0 Introduction

Electricity represents an important basis of the national economy. The power industry supports the development of other industries in an indispensable role. Since a key feature of electricity is that it cannot be stored in large-scale, and its consumption can well reflect the actual situation of economic development, thus being regarded as the "benchmark" of the macroeconomy. Therefore, electricity consumption is a good indicator of the macroeconomic growth and can be used in economic forecast.

The divergence between the electricity demand and gross domestic product (GDP) growth in recent years is attracting much attention from the academic community. At the present stage, the trend of electricity consumption and macroeconomic growth do not maintain complete consistency. Taking Zhejiang province as an example: in the second half of 2015, the total electricity consumption decreased by 1.35%, but its GDP increased by 6.7% in total. Similarly, there has also been a nationwide divergence in the cumulative growth of electricity consumption while the macro economy has maintained positive growth. The divergence is even far higher than in the period of the Asian financial crisis of 1998. Considering this phenomenon, it is important to investigate how to build appropriate models to accurately reflect the correlation and possible divergence between electricity consumption and economic growth.

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The electricity consumption of different industries have significant values for economic modeling. In addition, the electricity consumption are suitable for economic analysis because of the following key features:

(a) The electricity consumption of more than 50 industries, which include primary, secondary and tertiary industries, can be collected. It can, therefore, provide a comprehensive big picture of the national economy;

(b) Electricity cannot be stored on a large scale. Moreover, the power consumption data are cross-validated using both the generation side and customer side meters. The timeliness, reliability and accuracy of the power consumption can, therefore, be guaranteed.

For analyzing these data, the classical econometric method is based on linear regression. The advantages of the traditional method are: (a) each coefficient before the explanatory and control variables has its specific economic meaning; and (b) it does not require a large number of data samples for the case study. However, since linear regression is based on a linear model, it will usually suffer from the under-fitting problem. It thus can only be sufficient for qualitative analysis. Moreover, even if all the coefficients have passed the statistical testing and economic testing, the model may still generate invalid results due to the heteroskedasticity and multicollinearity of the data[1]. Therefore, linear regression based methods usually have poor performance if used for forecasting. To tackle the difficulties discussed above, a possible solution is employing a machine learning based method which is commonly nonlinear.

Extreme Learning Machine (ELM) is a novel machine learning method for training single hidden layer feed-forward neural networks (SLFNs)[2]. In ELM, all the input weights and the parameters of hidden layer activation function are assigned randomly. The output weights of the network are then analytically optimized. Therefore, the parameters of ELM can be determined in one pass rather than being solved iteratively. The ELM method has been verified with a lot of benchmark problems and Engineering applications and demonstrated a faster-learning speed and better generalization capability[3-8].

The input of the ELM model is the daily electricity consumption of each industrial sector and the output is monthly industrial year-to-year growth ratio. For the hidden layer, there are 10 sigmoid nodes in a single layer. The mean square error (MSE) is employed as the measure of the model accuracy. Comparisons between these two methods are shown in Table 4.

下降流进入锥体部分以后，由于受到锥体向上推力的影响，轴向分速度减小，中高密度颗粒由上而下逐渐集中；同时颗粒旋转半径逐渐减小，切向分速度增大，离心力增大；当颗粒离心力与重力的合力与锥体表面成直角时，在锥体下部空气柱与锥壁环形空间形成悬浮转动层，起到重介质作用。当颗粒由于惯性作用不改变运动方向而下落到悬浮转动层时，高密度颗粒可以穿过床层，低密度颗粒则受到阻拦，又被卷入上升流，形成二次分选[5]。

The rest of the paper is organized as follows. Section 1 reviews the previous works both in economic modeling and forecasting considering electricity consumption (1.1) and the applications of ELM (1.2). Section 2 describes the features studied in this paper and formulates the mathematical model of ELM. Section 3 presents the experimental design and model development. Section 4 discusses the experimental results of performance evaluation and comparison. Section 5 concludes this paper and provides guidelines for future work.

1 Related works

1.1 Econometric modeling of electricity

Electricity is closely related to the domestic production. The researchers classify the studies on electricity consumption based economic modeling into two categories: long-term co-integration relations and short-term causal relations.

Previously, researchers pay much attention on the correlation between electricity consumption and domestic income. Li and Liang (2005) used the economic cycle theory and state-space model to measure the variation of the demand for electric power in China and concluded that the variation of electricity demand is synchronous with the economic cycle[9]. Cai (2008) found that the electricity consumption is mainly affected by GDP, energy structure adjustment, the adoption of new technology, and the unit energy consumption, using the linear regression model[10].

In recent years, Han and Wu (2011) applied multi-variable linear regression for forecasting the social electricity demand in the Jing-Jin-Tang area. The result shows that the electricity demand is highly correlated with the economic growth and population, however, it is positively related to the economic growth but not synchronous[11]. Furthermore, Gao (2011) used error correction model with boom analysis to analyze the electricity industrial long-run variation and short-run dynamic adjustment effect. Her result has shown that the power industry boom and macroeconomic fluctuations have a consistent trend but the violation is uncertain[12].

From the above,it can be observed that at the current stage economists only apply the linear model to do quantitative analysis, which is insufficient for economic forecasting. Since a more accurate nonlinear model is highly demanded, a machine learning based method for economic modeling may be an attractive solution.

1.2 The application of ELM

The extreme learning machine (ELM)method was originally developed for training the single-layer feedforward neural network (SLFN)[2-3,13] and then applied to many engineering and social fields.

[1] STUDENMUND A H, HENRY J C. Using econometrics: A practical guide[M]. Addison-Wesley Educational Publishers, 1992: 2, 163, 215.

In this paper, ELM is employed for macro economy prediction, and comparisons are made with the traditional linear regression model.

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2 Models

In the regression analysis, the T-test is used to justify whether the coefficients are reliable; and calculating R2, the square of Pearson coefficient, to determine the correlation ratio between the samples and the regression model.

The first part of the model is used to describe the qualitative relations between the electricity and the industrial outcome. The well-established log-linear regression is utilized here to examine the effect of heteroskedasticity. Then the second part of the model applies the ELM method for quantitative forecasting. These methods will be evaluated and compared empirically in the experiment part.

2.1 Log-linear regression model

Linear regression is the most commonly used method in econometrics. And the regression analysis is to make quantitative estimates of economic relationships that previously have been completely theoretical in nature. The simplest linear regression model behaves like:

Y=α0+α1X+ε

(1)

where Y is the dependent variable, and in this paper, is the industrial GDP; X is the independent variable (corresponding electricity consumption); ε is the residual term caused by the omitted statistical error.

Theoretically, the residual ε should follow the homoskedasticity assumption, which states the observations of the error term are drawn from a distribution with a constant variance. However, in the real world, the heteroskedasticity is always presented and violates this assumption. In this case, the ordinary least square (OLS) solution is no longer the minimum-variance estimator (of all the linear unbiased estimators). There are many modified models for avoiding this problem, such as ARIMA model[19] or GARCH model[20]. Since in this analysis, only the linear model is needed to show the qualitative result, then the logarithm operation is applied for both dependent and independent variables. The model takes the following form:

log(Y)=α0+α1log(X)+ε

(2)

Our problem is to estimate the coefficients α0 and α1. The most widely used method for obtaining these estimates is the so-called Ordinary Least Square (OLS).

Ordinary Least Square is a regression estimation technique that calculates so as to minimize the sum of the squared residuals, thus:

(3)

Here these residuals (εi) are the differences between the actual logY and the estimated logY produced by the regression

For the equation with just one independent variable, the coefficients are:

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(4)

Given this estimate of α1,

(5)

where E[logX] and E[logY] represent the sample means of logX and logY. The estimates represented by and are then the solutions for qualitative analysis.

A structural economic model is formulated in this sector based on electricity consumption data. Since most electric power is consumed by the secondary industry, our work will mainly focus on studying the electricity consumption and the growth of the secondary industry.

2.2 Extreme Learning Machine

To effectively forecast the economic growth periodically in the different industry based on the historical electric consumption, ELM is applied as the learning algorithm in this work.

Although deep learning has a powerful ability of data feature extraction, cause it consists of many layers, a large number of parameters need to be optimized. The computational cost of model training is therefore very high. Extreme Learning Machine (ELM) refers to a class of stochastic machine learning algorithms that can be used to speed up the training of deep learning models. The basic mathematical form of ELM can be expressed as:

针对某个电网运行方式，调整柔直系统有功，进行含柔直系统的电网静态安全分析。即根据N-1原则，求取满足交流系统以及柔直系统安全性约束条件的柔直系统有功功率。由于环网中各通道潮流的非同向性，调节柔直系统有功功率在减轻部分通道负载的同时，势必会加重其他通道负载，因此该步骤得到柔直系统有功功率的优化区间。

(6)

where X is the input vector; B=[β1,…,βL]T is the weight vector for output layer; and H=[h1(X),…,hL(X)]T is a group of nonlinear feature transformation functions which satisfies the continuity hypothesis. Unlike the traditional neural network training algorithms, ELM does not optimize the input and hidden layer parameters, but generates them randomly. The general architecture of an ELM network is shown in Fig. 1.

After randomly generating input layer and hidden layer parameters, the output layer weights of the network can be obtained by solving the following optimization problem:

min||HB-T||2

(7)

where H is the hidden layer mapping function matrix; T is the matrix of training data; and ||·||is the Frobenius norm.

Fig.1 Typical structure of an ELM

(8)

The optimal solution of the problem can be solved by

B*=H+T

(9)

where H+ denotes the mapping function matrix H’s Moore-Penrose general inverse matrix.

The independent variable of the model is yearly electricity consumption and the dependent variable is the related industrial sector’s outcome. The result of log-linear regression for each sector is shown as below in Table 3. The unit for electricity consumption (X) is kW·h and for the related GDP is hundred million Yuan.

3 Numerical experiment

To empirically demonstrate the effectiveness of the proposed approach, the daily industrial electricity consumption and monthly industrial income data of a major province in the past 5 years are employed to train and test the log-linear regression model and ELM. The performances of these methods are compared then.

3.1 Data description

In the two cases study, 21 sectors in the secondary industry are selected. The details are shown in Table1.

Table 1 List of 21 Sectors in the Secondary Industry

An individual model is built for each sector. The daily electricity consumption of each sector is chosen as the independent variable, while the corresponding monthly industrial outcome is set as the dependent variable. The data are collected in a five-year period from Jan. 1, 2012 to Dec. 31, 2017. The data are from the Statistics Bureau and the electric power company of a Province in China.

3.2 Model selection

For the first experiment, the log-linear regression is applied for qualitative analysis, and the parameters will be estimated using ordinary least square method. This linear model would be regarded as a baseline model for the comparison.

In the second experiment, the ELM model should be set with a certain activation function. The commonly used ELM mapping functions are shown in Table 2.

Table 2 Commonly Used Feature Mapping Functions in ELM

[9] LI X, LIANG Y. Comparative study on trend decomposition of electricity demand and GDP[J]. Modern Electric Power, 2005, 22(5): 84-86.

4 Empirical results and analysis

4.1 Results of the linear analysis

Because ELM input layer and hidden layer parameters can be assigned randomly, and the output layer weights do not need to be optimized, which can be obtained by the matrix inversion. Therefore, compared with other mainstream machine learning methods, the computational efficiency of ELM is significantly higher. Generally speaking, ELM can improve the training speed of neural networks by the order of magnitude compared with the traditional methods such as support vector machines. ELM can be several hundred times faster compared with mainstream depth learning methods, and thus can be applied to the online processing of big data. In addition, both the theory and practices have proven that ELM has global approximation ability to any nonlinear functions. Also, it is relatively insensitive to the noisy data due to the randomly assigned hidden layer parameters, which can help avoid overfitting.

According to the result shown above,the following observations are attained:

(1) The economic outcomes of most sectors in the secondary industry are positively correlated to its electricity consumption as shown by the p-value of T-test and R2.

(2) The linear regression method is not always well fitted with the data, as most R2 are smaller than 0.8. And in some cases, the model fails to interpret the data (R2 < 0.5).

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(3) There is still strong heteroskedasticity affecting the linear regression even the logarithm is carried out firstly (some p-value is larger than 0.15).

4.2 Results of the nonlinear analysis

To forecast the economic growth based on electricity consumption, our work selects ELM to build the correlation model between the industry electricity consumption and economic indicators such as GDP. In particular, economic variables (such as GDP of different industries) will be selected as dependent variables and the electricity consumption as the independent variable.

Table 3 Results of Log-linear Regression for 21 Sectors

Table 4 Comparison of the MSEs between ELM and Log-Linear Regression

The most reliable sector in the log-linear regression (the R2 > 0.85 and the p-values are significant) is chosen to draw the figure of forecasting on training data. And it shows the comparison with ELM figure (in order to compare in the same magnitude, the logarithms of the ELM inputs and outputs are also calculated). The sectors chosen are transportation equipment manufacturing and electricity and heat production/supply industry. The forecasting results are shown in Fig. 2-5.

我院从2012年开始，构建以病种管理为核心的医疗质量精细化评价体系，把病种管理作为全面医疗过程质量管理的导向与核心，依托智能化信息系统，对医疗大数据的提取、整合与分析，实现医院运行质量监测与医院经营成本控制相结合的全面精细化管理体系。在医院运行管理体系中密切监测和分析病种质量、效率、效益、难度、缺陷等指标，形成关于病种质量和人员质量的评价结果和优化分析建议；在医院经营管理体系中则从病种收入、支出、可控成本、医保补偿等角度进行综合测算，形成分析报告，提出成本控制、优化收支结构的改进建议。

Fig.2 The forecasting result for Transportation Equipment Manufacturing sector by linear regression

Fig.3 The forecasting result for Transportation Equipment Manufacturing sector by ELM

Fig.4 The forecasting result for Electricity and heat production/supply sector by linear regression

Fig.5 The forecasting result for Electricity and heat production/supply sector by ELM

In these figures, the blue lines represent the forecasting result, while the red ones are logarithm of the original data.

According to the results,the following intuitions are observed:

(1) For most cases (in 13 industries), ELM has a better performance in forecasting than the classical linear regression.

(2) However, there are still 8 industries, where linear regression has a better performance than the ELM.

(3) There are a few industries (like oil and gas exploration industry and abandoned resources and waste materials recycling processing industry), whose MSEs for both methods are too large, and cannot easily be forecasted using only the electricity consumption data.

5 Conclusion

In this paper, an ELM and electricity consumption data based industrial economic growth model is proposed. In this model, ELM is firstly used to predict the macroeconomy. The empirical study applying data from the Statistics Bureau shows that in most sectors of the secondary industry, ELM demonstrates a higher accuracy. This result can be used as a more accurate benchmark for the local government to make decisions on its industrial development.

6 References

ELM has great potential in system modeling and prediction. In normal goods market, ELM was applied in sales forecasting in fashion retailing by Sun, et al. (2009), which was evaluated by real data from a fashion retailer in Hong Kong[14]. Heeswijk (2009) applied adaptive ensemble models of ELM to the problem of one-step-ahead prediction in stationary/non-stationary time series[15]. On the electricity spot market, Chen, et al. (2012) investigated the electricity price forecasting based on ELM and bootstrapping, using the chaotic time series and Australian National Electricity Market price series[16]. In electrical engineering, Xu, et al. (2013) developed an ELM-based predictor for real-time frequency stability assessment (FSA) of the power system. And the predictor trained off-line with a frequency stability database can be online applied for real-time FSA[17]. And also ELM shows a better performance in the stock market than the classical empirical methods[18].

本文构建了基于费控策略的电力营销管理体系，指出了该管理体系的主要功能，结合远程费控电力系统体系的功能，分析了远程费控电力营销对供电企业的经济效益。

[2] HUANG G, ZHU Q, CHEE K S. Extreme learning machine: a new learning scheme of feedforward neural networks [C]//Neural Networks, 2004. Proceedings. 2004 IEEE International Joint Conference, 2004, 2: 985-990.

[3] HUANG G, LEI C, CHEE K S. Universal approximation using incremental constructive feedforward networks with random hidden nodes[J]. IEEE Trans. Neural Networks, 2006, 17(4): 879-892.

[4] HUANG G, LEI C. Convex incremental extreme learning machine [J]. Neurocomputing, 2007, 70(16-18): 3056-3062.

[5] HUANG G, LEI C. Enhanced random search based incremental extreme learning machine[J]. Neurocomputing, 2008, 71(16-18): 3460-3468.

[6] FENG G,HUANG G, LIN Q, et al. Error minimized extreme learning machine with growth of hidden nodes and incremental learning[J]. IEEE Transactions on Neural Networks, 2009, 20(8): 1352-1357.

[7] NIZAR A H, DONG Z, WANG Y. Power utility nontechnical loss analysis withextreme learning machine method[J]. IEEE Transactions on Power Systems, 2008, 23(3): 946-955.

[8] XU Y,DONG Z, MENG K, et al. Real-time transient stability assessment model using extreme learning machine[J]. IET generation, transmission & distribution, 2011, 5(3): 314-322.

研究中发现，单一层面切片的HE染色，前哨淋巴结发现45枚(8例)(17.7%)、非前哨淋巴结41枚(14例)(34.1%)发现转移。对365枚前哨淋巴结行多层切片HE染色及免疫组化染色检测，发现单层切片常规HE染色前哨淋巴结均有微小转移，余下HE染色阴性的前哨淋巴结有微小转移灶，直径均小于2 mm，累计有96枚前哨淋巴结内有转移灶。

The sigmoid function is selected in the experiment with a = 1 and b = 0 specified as constants.

[10] CAI H, HAN Z, MA W. Multiple regression analysis on electric power consumption in China[J]. Statistics and Decision, 2008, 1(14): 101-103.

[11] HAN Z, WU H. Electric consumption forecasting of Jingjintang grid based on multiple linear regression[J]. North China Electric Power, 2011, 1(4): 22-24.

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美国：自2009年以来，美国住宅市场一直稳步复苏。但是近年来也出现了一些阻碍住宅市场发展的限制因素，包括：经济脆弱，失业率增加，银行贷款新政，越来越多的80后优先选择和父母住在一起。另外，人们对于住宅所有权的态度也发生了变化，越来越多的人选择租房而非买房。这些因素都将对北美未来住宅市场的发展产生影响，减缓住宅市场复苏的步伐。根据美国建筑协会的预测，美国2016年新建独立住宅的销售量为57.4万套，2017年为66.9万套，2018年为70.2万套;而现有住宅的销售量为2016年547.2万套，2017年576.8万套，2018年588.5万套。

[12] LIU C, GAO T. Characteristics of electricity industry cycle fluctuation and influential factors of electricity demand based on business analysis and the error correction model[J]. Resources Science, 2011, 33(1): 169-177.

[13] HUANG G, ZHU Q, CHEE K S. Extreme learning machine: theory and applications[J]. Neurocomputing, 2006, 70(1-3): 489-501.

[14] SUN Z,CHOI T, AU K, et al. Sales forecasting using extreme learning machine with applications in fashion retailing[J]. Decision Support Systems, 2008, 46(1): 411-419.

[15] VAN H M,MICHE Y, LINDH-KNUUTILA T, et al. Adaptive ensemble models of extreme learning machines for time series prediction[C]//International Conference on Artificial Neural Networks. Berlin: Springer, 2009: 305-314.

[16] CHEN X,DONG Z, MENG K, et al. Electricity price forecasting with extreme learning machine and bootstrapping [J]. IEEE Transactions on Power Systems, 2012, 27(4): 2055-2062.

[17] XU Y,DAI Y, DONG Z, et al. Extreme learning machine-based predictor for real-time frequency stability assessment of electric power systems[J]. Neural Computing and Applications, 2013, 22(3-4): 501-508.

[18] LI X,XIE H, WANG R, et al. Empirical analysis: stock market prediction via extreme learning machine[J]. Neural Computing and Applications, 2016, 27(1): 67-78.

[19] BOX, GEORGE E P, DAVID A P. Distribution of residual autocorrelations in autoregressive-integrated moving average time series models[J]. Journal of the American Statistical Association, 1970, 65(332): 1509-1526.

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[20] ENGLE R F. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation [J]. Econometrica: Journal of the Econometric Society, 1982, 50(4): 987-1007.