Dynamic neural networks to analyze the behavior of phase change materials embedded in building envelopes

Highlights

• Behavior of Artificial Neural Networks is done, for building envelopes with PCMs.

• The network trained adjusts well to experimental data, with MSE of 0.0584 W/m².

• The ANN shows bad generalization under conditions different to the training data.

• ANN generalization should always be analyzed.

• Bad generalization can be due to high variability of boundary conditions.

Abstract

Heat transfer during melting and solidifying processes in phase change materials, is a highly non-linear phenomenon. Artificial Neural Networks seem a suitable approach to deal with highly non-linear processes. The present work uses dynamic neural networks to simulate the behavior of a phase change material layer of a building envelope, which typically are under strongly varying conditions, with temperatures and heat fluxes changing at different rates inside a wide range of values. In the present work, the experimental procedure to obtain the training dataset is explained; then, an ANN is trained using experimental data, together with additional data related to the thermal behavior of PCMs; finally, generalization of the ANN is analyzed, and the results are evaluated.

Initial training attempts, show a perfect match between experimental data and simulation results of the neural networks, with absolute mean errors below the accuracy of the fluximeters. However, when analyzing the simulations carried out with data different to those used to train the networks, the results differ strongly to those expected. This means that neural networks seem to have a bad generalization when dealing with phase change materials under strongly varying conditions, probably due to the high variability of the input data, and the strongly non-linear behavior of phase change processes.

Introduction

Phase Change Materials (PCMs), can be useful to improve the efficiency of building envelopes. PCMs can store large amounts of thermal energy, without increasing their temperature, avoiding overheating. Embedding PCMs in building envelopes, it is possible to store solar thermal energy during the day, and use it at night, reducing the heating demand of the building. They can also be used to reduce the cooling demand in summer, by solidifying the PCM at night making use of lower outside temperatures, allowing to keep the rooms cooler. PCMs in building envelopes can be understood as a distributed thermal energy storage system in the building, that enhances the use of passive solar energy, and free cooling, to have a higher energy efficiency at the building level [1].

In order to obtain the best performance of the PCMs, the definition of the optimal thermo-physical properties is very important. Taking into account the high variability of the outdoor climatological conditions of a building, this can only be achieved through simulation of whole building performance in a typical year.

Heat transfer during melting and solidifying processes in phase change materials (PCMs), is a highly non-linear phenomenon, that can only be analytically solved in very simple situations. The most common approach to deal with the phase change problem, is to use finite difference methods, discretizing both space and time. The accuracy of these methods, is directly linked to the timestep, and the space discretization size [2]. In order to obtain accurate results, short timesteps and small space discretization needs to be used, what implies large computational costs.

However, Artificial Neural Networks (ANN), seem to be a suitable alternative to tackle with this problem. ANNs replicate the behavior of biological neurons. Neurons are highly interconnected cells, each of them doing simple operations, but when connected together, they are capable of handling complex problems [3]. Following this behavior, artificial neurons are simple mathematical functions, interconnected with other similar neurons. The outputs of the neurons act as inputs of neurons in the next layer, obtaining a powerful parallel computing scheme. ANNs are able to deal with non-linear problems, can learn from examples, are fault tolerant, can handle noisy and incomplete data, and once trained, can resolve the problems at high speed [4]. They do also have some limitations, that need to be taken into account, such as overtraining and extrapolation errors, network optimization, or the requirement of experimental or validated data to perform the training of the ANN [5].

Despite their advantages and suitability to handle phase change problems, ANNs have not been widely used so far to simulate the thermal behavior of PCMs.

One of the common problems with neural networks, is that while they can be trained to fit almost any process, sometimes they do not generalize correctly. Generalization is the ability of the ANN to answer correctly to data different to the one it has been trained with. When the input data has many different combinations, the network cannot simulate correctly all the possible variations, and turns to be useless [6]. The most common ways to enhance the generalization of the ANN is to use special training algorithms that avoid overtraining, like Bayesian Regularization, or to use only part of the available experimental data to train the network, and test the performance with the remaining data. Usually both methods are used together.

Many articles deal with the use of ANNs to calculate single bulk values, such as charging or discharging time, or stabilization temperature. They do not work with dynamic, time-dependent values, like temperature evolution or instant thermal performance.

Artificial Neural Networks have been used to analyze and optimize different configurations of heat sinks for electronic devices. Kanesan et al. [7] used ANNs to simulate the thermal behavior of heat sinks with fins, and PCM between them, when heated from the base at a constant heat flux. They used ANNs to obtain stabilization time and maximum operating temperature, when heated at a constant heat flux. The data used to train the ANNs was obtained from a validated numerical models. Then, they used Genetic Algorithms (GA) to optimize fin thicknesses, fin height, number of fins and PCM volume.

The same approach (i.e. the use of a validated numerical method to train an ANN, and then GA to optimize the heat sink) has been used by Baby et al. [8], for heat sinks with pin type fins, where they optimize the number of pins in order to maximize the time needed to achieve a certain temperature. Alayil et al. [9] analyzed heat sinks with cross plate fins, and optimized the number and width of the fins, to maximize the time needed to achieve a temperature of 312 K at the base. Srikanth et al. [10] analyzed heat sinks with matrix type fins. In this case, the heat sink is heated at a constant heat flux until the base reaches 318.2 K, and then is cooled down. The optimization with GA is done to maximize the heating time, and simultaneously minimize the cooling time. Srivatsa et al. [11] analyze different geometries of heat sinks with PCM, and optimize the configurations to maximize the time needed to melt all the PCM.

Najafian et al. [12] use a similar approach to optimize the integration of PCMs in domestic hot water tanks. In this case, they simulate different configurations of PCM amount, size and placement in a water tank, to obtain the total discharge time. Then, they train ANNs to relate the configurations with the discharge time, and finally they use GAs to maximize the discharge time.

Delcroix et al. [13] use ANNs to predict the thermal capacity of a PCM, using experimental data from Differential Scanning Calorimetry, and from experiments. They obtain a good agreement when working with DSC data, but a lower agreement when using experimental data.

On the other hand, some authors have used ANNs to simulate the dynamic behavior of thermal systems, to obtain time-dependent values, such as temperature evolution, or instant thermal performance.

Latent Heat Thermal Energy Storage (LHTES) systems, which include PCMs to store thermal energy, have also been analyzed with ANNs. Ermis et al. [14] used ANNs to calculate the total amount of energy stored in a latent heat thermal energy storage system with PCMs, when heated by a constant temperature fluid, at a constant fluid rate. To train the ANN, they used both experimental data, and data obtained from a finite volume model.

El-Sawi et al. [15], analyze the thermal performance of a centralized PCM storage system, used in the mechanical ventilation system of a building. In this case, they use a special type of neural network called GMDH (Group Method of Data Handling), in which the relation between different layers of neurons is polynomial. They train the network to obtain the air temperature at the outlet of the storage system. The training is done with data obtained from a validated CFD model. They simulate the first days of every week with the CFD model, to obtain the training data, and then use the ANN to simulate the whole summer period.

Kanimozhi et al. [16] use ANNs to analyze the enhancement of heat transfer in a thermal storage system with PCM. The storage system is charged at constant temperature and mass flow rate, and discharged at constant temperature and three different mass flow rates.

Different types and configurations of solar collectors with PCM have also been simulated with ANNs. Varol et al. [17] analyze the use of different Machine Learning methods, among them ANNs, to obtain useful energy and thermal performance evolution in time.

Kumar et al. [18] use ANNs to obtain the thermal performance, exergetic performance and outlet air temperature, of a solar air heater. The values obtained from the ANNs show a good adjustment to experimental data used for training, but they only use data from a single day to train the network.

Al-Waeli et al. [19], [20] analyze the behavior of PV/T solar panels. Among the cooling fluids for the thermal heating, they use nano-fluids with PCM. They use ANNs to simulate the behavior of the PV/T panel, but only to predict the electricity generation, and not to simulate the thermal behavior and heat transfer process in the PCM.

Fadael et al. [21] analyze the thermal behavior of a solar chimney with PCMs. The input for the ANN is the surface temperature at different positions inside the solar chimney, and the output is the air temperature. In this case, the ANN is simulating the heat transfer between the inside of the solar chimney and the air in contact with that surface, and not the thermal process inside the PCM. Apart form this, they only use hourly data from a single day to train the network.

Ghani et al. [22] use Layered Digital Dynamic Neural (LDDN) type networks to simulate the dynamic behavior of a thermal storage tank with PCMs, during charging and discharging processes. Both charging and discharging are done at constant temperature and constant mass flow rates. They used data from 20 experiments, and validated the network with the data from an additional experiment, showing good generalization of the network for this setup.

Urresti et al. [23] tested the thermal behavior of a building envelope layer with PCMs, and used experimental data to train an ANN. The ANN trained uses the temperature evolution on both surfaces of the envelope, and simulates the heat flux on both sides of the sample as output. The experimental data was obtained from a conductivimeter test, and the trained ANN showed a good accuracy.

All the articles show good agreement between experimental training data, and the results of the simulation with ANN, but most of them do not analyze the generalization of the network, that is, they do nor perform simulations with input data different from those used for training. Only the work by El-Sawi et al. [15], and the work by Ghani et al. [22], analyze the generalization of the network.

The objective present work is to acquire a deeper understanding of the ability of Artificial Neural Networks to simulate the dynamic behavior of building envelope components with PCMs. As can be seen from the bibliographic analysis presented, there are not many articles published that deal with dynamic thermal behavior of systems with PCMs, and most of them do not analyze the generalization of the trained network. Additionally, only one work has been published that deals with the dynamic behavior of building envelopes with PCMs, but it also lacks an analysis of the generalization of the network.

As mentioned before, in order to obtain the best performance of the PCMs, the definition of the optimal thermo-physical properties is very important. Taking into account the high variability of the outdoor climatological conditions of a building, a large dataset of experimental values is needed to obtain the training data for the ANN, and also an analysis of the generalization should be carried out.

In the present work, the experimental procedure to obtain the training dataset is explained; then, an ANN is trained using experimental data, together with additional data related to the thermal behavior of PCMs; finally, generalization of the ANN is analyzed, and the results are evaluated.