A water demand prediction method based on bayesian support vector machine and two-step factor analysis

Abstract

The application discloses a water demand prediction method based on a Bayesian support vector machine and two-step factor analysis, and comprises the following steps: A, coupling the Bayesian and support vector machine methods, and predicting the water demand in a basin on the basis of social and economic development data; B, adopting a Taguchi design method to quantize the contribution rate of each factor to the change of the water demand, identifying the influence of the main effect and interaction of the factors on the water demand, and thus screening out key influence factors; and C, performing full-factor analysis on the key factors, predicting future water demand based on the trained Bayesian support vector machine model, and comprehensively analyzing the influence of the key factors on the water demand. The application considers the influence of social and economic development indexes, predicts the water demand change trend under multiple scenarios, provides more scientific and reliable data input for sustainable water resource management, and can provide decision support for water resource managers.

Description

Technical Field

[0001] This invention relates to the field of water demand prediction technology, and in particular to a water demand prediction method based on Bayesian support vector machine and two-step factorial analysis. Background Technology

[0002] Accurate water demand forecasting is fundamental to the rational allocation and utilization of water resources. However, water demand is influenced by many factors. Traditional methods, such as time series extrapolation, neglect the interrelationships among multiple factors in the water resource system and often select single variables, resulting in weak model applicability and distorted water demand forecasts. To a certain extent, the socio-economic development of a river basin can reflect the changing trends in water demand; therefore, water demand forecasting should be based on the level of socio-economic development. Thus, analyzing the relationship between socio-economic development data and water demand is crucial for accurately predicting water demand in a river basin, enabling the fair and rational allocation of water resources, improving water resource utilization efficiency, and providing a scientific basis for the long-term sustainable development of the basin.

[0003] Purpose of the invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by providing a water demand prediction method based on Bayesian support vector machine and two-step factorial analysis, which saves water demand prediction time and improves operational efficiency and simulation accuracy. Summary of the Invention

[0005] This invention provides a water demand prediction method based on Bayesian support vector machine and two-step factorial analysis, comprising the following steps:

[0006] Step A: Based on previous research on water demand forecasting, select relevant socioeconomic indicators as input data to construct a Bayesian support vector machine model;

[0007] Step B: Use a two-step factorial analysis method. First, by establishing an appropriate orthogonal array, quickly find the optimal combination of factors. Then, use Taguchi design to screen out the key factors affecting water demand.

[0008] Step C, Two-Step Factorial Analysis: The second step involves conducting a full factorial analysis on the key factors selected by the Taguchi design, predicting and simulating water demand under various future scenarios, and comprehensively analyzing the impact of key factors on water demand.

[0009] Preferably, step A further includes the following steps:

[0010] Step A1: By referring to previous research and analyzing the factors affecting water demand structure, we initially selected relevant socio-economic indicators that affect water demand, and searched and collected relevant data on each influencing factor and water demand.

[0011] Step A2: Couple Bayesian and Support Vector Machine methods, and use Bayesian inference methods to optimize the parameters of the Support Vector Machine and select the optimal model;

[0012] Step A3: Considering the uncertainty of model parameters, establish a nonlinear statistical relationship between water demand and socioeconomic indicators, thereby constructing a water demand prediction model based on Bayesian support vector machine, and evaluate the simulation effect of the model.

[0013] More preferably, in step A3, a deterministic correlation coefficient R is selected. 2 The Nash coefficient (NSE) and root mean square error (RMSE) reflect the relationship between simulated and measured values, and are used to evaluate the effectiveness of the water demand prediction model based on Bayesian support vector machine. The deterministic correlation coefficient R0 2 The formulas for calculating the Nash coefficient (NSE) and the root mean square error (RMSE) are shown in equations (1)-(3), respectively:

[0014]

[0015]

[0016]

[0017] Where n is the total number of sample points; y obs,i和 y sim,i These represent the observed value and the simulated value, respectively; y obs This is the mean of the observed values.

[0018] Preferably, step B further includes the following steps:

[0019] Step B1: Based on previous research, 12 factors were initially selected, each with high and low levels. Based on the number of factors and their levels, L values ​​corresponding to 32 scenarios were selected. 32 Orthogonal arrays;

[0020] Step B2: Use the Taguchi design method to quantify the contribution rate of each factor to the change in water demand, identify the influence of single-factor main effects and multi-factor interactions on water demand, and screen out the factors that have the greatest impact on the change in water demand. On this basis, conduct a full factorial design.

[0021] More preferably, step B2 further includes: defining the contribution of a single factor to the system response as the proportion of its sum of squares to the total sum of squares; quantifying the magnitude of the influence of factors on water demand by calculating the sum of squares of individual factors and combinations of factors; in the case of three factors, the main effect calculation formulas of the factors are shown in equations (4)-(6):

[0022]

[0023]

[0024]

[0025] Among them, SS A SS B SS C Y represents the sum of squares of factors A, B, and C, respectively; ijt Let I represent the system response value of factor A at level i, factor B at level j, and factor C at level t; I, J, and T represent the level numbers of factors A, B, and C, respectively; the formulas for calculating the sum of squares of the interaction between the two factors are shown in equations (7)-(9):

[0026]

[0027]

[0028]

[0029] Among them, SS A×B SS A×C SS B×C These represent the sum of squares of the interactions between two factors in factors A, B, and C, respectively.

[0030] Preferably, step C further includes the following steps:

[0031] Step C1: Select the main influencing factors, including irrigation efficiency, water price, proportion of cash crop area and total planting area, and set high and low levels respectively. Based on the trained Bayesian support vector machine model, predict and simulate the future water demand of various countries or regions.

[0032] Step C2: Investigate the future water demand trends under multiple economic scenarios and the impact of key factors on water demand. Attached Figure Description

[0033] Figure 1 A schematic diagram of the framework of a water demand prediction method based on Bayesian support vector machine and two-step factorial analysis developed in this invention;

[0034] Figure 2 A diagram illustrating the interaction of socioeconomic indicators;

[0035] Figure 3 Schematic diagram of future water demand changes under various scenarios. Detailed Implementation

[0036] The specific implementation method of the present invention will be further described in detail below with reference to the accompanying drawings.

[0037] like Figure 1 As shown, this invention couples Bayesian, support vector machine, Taguchi design, and full factor analysis methods to develop a water demand prediction model under the influence of socio-economic factors. This method can effectively establish the correlation between water demand in various countries and its influencing factors, quantitatively identify key driving factors of water demand changes and the interactions between these factors. Therefore, based on the identified key factors affecting water demand changes, multiple socio-economic development scenarios are set up, and the multi-scenario set predicts the future trend of water demand changes in various countries.

[0038] In practice, the implementation process includes the following steps:

[0039] Step A: Based on previous research on water demand forecasting, select relevant socioeconomic indicators with complete data, and use these as input data to construct a Bayesian support vector machine model to predict national water demand under various scenarios; Step A is further divided into:

[0040] Step A1: By referring to previous research and analyzing the factors affecting water demand structure, we initially selected relevant socio-economic indicators that affect water demand, and searched and collected relevant data on each influencing factor and water demand.

[0041] In this embodiment, the preliminary selected socio-economic indicators affecting water demand are: Gross Domestic Product (GDP), agricultural share, industrial share, total crop planting area, cereal crop area share, cash crop area share, forage crop area share, agricultural irrigation efficiency, animal husbandry, total population, urbanization rate, and water price.

[0042] Step A2: Couple Bayesian and Support Vector Machine methods. To improve model performance and simulation accuracy, Bayesian inference methods are used to optimize the parameters of the Support Vector Machine and select the optimal model.

[0043] Step A3: Considering the uncertainty of model parameters, establish a nonlinear statistical relationship between water demand and socioeconomic indicators, thereby constructing a water demand prediction model based on Bayesian support vector machine, and evaluate the simulation effect of the model.

[0044] In this embodiment, monthly water demand and influencing factor data from 1980 to 2015 were selected to calibrate and validate the Bayesian support vector machine model. The calibration period was from 1980 to 2005, and the validation period was from 2006 to 2015. A deterministic correlation coefficient (R0.05) was used. 2 The Nash coefficient (NSE) and root mean square error (RMSE) reflect the relationship between simulated and measured values, and evaluate the simulation effect of the Bayesian support vector machine model. The calculation formulas for the above evaluation indicators are shown in equations (1)-(3) respectively:

[0045]

[0046]

[0047]

[0048] Where n is the total number of sample points; y obs,i和 y sim,i These represent the observed value and the simulated value, respectively; y obs This is the mean of the observed values.

[0049] Step B, Two-Step Factorial Analysis: Step 1: By establishing an appropriate orthogonal array, quickly find the optimal combination of factors, and then use Taguchi design to screen out the key factors affecting water demand; Step B is divided into:

[0050] Step B1: Based on previous research, 12 factors were initially selected, each with high and low levels. Based on the number of factors and their levels, L was selected. 32 Orthogonal array (corresponding to 32 scenarios);

[0051] Step B2: The Taguchi design method is used to quantify the contribution rate of each factor to the change in water demand, identify the main effects of single factors and the interactions of multiple factors on water demand, and thus screen out the factors with the greatest impact on the change in water demand. Based on this, a full factorial design is performed. Step B2 further includes:

[0052] The contribution of a single factor to the system response is defined as the proportion of its sum of squares to the total sum of squares. The magnitude of the influence of factors on water demand is quantified by calculating the sum of squares of individual factors and combinations of factors. Taking three factors as an example, the main effect calculation formulas of the factors are shown in equations (4)-(6):

[0053]

[0054]

[0055]

[0056] Among them, SS A SS B SS C Y represents the sum of squares of factors A, B, and C, respectively; ijt Let I represent the system response value of factor A at level i, factor B at level j, and factor C at level t; I, J, and T represent the level numbers of factors A, B, and C, respectively. The formulas for calculating the sum of squares of the interaction between the two factors are shown in equations (7)-(9):

[0057]

[0058]

[0059]

[0060] Among them, SS A×B SS A×C SS B×C This represents the sum of squares of the interaction between the two factors.

[0061] Step C, Two-Step Factorial Analysis: The second step involves conducting a full factorial analysis on the key factors selected by the Taguchi design to predict and simulate water demand under various future scenarios, and comprehensively analyzing the impact of key factors on water demand. Step C is further divided into:

[0062] Step C1: Set the main influencing factors (irrigation efficiency, water price, proportion of cash crop area and total planting area) selected above to high and low levels respectively, and predict the future water demand of various countries based on the trained Bayesian support vector machine model;

[0063] Step C2: In-depth investigation of the future water demand trends under multiple economic scenarios and the impact of key factors on water demand.

[0064] The results showed that the combined contribution of irrigation efficiency, water price, proportion of cash crop area, and total planting area to water demand was 91%, with irrigation efficiency contributing 66%. This indicates that irrigation efficiency is the main factor affecting water demand, followed by water price (contribution rate of 11%). Figure 2 This illustrates the impact of interactions among socioeconomic factors on water demand, showing interactions between factors such as GDP * the proportion of cash crop area, GDP * irrigation efficiency, and livestock farming * water price. Taking the interaction between GDP and irrigation efficiency as an example, the dashed line represents the response of water demand to irrigation efficiency when GDP is at a high level. The fact that the two lines are not parallel indicates that the effect of irrigation efficiency on water demand is influenced by the value of GDP, meaning that GDP and irrigation efficiency have a significant interaction effect on water demand.

[0065] Figure 3 Figures (a) and (b) show the monthly water demand trends in Tajikistan from 2020 to 2050 under 16 different scenarios. The results indicate that water demand initially increases and then decreases, peaking in 2026 at an annual demand of 16.78 billion m³. 3 Then it shows a decreasing trend, with the water demand in 2050 estimated at 11.67 billion m³. 3 Figure (c) shows the annual water demand under various scenarios in 2030 and 2050. The figures in the figure represent the growth rate of annual water demand under scenarios 2 to 16 compared to scenario 1.

[0066] In summary, this invention combines Bayesian methods, support vector machines, Taguchi design, and factorial analysis to generate a two-step factorial method based on Bayesian support vector machines. This method is then applied to water demand prediction, which can effectively reflect the nonlinear and complex relationship between influencing factors and water demand, and identify the key driving factors of water demand changes and the interactions between factors.

[0067] Compared with existing water demand prediction methods, the present invention has the following advantages:

[0068] (1) By using the Bayesian inference method to optimize the parameters and select the optimal model for the support vector machine, the frequent manual adjustment of parameters is avoided, which saves a lot of time and improves the running effect and simulation accuracy.

[0069] (2) A two-step factorial analysis method was applied. First, Taguchi design was used to screen out the key factors affecting water demand. Then, multi-scenario simulations were conducted through full factorial design to explore the impact of the main factors on water demand in detail. The biggest advantage of this method is that a Taguchi design is performed before the full factorial analysis, which quickly finds the optimal parameter combination with the fewest number of experiments, thereby greatly reducing the number of experiments, lowering experimental costs, and improving efficiency.

Claims

1. A water demand prediction method based on Bayesian support vector machine and two-step factorial analysis, characterized in that, Includes the following steps: Step A: Based on previous research on water demand forecasting, select relevant socioeconomic indicators as input data to construct a Bayesian support vector machine model; Step B: Use a two-step factorial analysis method. First, by establishing an appropriate orthogonal array, quickly find the optimal combination of factors. Then, use Taguchi design to screen out the key factors affecting water demand. Step C, Two-Step Factorial Analysis: The second step involves conducting a full factorial analysis on the key factors selected by the Taguchi design, predicting and simulating water demand under various future scenarios, and comprehensively analyzing the impact of key factors on water demand. Step B further includes the following steps: Step B1: Based on previous research, 12 factors were initially selected, each with high and low levels. Based on the number of factors and their levels, L values ​​corresponding to 32 scenarios were selected. 32 Orthogonal arrays; Step B2: Use the Taguchi design method to quantify the contribution rate of each factor to the change in water demand, identify the influence of single-factor main effects and multi-factor interactions on water demand, and screen out the factors with the greatest influence on the change in water demand. On this basis, conduct a full factorial design. Step B2 further includes: defining the contribution of a single factor to the system response as the proportion of its sum of squares to the total sum of squares; quantifying the magnitude of the influence of factors on water demand by calculating the sum of squares of single factors and combinations of factors. In the case of three factors, the main effect calculation formulas of the factors are shown in equations (4)-(6): （4）， （5）， （6）， Among them, SS A SS B SS C Y represents the sum of squares of factors A, B, and C, respectively; ijt Let I represent the system response value of factor A at level i, factor B at level j, and factor C at level t; I, J, and T represent the level numbers of factors A, B, and C, respectively; the formulas for calculating the sum of squares of the interaction between the two factors are shown in equations (7)-(9): （7）， （8）， （9）， Among them, SS A×B SS A×C SS B×C These represent the sum of squares of the interactions between two factors in factors A, B, and C, respectively. Step C further includes the following steps: Step C1: Select the main influencing factors, including irrigation efficiency, water price, proportion of cash crop area and total planting area, and set high and low levels respectively. Based on the trained Bayesian support vector machine model, predict and simulate the future water demand of various countries or regions. Step C2: Investigate the future water demand trends under multiple economic scenarios and the impact of key factors on water demand.

2. The water demand prediction method based on Bayesian support vector machine and two-step factorial analysis according to claim 1, characterized in that, Step A further includes the following steps: Step A1: By referring to previous research and analyzing the factors affecting water demand structure, we initially selected relevant socio-economic indicators that affect water demand, and searched and collected relevant data on each influencing factor and water demand. Step A2: Couple Bayesian and Support Vector Machine methods, and use Bayesian inference methods to optimize the parameters of the Support Vector Machine and select the optimal model; Step A3: Considering the uncertainty of model parameters, establish a nonlinear statistical relationship between water demand and socioeconomic indicators, thereby constructing a water demand prediction model based on Bayesian support vector machine, and evaluate the simulation effect of the model.

3. The water demand prediction method based on Bayesian support vector machine and two-step factorial analysis according to claim 2, characterized in that, In step A3, the deterministic correlation coefficient R is selected. 2 The Nash coefficient (NSE) and root mean square error (RMSE) reflect the relationship between simulated and measured values, and are used to evaluate the effectiveness of the water demand prediction model based on Bayesian support vector machine. The deterministic correlation coefficient R0 2 The formulas for calculating the Nash coefficient (NSE) and the root mean square error (RMSE) are shown in equations (1)-(3), respectively: （1）， （2）， （3）， Where n is the total number of sample points; y obs,i和 y sim,i These represent observed and simulated values, respectively. This is the mean of the observed values.

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