## 5 Conclusions  
This paper developed a framework of data imputation for sensors from building energy systems. The first module of this framework is developed based on pattern recognition, which identifies good data points that have similar characteristics with the missing data. The selected good data can mimic missing data but with truth value, which create testing scenarios to validate the effectiveness of the data imputation method. In the second module of this framework, a pool of data imputation methods is tested under the validation dataset to find an optimal imputation method for each sensor, which is termed as an ensemble method. The selected imputation method is expected to vary from sensor to sensor, which can reflect the specific mechanism and randomness of missing data from each sensor.  
The effectiveness of the framework is demonstrated in a real-building case study. The results show the importance of the ensemble method to automatically customize the selection of the imputation method based on different sensor types and missing data characteristics, after finding in the case study that (1) the ensemble method outperforms the best single imputation method by 18.2% and (2) the single imputation method cannot achieve good performance in all types of sensors and missing data characteristics.  
The framework can automate the data cleaning process due to very little domain knowledge being required. Users of this framework do not need any knowledge on the characteristics of the sensor and its missing data. Instead, the pool-based ensemble imputation method can automatically evaluate each single imputation method and find the most suitable one for each sensor. The automation process is essentially important with the development of BAS and Internet of Things, where a high automation is required for building analysis, modeling, and control.  
In terms of the limitation and future work, first, the framework only considers offline missing data. In the future, it can be extended for an online process. Second, the pool of imputation methods does not exhaust all the existing imputation methods. More sophisticated data imputation methods, such as Amelia, Self-Organization Maps, and K-nearest neighbors, can be included into the pool of imputation methods to further improve the performance of the whole framework. Moreover, the frequency of readings in this paper is 5 min for all sensors; in the future, the impact of sensor reading frequency on the accuracy of the developed framework can be further studied. Finally, the validation data generation module will not find appropriate (or similar enough) validation data when the missing data is a very rare case (in terms of weather and happening time) or no such pattern appears in the dataset. In the future, the impact of this situation on imputation accuracy should be evaluated. Generally speaking, the future work should focus on extending the developed framework to a more generic and plug-n-play tool for BAS.  
This work was authored in part by the National Renewable Energy Laboratory, operated by Alliance for Sustainable Energy, LLC, for the U.S. Department of Energy (DOE) under Contract No. DE-AC36-08 GO28308. Funding provided by the U.S. Department of Energy Office of Energy Efficiency and Renewable Energy Building Technologies Office. The views expressed in the article do not necessarily represent the views of the DOE or the U.S. Government. The U.S. Government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for U.S. Government purposes.  
The author declares no conflict of interest.