Soft Computing Approach in Modeling Energy Consumption

B. Murgante et al. (Eds.): ICCSA 2014, Part VI, LNCS 8584, pp. 770–782, 2014. © Springer International Publishing Switzerland 2014

Soft Computing Approach in Modeling Energy Consumption

Haruna Chiroma1, Sameem Abdulkareem1, Eka Novita Sari2, Zailani Abdullah3, Sanah Abdullahi Muaz4, Oguz Kaynar5, Habib Shah6, and Tutut Herawan7,8

1 Department of Artificial Intelligence 4 Department of Software Engineering

7 Department of Information system University of Malaya

50603 Pantai Valley, Kuala Lumpur, Malaysia 2 AMCS Research Center, Yogyakarta, Indonesia 3 School of Informatics & Applied Mathematics

Universiti Malaysia Terengganu Gong Badak, Kuala Terengganu, Malaysia

6 Faculty of Computer Science and Information Technology Universiti Tun Hussein Onn Malaysia

86400 Parit Raja, Batu Pahat, Malaysia 5 Department of Management Information System

Cumhuriyet University, 58140, Turkey 8 AMCS Research Center, Yogyakarta, Indonesia

[email protected], {sameem,tutut}@um.edu.my, [email protected], [email protected], [email protected],

[email protected], [email protected]

Abstract. In this chapter, we build an intelligent model based on soft computing technologies to improve the prediction accuracy of Energy Consumption in Greece. The model is developed based on Genetic Algorithm and Co-Active Neuro Fuzzy Inference System (GACANFIS) for the prediction of Energy Consumption. For verification of the performance accuracy, the results of the propose GACANFIS model were compared with the performance of Backpropagation Neural network (BP-NN), Fuzzy Neural Network (FNN), and Co-Active Neuro Fuzzy Inference System (CANFIS). Performance analysis shows that the propose GACANFIS improve the prediction accuracy of Energy Consumption as well as CPU time. Comparison of the results with previous literature further proved the effectiveness of the proposed approach. The prediction of Energy Consumption is required for expanding capacity, strategy in Energy supply, investment in capital, analysis of revenue, and management of market research.

Keywords: Genetic algorithm, Co-Active Neuro Fuzzy Inference System, Energy Consumption, Prediction.

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1 Introduction

Human’s require energy for their daily activities to properly function. Almost all activities in the society require energy [1]. The consumption of energy has significantly improved in the last decade across the globe as a result of population increase as well as economic development. In both social and economic development, energy is viewed as a critical factor which impact on the wealth of individuals [2]. The world energy demand increases by 2.5% annually and it will continue to increase in the future as expected. In Greece, energy consumption includes the energy delivered to the industrial, transportation, household, among others. In the last sixteen years (16), from 1992 to 2007 energy uses in Greece increase from 14, 079,000 to 22,552,000 Tones of Oil Equivalent (TOE). In terms of percentage, the energy increases by 60% with about 4.1% yearly increment [1]. The prediction of energy consumption are required for expanding capacity, strategy in energy supply, investment in capital, analysis of revenue, and management of market research. Though, high level of uncertainty characterized the prediction of long term energy consumption, in some instances the prediction covers thirty (30) years into the future. This attracted the interest of scientist to propose novel methods for a relatively reliable and accurate prediction of long-term Greek Energy Consumptions (GEC) [2].

GEC was forecast using a model developed based on Backpropagation neural networks (BP-NN) [2]. Hernandez et al. [3] proposes a model based on NNs for the forecasting of electricity load for microgrids. An NNs model was build to predict the monthly energy consumption of Iran [4]. However, NNs is well known to be slow and can easily be trapped in local minima. In another study, the demand for fossil fuels in Turkey was estimated using Genetic Algorithm (GA) model [5]. The GA can effectively improve the performance of NNs [6] which motivated Azadeh et al. [7] to hybridized NNs through GA searches to build a model for the prediction of electrical energy consumption in Turkey. Padmakumari et al. [8] applied fuzzy NNs (FNN) since it combined the power of NNs and fuzzy logic to create more effective hybrid model to build a synergistic model for the prediction of long-term energy consumption. Experimental evidence in [9] indicated that Co-active neuro fuzzy inference system (CANFIS) performs better than the FNN. Yet, CANFIS has been trained using the backpropagation algorithm (BP) which is susceptible to the limitations earlier mentioned. The GA can be applied for training without being trapped in the local minima and is faster than the BP in convergence to the optimal solution [10]. Fuzzy regression has a unique advantage of modeling using a small amount of datasets [11].

To improve the performance of CANFIS and considering the relatively few experimental data at our disposal, we propose to genetically optimize the parameters of CANFIS to build a GACANFIS model for the prediction of GEC.

The rest of this chapter is organized as follows. Section 2 presents a detailed description of the soft computing methodologies. Section 3 presents the results and a discussion of the study before concluding remarks and further works in Section 4.

772 H. Chiroma et al.

2 Proposed Method

2.1 Genetic Algorithm

The GA operates by the initialization of the random generation of chromosomes in a population believe to have the solution to the problem. Fitness for each of the chromosomes in the population is evaluated to select those with the best fitness value for mating. The iteration is terminated when the criteria set for termination is reached. For example, if the error is reduced to a predefine threshold, number of generations exceed predefine limits, predefine time, exceed predefine number of generations without improvement, etc. The chromosomes in the population are selected based on their fitness, many selection methods exist, e.g. Roulette wheel, ranking, Boltzmann etc. Genetic operators such as crossover, mutation rate, selection generation gap, elitism etc. is applied to reproduce the next generation. The reproduction continues in an iterative manner until the predefine stoppage criteria is reached and the optimal chromosome typically in the current population is returned as the best solution to the problem [12].

2.2 Co-Active Neuro Fuzzy Inference System

Jang et al. [13] CANFIS is a more general category of neuro fuzzy inference systems. It can be used as a universal approximation model for the mapping nonlinear function of any type. The capability and strengths of CANFIS lie on the advantages of hybridizing modular neural network and fuzzy inference systems. Mostly, the strength of CANFIS comes from the weights between the consequent layer and fuzzy association layer. The major constituent of CANFIS is fuzzy neurons through which membership function (MFs) is applied to the CANFIS inputs that are fed externally to the network. There are two commonly MFs that are used in the literature, namely, generalized bell and Gaussian [14]. The output of CANFIS is expanded by normalized axon within the range of 0 to 1 and the modular network supply function rules to inputs. The number of experts contain in the modular network correspond to the number of outputs and the number of neurons in each expert correspond to the number of MFs. This hybrid intelligent system has a combination of axon which applies MFs outputs to the modular neural network outputs. In the final stage of CANFIS operations the ensemble outputs pass through the last output layer. The error in the output is propagated to MFs as well as the modular neural network, every node in the first layer is the membership grade of the fuzzy set and the degree to which the input vectors belongs to one of the fuzzy set. The product of all outputs from the first layer is computed and transmits to the second layer. The upper, and lower components of the third layer, apply MFs to every input and represent modular neural network that carry out summation computation for each output [15].

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2.3 Design of the Proposed GACANFIS for Modeling the Greek Energy Consumption

2.3.1 Greek Energy Consumption Datasets The data required for the modeling of GEC in this research are collected from different sources. The installed power capacity (IPC) and the residence yearly/electricity consumption (RYEC) data were collected from [16]. The yearly ambient temperature (YAT) data were extracted from [17] and [1] supply the Greek gross domestic product (GGDP) and the GEC data. Though, there are other factors that determine the energy consumption, such as the amount of CO2 pollution, number of air conditioners, electricity price, installation of renewable energy technologies among others, but the record of the historical data are not available as pointed out in [2].

Table 1. Descriptive statistics of the GEC

Observation Minimum Maximum Mean Std Deviation GEC 22 2 72 31.95 20.37

Therefore, we decided to use only the variables with available data since it was argued in [18] that data availability is one of the criteria’s for the selection of independent variables for modeling purposes.

Fig. 1. Fluctuation of GEC from 1990 to 2011

The dependent variable is the GEC because its fluctuation as depicted in Fig. 1 depends on the independent variables, the descriptive statistics on the GEC data is presented in Table 1, in which the standard deviation computed based on Eq. (1) shows the dispersion of distribution in the data.

= =

−=

n

i

n

iii x

nx

n 0

2

0

2 11σ , (1)

where σ , n and xi represent the standard deviation, observations in the sample dataset, and real number of the random variable respectively.

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Fig. 1 clearly shows the increase in the demand of energy consumption in Greece and a sudden fall, which could likely be attributed to the financial crises, but the details is not within the focus of this research. The raw data were not normalized to prevent the destruction of the original pattern in the historical data, a practice suggested by [19].

2.3.2 Design of the Proposed GACANFIS Model The GACANFIS approach proposes to model the GEC. The structure of the CANFIS used in this study comprised of four input vectors representing RYEC, YAT, GGDP, and IPC. The output layer contained the output neuron which produces the GEC. The objective of the GA is to turn the CANFIS in order to determine the optimal parameter settings of fuzzy weights, mean and standard deviation of the MFs since they significantly affect the prediction performance of the CANFIS model. The datasets described in sub-section 2.3.1 are partitioned into 80% (1990 - 2008) for training and 20% (2007 - 2011) for testing the efficacy of the propose GACANFIS model. The CANFIS fitness function is the accuracy between the predicted values of GEC and the actual values. In this research, we chose Mean Square Error (MSE) computed using Eq. (2) as the fitness function because [20] argued that the MSE is more preferable than other measurement metrics such as normalized mean square error, mean absolute error, relative mean absolute error among others in measuring the accuracy of several algorithms on the same datasets.

nk

xa

MSE

n

iijij

k

j==

−

= 0

2

0

)(

,

(2)

where k = Neurons in the output layer n = Observations in the dataset xij = CANFIS output for observation i at neuron j aij = Actual GEC for observation i at neuron j

The initial population of the chromosomes is randomly selected, typically fifty (50)

chromosomes in the population based on the GA standard parameter values proposes by De Jong in 1975, reported in [21]. Each of the chromosomes in the population is evaluated using MSE.

The GA stop execution if the criteria set for termination is reached, otherwise the new generation of the chromosomes is created using crossover and mutation operators. The new population is created from chromosomes selected based on their fitness values. The chromosomes with the best fitness values are selected for mating whereas those with poor fitness values were rejected. Roulette wheel was the selection technique after trials with Boltzmann and rank selection. The crossover and mutation rates use in this simulation are 0.6 and 0.001 respectively, adopted from [21]. The value of generation gap, generation gap strategy, and chromosome length were selected after experimentations. The children resulted from the mating replace the older population of the chromosomes and iteratively continue searching the

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problem space. The iteration typically results to improve performance of the GACANFIS fuzzy weights, mean and standard deviation of the MFs. The generations of the population in our simulation was set to terminate when the GA runs for thirty (30) generations without improvement in the best fitness value found in the last population. Subsequently, the optimal chromosome is returned as the candidate solution, in our case the best GACANFIS model with the best fuzzy weights, mean and standard deviation of the MFs is returned as the final model for the prediction of GEC. The conceptual framework for the propose methodology is presented in Fig. 2. For comparison, BP-NN, FNN, Autoregressive Integrated Moving Average (ARIMA), and CANFIS were applied to predict the GEC. The models of the comparison methods were realized through trial and error technique to obtain the best model with the optimal performance.

Fig. 2. The optimization of CANFIS through GA operation to build GACANFIS

3 Results and Discussion

3.1 The Performance Accuracy of the Propose GACANFIS Model and Its Evaluation

The approach proposed in the study was implemented in GeneHunter, PB-NN implemented in MATLAB 2013a Neural Network ToolBox and CANFIS was implemented in Neurosolution on a computer system (HP L1750 model, 4 GB RAM, 232.4 GB HDD, 32-bit OS, Intel (R) Core (TM) 2 Duo CPU @ 3.00 GHz).

The optimal parameters of the GA that build the GACANFIS are: the GA operators - crossover rate was set to 0.6, mutation rate 0.001, population size fifty (50), roulette wheel was the selection technique. The generation gap was 0.76 with elitist strategy,

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chromosome length was 32 bits. The GA was set to terminate evolution when the best fitness runs for thirty (30) generations without improvement. The structure of the CANFIS was Gaussian. Fig. 3 is the simulation of the GA during building the GACANFIS, the straight line at the end of the learning curve shows convergence to the optimal solution and the GACANFIS with the optimal fuzzy weights, mean and standard deviation of the MFs was returned as the best model for the prediction of GEC.

Fig. 3. GA Search results for modeling CANFIS for the prediction of Greek energy consumption

For verification of the performance accuracy of the propose GACANFIS, this chapter predict the GEC using BP-NN, CANFIS, and FNN as earlier mentioned. Table 2 report the results of the comparison methods with the performance of our propose method.

Table 2. Comparing performances of the propose GACANFIS with other methods

Methodology MSE CPU time r

BP-NN 0.05132 13 0.7191 CANFIS 0.0156 16 0.8137 ARIMA 0.593 21 0.5321 FNN 0.02311 15 0.8691 Propose GACANFIS 0.0000627 9 0.9213

Table 2 shows the performances of the soft computing methods applied for the prediction of GEC. The results suggest that the propose GACANFIS significantly improve the performances of the methods previously utilized in the literature for the modeling of energy consumption. The performance criteria’s display in Table 2 clearly indicates the robustness and effectiveness of the propose method. Also, the propose GACANFIS was found to be faster than the other comparison methods in converging to the optimal solution. The probable reason for this performance could be as a result of the GA capability to avoid being trapped in a local minimum, and

Soft Computing Approach in Modeling Energy Consumption 777

searches for a very large space to obtain the optimal fuzzy weights, mean and standard deviation of the MFs which have not been possible without the GA. The performance of the our proposal is more evident when considering MSE and CPU time as performance criteria’s whereas in terms of correlation coefficient (r) between the GACANFIS output (y) and actual GEC (a) computed using Eq. (3), though the GACANFIS has the best values, but is close to the r values of the other methods.

n

yy

n

aa

n

aayy

r

ii

iii

−−

−−

=2

22 )()(

))((

(3)

This is not surprising as r indicates directional movement of the predicted and observed GEC. On the other hand, MSE shows error between predicted and observed values of GEC. This means that MSE can be changed without r being affected and vice versa. Among the other methods, including BP-NN, FNN, and CANFIS, their respective MSE values are close to each other. The worst performance was recorded by ARIMA model the probable reason for this performance can likely be caused by its linear nature which makes it unsuitable for solving complex and nonlinear problems including modeling of energy consumption. Though, the results generated by ARIMA are not surprising because experimental evidence in [22] among other literature with similar findings prove the superiority of soft computing techniques over statistical methods.

Fig. 4 display the performances of the propose GACANFIS and the comparative methods on the GEC test dataset to show the generalization ability of the methods in the prediction of GEC. The propose GACANFIS performs better than the BP-NN, CANFIS, and FNN as the predicted values of GEC from 2007 to 2011 are more closer to the actual GEC values than the GEC values predict by BP-NN, CANFIS, and FNN. Based on the promising values of GEC predict by the GACANFIS and the significant value of r as shown in Table 2. Therefore, the propose GACANFIS model can comfortably be applied to predict long-term GEC. The results of the study can favorably be compared with the results in the literature.

Table 3. The percentage error between actual GEC and GEC predict by GACANFIS

Year % Error 2011 0.27 2010 0.14 2009 0.22 2008 1.10 2007 0.12

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100GECActual

GECpredictedGACANFISGECActual%Error ×−= . (4)

We found only the work of [2] which predicts the GEC uses soft computing

techniques in the context of Greece. Thus, we select it for fair comparison since we also applied soft computing techniques to predict GEC in the context Greece. The percentage error of the propose GACANFIS presented in Table 3 computed using Eq. (4) indicates performance improvement over the 2% percentage error reported in [2]. The difference in the results could be attributed to the effectiveness of our approach which probable reason was earlier explained.

Fig. 4. Comparing GEC prediction performances of the soft computing technologies

Fig. 4 display the performances of the propose GACANFIS and the comparative methods on the GEC test dataset to show the generalization ability of the methods in the prediction of GEC. The propose GACANFIS performs better than the BP-NN, CANFIS, and FNN as the predicted values of GEC from 2007 to 2011 are more closer to the actual GEC values than the GEC values predict by BP-NN, CANFIS, and FNN. Based on the promising values of GEC predict by the GACANFIS and the significant value of R2 as shown in Table 2. Therefore, the propose GACANFIS model can comfortably be applied to predict long-term GEC. The results of the study can favorably be compared with the results in the literature.

3.2 Statistical Test

Non parametric statistical test was deployed for assessing the performances of the propose GACANFIS, FNN, BP-NN, ARIMA, and CANFIS on the GEC test datasets. The analysis of variance (ANOVA) was employed due to multiplicity of the independent datasets predict by each of the five (5) models which t-test cannot explore the significant difference among those models as t-test is limited to two independent samples. The ANOVA is a statistical test among several means under the hypothesis that they are equal. The ANOVA test result is determined based on p-values typically 0.05 at 95% confidence interval. The result based on p-value is that, if the critical value is less than the p-value, then the null hypotheses are rejected otherwise the research hypothesis is accepted.

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Table 4. Post hoc multiple comparison test results

(I) Group (J) Group

Mean Difference

(I-J) P

0.05 Confidence Interval

Lower Bound

Upper Bound

1.00 2.00 .07708 1.000 -49.8262 49.9804

3.00 9.73140 .990 -40.1719 59.6347

4.00 11.55070 .978 -38.3526 61.4540

5.00 11.42729 .979 -38.4760 61.3306

6.00 17.50530 .883 -32.3980 67.4086

2.00 1.00 -.07708 1.000 -49.9804 49.8262

3.00 9.65432 .990 -40.2490 59.5576

4.00 11.47362 .979 -38.4297 61.3769

5.00 11.35022 .980 -38.5531 61.2535

6.00 17.42822 .885 -32.4751 67.3315

3.00 1.00 -9.73140 .990 -59.6347 40.1719

2.00 -9.65432 .990 -59.5576 40.2490

4.00 1.81929 1.000 -48.0840 51.7226

5.00 1.69589 1.000 -48.2074 51.5992

6.00 7.77390 .996 -42.1294 57.6772

4.00 1.00 -11.55070 .978 -61.4540 38.3526

2.00 -11.47362 .979 -61.3769 38.4297

3.00 -1.81929 1.000 -51.7226 48.0840

5.00 -.12340 1.000 -50.0267 49.7799

6.00 5.95460 .999 -43.9487 55.8579

5.00 1.00 -11.42729 .979 -61.3306 38.4760

2.00 -11.35022 .980 -61.2535 38.5531

3.00 -1.69589 1.000 -51.5992 48.2074

4.00 .12340 1.000 -49.7799 50.0267

6.00 6.07801 .999 -43.8253 55.9813

6.00 1.00 -17.50530 .883 -67.4086 32.3980

2.00 -17.42822 .885 -67.3315 32.4751

3.00 -7.77390 .996 -57.6772 42.1294

4.00 -5.95460 .999 -55.8579 43.9487

5.00 -6.07801 .999 -55.9813 43.8253

Actual GEC (1), GACANFIS (2), BP-NN (3), FNN (4), CANFIS (5), and ARIMA (6).

780 H. Chiroma et al.

The ANOVA [F (Sig. = 0.86, df = 5, 29, P > 0.05) = 0.374], and Tukey results tabulated in Table 4 shows that there is no significant difference among the GEC values predicted by propose GACANFIS, FNN, BP-NN, ARIMA, CANFIS and the original GEC values. However, the mean difference of the propose GACANFIS predicted GEC and the Original GEC is very low and very close to the p-value (column 3 of Table 4) whereas others are very high. Implies that the propose GACANFIS predicted GEC values are promising than other GEC values produce by the comparison models. The means difference between the GEC values predicted by ARIMA model and the original once is very high and more than all other methods which signify poor performance.

3.3 Long – Term Prediction of Energy Consumption

The performance accuracy of the propose GACANFIS is promising and robust. The sigficant r values of original GEC and predicted once shows that the model has a capability of representing a real life system. Therefore, the model can be relied upon and applied to predict future values of GEC considering its performance and improvement made over approaches in the literature. As pointed out in [23], a model with a significant r constitute a true representation of the real system. Thus, we applied the propose GACANFIS to predict the long term GEC presented in Figure 5. Fig. 5 is a long term prediction of the GEC from 2014 up to 2023, the trend depicted by the figure indicated that the GEC will continue to fluctuate in the future but as a whole, the GEC demand will experience growth. This implies there will be economic development in Greece since energy consumption is positively correlated with economic development as reported in [1]. The policy makers in Greece can fine our propose GACANFIS model useful in the decision making process, especially on issues related to energy consumption and economic development.

Fig. 5. Long term GEC predicts by GACANFIS

4 Conclusion and Future Work

The research presented in this chapter is to improve the prediction accuracy of Greek energy consumption. The soft computing technologies applied for modeling the Greek

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energy consumption comprised of GA [24], fuzzy logic [25-27], inference system, and modular NNs. Specifically, in hybrid form is referred to as GACANFIS. Datasets were collected from various sources and use to build the propose GACANFIS model for the prediction of Greek energy consumption. For evaluation purposes, FNN, BP-NN, ARIMA, and CANFIS were also applied to predict Greek energy consumption for comparing the results with that of the propose GACANFIS. Simulation of the comparative analysis indicates that the propose GACANFIS outperform the FNN, BP-NN, ARIMA, and CANFIS in terms of MSE, R2, and CPU time. We take additional steps to compare the results with existing results in the literature and it was found to perform better than the results reported in the literature. The prediction of energy consumption is required for expanding capacity, strategy in energy supply, investment in capital, analysis of revenue, and management of market research. These can be applied in the context of Greece based on our propose model. Further research will be conducted to predict energy consumption of six (6) European countries and six (6) African countries based on data mining techniques selection criteria’s proposed by Chiroma et al. [28]. Uncertainties will be considered in the future work by modifying the framework of Chiroma et al. [29] to suit the prediction of GEC while considering uncertainties.

Acknowledgments. This work is supported by University of Malaya High Impact Research Grant no vote UM.C/625/HIR/MOHE/SC/13/2 from Ministry of Education Malaysia.

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