CN116451905A - Water demand prediction method based on Bayesian support vector machine and two-step factorization analysis - Google Patents
Water demand prediction method based on Bayesian support vector machine and two-step factorization analysis Download PDFInfo
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Abstract
The invention discloses a water demand prediction method based on a Bayesian support vector machine and two-step factorization analysis, which comprises the following steps: A. coupling Bayes and a support vector machine method, and predicting the water demand in the river basin on the basis of socioeconomic development data; B. the contribution rate of each factor to the change of water demand is quantified by adopting a field design method, and the influence of the main effect and interaction of the factors on the water demand is identified, so that key influence factors are screened out; C. and carrying out total factor analysis on the key factors, predicting the future water demand based on a trained Bayesian support vector machine model, and comprehensively analyzing the influence of the key factors on the water demand. The invention predicts the water demand change trend under multiple situations by considering the influence of social economic development indexes, provides more scientific and reliable data input for sustainable water resource management, and can provide decision support for water resource managers.
Description
Technical Field
The invention relates to the technical field of water demand prediction, in particular to a water demand prediction method based on a Bayesian support vector machine and two-step factorization analysis.
Background
Accurate water demand prediction is the basis for reasonably distributing water resources and promoting reasonable development and utilization of the water resources. However, the water demand is affected by a plurality of factors, the traditional methods based on time series extrapolation and the like neglect the correlations among a plurality of factors in the water resource system, and the selected variables are mostly single variables, so that the model has weaker applicability and the water demand prediction result is distorted. To a certain extent, the socioeconomic development of the river basin can reflect the change trend of the water resource demand, and the water demand prediction should be determined based on the socioeconomic development degree. Therefore, the relation between the socioeconomic development data and the water resource demand is analyzed to accurately predict the water demand of the river basin, so that the water resource quantity in the river basin is fairly and reasonably distributed, the water resource utilization efficiency is improved, and a scientific basis is provided for the long-term sustainable development of the river basin.
Object of the Invention
The invention aims to overcome the defects in the prior art, and provides a water demand prediction method based on a Bayesian support vector machine and two-step factorization analysis, which saves the water demand prediction time and improves the operation effect and simulation precision.
Disclosure of Invention
The invention provides a water demand prediction method based on a Bayesian support vector machine and two-step factorization analysis, which comprises the following steps:
step A, according to the related study of the predecessor on water demand prediction, selecting related socioeconomic indexes as input data to construct a Bayesian support vector machine model;
and step B, adopting a two-step factorial analysis method, wherein the first step is as follows: by establishing a proper orthogonal table, the optimal factor combination scene is quickly searched, and then key factors influencing water demand are screened out by using a field design;
and C, analyzing the factor of the two steps, namely, the second step: and carrying out full factor analysis on the key factors screened by the field opening design, predicting and simulating the water demand in each future situation, and comprehensively analyzing the influence of the key factors on the water demand.
Preferably, the step a further comprises the steps of:
step A1, preliminary selecting relevant social and economic indexes influencing water demand through reference predecessor research and influence factor analysis on a water demand structure, and searching and collecting relevant data of each influence factor and the water demand;
a2, coupling the Bayesian and the support vector machine method, and carrying out parameter optimization of the support vector machine and selection of an optimal model by using a Bayesian inference method;
and A3, under the condition of considering the uncertainty of model parameters, establishing a nonlinear statistical relationship between the water demand and the socioeconomic index, thereby constructing a water demand prediction model based on a Bayesian support vector machine, and evaluating the simulation effect of the model.
More preferably, in step A3, the deterministic correlation coefficient R is selected 2 The Nash coefficient NSE and the root mean square error RMSE reflect the relation between the simulation value and the actual measurement value, the effect of the water demand prediction model based on the Bayes support vector machine is estimated, and the correlation coefficient R is determined 2 The calculation formulas of the Nash coefficient NSE and the root mean square error RMSE are shown in formulas (1) - (3) respectively:
wherein n is the total number of sample points; y is obs, i and y sim,i respectively representing an observed value and an analog value; y is obs Is the mean of the observations.
Preferably, the step B further comprises the steps of:
step B1, primarily selecting 12 factors according to previous researches, wherein each factor is respectively provided with a high level and a low level, and L corresponding to 32 scenes is selected based on the number and the level value of the design factors 32 An orthogonal table;
and B2, quantifying the contribution rate of each factor to the water demand change by adopting a field design method, and identifying the influence of the interaction of the single factor main effect and the multiple factors on the water demand, thereby screening out the factor with the largest influence on the water demand change, and carrying out full factor design on the basis.
More preferably, the step B2 further includes: defining the contribution of a single factor to the system response as the proportion of the sum of squares to the total sum of squares; the size of the influence of the factors on the water demand is quantified by calculating the sum of squares of the combination of the single factors and the two factors, and in the case of three factors, the main effect calculation formulas of the factors are shown as formulas (4) - (6):
wherein the SS A 、SS B 、SS C Respectively representing the sum of squares of the factors A, B, C; y is Y ijt Representing the system response value of factor A at the ith level, factor B at the jth level, and factor C at the tth level; I. j, T each represents the number of levels of the factor A, B, C; the sum of squares calculation formula of the two-factor interaction is shown in formulas (7) - (9):
wherein the SS A×B 、SS A×C 、SS B×C Representing the sum of squares of the two-factor interactions in the factor A, B, C, respectively.
Preferably, the step C further comprises the steps of:
step C1, respectively setting the main influence factors including irrigation efficiency, water price, economic crop area occupation ratio and total planting area, and predicting and simulating water demand of various countries or places in the future based on a trained Bayesian support vector machine model;
and C2, exploring the change trend of the future water demand under the multi-economic situation and the influence of main factors on the water demand.
Drawings
FIG. 1 is a schematic diagram of a water demand prediction method framework based on a Bayesian support vector machine and two-step factorization analysis;
FIG. 2 is a schematic illustration of the interaction of socioeconomic performance metrics;
fig. 3 is a schematic diagram of future water demand change in each scenario.
Detailed Description
The following describes the embodiments of the present invention in further detail with reference to the accompanying drawings.
As shown in figure 1, the invention couples Bayes, support vector machines, field port design and full factor analysis methods, and develops a water demand prediction model under the influence of socioeconomic performance. The method can effectively establish the association relation between the water demand of each country and the influence factors thereof, and quantitatively identify key driving factors of water demand change and interaction among factors. Therefore, based on the identified key factors influencing the water demand change, various socioeconomic development scenes are set, and the multi-scene set predicts the change trend of the water demand of each country.
In specific practice, the implementation flow comprises the following steps:
step A, according to the related study of the predecessor on water demand prediction, selecting related socioeconomic indexes with complete data, taking the related socioeconomic indexes as input data to construct a Bayesian support vector machine model, and predicting the national water demand under each situation; the step A is specifically divided into:
step A1: preliminary selecting relevant social and economic indexes influencing water demand through reference to previous study and influence factor analysis on a water demand structure, and searching and collecting relevant data of each influence factor and water demand;
in this embodiment: the relevant socioeconomic indexes which are preliminarily selected and influence the water demand are respectively as follows: national production total (GDP), agricultural duty, industrial duty, total crop area, cereal crop area duty, cash crop area duty, feed crop area duty, agricultural irrigation efficiency, animal husbandry, total population, urbanization rate, water price.
Step A2: the Bayesian inference method is used for carrying out parameter optimization of the support vector machine and selection of an optimal model in order to improve the model operation effect and simulation precision;
step A3: under the condition of considering the uncertainty of model parameters, a nonlinear statistical relationship between the water demand and the socioeconomic index is established, so that a water demand prediction model based on a Bayesian support vector machine is established, and the simulation effect of the model is evaluated.
In the embodiment, the Bayesian support vector machine model is subjected to parameter calibration and verification by selecting water demand and influence factor data of the 1980-2015 year and month scale, wherein the rate is in the period of 1980-2005, and the verification period is in the period of 2006-2015. Using deterministic correlation coefficients (R 2 ) The Nash coefficient (NSE) and Root Mean Square Error (RMSE) reflect the relation between the simulation value and the actual measurement value, and the simulation effect of the Bayesian support vector machine model is evaluated. The calculation formulas of the evaluation indexes are shown in formulas (1) - (3), respectively:
wherein n is the total number of sample points; y is obs, i and y sim,i respectively representing an observed value and an analog value; y is obs Is the mean of the observations.
Step B, analyzing two factorization factors, namely: by establishing a proper orthogonal table, the optimal factor combination scene is quickly searched, and then key factors influencing water demand are screened out by using a field design; the step B is divided into:
step B1: according to the previous study, primarily selecting 12 factors, each factor is respectively provided with a high level and a low level, and selecting L based on the number and level values of the design factors 32 (corresponding to 32 scenarios) orthogonal tables;
step B2: and quantifying the contribution rate of each factor to the water demand change by adopting a field design method, and identifying the influence of the single factor main effect and the multi-factor interaction on the water demand, thereby screening out the factor with the largest influence on the water demand change, and carrying out full factor design on the basis. Step B2 further comprises:
the contribution of a single factor to the system response is defined as the ratio of its sum of squares to the total sum of squares. The size of the influence of the factors on the water demand is quantified by calculating the sum of squares of the combination of the single factors and the two factors, and taking three factors as examples, the main effect calculation formulas of the factors are shown as formulas (4) - (6):
wherein the SS A 、SS B 、SS C Respectively representing the sum of squares of the factors A, B, C; y is Y ijt Representing the system response value of the factor A at the ith level, the factor B at the jth level and the factor C at the tth level; I. j, T each represent a horizontal number of A, B, C factors. The sum of squares calculation formula of the two-factor interaction is shown in formulas (7) - (9):
wherein the SS A×B 、SS A×C 、SS B×C Representing the sum of squares of two-factor interactions.
And C, analyzing the factor of the two steps, namely, the second step: and carrying out full factor analysis on the key factors screened by the field opening design, predicting and simulating the water demand in each future situation, and comprehensively analyzing the influence of the key factors on the water demand. Step C is divided into:
step C1: the main influence factors (irrigation efficiency, water price, economic crop area occupation ratio and total planting area) screened out are respectively set to be high and low, and the water demand of each country in the future is predicted based on a trained Bayesian support vector machine model;
step C2: the influence of the change trend of the future water demand and the main factors on the water demand under the multi-economic situation is explored in detail.
The results showed that the sum of the irrigation efficiency, water price, cash crop area ratio and total planting area contribution to water demand was 91%, with 66% contribution to irrigation efficiency, indicating that irrigation efficiency is the primary factor affecting water demand, and secondly water price (contribution 11%). Figure 2 shows the effect of socioeconomic factors on water demand, total domestic production volume ratio, total domestic production volume irrigation efficiency, animal husbandry water price, etc. Taking the interaction of the domestic total production value with the irrigation efficiency as an example, the dashed line represents the response process of the water demand to the irrigation efficiency when the domestic total production value is at a high level. The two lines are not parallel to indicate that the effect of irrigation efficiency on water demand is influenced by the value of the domestic production total value, namely the domestic production total value and the irrigation efficiency have obvious interaction on the water demand.
Fig. 3 (a) and (b) show the trend of the monthly water demand of tagatotan in 2020 to 2050 under 16 conditions. The results show that the water demand shows a trend of increasing and then decreasing, reaches a peak in 2026 and has a water demand of 167.8 hundred million m 3 Then the water demand for 2050 is 116.7 hundred million m in a decreasing trend 3 . Graph (c) is annual water demand in each scenario of 2030 and 2050. The figures indicate the rate of increase of annual water demand for scenario 2 to 16 compared to scenario 1.
In summary, the invention combines Bayes, support vector machines, field port design and factorization analysis to generate a two-step factorization method based on the Bayes support vector machines, and the method is applied to water demand prediction, thus effectively reflecting nonlinear complex relations between influencing factors and water demand and identifying key driving factors and interaction among factors of water demand change.
Compared with the existing water demand prediction method, the method has the following advantages:
(1) The Bayesian inference method is used for carrying out parameter optimization of the support vector machine and selecting an optimal model, so that frequent manual adjustment of parameters is avoided, time is greatly saved, and the operation effect and simulation precision are improved.
(2) The two-step factor analysis method is applied, the field design is adopted to screen out key factors influencing the water demand, then the full factor design is used for carrying out multi-scenario simulation, and the influence of the main factors on the water demand is explored in detail. The method has the greatest advantages that the method is firstly designed in one step before full factor analysis, and the optimal parameter combination is quickly searched through the minimum experiment times, so that the experiment times are greatly reduced, the experiment cost is reduced, and the efficiency is improved.
Claims (6)
1. A water demand prediction method based on a Bayesian support vector machine and two-step factorization analysis is characterized by comprising the following steps:
step A, according to the related study of the predecessor on water demand prediction, selecting related socioeconomic indexes as input data to construct a Bayesian support vector machine model;
and step B, adopting a two-step factorial analysis method, wherein the first step is as follows: by establishing a proper orthogonal table, the optimal factor combination scene is quickly searched, and then key factors influencing water demand are screened out by using a field design;
and C, analyzing the factor of the two steps, namely, the second step: and carrying out full factor analysis on the key factors screened by the field opening design, predicting and simulating the water demand in each future situation, and comprehensively analyzing the influence of the key factors on the water demand.
2. The water demand prediction method based on bayesian support vector machine and two-step factorization analysis according to claim 1, wherein the step a further comprises the steps of:
step A1, preliminary selecting relevant social and economic indexes influencing water demand through reference predecessor research and influence factor analysis on a water demand structure, and searching and collecting relevant data of each influence factor and the water demand;
a2, coupling the Bayesian and the support vector machine method, and carrying out parameter optimization of the support vector machine and selection of an optimal model by using a Bayesian inference method;
and A3, under the condition of considering the uncertainty of model parameters, establishing a nonlinear statistical relationship between the water demand and the socioeconomic index, thereby constructing a water demand prediction model based on a Bayesian support vector machine, and evaluating the simulation effect of the model.
3. A water demand pre-measurement based on bayesian support vector machine and two-step factorization analysis according to claim 2A measuring method is characterized in that in the step A3, a deterministic correlation coefficient R is selected 2 The Nash coefficient NSE and the root mean square error RMSE reflect the relation between the simulation value and the actual measurement value, the effect of the water demand prediction model based on the Bayes support vector machine is estimated, and the correlation coefficient R is determined 2 The calculation formulas of the Nash coefficient NSE and the root mean square error RMSE are shown in formulas (1) - (3) respectively:
wherein n is the total number of sample points; y is obs, i and y sim,i respectively representing an observed value and an analog value;is the mean of the observations.
4. The water demand prediction method based on bayesian support vector machine and two-step factorial analysis according to claim 1, wherein the step B further comprises the steps of:
step B1, primarily selecting 12 factors according to previous researches, wherein each factor is respectively provided with a high level and a low level, and L corresponding to 32 scenes is selected based on the number and the level value of the design factors 32 An orthogonal table;
and B2, quantifying the contribution rate of each factor to the water demand change by adopting a field design method, and identifying the influence of the interaction of the single factor main effect and the multiple factors on the water demand, thereby screening out the factor with the largest influence on the water demand change, and carrying out full factor design on the basis.
5. The method for predicting water demand based on bayesian support vector machine and two-step factorial analysis according to claim 4, wherein the step B2 further comprises: defining the contribution of a single factor to the system response as the proportion of the sum of squares to the total sum of squares; the size of the influence of the factors on the water demand is quantified by calculating the sum of squares of the combination of the single factors and the two factors, and in the case of three factors, the main effect calculation formulas of the factors are shown as formulas (4) - (6):
wherein the SS A 、SS B 、SS C Respectively representing the sum of squares of the factors A, B, C; y is Y ijt Representing the system response value of factor A at the ith level, factor B at the jth level, and factor C at the tth level; I. j, T each represents the number of levels of the factor A, B, C; the sum of squares calculation formula of the two-factor interaction is shown in formulas (7) - (9):
wherein the SS A×B 、SS A×C 、SS B×C Representing the sum of squares of the two-factor interactions in the factor A, B, C, respectively.
6. The water demand prediction method based on bayesian support vector machine and two-step factorization analysis according to claim 1, wherein the step C further comprises the steps of:
step C1, respectively setting the main influence factors including irrigation efficiency, water price, economic crop area occupation ratio and total planting area, and predicting and simulating water demand of various countries or places in the future based on a trained Bayesian support vector machine model;
and C2, exploring the change trend of the future water demand under the multi-economic situation and the influence of main factors on the water demand.
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