Journal of Physics: ConferenceSeries       PAPER • OPEN ACCESS Performance Comparison of Indoor Humidity Modeling: A Novel Hybrid Model vs. the Simplified Calculation Model by EN ISO 13788 To cite this article: Tao Lu et al 2023 J. Phys.: Conf. Ser. 2654 012052   View the article online for updates and enhancements. 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Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd 13th Nordic Symposium on Building Physics (NSB-2023) Journal of Physics: Conference Series 2654 (2023) 012052 IOP Publishing doi:10.1088/1742-6596/2654/1/012052 1 Performance Comparison of Indoor Humidity Modeling: A Novel Hybrid Model vs. the Simplified Calculation Model by EN ISO 13788 Tao Lu1, Xaoshu Lü1,2 and Heidi Salonen2 1 Department of Electrical Engineering and Energy Technology, University of Vaasa, P.O. Box 700, FIN-65101, Vaasa, Finland 2 Department of Civil Engineering, Aalto University, P.O. Box 11000, 02150, Espoo, Finland * Corresponding author. xiaoshu.lu@aalto.fi Abstract. Ventilation is essential for maintaining indoor air quality and human comfort, particularly in buildings with mechanical ventilation systems. However, modeling the complex relationship between ventilation rate and measurable indoor environmental parameters, such as humidity, poses significant challenges. Current methods for modeling this relationship are often inefficient. For example, data-driven models frequently require sufficient information on ventilation, which may not be available for constant air volume (CAV) systems. On the other hand, simulation programs can be time-consuming and require expert engagement. In this study, we present two simplified calculation models, including a hybrid model developed by the authors, and a well-known model introduced by EN ISO 13788. We compare their performance in evaluating the impact of ventilation rate on indoor humidity. The hybrid model uses a novel analytical method to upgrade a single-input regression model (which considers only outdoor humidity as input) to enable the evaluation of indoor humidity based on both outdoor humidity and ventilation rate. We used the commercial TRNSYS program to model two scenarios: increasing the reference ventilation rate and decreasing the reference ventilation rate. The results showed that both models matched TRNSYS simulations with satisfactory accuracies, but the hybrid model demonstrated superior performance to the EN ISO 13788 model in both scenarios. The hybrid model's higher accuracy and hybrid features make it better suited for big data analysis and field studies. 1. Introduction Ventilation plays a crucial role in controlling indoor air quality (IAQ) and human thermal comfort, and indoor humidity is an essential indicator of IAQ [1]. Mechanical ventilation is the most significant factor affecting indoor humidity [2]. State-of-the-art methods typically use physics-based models [3-6] to investigate the nonlinear relationship between ventilation rate and indoor humidity. However, certain factors, particularly the moisture buffering effects of building materials, can be challenging to account for in physical models [7]. Data-driven models face challenges in collecting the necessary data. To model ventilation performance using artificial neural networks, researchers collected data on IAQ, temperature, humidity, wind speed, and window and door characteristics in a residential building [8]. In our previous research, we introduced a novel hybrid model that utilizes only measured indoor and outdoor humidity data to effectively model the influence of outdoor humidity, ventilation rate, and 13th Nordic Symposium on Building Physics (NSB-2023) Journal of Physics: Conference Series 2654 (2023) 012052 IOP Publishing doi:10.1088/1742-6596/2654/1/012052 2 internal moisture production rate on indoor humidity in mechanically ventilated buildings/spaces [9]. This approach hybridizes a novel analytical method with a simple linear regression model, making it suitable for all types of ventilation systems, including constant volume ventilation (CAV). In this study, we aim to compare the performance of the novel hybrid model [9] with the simplified calculation method proposed in EN ISO 13788 [10] for modeling the impact of ventilation on indoor humidity. This comparison was lacking in our original work [9] and is crucial from a literature perspective. This work is an extension of our previous research [9]. 2. Methodology The novel hybrid model developed in [9] aims to upgrade the following model to model the impact of outdoor humidity, ventilation rate (𝑉̇𝑉, m3/h) and internal moisture production rate on indoor humidity: 𝑣𝑣𝑖𝑖 = 𝑎𝑎𝑣𝑣𝑒𝑒 + 𝑏𝑏 (1) where 𝑣𝑣i and 𝑣𝑣e are the indoor and outdoor humidity in [g/m3]. The model coefficients, 𝑎𝑎 and 𝑏𝑏, are determined based on the measured indoor and outdoor humidity. In this study, daily averaged values were used for the sampling interval, although shorter intervals may be possible depending on internal moisture production rates and other influential factors. While this linear model (Equation (1)) has been widely reported and studied in [6, 8-9, 11-12], it only has one input (i.e., ve), and assumes a fixed ventilation rate, which is the averaged ventilation rate over the measurement duration. In this paper, we refer to this fixed ventilation rate as the reference ventilation rate ( 𝑉̇𝑉𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟). In order to quantify the internal moisture change (∆m) induced by varying the reference ventilation rate while keeping the outdoor humidity constant, a novel theory was developed in [9]. According to this theory, only the change in the outdoor absolute humidity (AH) contributes to ∆m. Therefore, the change in the reference ventilation rate does not affect ∆m, and the linear relationship between indoor and outdoor humidity given by Equation (1) holds [9]. To account for ∆m, the true outdoor humidity (i.e., ve) in Equation (1) is replaced by a fictitious outdoor humidity called "pseudo-outdoor humidity" in this paper, which includes both the true outdoor humidity and a fake humidity term accounting for ∆m. For a fixed reference ventilation rate 𝑉̇𝑉𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟, increasing the reference ventilation rate l times is equivalent to drawing in outdoor humidity into the space l-1 times, which also results in l-1 times indoor humidity being drawn out of the space. Further details can be found in [9]. Based on mathematical calculations, the pseudo-outdoor humidity can be calculated as 𝑣𝑣𝑒𝑒 + (𝑙𝑙 − 1)𝑣𝑣𝑒𝑒 − (𝑙𝑙 − 1)𝑣𝑣𝑖𝑖 . By substituting the pseudo-outdoor humidity for 𝑣𝑣𝑒𝑒 in Equation (1), we obtain: 𝑣𝑣i = 𝑙𝑙𝑙𝑙 (1+𝑎𝑎(𝑙𝑙−1)) 𝑣𝑣e + 𝑏𝑏 (1+𝑎𝑎(𝑙𝑙−1)) (2) where l can be less than 1. The adoption of pseudo-outdoor humidity is a novel concept introduced in our previous research [9], which can also be utilized to incorporate internal moisture production rate as an additional input to Equation (1). However, in this paper, we will solely focus on the case of ventilation rate as an additional input. EN ISO 13788 [10] introduces a simplified steady-state model to evaluate the influence of outdoor humidity, ventilation rate, and internal moisture production rate on indoor humidity. The model is expressed as: 𝑣𝑣𝑖𝑖 = 𝑣𝑣𝑒𝑒 + 𝐺𝐺 1000𝑉̇𝑉 (3) where 𝑉̇𝑉 is ventilation rate (m3/h), and G is internal moisture production rate (kg/h). It should be noted that the EN ISO 13788 model, represented by Equation (3), does not take into account the hygroscopic moisture capacity of building materials, i.e., moisture buffering effects. In this work, we aim to compare the performance of two models, namely Equation (2) and Equation (3), in the case of varying ventilation rates. 13th Nordic Symposium on Building Physics (NSB-2023) Journal of Physics: Conference Series 2654 (2023) 012052 IOP Publishing doi:10.1088/1742-6596/2654/1/012052 3 3. Case studies A bedroom in a single-story and single-family house (Figure 1) was selected as a case study for the two models, Equation (2) and Equation (3). Synthetic data, including indoor humidity, at 10-minute intervals were generated using the commercial software TRNSYS 18 and its effective capacitance humidity module [13]. Table 1 lists the important parameters for the TRNSYS model. Figure 1. Bedroom with 2.6 m ceiling height. Table 1. Information about the bedroom in the TRNSYS model Element Property U-value (W/m2K) External wall 13 mm gypsum board + 540 mm mineral wool (wooden framed), 9 mm wind shield board 0.08 Roof 13 mm gypsum board + 650 mm mineral wool (wooden framed) + 10 mm waterproof sheet 0.07 Base floor 14 mm parquet + 80 mm concrete +365 mm EPS- insulation + 1000 mm ground layer 0.1 Internal wall 13mm gypsum board + 50 mm air gap (wooden framed) + 13 mm gypsum board 2.42 Windows g-value: 0.26 0.80 Ventilation system Mechanical supply and exhaust ventilation system Constant Air Volume system (100% outdoor air system) Operation schedule Monday–Sunday 00:00–24:00 Supply and exhaust air flow rate 25.92 m3/h Setpoint 21 ◦C for heating and 27 ◦C for cooling Internal moisture production rate 0.162 kg/h for 22:00–7:00 (occupied period), Monday–Sunday One-year weather data from Changchun, a city in Northern China, were extracted from an open- source dataset as it is similar to the Nordic climate. Based on the generated indoor humidity data for the bedroom, values of 𝑎𝑎 and 𝑏𝑏 were obtained as 0.9897 and 2.1105, respectively, for Equation (2). Furthermore, we assumed an ideal situation for the EN ISO 13788 model (Equation (3)), where the true internal moisture production rate (i.e., 0.162 kg/h for 22:00–7:00, Monday–Sunday) and ventilation rate (i.e., 25.92 m3/h) were known. Then, Equations (2) and (3) were used to estimate indoor humidity for two scenarios: 13th Nordic Symposium on Building Physics (NSB-2023) Journal of Physics: Conference Series 2654 (2023) 012052 IOP Publishing doi:10.1088/1742-6596/2654/1/012052 4 Scenario 1 (ventilation rate is increased by two times, i.e., l=2 in Equation (2)) Scenario 2 (ventilation rate is reduced by 50%, i.e., l=0.5 in Equation (2)). We utilized commonly used measures, including root mean square error (RMSE), mean absolute percentage error (MAPE), and coefficient of determination (R2), to assess the performance of Equations (2) and (3) for model fit. 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 = �∑ (𝑦𝑦�(𝑘𝑘)−𝑦𝑦(𝑘𝑘))2𝑁𝑁 𝑘𝑘=1 𝑁𝑁 (4) 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀(%) = 100∑ |𝑦𝑦�(𝑘𝑘)−𝑦𝑦(𝑘𝑘)| 𝑦𝑦(𝑘𝑘) 𝑁𝑁 𝑘𝑘=1 𝑁𝑁 (5) 𝑅𝑅2 = 1 − ∑ (𝑦𝑦�(𝑘𝑘)−𝑦𝑦(𝑘𝑘))2𝑁𝑁 𝑘𝑘=1 ∑ (𝑦𝑦�(𝑘𝑘)−𝑦𝑦�(𝑘𝑘))2𝑁𝑁 𝑘𝑘=1 (6) where 𝑦𝑦�(𝑘𝑘) is the simulations by Equation (2) or Equation (3), 𝑦𝑦(𝑘𝑘) is the TRNSYS generation, and 𝑦𝑦�(𝑘𝑘) presents the mean of y(k) 4. Results and discussion Figure 2 shows the comparisons of the simulations by the commercial software TRNSYS and by Equations (2) and (3) in Scenario 1 and Scenario 2. Table 2 displays their performance. Figure 2. Comparison of simulations by TRNSYS and by Equation (2) and Equation (3) (i.e., EN ISO 13788). The time step is day: (a) Scenario 1 and (b) Scenario 2. 13th Nordic Symposium on Building Physics (NSB-2023) Journal of Physics: Conference Series 2654 (2023) 012052 IOP Publishing doi:10.1088/1742-6596/2654/1/012052 5 Table 2. The performance of the two models: Equation (2) (the hybrid model by the authors) and the EN ISO 13788 model (Equation (3) (the time step is day) RMSE MAPE (%) R2 Equation (2) Scenario 1 0.38 4.63 0.99 Scenario 2 0.88 5.75 0.97 EN ISO 13788 Scenario 1 0.44 6.7 0.99 Scenario 2 1 8.23 0.97 The results of both models were satisfactory. However, the hybrid model (Equation (2)) outperformed the EN ISO 13788 model (Equation (3)) for both scenarios, even though the true internal moisture production rate was assumed to be known for the EN ISO 13788 model. In practice, it is difficult to obtain the true internal moisture production rate due to moisture buffering effects. For the hybrid model, over 85% of the simulations have an MAPE of less than 10% (for both scenarios combined). This figure is 69% for the EN ISO 13788. There are two factors that contribute to the greater accuracy of the hybrid model. Firstly, the hybrid model is based on a data-driven model (Equation (1)) which generally yields more precise results than a physical model like the EN ISO 13788 model. Secondly, the hybrid model takes moisture buffering effects into consideration, whereas the EN ISO 13788 model neglects this aspect. Equation (1) includes two parameters with physical interpretations: 𝑎𝑎𝑣𝑣e and 𝑏𝑏. Specifically, 𝑎𝑎𝑣𝑣e represents the portion of indoor humidity that originates from outdoor humidity, while 𝑏𝑏 represents the portion of indoor humidity that arises from internal moisture sources and sinks, such as occupants, furniture, and building materials. The moisture buffering effects of building materials, which involve the uptake and release of moisture, are also included in 𝑏𝑏. Both models showed reduced performance in Scenario 2 compared to Scenario 1, but the EN ISO 13788 model exhibited a greater decline. The hybrid model, for example, decreased by about 1.12% (=5.75%-4.53%) in terms of MAPE, whereas the EN ISO 13788 model decreased by 1.53% (=8.23%-6.7%). It is a well- established fact that moisture buffering effects are more pronounced at lower ventilation rates [6]. The EN ISO 13788 model is a physical model that operates under steady-state conditions. To model indoor humidity based on outdoor humidity and ventilation rate, internal moisture production rate information is required. Conversely, the hybrid model only requires the measurement of indoor and outdoor humidity to determine the two parameters, 𝑎𝑎 and 𝑏𝑏 in Equation (2). As previously discussed, the values of 𝑎𝑎 and 𝑏𝑏 implicitly incorporate information about internal moisture production rate and moisture buffering effects. This characteristic makes the hybrid model highly convenient for use, especially in big data analysis and field studies. 5. Conclusions This study compared two simplified indoor humidity models, namely the hybrid model by the authors in [9] and the EN ISO 13788 model in [10], for modeling the influence of ventilation rate on indoor humidity in two scenarios: increased and decreased reference ventilation rate. The hybrid model outperformed the EN ISO 13788 model in terms of accuracy for both scenarios. In section 4, we discussed the advantages and limitations of both models. The EN ISO 13788 model requires information about internal moisture production rate and ignores moisture buffering effects. On the other hand, the hybrid model does not have these limitations, but it is a regression model, meaning its accuracy is dependent on the quality of measurements. However, with the increasing use of IoT ( Internet of Things) sensors, long-term measurements are readily available, making the proposed methodology more suitable for this trend and producing higher accuracy than the EN ISO 13788 model. 13th Nordic Symposium on Building Physics (NSB-2023) Journal of Physics: Conference Series 2654 (2023) 012052 IOP Publishing doi:10.1088/1742-6596/2654/1/012052 6 One area of focus for future work is enhancing the quality of the hybrid model. One potential avenue for improvement is to employ pseudo-outdoor humidity, rather than actual outdoor humidity, in the construction of Equation (2) in order to increase the R2 value. Acknowledgements This research was supported by the Academy of Finland (STARCLUB, Grant No. 324023, CleanSchool, Grant No. 330150). 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