Integrated IDA–ANN–DEA for assessment and optimization of energy consumption in industrial sectors

This paper puts forward an integrated approach, based on logarithmic mean divisia index (LMDI) – an index decomposition analysis (IDA) method, an artificial neural network (ANN) and a data envelopment analysis (DEA) for the analysis of total energy efficiency and optimization in an industrial sector. The energy efficiency assessment and the optimization of the proposed model use LMDI to decompose energy consumption into activity, structural and intensity indicators, which serve as inputs to the ANN. The ANN model is verified and validated by performing a linear regression comparison between the specifically measured energy consumption and the corresponding predicted energy consumption. The proposed approach utilizes the measure-specific, super-efficient DEA model for sensitivity analysis to determine the critical measured energy consumption and its optimization reductions. The proposed method is validated by its application to determine the efficiency computation and an analysis of historical data as well as the prediction and optimization capability of the Canadian industrial sector.

To put an end to the rapid depletion of world's fossil-fuel reserves, energy has to be used efficiently. A primary need for sustainable development is the availability of energy of the required quality, in adequate amounts and at a realistic cost [1]. Energy is a cardinal element of any study of progress in sustainable development [2]. This study survey tries to track energy trends from the perspective of industrial consumption. Discovering a means to decrease the amount of energy required to deliver a service or a unit of economic output, and indirectly, to reduce energy-related emissions, is the objective of energy analysis and policy in the framework to ensure sustainable development [3]. Currently 37 percent of global energy usage is consumed by the industrial sector [4]; therefore this represents a key area in which to develop methods for energy efficiency and optimization. Energy efficiency and optimization could lead to more economical use of energy and related developments in the industrial sector.

Energy consumption in the industrial sector is influenced by three indicators, namely changes in activity, structure and efficiency. Energy is an essential requirement for a variety of reasons in industrial facilities around the world. In the 1970s, energy efficiency in the industrial sector began to be viewed as a major factor. Since then, the world has trimmed its energy account through greater efficiencies, while still expanding economically, and conserving the environment [5].

Energy efficiency in industry can be increased among three different strategies [5]: energy saving promoted by management; energy saving backed up by technologies; and energy saving enforced by policies/regulations. A management approach using integrated energy research tools is the focus of this study. Energy management can be defined as the strategy of meeting demand for energy when and where it is essential. This can be achieved by optimizing and regulating high energy processes and systems thereby decreasing energy requirements per unit of output, while maintaining or even decreasing the total cost of manufacturing the output from these systems [5], [6].

Successful energy-management programmes should comprise four main sections [5], [6], [7]. These are: analysis of historical data; energy auditing and accounting; engineering analysis and investment proposals based on feasibility studies; and staff training and relevant information. This study focuses on the analysis of historical data to enable reducing energy usage without affecting production negatively.

The motivation for reducing the energy usage of any organization today is not merely to save energy, because there are two crucial factors that need to be taken into consideration. First, higher profits can be generated by improved energy efficiency. Secondly, in view of the fact that improved energy efficiency is one of the most immediate and cost effective answers to the threat of global warming, energy saving has a major positive impact on the environment [8].

The aim of this study is to assist energy managers to analyze historical data, determine the level of efficiency, as well as to predict and optimize energy consumption of the industrial sector by using tools such as index decomposition analysis (IDA), data envelopment analysis (DEA) and an artificial neural network (ANN).

The rest of this paper is organized as follows: background of the study is followed by the literature review. A description of the general integrated method based on LMDI (logarithmic mean divisia index), ANN and DEA is presented. Details of the proposed method are discussed. These include use of: the LMDI, the ANN model for prediction; regression analysis for authentication; and, the DEA sub-model for sensitivity analysis. The case study in which the proposed model was applied comprises 15 Canadian industrial sectors. Results and discussion are presented as well as the conclusion.

2. Background of the study

Index decomposition analysis that is designed to understand activity growth, structure and efficiency change factors that have a bearing on energy consumption, is derived from index numbers used to link the contributions of price and quantity levels to changes in aggregate commodity consumption [9]. The use of IDA which evaluates energy consumption patterns and identifies the dynamic factors leading to changes in energy consumption to analyze historical and estimate future requirements is of immense value to researchers who are interested in decomposing aggregate indicators. In this study, the purpose of implementing IDA is to understand changes that contribute to variable energy consumption.

Since IDA cannot be used for prediction, an artificial neural network (ANN) was used to determine the relationship between energy consumption and its driving factors. This network is able to forecast energy consumption accurately, while taking into consideration the input factors that lead to the changes in energy consumption. The accuracy of the artificial neural network (ANN) model used in this study is measured by performing a linear regression analysis between the measured energy consumption (output from the neural network) and the predicted energy consumption.

For this study, DEA which is held in high regard for measuring energy efficiency accurately requires only the measured quantities of energy consumption as an input and predicted energy consumption as an output. DEA has also gained acceptance as an energy-efficient optimization tool. DEA is employed to determine the optimal consumption of energy to ensure potential energy saving. For this study, it is postulated that the integration of IDA, ANN and DEA will result in energy-efficient assessment and optimization.

3. Literature review

In a study by [10], various index decomposition analysis methods are evaluated and it is concluded that the LMDI method is the ideal method. LMDI is regarded as ideal method [10], [11], [12], [13] of decomposition for the following reasons: its consistency in aggregation; its perfect decomposition; its adaptability; its simplicity of use and result analysis; its solid theoretical basis; and no inexplicable residual term. This method is deemed “robust”.

The Divisia method was employed by [14] to decompose industrial energy demand in the Korean manufacturing industry between 1981 and 1992. The results obtained show that increases in aggregate intensity for total energy consumption since 1988 are due primarily to the effect of increased real-energy intensities, whereas the contributions from structural changes and inter-fuel substitution have been relatively small. Gonzalez and Suarez [15]studied the changes in electricity intensity in the Spanish industry by decomposition to identify the factors that contributed to the changes. Combined with an analysis of electricity cost, the results of their study indicate the negligible contribution of structural change to substantial reductions in aggregate electricity intensity.

Salta et al. [16] employed LMDI decomposition analysis to determine the influence of production, structure and energy efficiency effects to changes in sub-sectoral manufacturing energy, to selected sub-sectors of the Greek manufacturing sector from 1985 to 2002 for electricity, fossil fuels and total energy use. Factors affecting the trends in energy efficiency in South Africa from 1993 to 2006 were identified by [17]. It was established that structural changes in the economy impacted negatively on increasing across-the-board energy efficiency, whereas the energy usage intensity was a contribution factor to the decreasing trend in energy efficiency. Ozawa et al. [18] analyzed energy use for the Mexican iron and steel industry from 1970 to 1996 using decomposition analysis based on physical indicators. According to the analysis, the substantial growth in activity was the main driver behind the huge increase in energy consumption.

Many improvements have been made by exploiting existing intelligent systems – some inspired by biological neural networks, fuzzy systems and/or a combination of them [19]. Nevertheless, artificial neural networks (ANN) indisputably gained the widest application, sharing a spot with the most potent computational mechanisms ever built [20].

ANNs have become a useful tool in energy studies. Wong and Lam [21] developed an ANN model for office buildings with day-lighting (in subtropical climates). To predict regional load in Taiwan [20] and green house gases in Turkey [22]. Analyzing and predicting wind power generation [23], prediction of net energy consumption in Turkey [24] and forecasting daily electric load profiles of a suburban area [25] are among the ANN studies undertaken. Other studies include [26], [27], [28]. Kusiak and Xu [26] optimized energy consumption of a heat ventilation and an air-conditioning (HVAC) system using a dynamic neural network. The ensemble algorithm outperformed the other algorithms used in their study. The ANN model was used successfully to predict energy use in wheat production [27]. Several direct and indirect factors were included in the study to create the ANN model that predicted energy use with an error margin constituting +12% on the Canterbury arable farms. Ekonomou [28]used ANN to predict Greek long-term energy consumption, exploiting its computational speed, ability to handle complex non-linear functions, robustness and high efficiency even in cases where full information for the problem under study was non-existent.

A known mathematical technique that employs a linear programming method to evaluate the efficiencies of decision-making units (DMU) is DEA. This linear program uses multiple input and output variables as was first determined by Charnes et al. (1978). DEA is a nonparametric methodology where a single measure of efficiency for each unit relative to its peers is generated. It has been identified as a dynamic mechanism employed for evaluating the performance of organizations [29]. DEA has been used in many energy-related studies. Farmers' levels of efficiency in energy use in rice production activities using DEA methodology were investigated [30]. About 11.6% of the total energy usage could be saved, if farmers were to adhere to the input package suggested by the study. Hu and Kao [31] set the energy-savings target using DEA for APEC (Asia-Pacific Economic Cooperation) economies without lowering their maximum potential gross domestic product in any year. It was found that China was in the lead with energy-saving goals. The operational performance of thermal power plants in Taiwan using data envelopment analysis was assessed [32]. The power plants investigated achieved acceptable overall operational efficiency from 2004 to 2006, with the combined cycle power plants being the most efficient.

In our investigation, in the assessment of energy efficiency analysis, LMDI decomposed the energy consumption into changes in activity growth, structure and efficiency. ANN includes all variation sources, namely measured energy consumption, activity growth, structure and efficiency changes in the Canadian industrial sector into the assessment by considering them as inputs and output indicators. DEA, on the other hand, includes the measured and predicted energy consumption in evaluation by regarding them as input and output indicators. The result of the ANN is validated by carrying out a linear regression analysis between the observed and predicted energy consumption where a coefficient of correlation was noticed. In addition, with the aid of DEA sensitivity analysis, the relevant energy consumption can be determined and the optimization reductions in the energy consumption can be proposed.

4. Proposed model

This study employs an integrated approach based on LMDI, ANN and DEA for total energy efficiency assessment and optimization of energy consumption in the Canadian industrial sector. Fig. 1 presents a schematic view of the generic proposed model. Steps to be followed in the generic proposed model can be summarized as follows:

I.

An IDA based on LMDI is performed to assess the respective contributions of activity, structural and intensity effects on the 15 industrial sectors.

II.

Energy consumption, activity, structural and intensity effects are selected as ANN input and output indicators. The energy consumption indicator is the output indicator, while activity, structural and intensity indicators are the input indicators.

III.

The predicted results of ANN are verified and validated using the result of regression analysis.

IV.

With the aid of a super-efficient DEA sub-model, energy consumption is calculated using a sensitivity-analysis approach.

V.

Suggestions for optimization of energy consumption are proposed to be applied in the Canadian industrial sectors.

1. Download full-size image

Fig. 1

4.1. LMDI

The LMDI the preferred IDA, similar to other IDA methods, can adopt either a multiplicative or an additive mathematical form in a time-series or base-year method. The differences between the time-series and the base-year method can be found [33] and [34]. For our study, the time-series multiplicative mathematical form was adopted. The multiplicative decomposition form decomposes the relative growth of an indicator I into determinant effects [35].

(1)$\frac{I^t}{I^{t-1}}=\text{Determinant}\text{effect}\times \text{Determinant}\text{effect}\times \text{Determinant}\text{effect}\times \text{Residual}$

The residual term for LMDI decomposition is always unity. Where energy consumption is the indicator for this study, equation (1) can be rewritten as

(2)$\frac{E^t}{E^{t-1}}=D_{\mathrm{tot}}=D_{\mathrm{act}}·D_{\mathrm{str}}·D_{\mathrm{int}}$

The LMDI (multiplicative) takes the following form

(3)$E=\sum _i{E}_i=\sum _{i}Q\frac{Q_i}{Q}\frac{E_i}{Q_i}=\sum _{i}Q{S}_i{I}_i$

$D_{\mathrm{act}}=\exp \left[\sum _i{w}_i\ln \left[\frac{Q^T}{Q^0}\right]\right]$$D_{\mathrm{str}}=\exp \left[\sum _i{w}_i\ln \left[\frac{S^T}{S_i^0}\right]\right]$$D_{\mathrm{int}}=\exp \left[\sum _i{w}_i\ln \left[\frac{I^T}{I_i^{\text{0}}}\right]\right]\text{;}$

where

(7)$w_i=\frac{\left(E_i^T-E_i^0\right)/\left(\ln E_i^T-\ln E_i^0\right)}{\left(E^T-E^0\right)/\left(\ln E^T-\ln E^0\right)}$

where Dtot represents the total energy consumption, Dact the activity involved, Dstr the structural change and Dint the change in intensity. The derivation of the above equations can be found in [36]

4.2. ANN

ANNs are well-known massive, parallel computing models which exhibit excellent behavior in solving problems associated with engineering, economics, etc. The most commonly applied network is the multilayer perceptron with the error backpropagation learning algorithm [37]. For the neural network methodology, we refer interested reader to the paper [38] for details of the methodology.

4.2.1. Problem formulation

The objective function chosen for this problem is the mean square error (MSE) between the outputs from the neural network and the target value which is the energy consumption. The inputs are applied to the network; and similarly the network output is compared to the target. The error is calculated as the difference between the target output and the neural network output. The goal is to minimize the average of the sum of these errors.

(8)$\mathrm{mse}=\frac{1}{Q}\sum _{k=1}^{Q}e{\left(k\right)}^2=\frac{1}{Q}\sum _{k=1}^Q{\left(t\left(k\right)-a\left(k\right)\right)}^2$

The least mean square error (LMS) algorithm adjusts the weights and biases of the linear network so as to reduce the mean square error. The architecture of this network comprises of three layers namely the input, hidden and output layers, with each layer having one or more neurons, in addition to the bias neurons connected to the hidden and output layers. The computational procedure of the network is described below [20]:

(9)$Y_j=f\left(\sum _i{w}_{ij}{x}_{ij}\right),$

where Yj is the output of node j, f(.) the transfer function, wij the connection weight between node j and node i in the lower layer, and Xi the input signal from node i in the lower layer. The backpropagation is based on the steepest descent technique with a momentum weight (bias function) which calculates the weight change for a given neuron. It is expressed as follows [20], [39]: let 

$\Delta w_{ij}^p\left(n\right)$

 denotes the synaptic weight connecting the output of neuron ito the input of neuron j in the pth layer at iteration n. The adjustment 

$\Delta w_{ij}^p\left(n\right)$

 to 

$w_{ij}^p\left(n\right)$

 is presented as

(10)$\Delta w_{ij}^p\left(n\right)=-\eta \left(n\right)\frac{\partial E\left(n\right)}{\partial w_{ij}^p},$

where η (n) is the learning-rate parameter. By applying the chain rule of differentiation, the weight of the network with the backpropagation learning rule is updated, using the following formulas:

(11)$\Delta w_{ij}^p\left(n\right)=\eta \left(n\right){\partial }_j^p\left(n\right)X_i^{p-1}\left(n\right)m\left(n\right)\Delta w_{ij}^p\left(n-1\right),$

$\Delta w_{ij}^p\left(n+1\right)=w_{ij}^p\left(n\right)+\Delta w_{ij}^p\left(n\right),$

where 

${\partial }_j^p\left(n\right)$

 is the nth error signal at the jth neuron in the pth layer, 

$X_i^{p-1}\left(n\right)$

 is the output signal of neuron i at the layer below and m is the momentum factor.

4.2.2. Linear regression analysis

Performance of neural networks can be measured to some extent by the sum squared error, but it is useful to investigate the response in more detail. One of the options is to perform a regression analysis between the network response and the corresponding targets [40].

According to [40], the validation analysis leads to 3 parameters. The first two m and bcorrespond to the slope with the y-intercept of the best linear regression, relating targets to neural network outputs. To ensure a perfect fit (outputs exactly equal to targets), the slope would be 1, and the y-intercept would be 0. The third parameter is the correlation coefficient (R-value) between the outputs and targets. There is a perfect correlation between the targets and outputs if the R-value is equal to 1.

4.3. DEA

This study makes use of the input-oriented Charnes-Cooper-Rhodes (CCR) model of a DEA. The input model reduces the inputs while satisfying the lowest given output [32]. The efficiency scores obtained from the input-oriented model for inefficient years (DMU) deal with the potential of conservation in the observed energy consumption.

The model to the CCR is given below [32], [41]

(13)$\begin{array}{l}\min {\mathit{\theta }}_{\mathit{k}}-\epsilon \left(\sum _{i=1}^m{s}_{ik}^{-}+\sum _{r=1}^s{s}_{rk}^{+}\right)\\ \text{subject}\text{to}\\ {\theta }_k{x}_{ik}-\sum _{j=1}^n{\lambda }_j{x}_{ij}-s_{ik}^{-}=0;i=1,\mathrm{..},m\\ y_{rk}-\sum _{j=1}^n{\lambda }_j{y}_{rj}+s_{rk}^{+}=0;r=1,\mathrm{..},s\\ {\lambda }_j,s_{ik}^{-},s_{rk}^{+}\ge 0\forall i,\end{array}$

where θk is the measure of efficiency of DMU “k”, the DMU in the set of j = 1,2,..n DMUs rated relative to the others; ε an infinitesimal positive number used to make both the input and output coefficients positive; 

$s_{ik}^{-}$

 slack variables for input constraints, which are all constrained to be non-negative; 

$s_{ik}^{+}$

 slack variables for output constraints, which are all constrained to be non-negative; and λj the dual weight assigned to DMUs.

4.3.1. “Sensitivity analysis and optimization” using the DEA sub-model

The input-oriented, measure-specific super-efficiency DEA model proposed by Zhu [42] was adopted for the sensitivity analysis. Constant return to scale (CRS) was assumed. In the model 14, the input is given priority to change to its value.

(14)$\begin{array}{l}\min {\mathit{\theta }}_{\mathit{k}}\\ \mathrm{s}\text{.}\mathrm{t}\sum _{\begin{array}{l}j=1\\ j\ne 0\end{array}}^n{\lambda }_j{x}_{ij}\le {\theta }_k{x}_{io},i=k,\\ \sum _{\begin{array}{l}j=1\\ j\ne 0\end{array}}^n{\lambda }_j{x}_{ij}\le x_{io},i\ne k\\ \sum _{\begin{array}{l}j=1\\ j\ne 0\end{array}}^n{\lambda }_j{y}_{rj}\ge y_{ro},r=1,2,\mathrm{..},s\\ {\theta }_k,{\lambda }_j,\left(j\ne 0\right)\text{;}\end{array}$

The sensitivity analysis result for an efficient DMU will assist in determining the increase in energy consumption, yielding an inefficient DMU. It can be assumed that the decrease in energy consumption could make an efficient DMU of an inefficient DMU.

4.3.2. Optimization of energy consumed

The optimal value of a DEA sub-model shown in model 13 (θ*) for an inefficient DMUo, is the minimum reduction in energy consumption that causes DMUo to be a best-practice DMU and an efficient DMU on the frontier for the observed energy consumption (input). When xiois the energy consumption of DMUo, θ*xi0 is the amount of potential reduction in energy consumption, that can be compared to the best observed DMU. The potential of a saving in energy consumption decreases as the optimal value of the energy consumption in model 13 increases. The reduction (θ*xi0) in the input is the optimal reduction in energy consumption that makes DMUo an efficient DMU.

5. Case study

In this paper, 15 aggregated sectors between 1990 and 2000 of the Canadian industrial sector were analyzed. Data used came from Granel's study [33]. The 15 aggregated sectors are metal mining, nonmetal mining, food industry, beverage industry, rubber products, plastic products, leather and allied products, primary textile, textile products, clothing industry, wood, furniture and fixtures, paper and allied products, printing public as well as allied and primary metal. Production is given based on the gross domestic product (GDP) output expressed in 1986 in U.S $.

6. Results and discussion

6.1. LMDI

The results of the decomposition analysis are provided in Table 1. It shows, among others, the increase in the energy consumption in the 15 Canadian industrial sectors from 1990 to 2000 amounting to 1.2264 PJ. Many underlying factors contributed to the increase in energy consumption for the period under investigation.

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