## 1 Introduction  
It is reported by U.S. Energy Information Administration that buildings consumed 32% of primary energy in 2019 in the United States and global energy consumption in buildings will grow by 1.3% per year on average from 2018 to 2050 [1]. Building operation data are playing an important role in building design, retrofit, commissioning, maintenance, operations, monitoring, analysis, modeling, and control. With the wide adoption of building automation system (BAS), smart sensors, and Internet of Things in buildings, massive measurements from sensors and meters are continuously collected, providing a +great amount of data on equipment and building operations and great opportunities for data-driven tools to improve building energy efficiency based on collected data [2]. Data quality is essential for data-driven tools and missing data is one of the most common and important issues for data quality. During building operations, it is common for sensors to fail to record data for several reasons, including malfunctioning equipment or sensors, power outage at the sensor's node, random occurrences of local interferences, and a higher bit error rate of the wireless radio transmissions as compared with wired communications [3]. [PERSON] and [PERSON] [4] summarized that missing data can be grouped depending on the reason they are missing: (a) missing not at random, or systematic missing: when the probability of an observation being missing depends on the information that is not observed; (b) missing at random: when the probability of an observation being missing depends on other observed values; and (c) missing completely at random: when the probability of an observation being missing is completely at random and not related to any other value. In statistics, imputation is the process of replacing missing data with substituted values ([PERSON] et al., 2017). The theories of imputation are well studied. Early in 2001, [PERSON] (1996) wrote a review of methods for missing data imputation and he summarized that ad hoc methods, such as complete case analysis, available case analysis (pairwise deletion), or single-value imputation, are widely studied. Ad hoc methods can be easily implemented, but they require assumptions about the data that rarely hold in practice. However, model-based methods, such as maximum likelihood using the expectation-maximization algorithm and multiple imputation, hold more promise for dealing with difficulties caused by missing data. While model-based methods require specialized computer programs and assumptions about the nature of the missing data, these methods are appropriate for a wider range of situations than the more commonly used ad hoc methods. [PERSON] and [PERSON] (2017) reviewed some key theoretical ideas, forming the basis of multiple imputation and its implementation, provided a limited software availability list detailing the main purpose of each package, and illustrated by example the practical implementations of multiple imputation, dealing with categorical missing data. [PERSON] et al. (2018) reviewed four common approaches for inference in generalized linear models with missing covariate data: maximum likelihood, multiple imputation, fully Bayesian, and weighted estimating equations. They studied how these four methodologies are related, the properties of each approach, the advantages and disadvantages of each methodology, and computational implementation. They examined data that are missing at random and nonignorable missing. They used a real dataset and a detailed simulation study to compare the four methods. Many existing studies are found to apply data imputation in missing data in buildings. Deleting the missing data is the most direct way to deal with them and, on some occasions, it can be counted as a data imputation method. In the research from [PERSON] et al. (2019), all corrupted and missing data instances due to instrumentation limitations were excluded from further analysis.