Multi-gene genetic programming for predicting the heat gain of flat naturally ventilated roof using data from outdoor environmental monitoring
Introduction
Buildings represent the sector that consumes more energy, with over one-third of all energy produced in the world, and around one-half of global electricity [1]. This amount of energy is expected to increase in the next decades due to the growing demand for cooling and heating needs for the conditioning of residential and commercial buildings. The design of building envelope, the barrier between the indoor and outdoor environment, is one of the key steps to ensure the thermal comfort and energy efficiency of buildings. All envelope components such as walls, windows, roof, doors, and floor contribute to the thermal energy gains and losses of a building. However, building roofs receive solar energy during more hours than other components, and also, they have the greatest temperature fluctuations. According to Nahar et al. [2], a roof can contribute up to 50% of the total energy gain for buildings located in a warm climate. Therefore, this component has a vital role in the energy consumption of buildings.
Several technologies have been developed during the last decades to regulate energy gains from building roofs. Among these technologies, one can find thermal insulation (insulated roofs) [3], [4], reflective materials (cool roofs) [5], [6], phase change materials (PCM) [7], [8], airspaces and naturally ventilated cavities (ventilated roofs) [9], [10], [11], [12], [13], or even vegetation (green roofs) [14], [15], [16]. In this sense, naturally ventilated roofs have proven to be an actractive alternative to reduce energy gains into the buildings compared to the traditional components [9], [11], [17], because of two important features. First, they block the direct solar irradiance, which is the main source of energy gains for components exposed to the outdoor environment; and second, they prevent building overheating because the airflow in between the plates removes a great amount of heat.
In order to establish strategies for the construction of energy efficient buildings, the development of heat gain predictive models has become an essential practice [18]. Based on this, studies on the modeling of naturally ventilated roofs have been carried to analyze their thermal performance and establish the appropriate configurations that provide comfort to occupants [10], [11], [12], [13], [19], [20], [21]. In this sense, most of the documented models have been developed for steady-state conditions or have performed indoor experiments to estimate the heat transfer inside the building. The reason is that being exposed to the outdoor environment, heat transfer processes on the roof surface are affected by the fluctuating climatic factors and the time dependence. This interaction results in a complex procedure to predict the heat flux transferred through the naturally ventilated roof [10]. As a consequence, alternative modeling techniques can be used for the study of measurements made in outdoor conditions. The above in order to understand the complex multivariable nonlinear correlation among the environmental variables, the ventilated roof configuration, and its thermal performance.
Recently, machine learning techniques have been used as alternative tools for modeling and predicting the buildings thermal behavior in outdoor environment experiments due to their low computational cost, good reliability, and their flexibility to work with non-linear processes databases [22], [23], [24], [25], [26]. Mba et al. [22] proposed a recurrent artificial neural networks (RNN) modeling approach for the forecasting of indoor air temperature and relative humidity in buildings. Erdmir [23] and Ayata [24] examined the effects of temperature reduction inside buildings provided by a green roof using predictive models based multi-layer perceptron neural networks (MLP-ANN) and genetic programming, respectively. Similarly, artificial neural networks (ANN) models for predicting indoor temperature using different passive cooling techniques in test cells roof were studied by Pandey et al. [25]. Chong et al. [26] determined the predominant variables that affect the thermal comfort in forced attic ventilated buildings by using adaptive neuro-fuzzy inference systems (ANFIS).
Under this scenario, there is no evidence of coupling data from outdoor experiments and machine learning techniques to predict the thermal performance of naturally ventilated roofs. According to the literature review [22], [23], [24], [25], [26], the existing works based on machine learning are focused on the prediction of indoor temperature. This is because the measurement of the incoming heat flux in outdoor environmental conditions requires sophisticated facilities to isolate the other envelopes of the building. A suitable solution to this inconvenience is the implementation of test cells. These represent reliable tools widely used among building researchers for testing building components [27], [28], [29], [30], [31], [32], [33]. Compared to field measurements in real-scale buildings, test cell experiments ensure a higher quality of instrumentation and acquisition systems, and more homogeneous indoor conditions. Therefore, all the most influencing variables are thus controlled, while climatic conditions are continuously monitored. On the other hand, another important aspect to consider is that most of the models are focused on the analysis of ventilated inclined roofs. However, in various regions around the world flat roofs represent the most common configuration for housing construction [34], [35]. Therefore, in conjunction with the need to develop predictive models with real conditions, it is necessary to establish adequate facilities for the measurement and evaluation of thermal behavior on flat ventilated roofs.
Based on the aforementioned, the current work study the implementation of an evolutionary programming approach for the modeling of heat flux in naturally ventilated roof under outdoor environmental conditions. In this work, an outdoor test cell was designed and adequately instrumented for measuring temperatures and voltages that allowed us to determine the heat flux through the roof with different channel widths. Experimental measurements were conducted in the city of Cuernavaca, Mexico. The machine learning technique multi-gene genetic programming (MGGP) was selected for the development of mathematical models considering as input data the solar irradiation, wind speed, relative humidity, ambient air temperature, and different channel widths of the roof. The performance of the model was assessed and statistically compared with the multivariate analysis methods artificial neural networks, support vector regression, regression tree model, and multi-variate linear regression. Besides, the relative importance of the input parameter with respect to the thermal behavior was determined by a sensitivity analysis. The computational methodology developed by experimental samples is useful to estimate the annual panorama of the heat gain per square meter throughout the year, detecting the possible optimal ventilation widths for each month.
The contribution of this work focuses, in the first instance, on presenting a novel facility design for the measurement and evaluation of thermal behavior in flat naturally ventilated roof under external ambient conditions. On the other hand, the proposed simulation methodology based on evolutionary programming provides a useful tool for the projection of annual heat flux using data from outdoor environmental monitoring; which can gradually improve its estimation capacity when incorporating new training data. Thus, the proposed methodology can be used in order to identify the most suitable comfort zones aimed at energy saving.
Section snippets
Experimental facility and measurements
In this work, an outdoor test cell with dimensions 1.0 m × 1.0 m × 1.0 m (long, wide, and high) was designed, built, and characterized to assess the heat gain of ventilated roofs. The ventilated roof was formed using a concrete slab as a primary roof and a thin steel layer as the secondary roof. An adjustable channel width (d) was included in order to evaluate the roof thermal gain under various configurations.
Fig. 1 shows the experimental model of the test cell, the heat flows through the
Multi-gene genetic programming
MGGP is a robust variant of the genetic programming technique developed by Koza [36], based on the principle of Darwinian natural selection. It has proven to be a powerful tool for the solution of complex non-linear multivariate problems [37], [38], [39], [40], [41]. MGGP differs from the traditional statistical and machine learning techniques because it can generate prediction equations without assuming any prior form of the existing relationships.
In MGGP, a mathematical formula population,
Computational methodology
In this work, the MGGP is applied to identify the relationship of the incident heat gain per square meter in a flat ventilated roof with respect to the channel width and the effects of exposure to climatic parameters. Therefore, the computational methodology presented in Fig. 5 was used to estimate the thermal performance, modeling the heat flux passing through the roof (Q) at different dvalues. The procedure used to model Q consists of three steps:
(I) In the first step, a working database was
Sensitivity analysis
Sensitivity analysis (SA) was used to determine the influence of the input variables on the result of the MGGP model. It also defines the capability of the model to interpret the nature of the phenomenon. In this work, the SA technique implemented was the Elementary Effect Test (EET) [58]. It is a global SA technique based on the calculation of the mean () and standard deviation () of the so-called effective elements (EEs). The procedure consists in generate r random samples for each input
Model theoretical implementation
Based on statistical results of Section 4.1 and the robustness of the model tested in Section 5, the predictive MGGP model can be used to estimate the heat flux through the roof for theoretical channel widths within the model range (0.0–14.0 cm). According to [18], the calculation of these approximations should consider the deviation between the predicted value and the real measure, known as the performance gap. For the presented case this equals ±5.0 W/m2, corresponding to the standard
Conclusions
This paper studies the implementation of multi-gene genetic programming for the modeling of thermal gains in a naturally flat ventilated roof under outdoor environmental conditions. The experimental data were collected using a meteorological station and an adequately instrumented (thermally isolated) test cell for the measurement of heat transfer through the roof at different channel widths. Applying a computational methodology, a multi-gene genetic programming based model was developed as a
Acknowledgments
The authors acknowledge Miguel Beltrán for his support to perform the experimental tests. We also thank Carlos Torres for his help to manufacture the secondary steel roof. Finally, we appreciate the support of Rasikh Tariq for the language revision.
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