## 3 Data and Method
### Energy Benchmarking  
Benchmarking energy performance helps energy managers to identify best practices that can be replicated, either within a building or across a portfolio of buildings. Benchmarks can be reference points for measuring and rewarding good performance, as they allow an organization to identify top-performing facilities for recognition and to prioritize poorly performing facilities for immediate improvement.  
The most commonly used statistical method to develop benchmark tools is the linear regression technique. It is a statistical method used to model a linear relationship between a scalar dependent variable 'y' and one or more explanatory variables indicated by 'X'. Regression modeling is an easy method to estimate energy use intensity (EUI) for benchmarking purposes. Clear correlation between affected variables and energy consumption has to be recognized to ensure accurate estimation and a useful benchmark.  
The regression model is used to develop the benchmark Equation (1) for the energy performance. The benchmark formula estimates energy use intensity (EUI) based on affected variables such as electricity, city gas, and water consumption.  
Energy use intensity (EUI) unite is (MJ/m\({}^{2}\)) per month, year, room, person or other similar indicator, it can be normalized base on building function or the purpose of study.  
\[EUI= \propto+b_{1}\times X_{1}+\cdots\ldots+b_{k}\times X_{k}+\varepsilon \tag{1}\]  
where \(\alpha\) is the intercept; \(b_{1}\),..., \(b_{k}\) are the regression coefficients; \(X_{1}\),..., \(X_{k}\) are the significant standardized factors; and \(\varepsilon\) is the random error.  
The examined factors are selected based on their impact on energy intensity; other factors are neglected because they have less effect or an unclear effect on energy use in this category of buildings.  
Artificial neural networks (ANNs) imitate the working principles of human brains and perform learning and prediction. They are structured like a nervous system and are based on biological learning. In this study, an ANN was trained and tested using the software MATLAB. MATLAB provides built-in transfer functions that have been used for the hidden layers and outputs a pure linear function for the output neurons. The output of an artificial neuron can be mathematically expressed using Equation (2):  
\[y=\text{f.}\{\sum_{i=1}^{h}(W_{i}X_{i}+b)\} \tag{2}\]  
where \(y\) is the output of one neuron, \(h\) is the number of hidden layers, \(W\) is the connection weight, \(X\) is the input data, \(b\) is the bias value and f is the transfer function.  
ANNs is common method to model different categories of building energy consumption in a variety of conditions, such as heating/cooling load, electricity consumption, sublevel component operation and optimization, and estimation of usage parameters.  
In Figure 2, the topology of the MLP network shows the input and output of the ANN model for current study.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Cluster No.** & **Size Range (m\({}^{2}\))** & **Sample\({}^{\prime}\) No.** \\ \hline
**Cluster 1** & 300–2000 & **29** \\
**Cluster 2** & 2000–10,000 & **157** \\
**Cluster 3** & 10,000–30,000 & **101** \\
**Cluster 4** & \(\geq\)**30,000** & **52** \\ \hline \hline \end{tabular}
\end{table}
Table 1: Clusters of DECC samples.  
The ANN model in this research used the following inputs: Electricity, gas, and clean water consumption from the DECC data of accommodation facilities in the Kanto region.