2.1. Experimental setup and procedures

An experimental setup is designed and implemented to obtain real-time greenhouse conditions specifically for the UK environmental conditions. The current packed bed system is designed for lettuce cultivation in the greenhouse. Figure 1 details the various components and their interconnections, which work together to increase humidity levels in the greenhouse. The experimental procedures involve the installation of packing material with variations in air temperature, humidity, and flow rates. Ambient air is drawn into the system through the air inlets. The air then passes through the packed bed chamber, where the packing materials are installed. Here, the air interacts with the water, increasing the air’s moisture level. The relatively humid air is then directed to the air outlet for introduction into the greenhouse environment. After releasing water vapour into the air, the water goes to the tank and is again pumped to the packed bed chamber. Data collection instruments like sensors and loggers are utilised to monitor environmental parameters and system performance.

Figure 1 Schematic of experimental setup.

The system is compact, with overall dimensions of 1.6 m × 0.9 m × 0.9 m, and utilises a counter-flow pattern for efficient air and water interaction. The core of the system is the packed bed, which is constructed using PVC corrugated sheets with dimensions of 0.4 m × 0.15 m × 0.4 m. The packing material of the packed bed chamber has a specific surface area of 256 m²/m³ that facilitates effective interaction between working fluids. The system features two liquid pumps, specifically Iwaki Magnet Pumps MX-70VM-13, with a capacity range of 90–100 L/min, which circulates the water between the packed bed and the water tank. Additionally, two blowers ensure a nominal air volume of 300 m³/h. The dehumidifier and regenerator are connected via 0.02 m diameter pipes, and the outlet/inlet ducts have a diameter of 0.1 m. The air velocity is measured using a Testo 405I hot wire thermo-anemometer, which has an accuracy of ±0.1 m/s and a range of 0 to 20 m/s. It was calibrated against a standard air velocity at the wind tunnel lab to verify its accuracy. Water temperature is monitored with a K-type thermocouple, accurate to ±0.5 °C, capable of measuring within a broad range of -200 to 1100 °C. The thermocouple was calibrated using an ice bath for low temperatures and a temperature-controlled water bath for high temperatures, ensuring accuracy across the desired range. Air humidity is assessed with Venatronics LLC THS14-A11-30-N, which offers an accuracy of ±0.6 °C and ±2.5% within a humidity range of 0 to 100% RH and an operating temperature range of -30 °C to 75 °C. Dry and wet bulb temperature readings are used to calibrate humidity sensors. Subsequently, the relative humidity values were obtained from a psychrometric chart to verify its accuracy. The water flow rate is measured by an RS 257-133 radial flow turbine flow meter, which has a similar accuracy of ±2% L/h and a flow range of 1.5 L/min to 30 L/min. The corresponding calibration was performed by comparing the flow meter readings with those obtained using the catch bucket method, where the volume of water collected over a specific time period was measured.

2.2. Methodology of intelligent models

The intelligent modelling approach involves machine learning algorithms to predict the behaviour of packed bed systems. Training datasets are generated using experimental data collected from the packed bed setups, including input parameters such as humidity, air flow rates, and corresponding output parameters representing system performance (Δω_a). Artificial neural network (ANN) is considered in the present study. An ANN is a standard method of artificial intelligence constructed in a manner analogous to the human brain’s information-processing system. They serve as computational tools for modelling complex non-linear relationships between independent and dependent variables, with extensive applications in various energy systems as documented in existing literature [9–12]. Among the various types of ANNs, the Multi-Layer Perceptron (MLP) neural network is particularly notable for regression tasks. MLPNNs are structured with an input layer, one or more hidden layers, and an output layer, each comprising numerous units known as neurons. This architecture enables MLPNNs to perform deep learning, accurately predicting both simple and complex functional behaviours. An MLPNN is characterised by having at least three layers: the input layer, which receives the initial data; the hidden layers, which process the data through transfer functions to identify patterns; and the output layer, which delivers the final prediction. The connections between neurons across these layers are established through weights, which adjust over time to strengthen or weaken the influence of each input. Generally, the number of neurons in the input and output layers is determined by the number of input and output variables. In the hidden layers, neurons work to pattern the behaviour of the input data, ultimately influencing the predictions made by the output layer neurons [13].

where d = target value of output layer for that neuron.

where T = target value of hidden layer for that neuron.

In the aforementioned context, X, b, and w denote the input, bias, and weight, respectively. This procedure is elucidated through a schematic representation, as depicted in Figure 2.

Figure 2 Schematic representation of an ANN illustrating overall model architecture and information flow.

Additionally, the output of the MLPNN model can be directly influenced by the choice of transfer (activation) function, which may exhibit either linear or non-linear characteristics. MATLAB offers three fundamental activation functions: purelin, logsig, and tansig, each tailored to different requirements. These functions are visually represented in Figure 3, accompanied by their respective function equations.

Figure 3 Comparative analysis of activation functions in ANN. (a) Purelin; (b) Logsig; (c) Tansig.

2.3. Performance parameters

In this context, ω_a,i represents the specific humidity of the incoming air, while ω_a,o denotes the specific humidity of the outgoing air.

3.1. Parametric study

Figure 4 represents the real-time experimental datasets obtained from the packed bed system that tracks the system’s performance. The constant air flow rate value in Figure 4 suggests that the system is designed to handle a particular air volume per hour.

Figure 4 Effect of air flow rate on outlet humidity ratios. Inlet and outlet humidity ratios over time for air flow rates of (a) 176 m³/hr, (b) 286 m³/hr, (c) 383 m³/hr, and (d) 428 m³/hr.

Figure 4 also presents a comprehensive parametric analysis to evaluate system performance under various operating conditions. This would involve the time-average water temperature and the water flow rate. The water, with a mean temperature of 15.7 °C, circulates through the system at a flow rate of 12.8 kg/min, which is maintained in the present study. Figure 4 contains four sub-figures that illustrate the relationship between air flow rate and humidity ratio throughout different times of the day to analyse the performance of a packed bed system designed to increase the humidity level of air using water as the working fluid. Figure 4(a) corresponds to an air flow rate of 176 m³/hr. It is observed that the inlet humidity ratio remains relatively constant over the time period, while the outlet humidity ratio exhibits more variability. This suggests that the packed bed system is effectively adding moisture to the air, as the outlet humidity is consistently higher than the inlet. Figure 4(b), at an air flowrate of 286 m³/hr, shows a similar pattern, with the outlet humidity ratio again being higher than the inlet, indicating successful humidification. Figure 4(c), with an air flow rate of 383 m³/hr, and Figure 4(d), at 428 m³/hr, both continue to display the trend of a higher outlet humidity ratio compared to the inlet. More specifically, for instance, when the inlet humidity ratio is 6 g/kg_da and the outlet is 9 g/kg_da, this would represent a 50% increase in humidity ratio due to the system’s operation. In summary, Figure 4 demonstrates the effectiveness of the packed bed system in humidifying air, with the outlet humidity ratio consistently higher than the inlet across various air flow rates.

Figure 5 represents quantitative data of Δω_a estimated over a specific time interval. The y-axis represents the change in a parameter denoted as Δω_a (g/kg_da), and the x-axis represents the duration in minutes. Figure 5 includes four different flow rate conditions, as indicated by the legend: 176 m³/hr (purple line), 286 m³/hr (blue line), 383 m³/hr (red line), and 428 m³/hr (black line). The general trend of Figure 5 indicates that the parameter Δω_a (g/kg_da) tends to decrease with time, especially at lower flow rates (176 m³/hr and 286 m³/hr). The higher flow rates (383 m³/hr and 428 m³/hr) show more stability in the parameter value over time.

Figure 5 Effect of air flow rate on humidity change, inlet and outlet humidity ratio basis.

3.2. AI modelling and its results

The MLPNN model was trained using comprehensive datasets that included multiple parameters: inlet air flow rate, humidity ratio, air temperature, liquid flow rate, and liquid temperature. These parameters were crucial for capturing the complex interactions affecting the system’s performance. However, in the context of the present study, the variations in air temperature (16 ± 0.7 °C), liquid flow rate (12 ± 0.8 kg/s), and liquid temperature (15 ± 0.9 °C), were relatively stable. Due to these constrained variations, their influence on the model’s predictions was less pronounced compared to the inlet air flow rate and humidity ratio. Therefore, the network inputs utilise two key variables, namely ṁ_a and ω_a. To establish an accurate and resilient model, Δω_a is trained through the different configurations of MLPNN. The optimum structure of the MLPNN model is depicted in Figure 6. This study employed 112 non-repeated datasets (comprising 56 input and 56 target data points) to map the input-output correlation. A feed-forward neural network, enhanced with a backpropagation learning algorithm, was employed for model training. From the total datasets, 70% were randomly selected for training purposes, while the remaining 30% were allocated for testing and validation. Various activation functions were utilised to ensure the MLPNN algorithm achieves commendable predictive accuracy. Details on the optimal hyper-parameters for the ANN model can be found in Appendix A. In the present MLPNN modelling, the primary stopping criterion used was epoch number 10,000, which monitored validation error during training and halted the process when improvements stagnated or declined, thus mitigating overfitting risks. Further, regularisation techniques were employed, specifically L1 and L2 regularisation, to penalise large weights and prevent the model from becoming overly complex. In addition, cross-validation played a crucial role; the dataset was divided into training, validation, and testing subsets. This approach allowed for hyperparameter tuning and performance evaluation, ensuring robust generalisation beyond the training datasets. The architecture, including the number of layers and neurons, was optimised based on empirical validation and domain expertise, balancing model complexity with generalisation to predict humidity variations in greenhouse conditions accurately.

Figure 6 Structure of proposed ANN model, featuring two hidden layers, each containing ten neurons (2-10-10-1 configuration).

The TrainLM training function was identified as the most appropriate for this present research study. The architecture of the neural networks utilised a tangent sigmoid activation function for both the output and hidden layers. To minimise the risk of overfitting during the training phase, a portion of the data samples, amounting to 15%, was allocated for validation purposes, while another 15% was set aside for testing the efficacy of the trained networks. The initial trials, which employed networks with a single hidden layer, did not yield satisfactory results due to a pronounced discrepancy between the experimental data and the predictions, attributed to the complexity of the problem at hand and regardless of other parameter settings. This observation led to the exploration of networks with multiple hidden layers for further testing and evaluation, aiming to enhance the accuracy of the predictions. Adjustments were made to the number of neurons within these layers, ranging from 8 to 12. The findings revealed that the optimal network configurations for predicting Δω_a were those with two hidden layers, specifically the 2-10-10-1 topology, which comprises two input neurons in the first layer, ten hidden neurons in each of the two hidden layers, and one output neuron, as depicted in Figure 6.

Figure 7 illustrates the predicted Δω_a values as obtained by the MLPNN model, alongside a comparison with the corresponding experimental data. The predictive patterns of the packed bed system’s output parameters generated by the AI model closely agree with the experimental outcomes across all tested conditions. The most significant observed discrepancy between the ANN predictions and the experimental Δω_a values was within a margin of ±2.5%.

Figure 7 Comparison between experimental and AI models outcomes for Δω_a.

Availability of Data and Material

Dataset available on request from the authors.

Funding

This research is funded by Innovate UK as part of the project “Protected Cultivation of Horticultural Crops: Setting a New Standard” (10054907).

Competing Interests

Anthony Paul Roskilly is the Editor-in-Chief of the journal Green Energy and Sustainability. The author was not involved in the journal’s review of or decisions related to this manuscript. The authors have declared that no other competing interests exist.

Author Contributions

Mrinal Bhowmik: Writing – Original Draft, Conceptualization, Methodology, Investigation, Software, Visualization, Validation, Data Curation; Alessandro Giampieri: Writing – Review & Editing, Conceptualization, Methodology, Investigation, Visualization, Data Curation; Anthony Paul Roskilly: Supervision, Funding Acquisition, Formal analysis; Zhiwei Ma: Writing - Review & Editing, Resources, Project Administration, Conceptualization, Methodology, Investigation, Visualization.