a dynamically parameter-improved Bass model, referencing... Figure 1-3This method first estimates the initial parameters of the Bass model using nonlinear least squares based on historical data, and then performs linear regression analysis on the innovation coefficient and imitation coefficient. Secondly, it uses principal component analysis (PCA) to identify five key factors influencing the promotion and application of electric passenger vehicles, including per capita GDP, charging infrastructure availability, government subsidies, electric passenger vehicle driving range, and battery energy density. Then, it uses Stata software to perform regression analysis on the innovation coefficient, imitation coefficient, and influencing factors, thereby analyzing the relationship between dynamic parameters and influencing factors. Finally, it constructs a Bass model that incorporates improved dynamic parameters to predict the number of electric passenger vehicles in China from 2025 to 2035. The method specifically includes the following steps:
[0053] S1: Obtain historical data on the number of electric passenger vehicles and multi-source influencing factors in the target region for 15 consecutive years through publicly available data from the National Bureau of Statistics and other sources;
[0054] S2: The initial innovation coefficient p and imitation coefficient q of the Bass model are calibrated based on the nonlinear least squares method. Taking the annual electric passenger vehicle ownership as input, the optimization objective is to minimize the error. Through iterative solution, the initial static parameter values that best fit the historical diffusion curve are obtained.
[0055] S3: Principal component analysis is used to extract three types of principal components—economic, policy, and technological—from the shadow factors, and multiple regression equations are established between p(t), q(t), the principal components, and time to achieve parameter dynamization.
[0056] S4: Substitute the dynamic p(t) and q(t) into the Bass diffusion differential equation to obtain the prediction curve of electric passenger vehicle ownership for the next 10 years and the prediction results for each year;
[0057] S5: Backtest the prediction curve using the actual holdings in historical years. When the mean absolute error (MAPE) is less than or equal to 5%, output the final prediction result.
[0058] In this embodiment, the model construction and parameter initialization method includes the following steps:
[0059] 1) Constructing the Bass diffusion model: using the basic form of the classic Bass model:
[0060]
[0061] 2) Introducing a dynamic parameter mechanism: To overcome the shortcomings of traditional models with fixed parameters that cannot reflect external influences, this invention proposes to set p and q as time functions, i.e., p(t) and q(t), and construct an improved Bass model in the following form:
[0062]
[0063] In this embodiment, the target number of electric passenger vehicles in China by 2035 is set at 200 million, representing a maximum market potential of m = 200 million vehicles. Considering the dynamic changes in the innovation coefficient p and the imitation coefficient q, the least squares method is used to fit the obtained p and q data, based on the known number of electric passenger vehicles in each year from 2010 to 2024. Using 2010 as the base year, the relationship between the innovation coefficient p and the imitation coefficient q affecting the number of electric passenger vehicles and time is obtained (t takes values of 1, 2, 3, ...).
[0064]
[0065]
[0066] Optionally, under the constraint of minimizing the predicted and actual values, the innovation coefficient p and imitation coefficient q for each year are calculated based on historical data, as shown in Table 1. The data in the table shows that there are significant differences between years, rather than a stable constant. The innovation coefficient p describes the probability that an individual will independently adopt a new product due to external influences (such as advertising, media promotion, and marketing). In the Bass model, the imitation coefficient q describes the likelihood that someone who has not yet used the product will be influenced by word-of-mouth from other users and begin using it. An increase in the p value indicates that external factors play a more important role in the diffusion of new products, accelerating the market penetration and diffusion speed. An increase in the q value indicates that internal influences (i.e., mutual influence among consumers) are increasing during product diffusion, and this increase also accelerates the market diffusion speed of the product.
[0067] Table 1. Number and Key Parameters of Electric Passenger Vehicles in China
[0068]
[0069] In this embodiment, SPSS software was used to perform correlation analysis on nine influencing factors and the number of electric passenger vehicles in China based on PCA principal component analysis to obtain a correlation matrix. The larger the absolute value of the correlation coefficient, the stronger the correlation. The results are shown in Table 2. It shows that the absolute values of the correlation coefficients between per capita GDP, charging infrastructure, government subsidies, electric passenger vehicle driving range, and battery energy density and the number of electric passenger vehicles are all greater than 0.85, indicating that these influencing factors are highly correlated with the number of electric passenger vehicles.
[0070] Table 2 Correlation Matrix of Each Variable
[0071]
[0072] After selecting the five most relevant influencing factors, principal component analysis was performed, and the results are shown in Table 3. The common factor variance ranged from 83.0% to 99.1%, and the absolute values of the component coefficients were all greater than 0.9. Based on the characteristics of internal and external factors, the factors with the greatest impact on the number of electric passenger vehicles were identified as: external factors (GDP per capita, charging infrastructure availability, and government subsidy level) and internal factors (vehicle driving range and battery energy density).
[0073] Table 3 Common Factor Variance and Component Coefficients
[0074]
[0075] In this embodiment, the development trend expression of internal and external influencing factors is as follows:
[0076] 1) GDP per capita: China's total GDP / 100 million yuan (by Y) GDP (t) represents:
[0077]
[0078] China's total population / 100 million (by Y) population (t) represents:
[0079]
[0080] Where T is the ordinal number of the predicted year, T∈{0,1,2,…}, and T=0 in 1995, then T=t+14.
[0081] From equations (12) and (13), we can obtain the GDP per capita in yuan:
[0082]
[0083] 2) The number of charging facilities in operation per 10,000 units is expressed as:
[0084]
[0085] Where t represents the time series, with t=1 for 2010, and so on.
[0086] 3) The level of policy subsidies per 10,000 yuan is expressed as follows:
[0087]
[0088] Based on data from the "Catalogue of New Energy Vehicle Models Exempt from Vehicle Purchase Tax" released by the Ministry of Industry and Information Technology, we statistically analyze the annual average values of battery energy density and driving range, and predict future values through fitting.
[0089] 4) Driving range / km is expressed as:
[0090]
[0091] 5) Battery energy density (Wh / kg) is expressed as:
[0092]
[0093] In this embodiment, the integration of the innovation coefficient p, the imitation coefficient q, and the influencing factors specifically involves: organizing and standardizing the collected data; using Stata software to perform regression analysis with the influencing factors as independent variables and p and q as dependent variables; and obtaining the following relationship based on the fitting results:
[0094]
[0095]
[0096] In this embodiment, the above-mentioned relationship between p(t) and q(t) is substituted into the improved Bass model to obtain the diffusion trend of electric passenger vehicles in China, resulting in a predicted curve for the number of electric passenger vehicles in use from 2025 to 2035. The results are as follows. Figure 2 As shown in Table 4.
[0097] The prediction results of this embodiment are compared with the actual data from 2020 to 2024 to calculate the mean absolute percentage error (MAPE):
[0098]
[0099] The results show that the five-year average MAPE of the method described in this embodiment is 4.66%, which is significantly better than the traditional Bass model with fixed parameters (MAPE is as high as 25% or more). The comparison curves are shown below. Figure 3 As shown, this invention demonstrates its high accuracy and strong adaptability in predicting the number of electric passenger vehicles.
[0100] Table 4. Error Comparison of the Improved Bass Model in This Embodiment with Other Bass Models
[0101]
[0102] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.
Claims
1. A method for predicting the number of electric passenger vehicles based on a dynamic parameter Bass model, characterized in that, Includes the following steps: S1: Obtain time series data on the number of electric passenger vehicles and multi-source influencing factors in the target area over the years through publicly available data; S2: The initial innovation coefficient p and imitation coefficient q of the Bass model are calibrated based on the nonlinear least squares method. Taking the annual electric passenger vehicle ownership as input, the optimization objective is to minimize the error. Through iterative solution, the initial static parameter values that best fit the historical diffusion curve are obtained. S3: Principal component analysis is used to extract three types of principal components—economic, policy, and technological—from the influencing factors. A multiple regression equation is established between the dynamic parameter p(t) of the innovation coefficient, the dynamic parameter q(t) of the imitation coefficient, and the principal components and time to achieve parameter dynamization. S4: Substitute the dynamic parameters p(t) of the innovation coefficient and q(t) of the imitation coefficient into the Bass diffusion differential equation to obtain the future electric passenger vehicle ownership prediction curve and the prediction results for each year; S5: Backtest the prediction curve using the actual holdings in historical years. When the mean absolute error (MAPE) is less than or equal to 5%, output the final prediction result.
2. The method for predicting the number of electric passenger vehicles based on the dynamic parameter Bass model according to claim 1, characterized in that, The influencing factors include: GDP per capita, the number of charging facilities, the intensity of government subsidies, the average driving range of electric passenger vehicles, and the energy density of battery mass.
3. A method for predicting the number of electric passenger vehicles based on a dynamic parameter Bass model according to claim 1 or 2, characterized in that, The cumulative variance contribution rate of principal component analysis is ≥98%, and the Kaiser-Meyer-Olkin test value is >0.
9.
4. The method for predicting the number of electric passenger vehicles based on the dynamic parameter Bass model according to claim 1, characterized in that, The initial values of the innovation coefficient p and the imitation coefficient q are fitted using the least squares method. The optimization estimation is based on minimizing the sum of squared errors between the predicted values and the actual data. Furthermore, there are significant differences between the years, and they are not stable.
5. The method for predicting the number of electric passenger vehicles based on the dynamic parameter Bass model according to claim 1, characterized in that, The multiple regression equation describes the relationship between the dynamic parameters p(t) of the innovation coefficient and q(t) of the imitation coefficient, and the influencing factors X(t) and Y(t), specifically: Principal component analysis (PCA) was used to study the relationship between various influencing factors and the number of electric passenger vehicles in operation, thereby extracting the main influencing factors. The external and internal influencing factors were denoted as vectors X(t) = [X1(t), X2(t), ..., X...]. n (t)] and Y(t)=[Y1(t),Y2(t),…,Y n [(t)], where X j (t) and Y j (t) represents the value of the j-th influencing factor at time t; Combining the future development patterns of internal and external influencing factors X(t) and Y(t), expressions for p(t) and q(t) are established based on multiple linear regression: Where, α j and β j The parameters to be estimated, j=0...n, are obtained through Stata regression estimation.
6. The method for predicting the number of electric passenger vehicles based on the dynamic parameter Bass model according to claim 1, characterized in that, The basic expression of the Bass diffusion differential equation is: Where f(t) is the adoption rate of the new product at time t, and F(t) is the cumulative adoption rate of the new product; The cumulative number of new products adopted before time t is expressed as: Where N(t) is the cumulative holdings in year t, and m is the maximum market potential, i.e., the maximum value used in the diffusion process.
7. A method for predicting the number of electric passenger vehicles based on a dynamic parameter Bass model according to claim 1 or 6, characterized in that, The dynamic parameter Bass diffusion model is as follows: 。 8. The method for predicting the number of electric passenger vehicles based on the dynamic parameter Bass model according to claim 1, characterized in that, The backtesting step in S5 includes: Calculate MAPE based on the actual holdings over the past five years. If MAPE > 5%, return to S3 to readjust the principal component weights or increase the number of sample years until MAPE ≤ 5%. Specifically: 。 Among them, a i represents the actual data, and a*i represents the model's predicted data.
9. The method for predicting the number of electric passenger vehicles based on the dynamic parameter Bass model according to claim 1, characterized in that, The diffusion solution module uses MATLAB to numerically solve the Bass differential equation, obtain the diffusion trend of electric passenger vehicles in China, and output data and curves of the number of electric passenger vehicles in China for the next 10 years.
10. The method for predicting the number of electric passenger vehicles based on the dynamic parameter Bass model according to claim 1, characterized in that, After the parameter dynamization step, the method further includes an economic rationality test on p(t) and q(t) to ensure that p(t)∈[0,1] and q(t)∈[0,1] and conform to the actual diffusion law.