A simple neural network for predicting operable window status

. A simple artificial neural network (ANN) is globally developed and broadly adopted in the building engineering field from many perspectives. It is a powerful tool to help engineer or predict future statements. There are many methods to introduce natural ventilation interior, and the simplest way is to conduct the airflow through windows. The general passive ventilation is practically in Spring and Autumn. This study aims to forecast the trends of indoor temperature and schedule the operation status of operable windows by using time-series differential data set. The building simulation has conducted during the transition periods to create training and testing data. A single-layer artificial neural network has been developed and performs training using the Levenberg-Marquardt algorithm. Additionally, the simulations have investigated in different seasons and places to validate the ANN model and find the best ANN model. From the result, the best trained ANN model is the training data that created covers the spring and autumn seasons with one hidden layer and 25 nodes. The training performances present in terms of MSE and R-values are 0.0507 and 88.25%, respectively. Finally, the best ANN model that has been built from a location is applicable and adapted to another location efficiently.


Introduction
Artificial neural networks (ANN) are used in many fields such as healthcare, image recognition, voice recognition, and engineering applications. ANN has been successfully applied across a wide range of problems in building engineering. The various applications of ANNs in renewable energy problems including solar steam generators, solar domestic water heating systems, photovoltaic systems, solar-radiation predictions, wind predictions, and building service systems, are presented in Kalogirou et al., (2001), [1]. Another reviewed work, [2], related to ANN on building energy applications. This work also presented the capabilities of ANN in building energy systems predictions. Applications of applying ANN in thematic problems are presented in [3][4][5][6]. Another paper, [7], reviewed researches related the modelling and prediction in building energy consumption, ANN is the most widely used artificial intelligence methods in summary.
ANNs have been widely used among researchers to predict indoor air environments and to obtain conducive environments. A large number of existing studies that related to have been reviewed. Indoor air temperature and humidity in a residential building under two different climate zones, Miami and Los Angeles have been controlled throughout the year by applying machine learning (ML) with reinforcement learning, [8]. The ANN was developed to predict the night ventilation rate in the bedroom of 24 buildings in China, [9]. The model has high accuracy and researchers have claimed * Corresponding author: thanyalak_s@meiji.ac.jp that it can be used to determine indoor air quality as a guideline. A research work validated an ANN model by using computational fluid dynamics (CFD), [10]. This work used CFD to create data set and validate the model. Air velocities and distributions had been predicted by a developed ANN model. One important point from this research is variations of pre-data processing have a high impact on the ANN model. Another work used CFD to train, test, and validate the ANN model, [11]. This work used the model to optimize the window size to achieve thermal comfort in naturally ventilated buildings. Another work controlled the window operations to reduce heat loss by developing a deep learning network. This work developed image recognitions from the camera to create the model, [12].
Training an ANN usually requires big data, but in a practical situation, data is limited. A challenge in developing the ANNs is the amount of training data to generate a model. A machine learning model was developed under data sparsity in the building operation by pre-processing data based on fundamentals of physics, [13].
This research extends the previous research that conducted the training data set with time series differentials data set to exploit the trends of indoor temperatures to predict the status of window operations, [14].
The main objective of this study is to investigate the performance of using the ANNs model that is built from limited data to predict a target with unknown test data under a different time of the year. Another objective is

Artificial Neural Network
This study is extending the results using ANNs for predicting operable windows referred on temperature change from the previous study, [14]. This study conducts the simplest ANN model to predict the trends of indoor temperatures to manage the status of window operations. MATLAB with the deep learning toolbox is used to develop the ANN model. The structure of the ANN model is presented in figure 1.
The number of nodes (N) in a hidden layer are varied to achieve the best-fit model. In this study, the number of nodes (N) are varied as 15, 20, 25, and 30 nodes. The network performances of the training model have been evaluated by the mean square error (MSE) and the correlation coefficient (R-value). For the testing performance is required by applying unknown data that have not been used in the training model. The test performances and number of nodes indexes in this study are presented in terms of standard deviation (S.D.) and percentage of positive direction (PP). PP is the correlation of the change of indoor air temperatures between predicted and simulated values. This term implies that the percentages of the predicted and simulated values move together in the same direction.   The ANNs model was a preliminary study using training data in Spring for Tokyo, Japan. The first step is using the ANNs model for predicting temperature changes in the Autumn period for a building in Japan. The second step is creating a new ANNs model for Spring and Autumn to predict temperature change both in Spring and Autumn. And the last step is testing the new ANNs model for a different place in Japan. Fukuoka city is chosen to test the model, it is located in the southern part of Japan where the weather zone is different from Tokyo. The case studies in this research are presented in table 1.

Simulation setting for creating a new data set to train the ANN model
The building model in Figure 2 is a standard model that has seven floors, which is generally used in building simulation in Japan, [15]. The floor plan has been shown in figure 3. Except for the third floor which is defined for studying natural ventilation is shown in figure 4. On the third floor, heat transfers and airflow are analyzed, therefore heat exchange between the connected floor (2 nd and 4 th floor) is set to zero. In figure 4, the vertical void space on each floor has merged into Office 1, this void space works as a stack to ventilate air from the openings on the lowest floor to the top floor. The airflow pathways of the analyzed zone induce natural flow from seven windows facing the south and flow up to the stack vent.    This study defines a particular setting for the openings. Two of seven windows always opened as fixed-opening windows. The other operable windows are on a mixed-mode operation that will be automatically opened when the outdoor temperature is over 20 °C. The opening area of all windows in Office 1 is approximately 3.4 m 2 . The vent area of the stack top is approximately 3.64 m 2 , and the discharge coefficient is 0.52.
The indoor air temperatures under the natural ventilation condition are determined on the Design Builder software. The predictors in this study are indoor temperature, outdoor temperature, wind speed, solar incident on windows, window status, lighting load, occupancy load, and equipment load. The natural ventilation is operated during Spring (April and May) and Autumn (October and November), every day between 7 am and 8 pm. Outside this specified time, the mechanical ventilation systems are turned on at 0.5 ac/h, to complete the 24-h ventilation of this building. For the internal heat load in the Office 1, the operation schedules are based on the standard Japanese building simulation. The occupancy density is 0.1 people/m 2 , except on the third floor, which has an occupancy density of 0.08 people/m 2 .
During custom schedules, the office equipment has a power density of 12 W/m 2 , except on the third floor, which has a power density of 8 W/m 2 . The lighting power density in the occupied zone has constantly been set at 7 W/m 2 . The schedules of internal load are presented in Table 2.

Effect of local climate data
This section is investigating the sensitivity of the ANNs model by simulating the identical building performance with different locations and testing it with the best ANNs model from the base building. The weather file adopted in this study contains data obtained from the Japan Meteorological Agency Weather Data of Tokyo, Japan, from the year 2016 to 2019. For the testing effect of local climate data, the weather file of Fukuoka city was obtained from the Japan Meteorological Agency Weather Data.

Results and Discussion
The performances of the ANN model in this study are assessed by the Mean Square Error (MSE), Correlation Coefficient (R-value), Standard Deviation (S.D), and Percentage of Positive direction (PP).
The simulation results in cases 1 to 5 has been done by using weather file from Tokyo, but weather file of Fukuoka city is used in case 6 and 7. In case 1, the training model is created from simulation results in Spring. In case 2, the training model is created from simulation results in Autumn. The testing data in cases 1 and 2 are created from simulation results in Autumn.
The number of trained and tested data in 1 and 2 are identical. In cases, 3 to 7, the numbers of training data are two times from previous cases because it has been created from simulation results in Spring and Autumn, but the testing data are the same except in case 3 where the testing data are twice. The training performances are divided into three groups that are case 1, case 2, and cases 3 to 7 as presented in figure 5. For the testing performances, it has presented for each case separately as in figure 6.
The best training model of Case 1 is the model with 15 nodes which has MSE and R-value of 0.0306 and 88.85%, respectively. The test performance indexes are S.D. and PP values of 0.3567 and 98.36%, respectively. The best training model of Case 2 is the model with 30 nodes which has MSE and R-value of 0.0575 and 91.42%, respectively. The test performance indexes are S.D. and PP values of 0.2367 and 98.85%, respectively. The best ANN model is case 3 because the number of training data is twice that compared to the other cases, and it covers whole periods for introducing natural ventilation into the buildings. The best ANN model for predicting trends of indoor air temperature is case 3 which has one hidden layer and 25 nodes. MSE and Rvalue of the training performances are 0.0360 and 0.8883 respectively. The testing performances are S.D. and PP values of 0.1923 and 99.67%, respectively. For case 4-7, the training performances are similar to case 3 because the best ANN model from case 3 is used to investigate different the test data set in cases 4 to 7. The testing performances in case 4 are S.D. and PP values of 0.1747 and 99.34%, respectively.  The next study is an investigation of the local climate effect by using simulation results from Fukuoka city. In cases 6 and 7, The testing performances in case 6 are S.D. and PP values of 0.1797 and 99.34%, respectively. The testing performances in case 7 are S.D. and PP values of 0.2213 and 99.34%, respectively. From the result, the training model created from the simulation result by using the Tokyo weather file can be used for Fukuoka city, the testing performances have high accuracy.
In the comparison between the use of Spring (Case 1) and Combined two season's data (Case 3), as in figure  5 and 6, the percentage change in MSE of Case 1 is lower than Case 3 by approximately 15%. The percentage change in the R-value of Case 1 is higher than Case 3 by less than 1 %. The percentage change in the S.D. value of Case 1 is higher than Case 3 by approximately 85%. In addition, the percentage change in PP of Case 1 is lower than Case 3 by approximately 1%.
In the comparison between the use of Autumn (Case 2) and Combined two season's data (Case 3), as in figure  5 and 6, the percentage change in MSE of Case 3 is lower than Case 2 by approximately 59%. The percentage change in the R-value of Case 2 is higher than Case 3 by approximately 3 %. The percentage change in the S.D. value of Case 2 is higher than Case 3 by approximately 23%.
In addition, the percentage change in PP of Case 2 is lower than Case 3 by approximately 1 %.
The preferred indoor air temperature for comfort in Japan ranges between 24 °C and 30 °C in the natural ventilation mode, [16]. The temperature setpoint for managing the window, open or close, should be set at the minimum value to cover the all comfortable range. The comfortable indoor air temperature at 24 °C with a tolerance of 0.5 °C is set as one of the criteria for a simple control strategy in this study.
In this study, the results of indoor air temperature trends have been used to settle how to designate the status of the operable window. An example plot of the difference in indoor air temperature and status of the windows in Case 3 is presented in Figure 7. Regarding the temperature trends (increase (positive value) or decrease (negative value) of the indoor air), if the indoor air temperature is less than 23.5 °C, the operable windows will be closed -assigned the binary number as 0. Suppose the trends of the indoor air temperatures increase (positive value) or decrease (negative value), but the current air temperature ranges between 23.5 and 24.5 °C. In that case, the operable windows will not change from their previous statusassigned in the graph as 0.5. If the trends of the indoor air temperatures increase (positive value) along with the air temperature greater than 24.5 °C, then the operable windows will be opened -assigned a binary number as 1.

Conclusion
A feedforward ANN is developed to predict the indoor air temperature and used to set the status of operable windows for a naturally ventilated building in Japan. This study is preliminary research that boards of natural ventilation in the office building during the Spring and Autumn season when the building is under moderate temperatures with no storm. This study investigates the performance of using the ANNs model that is built from limited data to predict a target with unknown test data under different seasons. From the result, the best trained ANN model is the training data that created covers the spring and autumn seasons with one hidden layer and 25 nodes. This study investigated the effect of local climate on the ANNs model prediction by using the trained model created from the Tokyo database and then applied to Fukuoka. The predictions of air temperature trends and window status in Fukuoka city have high accuracy. This study discovered that the ANNs model built from limited data can predict the naturally ventilated performance for different times and locations. And the ANN and simulation outputs of air temperature change gradually with good harmonization.