استفاده از روش فازی رگرسیون خطی برای معیار بهره وری انرژی ساختمان های تجاری

Benchmarking systems from a sample of reference buildings need to be developed to conduct benchmarking processes for the energy efficiency of commercial buildings. However, not all benchmarking systems can be adopted by public users (i.e., other non-reference building owners) because of the different methods in developing such systems. An approach for benchmarking the energy efficiency of commercial buildings using statistical regression analysis to normalize other factors, such as management performance, was developed in a previous work. However, the field data given by experts can be regarded as a distribution of possibility. Thus, the previous work may not be adequate to handle such fuzzy input–output data. Consequently, a number of fuzzy structures cannot be fully captured by statistical regression analysis. This present paper proposes the use of fuzzy linear regression analysis to develop a benchmarking process, the resulting model of which can be used by public users. An illustrative example is given as well.

In 2010, the Hong Kong government conducted a public consultation and consequently proposed the target of reducing Hong Kong’s carbon intensity (CO2/GDP) in 2020 by 50–60%. The Chinese government announced that the target for CO2 emission reduction per unit GDP in 2020 would be 40–45% compared with that in 2005. Moreover, in response to the increasing amount of end-use energy consumption, the Hong Kong government pledged an international commitment to reduce energy intensity by at least 25% by 2030, with 2005 as the base year, in a joint effort to address climate change through a reduction in energy intensity in Hong Kong. Currently, approximately 90% of the electricity consumed in Hong Kong is used in buildings [1]. Power generation accounts for almost 60% of the greenhouse gas emission, according to [2] and [3], and electricity intensity (kWh/m2/year) increases at an annual rate of 2.3% since 1996. Therefore, electricity must be used efficiently and wisely in the future, and the means to build energy efficiency must be improved as well. Other cities, such as Hong Kong, are facing the same challenge. Thus, benchmarking building energy efficiency is used to promote the efficient use of energy. As mentioned in [4], to conduct the benchmarking processes, benchmarking systems (or simulation models) from a sample of reference buildings must be developed to obtain “similar buildings”. The benchmarking system should consider several factors because the differences in a building’s energy efficiency may be affected by – random factors, such as unusual weather conditions; – physical characteristics, including age, number of floors, and so on; – incentives faced by building management or the owners; and – differences in how the building occupants utilize end-use devices. The actual energy use performances of the reference buildings should be normalized considering the abovementioned factors. The reference buildings can then be ranked according to their energy use performance using the normalized results. Benchmarking systems function as a public yardstick for energy use performance of the reference and other buildings. Some regulators may release benchmarking information to the media. This practice proves to be advantageous because owners/developers are needed to face with public pressure to act on poorly performing buildings. Benchmarking results can then be used to encourage poor performers (in energy efficiency) to improve their performance. Performance indicators, such as “kWh/ft2/year” or “MJ/m2/year”, provide information that makes building users, owners, management teams, or whoever pays the utility bills accountable for their energy use performance. Moreover, a comprehensive benchmarking system can promote competition in energy efficiency by providing information on the reasons for poor performance to building users or owners. A building’s energy use performance can be assessed relative to reference buildings or to its past performance. However, the different methods used to develop benchmarking systems do not allow public users (i.e., other non-reference building owners) to use all benchmarking systems. On the other hand, the present paper is partially motivated by and is based on a previous research [5]. In this previous work, a benchmarking energy efficiency model for commercial buildings by statistical analysis was developed. In the development process, data (or scores) on occupant behavior and maintenance condition, which is a subjective rating score with a fuzzy nature, were collected. However, the previous work may not be adequate to handle such fuzzy input–output data. Consequently, some fuzzy structures cannot be fully captured by statistical regression analysis. In summary, the following are the challenges: 1.1. Existing techniques are not suitable for a fuzzy environment From the literature, simple regression (SRA), stochastic frontier (SFA), and data envelopment analyses (DEA) were commonly used for benchmarking processes [4]. However, these approaches are incapable of dealing with fuzzy variables and/or parameters. In some comparative efficiency analyses, input and output data of buildings being evaluated are often fuzzy. Hence, a number of studies, such as that of Guo et al. [6], proposed the fuzzy DEA approach to deal with the efficiency analysis problem, given fuzzy input and output data.

The present research proposed a method for developing benchmarking models using fuzzy linear regression analysis. Through the standardization of the input data, the resulting fuzzy regression model can be used to build a benchmarking model. The results of the fuzzy regression model can be used to obtain a set of normalized center outputs to form the benchmarking table or figure. In the present work, the proposed method was used in a crisp input and output problem. Further studies may be required. If the approach is applied to crisp input and fuzzy output problems, or fuzzy input and fuzzy output problems, other reliable methods, such as the ones mentioned in [13] and [15], must be used to obtain the regression model and the resulting Yanorm(j). The resulting benchmarking model or figure is suitable for online applications. A website utilizing Eq. (7) for normalization calculation can be developed. New users can then provide the input and output values of their buildings this website to obtain their benchmarking scores.