CN108830417B - ARMA (autoregressive moving average) and regression analysis based life energy consumption prediction method and system - Google Patents
ARMA (autoregressive moving average) and regression analysis based life energy consumption prediction method and system Download PDFInfo
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Abstract
The invention discloses a life energy consumption prediction method and system based on ARMA and regression analysis, which are used for obtaining the life energy consumption items of everyone and the measured values thereof; establishing a first sample corresponding to the measured value of the average human life energy consumption, and establishing a time sequence; determining the order of the ARMA model according to the Bayesian information quantity criterion, and constructing the ARMA model; establishing a sample set of the influence factors of the reality factors and the time sequence as a second sample; carrying out regression analysis on the second sample to obtain a combined prediction model; and performing combined prediction on the time series by using a combined prediction model. The invention adopts a combined machine learning prediction model based on ARMA and regression analysis, can better adapt to the characteristics of time series and accurately describe the real influence factors, and has the advantage of high test accuracy.
Description
Technical Field
The invention relates to the field of energy prediction data mining, in particular to a life energy consumption prediction method and system based on ARMA and regression analysis.
Background
Energy plays an important role in economic development and is an important factor influencing national strategies and policies. In recent years, the brisk development of the energy industry in China provides continuous power for the economic growth of China, but in the development process of the energy industry, the problems of insufficient per-capita energy, low energy utilization efficiency, serious environmental pollution and the like are increasingly highlighted, so that the adjustment and control of the energy structure and energy consumption in China are needed, the prediction of the per-capita energy consumption in people is needed, the reasonable energy regulation and control measures are facilitated, and the important significance is brought to the healthy development of economy and environment. At present, a time series method is mostly adopted for predicting energy, the time series method predicts future data by searching for potential rules in historical data, but when a single time series model predicts a nonlinear chaotic sequence, a prediction result often has a large error. In addition, the value of the time series under the actual condition at a certain moment not only depends on the change rule of the time series, but also is influenced by factors such as population, economy and the like, and the time sequence model cannot describe the characteristic information of the real influence factors.
In summary, in the prior art, an effective solution is still lacking for the problem that the error of the prediction result is large and the time sequence model cannot describe the real influence factors.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides the life energy consumption prediction method and the life energy consumption prediction system based on the ARMA and the regression analysis.
The technical scheme adopted by the invention is as follows:
a life energy consumption prediction method based on ARMA and regression analysis comprises the following steps:
acquiring a human-average life energy consumption project and a measured value thereof;
establishing a first sample corresponding to the measured value of the average human life energy consumption, and establishing a time sequence;
determining the order of the ARMA model according to the Bayesian information quantity criterion, and constructing the ARMA model;
establishing a sample set of the influence factors of the reality factors and the time sequence as a second sample;
carrying out regression analysis on the second sample to obtain a combined prediction model;
and performing combined prediction on the first sample by using a combined prediction model.
Further, screening the measured value of the average human living energy consumption, and removing the missing value in the average human living energy consumption; and fitting the measurement deficiency value in the human-average living energy consumption measurement value, and performing format conversion on the screened and fitted human-average living energy consumption measurement value.
Further, the method for constructing the time sequence comprises the following steps:
establishing a first sample corresponding to the measured value of the average human life energy consumption, and taking the first sample as an initial sequence;
and performing k-order difference operation on the initial sequence to obtain a time sequence which is based on the energy consumption project of the average life of people and meets the requirement of stationarity.
Further, if the initial sequence is not a stationary sequence, k-order differential operation needs to be performed on the initial sequence, where k is the minimum differential operation frequency for the sequence to meet the requirement of stationarity; if the initial sequence meets the stability requirement, no difference operation is needed, and the k value is 0 at the moment.
Further, the method for performing regression analysis on the second sample includes:
taking the influence factors of the reality factors and the time sequence as independent variables of regression analysis, taking the values of the time sequence at a certain moment as dependent variables of the regression analysis to perform function fitting to obtain a plurality of regression analysis samples, and establishing a regression analysis sample set;
randomly selecting 3 samples from the regression analysis sample set as a verification set, and training the regression analysis model by using the rest samples as a training set;
and comparing the relative error of each regression analysis model on the verification set, and taking the first three models with the minimum relative error to construct a combined prediction model, wherein the combined prediction model comprises an ARMA model, a support vector machine regression model and a ridge regression model.
Further, a partial sequence with the length of n is cut out from the time sequence in sequence to serve as the value of the time sequence independent variable, the step length is 1, and n is the number of the time sequence independent variables in the regression analysis.
Further, the method for performing combined prediction on the first sample by using the combined prediction model includes:
and predicting the first sample by using an ARMA (autoregressive moving average) model, a support vector machine regression model and a ridge regression model to obtain the prediction results of the three models, distributing a certain weight to the prediction results of the three models, and carrying out weighted average to obtain the final prediction result.
Further, the method for calculating the weight includes:
wherein, tauiRepresenting the degree of fit of the model containing the mean and standard deviation, and the value of i is 1,2,3, omegaiRepresenting the weight of the model.
Further, the calculation function of the fitting degree of the model containing the mean value and the standard deviation is as follows:
wherein, sigma and mu respectively represent the standard deviation and the mean value of the true value of the verification set; xiiRepresenting the relative error of the model i on the verification set, wherein the value of i is 1,2 and 3; sigmaiAnd (3) standard deviation (mu) of a predicted value obtained by predicting the verification set by the representation model iiAnd representing the mean value of the predicted values obtained by predicting the verification set by the model i.
A system for forecasting energy consumption for life based on ARMA and regression analysis, the system comprising:
the energy detection device is used for acquiring the life energy consumption items and the measured values thereof; and
the processor is connected with the energy consumption detection device and is used for realizing the life energy consumption prediction method based on the ARMA and regression analysis; and
and the display unit is connected with the processor and used for outputting the prediction result of the processor.
Compared with the prior art, the invention has the beneficial effects that:
(1) the combined machine learning prediction model based on ARMA and regression analysis is adopted, so that the characteristics of a time sequence are better adapted, the actual influence factors can be accurately described, the change situation of future life energy consumption along with time can be predicted, reasonable energy regulation and control measures can be made, and the test accuracy is high;
(2) the method carries out optimal model screening, compares the relative error of each model on a verification set, and takes the first three models with the minimum relative error to construct a combined prediction model, so that the combined prediction model for the life energy consumption can better adapt to the characteristics of time series, the final prediction result is obtained by distributing certain weight to the prediction results of the three single models and carrying out weighted average, and the prediction is carried out in a weighted combination mode.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the application and, together with the description, serve to explain the application and are not intended to limit the application.
FIG. 1 is a flow chart of a method for predicting energy consumption based on ARMA and regression analysis;
FIG. 2 is a graph of dependent variables and time series independent variables of the present invention;
FIG. 3 is a graph of a regression analysis sample;
FIG. 4 is a graph of the relative error of a model on a validation set;
FIG. 5 is a graph of mean and standard deviation;
FIG. 6 is a diagram of predicted values and true values according to the present invention.
Detailed Description
The invention is further described with reference to the following figures and examples.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, 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 belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
Term interpretation part ARMA is an autoregressive moving average model
As introduced by the background art, the existing technology has the defects that the error of a prediction result is large, and a time sequence model cannot describe practical influence factors, and in order to solve the technical problems, the application provides a life energy consumption prediction method and a life energy consumption prediction system based on ARMA and regression analysis, so that the method and the system are better adapted to the characteristics of a time sequence, can accurately describe the practical influence factors, can predict the change situation of future life energy consumption along with time, further make reasonable energy regulation and control measures, and have the beneficial effect of high test accuracy.
In an exemplary embodiment of the present application, as shown in fig. 1, there is provided a life energy consumption prediction method based on ARMA and regression analysis, the method including the steps of:
step 101: and acquiring the human-average living energy consumption project and the measured value thereof, and screening, fitting and converting the human-average living energy consumption measured value.
The method for screening the human average living energy consumption measured value comprises the following steps:
screening the measured value of the human-average living energy consumption, and removing the missing value in the human-average living energy consumption.
The step of fitting the human average living energy consumption measurement value comprises the following steps:
and fitting the measurement missing values in the human average living energy consumption measurement value.
The step of converting the measured value of the average human life energy consumption comprises the following steps:
and carrying out format conversion on the filtered and fitted measured value of the human-average living energy consumption.
Step 102: and constructing a time sequence and a second sample based on the measured value of the average life energy consumption.
The construction method of the time sequence comprises the following steps:
establishing a first sample corresponding to the measured value of the average human life energy consumption, and taking the first sample as an initial sequence; and (4) performing k-order differential operation on the initial sequence (k is the minimum differential operation frequency for enabling the sequence to meet the stability requirement), and obtaining the time sequence which is based on the energy consumption project of the average human life and meets the stability requirement.
If the initial sequence is not a stable sequence, k-order differential operation needs to be carried out on the initial sequence, wherein k is the minimum differential operation frequency for enabling the sequence to meet the stability requirement; if the initial sequence meets the stability requirement, no difference operation is needed, and the k value is 0 at the moment.
The k value is calculated as:
Z＝{S′|S′is stationary} (1)
k＝min(Q) (3)
wherein Z represents a set containing all time sequences satisfying the stationarity requirement; s represents an initial time series; d (S, l) represents a new time sequence obtained by carrying out l-order differential operation on the initial time sequence S; q represents the set of all differential operation times that make the sequence meet the stationarity requirement.
And after the time series is obtained, establishing a sample set of the time series and an influence factor based on practical factors such as population, economy and the like as a second sample.
Step 103: and determining the order of the ARMA model according to the Bayesian information quantity criterion, and constructing the ARMA model.
And according to a Bayesian information quantity criterion, determining the order of the ARMA model to construct the ARMA model with the strongest generalization capability, and predicting future data.
The expression of the ARMA model is:
wherein, YtIs the value of the predicted object at time t, etThe average value is 0, the variance is larger than 0, the p and the q are orders of an ARMA model, and the order determination of the ARMA model is to determine proper p and q values.
The order of the ARMA model is determined by Bayesian Information Criterion (BIC) to overcome the defect of insufficient generalization capability of the model caused by under-fitting and over-fitting, and the calculation mode of the BIC index is as follows:
BIC＝-2lnL+KlnN (5)
wherein, L is the maximum likelihood estimation value of the model, K is the number of variables used by the model, and N is the number of data used by the model.
Step 104: and (5) performing regression analysis to construct a combined prediction model.
The regression analysis method includes various regression methods of linear regression And nonlinear regression, which are multivariate linear regression, ridge regression, random forest regression, decision tree regression, extreme random tree regression, gradient lifting tree regression, support vector machine regression, And LASSO (last Absolute Shrinkage And extension Operator, LASSO) regression, respectively.
The method comprises the following steps of taking an influence factor based on practical factors such as population, economy and the like and a time sequence as independent variables of regression analysis, and taking values of the time sequence at a certain moment as dependent variables of the regression analysis, wherein the independent variables are as follows:
wherein y represents a dependent variable, W1...Wm+nCoefficients representing independent variables, m, n respectively representing influence factor independent variables (f)1...fm) And time series argument (o)1...on) In order to intercept partial sequences of length n in time series as values of time series arguments, step size 1, e.g. for time series(s)1,s2,s3,s4,s5,s6,s7,s8) If the number of time-series independent variables in the regression analysis is 4 (n-4), that is, (o)1,o2,o3,o4) The values of the dependent variable and the time series independent variable are shown in fig. 2.
And taking the influence factors and the time sequence as independent variables of regression analysis, taking the value of the time sequence at a certain moment as a dependent variable of the regression analysis, performing function fitting to obtain a plurality of regression analysis samples, and constructing a regression analysis sample set.
Randomly selecting 3 samples from the regression analysis sample set as a verification set, and training the regression analysis model by using the rest samples as a training set; and comparing the relative error of each regression analysis model on the verification set on the training set, and taking the first three models with the minimum relative error to construct a combined prediction model, wherein the combined prediction model comprises an ARMA model, a support vector machine regression model and a ridge regression model.
Step 105: and performing combined prediction on the first sample by using a combined prediction model.
And performing combined prediction on the first sample by using a combined prediction model, and obtaining a final prediction result by distributing a certain weight and performing weighted average on the prediction results of the three single models. And presenting the prediction result of the per-capita energy consumption in the time sequence.
The weight is calculated as:
wherein, tauiRepresenting the degree of fit of the model, the value of i is 1,2,3, omegaiAnd representing the weight of the model, wherein the value of i is 1,2 and 3.
The model fit of the ARMA model was calculated as:
wherein ξiAnd the relative error of the model on the verification set is represented, and the value of i is 1,2 and 3.
The method and the device introduce the mean value and the standard deviation, and distribute larger weight for the model with the predicted value and the true value having the relatively close mean value and standard deviation. Replacing the fitness calculation function with a fitness calculation function containing a mean and a standard deviation, wherein the fitness calculation function comprises the following steps:
wherein ξiRepresenting the relative error of the model on the verification set, wherein the value of i is 1,2 and 3; sigma and mu respectively represent the standard deviation and the mean value of the true value of the verification set; sigmaiAnd (3) standard deviation (mu) of a predicted value obtained by predicting the verification set by the representation model iiAnd representing the mean value of the predicted values obtained by predicting the verification set by the model i. .
The life energy consumption prediction method based on ARMA and regression analysis provided by the embodiment of the invention enables a life energy consumption combined prediction model to better adapt to the characteristics of a time sequence, performs prediction in a weighted combination mode, has the beneficial effects of high test accuracy, strong reliability and stability, and is obviously superior to the traditional method for constructing the combined model.
In order to make those skilled in the art better understand the present invention, a specific calculation example is listed below, and the embodiment of the present invention provides a method for predicting energy consumption for life based on ARMA and regression analysis, including:
step 201: selecting the energy consumption of the life of each person every year.
The historical data adopted in the embodiment is the annual average human life energy consumption from 1983 to 2015, and the unit is kilogram of standard coal and the proportion of male population, as shown in tables 1 and 2; and the energy consumption of life per capita in 2008 to 2015 is predicted and verified. The established regression analysis model takes the proportion of males in the general population of China as the independent variable of the influence factor.
TABLE 1 energy consumption per capita
TABLE 2 proportion of male population in China
| Year of year | Specific gravity/% | Year of year | Specific gravity/% | Year of year | Specific gravity/% |
| 1983 | 51.6 | 1994 | 51.1 | 2005 | 51.53 |
| 1984 | 51.6 | 1995 | 51.03 | 2006 | 51.52 |
| 1985 | 51.7 | 1996 | 50.82 | 2007 | 51.5 |
| 1986 | 51.7 | 1997 | 51.07 | 2008 | 51.47 |
| 1987 | 51.5 | 1998 | 51.25 | 2009 | 51.44 |
| 1988 | 51.52 | 1999 | 51.43 | 2010 | 51.27 |
| 1989 | 51.55 | 2000 | 51.63 | 2011 | 51.26 |
| 1990 | 51.52 | 2001 | 51.46 | 2012 | 51.25 |
| 1991 | 51.34 | 2002 | 51.47 | 2013 | 51.24 |
| 1992 | 51.05 | 2003 | 51.5 | 2014 | 51.23 |
| 1993 | 51.02 | 2004 | 51.52 | 2015 | 51.22 |
Step 202: the energy consumption of the life of each person is screened every year.
Screening the annual average life energy consumption items and the measured values thereof, and removing the measurement missing values in the annual average life energy consumption; fitting the measured deficiency values in the annual average life energy consumption; and converting the formats of the screened and fitted measured values of the annual average living energy consumption.
First, missing value cleaning is performed. And observing the data, calculating the proportion of the missing values of the data, and determining the range of the missing values. And adopting different processing strategies according to the missing proportion and the field importance. For the characteristics of high importance and low deletion rate, filling is carried out through experience or business knowledge estimation; and for the characteristics of high importance and high deletion rate, other complex models are used for calculating completion. The importance is high, the deletion rate is low, and the method is supplemented by a fitting method; high deletion rate and low importance, and can be directly removed.
Next, data format conversion is performed. And manually processing the partial column misalignment problem and the over-column condition of the imported data.
Step 202: and (5) constructing a time sequence.
Establishing a first sample corresponding to a human-average living energy consumption measured value, carrying out k-order differential operation on the first sample (k is the minimum differential operation frequency for enabling the sequence to meet the stability requirement), obtaining a time sequence which is based on the human-average living energy consumption item and meets the stability requirement, and establishing a sample set which takes an influence factor based on real factors such as population, economy and the like and the time sequence as a second sample; and determining the order of the model as p-1 and q-0 according to the Bayesian information quantity criterion.
Step 20: 3: and (4) performing regression analysis, and constructing a combined prediction model for prediction.
For the regression analysis model, the dependent variable is the per-capita energy consumption in China in a certain year, the independent variable comprises the proportion of the male population and the time sequence variable, specifically, the invention takes 1 as the step length, cuts out a part of the time sequence with the length of 11 on the per-capita energy consumption time sequence in sequence, and the sample of the regression analysis is shown in figure 3. Randomly selecting 3 samples from the regression analysis sample set as a verification set, training the regression models by using the rest samples as training sets, wherein the relative errors of the ARMA model and each regression analysis model on the verification set are shown in FIG. 4.
Therefore, the obtained ARMA model, the support vector machine regression (linear kernel) and the ridge regression are three models with small relative errors, and the relative errors are 1%, 4% and 4% respectively, so that the prediction results of the three models are weighted and summed, and the prediction of the per-capita life energy consumption from 2008 to 2015 is realized. FIG. 5 shows the mean and standard deviation of support vector machine regression (linear kernel) and ridge regression over the validation set, the mean and standard deviation of the true values of the validation set.
In order to further determine the weight of each model, the relative error, the mean value and the standard deviation of the ARMA model are substituted, the fitting degree of the ARMA model is 97.1934463, the fitting degree of the support vector machine regression (linear kernel function) and the ridge regression are 4.22926306 and 3.291428455 respectively, the weight of the final ARMA model is 0.9281788, the weight of the support vector machine regression (linear kernel function) is 0.04038865, and the weight of the ridge regression is 0.0314325.
The predicted value and the true value of the combined prediction model constructed by the invention on the energy consumption of Chinese people in 2008-2015 are shown in fig. 6.
If three models with the largest error on the verification set are selected, the relative error of the predicted value is 50.3%; if the fitting degree of the regression analysis model is determined by the formula
Calculating to obtain a predicted value with a relative error of 5.3%; if the weights of the three models are 1/3, the relative error of the predicted value is 8.48%; the method provided by the invention not only can effectively screen the model suitable for predicting the life energy consumption sequence, but also can allocate reasonable weight for the screened model. In this embodiment, three models with the smallest error in the verification set are selected, and the fitting degree between the ARMA model and the regression analysis model is calculated according to formulas 9 and 10, respectively, so that the relative error of the obtained predicted value is 4.25%, which is obviously superior to other methods for constructing a combined model.
The ARMA and regression analysis-based life energy consumption prediction method provided by the embodiment of the invention effectively reflects the influence of the real factors on the time sequence, and the combined prediction model can screen out a proper single model according to the characteristics of the time sequence and allocate reasonable weight to the model, so that the ARMA and regression analysis-based life energy consumption prediction method has the beneficial effects of high test accuracy, strong reliability and stability.
According to another exemplary embodiment of the present application, there is provided a life energy consumption prediction system based on ARMA and regression analysis, the system including an energy detection device, a processor and a display unit connected in sequence.
And the energy detection device is used for acquiring the life energy consumption items and the measured values thereof.
The processor is used for realizing the life energy consumption prediction method based on ARMA and regression analysis;
and the display unit is used for outputting the prediction result of the processor.
The life energy consumption prediction system based on ARMA and regression analysis provided by the embodiment of the invention is better adapted to the characteristics of time series, can accurately describe the real influence factors, and can predict the change situation of future life energy consumption along with time.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the present invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive efforts by those skilled in the art based on the technical solution of the present invention.
Claims (4)
1. A life energy consumption prediction method based on ARMA and regression analysis is characterized by comprising the following steps:
acquiring a human-average life energy consumption project and a measured value thereof;
establishing a first sample corresponding to the measured value of the average human life energy consumption, and establishing a time sequence;
determining the order of the ARMA model according to the Bayesian information quantity criterion, and constructing the ARMA model;
establishing a sample set of the influence factors of the reality factors and the time sequence as a second sample; carrying out regression analysis on the second sample to obtain a combined prediction model;
performing combined prediction on the first sample by using a combined prediction model;
the construction method of the time sequence comprises the following steps:
establishing a first sample corresponding to the measured value of the average human life energy consumption, and taking the first sample as an initial sequence; k-order differential operation is carried out on the initial sequence, wherein k is the minimum differential operation frequency which enables the sequence to meet the requirement of stationarity, and a time sequence which is based on the human-average life energy consumption project and meets the requirement of stationarity is obtained;
if the initial sequence is not a stable sequence, k-order differential operation needs to be carried out on the initial sequence, wherein k is the minimum differential operation frequency for enabling the sequence to meet the stability requirement; if the initial sequence meets the stability requirement, differential operation is not needed, and the k value is 0 at the moment;
the method for performing regression analysis on the second sample comprises the following steps:
taking the influence factors of the reality factors and the time sequence as independent variables of regression analysis, taking the values of the time sequence at a certain moment as dependent variables of the regression analysis to perform function fitting to obtain a plurality of regression analysis samples, and establishing a regression analysis sample set;
randomly selecting 3 samples from the regression analysis sample set as a verification set, and training the regression analysis model by using the rest samples as a training set;
comparing the relative error of each regression analysis model on the verification set, and taking the first three models with the minimum relative error to construct a combined prediction model, wherein the combined prediction model comprises an ARMA model, a support vector machine regression model and a ridge regression model;
the method for performing combined prediction on the first sample by using the combined prediction model comprises the following steps:
predicting the first sample by utilizing an ARMA model, a support vector machine regression model and a ridge regression model to obtain prediction results of the three models, distributing a certain weight to the prediction results of the three models, and carrying out weighted average to obtain a final prediction result;
the calculation method of the weight comprises the following steps:
wherein, tauiRepresenting the degree of fit of the model containing the mean and standard deviation, and the value of i is 1,2,3, omegaiRepresenting the weight of the model;
the calculation function of the model fitting degree containing the mean value and the standard deviation is as follows:
wherein, sigma and mu respectively represent the standard deviation and the mean value of the true value of the verification set; xiiRepresenting the relative error of the model i on the verification set, wherein the value of i is 1,2 and 3; sigmaiAnd (3) standard deviation (mu) of a predicted value obtained by predicting the verification set by the representation model iiAnd representing the mean value of the predicted values obtained by predicting the verification set by the model i.
2. The method of claim 1, further comprising screening the measured value of average human energy consumption to remove missing values of the average human energy consumption; and fitting the measurement deficiency value in the human-average living energy consumption measurement value, and performing format conversion on the screened and fitted human-average living energy consumption measurement value.
3. The method of claim 2, wherein the partial sequence with length n is sequentially cut out in time series as the value of the time series independent variable, the step length is 1, and n is the number of time series independent variables in the regression analysis.
4. A life energy consumption prediction system based on ARMA and regression analysis is characterized by comprising:
the energy detection device is used for acquiring the life energy consumption items and the measured values thereof; and
a processor connected to the energy consumption detection device for implementing the ARMA and regression analysis based method for predicting life energy consumption according to any one of claims 1-3; and
and the display unit is connected with the processor and used for outputting the prediction result of the processor.
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| CN109854242B (en) * | 2019-01-08 | 2020-09-11 | 浙江大学 | Chaos theory-based automatic prediction system for coal mining machine roller |
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