1. Introduction
The process when chemical compounds are bound to a solid phase is generally known as sorption. Adsorption occurs when adsorption of a substance takes place at the surface, while absorption occurs when the substance is absorbed in the entire volume of the solid phase. These processes can apply to volatile substances and particles dissolved in a liquid medium associated with the solid phase particles. Molecules and atoms can attach to surfaces in two ways. In the process of physical adsorption process between the adsorbate and the adsorbent, there are van der Waals interactions. In the process of chemical adsorption, molecules or atoms join with the surface to form chemical bonds.
The adsorption chillers [
1] (
Figure 1) are quiet, non-corrosive, reliable, environmentally friendly, and economical in operation appliances. They are consist of an evaporator, a condenser, separating valves, and a sorption bed. In some solutions, more than one sorption bed may be used. Adsorption chillers are capable of utilizing low-grade waste heat and renewable heat (e.g., solar energy) to produce cool and/or desalinated water. The adsorption chiller with silica gel-water, powered by a waste heat source, has been successfully commercialized in Japan [
2]. Waste heat in the industry is rarely used and is currently usually discharged into the environment. The article [
2] presents a three-stage adsorption chiller and computer program to simulate the cycle to predict its operation. Most often, in scientific studies, sorption processes are predicted using the nonlinear autoregressive network with exogenous inputs (NARX) [
2,
3,
4] or feed forward neural network (FFNN) [
3].
Neural networks (NNs) are used to predict various dependencies, among others, to predict the traffic volume [
5], the efficiency and generator power of a supercritical coal-fired power plant [
6,
7], the hydrogen concentration in the syngas [
8], in order to optimize a heat exchanger and adsorption chillers [
8,
9,
10]. They come in many variants, feed-forward NN [
7,
11] fuzzy NN [
10,
12], recurrent NN (RNN) [
13], and hybrid NN [
14]. Recurrent Neural Networks (RNNs) by their chain-like structure and internal memory with loops are widely used. Recently, the deep learning model, such as RNNs, has been increasingly used [
15]. The disadvantage of RNN is the vanishing gradient problem, which prevents them from modeling time series with long-term relationships such as wind speed and wind direction [
16]. There have been several attempts to overcome the difficulty of training RNNs over the years. These difficulties were successfully addressed by the Long Short-Term Memory networks (LSTMs) [
17], a type of RNN capable of learning long-term dependencies.
Long Short-Term Memory (LSTM) as a deep learning method can process sequential data [
15] and is applied in many real-world problems, such as image captioning [
18], music composition [
19], predicting for COVID-19 [
20], speech recognition [
21], and human trajectory prediction in crowded places [
22]. The papers [
23,
24] show algorithms by which there is the time at the input of neural networks and the data entered into the network are given in chronological order. In the presented article, no time variable was given at the input of the network. In the last few years, LSTM has gained popularity due to its ability to model long-term dependencies [
25,
26]. The long-term dependencies are typically learned from chronologically arranged input data, considering only forward dependencies, while dependencies learned from randomly fed inputs data have never been explored. NARX, FFNN, and LSTM are neural networks mainly dedicated to modeling time series cases. In this study, LSTM was used, which turned out to be one of the best and easy to interpret neural networks suitable for time-series problems.
The architecture of the LSTM-based model sought to be capable of describing the dynamics of sorption processes. Since most of the newly proposed LSTM-based prediction models are of one hidden-layer shallow architecture [
27,
28,
29], their performance is poorer than those with several hidden layers models [
30,
31].
All time-series sets of data ought to be utilized during prediction by an LSTM model. Usually, the model’s dataset is chronologically arranged from time epoch
t−1 to
t [
32]. However, this may lead to filtering out, or ineffectively passing through the network structure of useful information. Therefore, it may be a good idea to consider randomizing data. Another reason for the sampling of data into our study is the periodicity of sorption cycles. Analyzing time-series data periodicity, especially in recurring patterns, will enhance the predictive performance from both forward and backward temporal perspectives [
33]. However, based on our literature review, the dataset fed to LSTM is chronologically arranged, and the network itself uses forward and/or backward data prediction dependencies. The use of chronological data in the LSTM network may cause the network to start learning training data and incorrectly predict data, which is why it was decided that data would be entered into the network randomly within the research.
Since the literature review has already reported the advantages of the LSTM approach over other networks such as FFNN or NARX [
34,
35,
36], the purpose of the paper is to use the LSTM network in the novel field of application, i.e., for adsorption processes in innovative fluidized adsorption beds. This work presents numerical research results related to predicting the adsorption bed mass using the Long Short-Term Memory. Therefore, the considered issue corresponds to the innovative concept of replacing the fixed adsorption beds in conventional adsorption chillers with fluidized beds described in detail in [
37,
38].
Adsorption chillers are promising appliances allowing to use of low-grade thermal energy [
39,
40,
41], including renewable sources of energy such as solar heat, wastewater, underground resources, and waste heat, instead of high valued energy sources, e.g., electricity and fossil fuels-driven appliances [
42,
43,
44].
The idea of fluidized bed application [
45,
46,
47] significantly increases the heat transfer coefficient between the adsorption bed and the surface of a heat exchanger and the bed conductance of fluidized bed adsorption chillers, improving the performance of adsorption cooling and desalination systems [
48,
49,
50]. Moreover, the set of experimental data used is unique because the advanced test stand was utilized, which allows for the fluidized state implementation into the adsorption bed under lowered pressure conditions, even up to 1500 Pa.
The present work is the first in the literature, dealing with the deep learning method, such as LSTM for modeling fluidized and fixed adsorption beds to the best of our knowledge. The data used in the deep learning network was recorded within the experimental research related to sorption processes. In the LSTM, the input dataset has been given in random order rather than in chronological order, and the network itself uses forward dependencies. This paper deals with an innovative approach consisting of a fluidized bed application. Such an idea allows for improving heat and mass transfer processes, with helps increase adsorption chiller’ performance.
The second chapter contains a description of the test stand and research equipment, experimental research results, and the discussion on the algorithms used during the numerical research. The third section depicts the LSTM network hyperparameters and the structure of the LSTM network inputs and outputs as well as the results and their discussion. The work is finalized with a conclusion and proposal for further research.
3. Results of Numerical Calculations
By adopting the assumptions, formulations, and experimental research results presented in the previous chapters, the LSTM network algorithm and a computer program were developed, which enabled predicting the sorption bed’s mass during the sorption process. The experimental test results for the first ten valve V
3 opening cycles (6 tests, see
Table 1) have been normalized to a range of 0 to 100 and divided into three parts. The training data is presented to the network during the training stage. Validation data is exploited to improve learning and possibly to stop training. Finally, the test data do not affect training and validation, and thus, provide an independent measurement of network performance after training. These data were randomized without duplication as follows:
- (a)
First numerical research (60-20-20):
training data—60% of all data,
validation data—20% of all data,
test data—20% of all data,
- (b)
Second numerical research (70-15-15):
training data—70% of all data,
validation data—15% of all data,
test data—15% of all data,
- (c)
Third numerical research (80-10-10):
training data—80% of all data,
validation data—10% of all data,
test data—10% of all data.
Figure 9,
Figure 10 and
Figure 11 show test data as the trend line (linear fit) for all studies and the 95% prediction interval of LSTM network results.
The first analysis of the prediction of mass in the sorption bed using the LSTM network concerned the division of data in the ratio of 60-20-20, the results of this study are shown in
Figure 9 and
Table 3.
Figure 9 shows the LSTM network operation results compared to the values obtained during the experiment. The LSTM network predicts the worst results for pure silica gel (100% SG) in a fluidized state.
Table 3 shows the fit for all data and individual mixture. The coefficient of determination for all data is 0.9515. The LSTM network predicts the worst values for pure silica gel (100% SG). In the case of fluidization, the coefficient of determination is 0.8934, and for the fixed bed, it is 0.9218, which may be the reason for the low repeatability of the cycles during the experiment. The network achieves the best match for the mixture 95% SG + 5%Al, where the coefficient of determination for fluidized and fixed bed was equal to 0.989, and 0.973, respectively.
The second analysis of mass prediction in the sorption bed using the LSTM network concerned the data division in the ratio of 70-15-15. The results of this study are presented in
Figure 10 and
Table 4.
Figure 10 shows the result of the LSTM network in comparison with the values obtained during the experiment. As in the previous study, the LSTM network predicts the worst results for pure silica gel (100% SG) in a fluidized state.
All datasets achieved a fit of 0.9507, and
Table 4 also shows the coefficient of determination of the individual mixture for the fit function. The coefficient of determination in this study is lower than in the previous study. The LSTM network predicts the worst values for pure silica gel (100% SG) in fluidized bed conditions. The coefficient of determination for fixed and fluidized bed was 0.9250 and 0.8404, respectively.
The model’s best accuracy, in this case, was achieved for the fluidized bed of 85% SG + 15%Al mixture with R2 equal to 0.98.
The third analysis of the prediction of mass in the sorption bed using the LSTM network concerned the distribution of data in the ratio of 80-10-10. The results of this study are presented in
Figure 11 and
Table 5.
Figure 11 shows the results of the LSTM in comparison with the values obtained during the experiment. As in previous studies, the LSTM network predicts the worst results for pure silica gel (100% SG), fluidized state. In this case, the network best predicts the results of the experimental research.
The coefficient of determination for all is equal to 0.9554. The accuracy of the developed model is the best of the two previous ones. Only a slight decrease in R2 be seen for the 95% SG + 5%Al(S), and 95% SG + 15%Al(S) blends. The LSTM network prediction is still worst for the fluidized bed of pure silica gel (100% SG) with R2 equal to 0.867. However, the best prediction was achieved for the fluidized bed of the mixture 95% SG + 5%Al with R2 = 0.9915.
4. Conclusions
This paper deals with an innovative concept of a fluidized bed instead of a fixed adsorption beds application, currently employed in conventional adsorption chillers. The model, developed in the study, correctly predicts the vapor mass adsorbed in the adsorption chillers.
In this work, the Long Short-Term Memory networks, classified as a deep learning method, were also used to predict the sorption bed’s mass. The LSTM network is one of the particular kinds of recursive networks that are capable of learning long-term dependencies.
The solution to predicting the results was based on the most accurate mapping of the experimental values by the LSTM network. In the mathematical model, all network inputs were normalized to the range <0–100> due to the different units of parameters used in the study.
The analysis was performed by splitting the input data set into three parts (training data, validation data, and test data), in three variants: 60-20-20, 75-15-15, 80-20-20. The LSTM network, while increasing the amount of data used for training, better reproduced the experimental results. By increasing the training data make it possible to increase the accuracy of LSTM. The division of data into training data, validation data, and test data in deep learning networks are problematic because increasing one of the above values reduces the other two. A better solution seems to be to increase the amount of data entered into the network, but in this case, it was impossible due to the number of sorption cycles that the adopted mixtures could perform. In order to increase the amount of data, the mass of the mixture should be increased, as well as the initial conditions under which the tests were performed, e.g., the absolute pressure in the adsorption chamber and evaporator.
The developed model using the LSTM network and the high accuracy of the obtained numerical results confirm that the LSTM network is suitable for predicting sorption processes.
The LSTM network predicted the worst experimental test for pure silica gel (100% SG) in the fluidized conditions where the coefficient of determination did not exceed the threshold of 0.9 since these experimental tests are the least repeatable. The test results for 100% SG are more difficult to predict because no additive in the mixture would stabilize the sorption processes during the experimental test, so the sorption cycles for 100% SG are not very repeatable. Due to its high thermal conductivity, aluminum’s addition to the silica gel stabilizes the mixture, improving the sorption bed’s thermophysical properties. The LSTM network achieved the best accuracy for the mixture of 95% silica gel with 5% aluminum of addition in the fluidized conditions. For data splitting of 80-10-10 the highest coefficient of determination was equal to 0.9915.
Future research is planned to conduct comparative studies of several deep learning methods.