Investigation of dehumidifier performance parameters using ANN-PSO algorithm

ABSTRACT

In this investigation, a performance analysis of a liquid desiccant-based dehumidification system was conducted by integrating a particle swarm optimization (PSO) algorithm and an artificial neural network. Experimental data are collected through past studies on falling film towers for flat plate and cylindrical surfaces, covering a wide range of liquid desiccant and air operating conditions. The neural network is fine-tuned through the use of the PSO algorithm. This optimization aims to enhance the accuracy of predicting the moisture absorption rate, change of specific humidity and dehumidification effectiveness of a liquid LiCl (Lithium chlorite) desiccant system. The effectiveness is contingent on various working parameters, including mass flow rate of moist air, mass flow rate of liquid LiCl solution desiccant, inlet air temperature, and relative humidity of inlet air, inlet temperature LiCl solution desiccant and desiccant concentration. The present ANN-PSO algorithm predicts the changes of absolute specific humidity, moisture absorption rate of water vapour from air and effectiveness of the dehumidification system. The present model precisely predict the performance parameters with R² = 0.9989.

Keywords:
Liquid desiccant; Dehumidifier; Polypropylene; Artificial Neural Network (ANN); Particle Swarm Optimization (PSO)

1. INTRODUCTION

In recent decades, there has been a rapid escalation in building energy consumption TUOMINEN et al. [¹]. In developed nations, the collective contribution of residential and commercial buildings to overall energy consumption has shown a consistent upward trend, comprising a substantial portion ranging from 20% to 40%. This surpasses other major sectors such as the transportation industry PÉREZ-LOMBARD et al. [²]. Within the spectrum of air conditioning, heating, ventilation (HVAC), and building energy services, systems emerge as the major energy-intensive components, accounting for over 50% of the total energy utilized by the building area. Notably, in humid regions, air-conditioning systems alone account for 54% and 23.5% of the total energy consumption in typical commercial and residential buildings, respectively [³]. Many researchers have explored hybrid systems to reduce energy consumption in air conditioning. ABBASI et al. [⁴] conducted a study on a hybrid system that combines a ground-source heat pump (GSHP) with a photovoltaic (PV) system. This system is intended to fulfill the cooling and heating requirements of a zero-energy residential building. Their results showed that this hybrid approach could significantly reduce CO₂ emissions by nearly 70 tons per year. Additionally, liquid desiccant systems, which can utilize solar energy, present a promising alternative to conventional air conditioning for managing latent loads. Traditional air conditioning systems, which rely on refrigerants, have the potential to contribute to ozone depletion. Over the past few decades, there has been a growing interest in liquid desiccant dehumidification, owing to its precise humidity control capabilities and significant potential for energy savings. In contrast to Vapor Compression Systems (VCS), which heavily depend on electrical energy, liquid desiccant systems demonstrate the ability to utilize low-grade energy [⁵,⁶,⁷]. This versatility enables a marked enhancement in system energy efficiency. A comparative analysis with traditional VCSs indicates that liquid desiccant cooling system (LDCS) exhibits potential for energy conservation ranging from 30% to 50% [⁸]. The evaluation of liquid desiccant dehumidifier performance commonly relies on key metrics, with effectiveness and condensation rate serving as primary Indies. Previous research has categorized the modelling techniques employed for predicting dehumidifier performance into three main classes: theoretical analysis models, experimental models, and artificial intelligence models.

In the study conducted by LIU et al. [⁹], a comparative analysis was undertaken between lithium chloride and lithium bromide water solutions. Experimental observations revealed the superior dehumidification capability of the lithium chloride solution. Subsequently, LIU and JIANG [¹⁰] developed a comprehensive mass transfer and heat transfer model, verifying it through both experimental data and numerical simulation. This model facilitated an analysis of the uncoupled mass and heat transfer processes, as well as the simultaneous consideration of enthalpy differences and a discussion of relative humidity (RH) between the air and solution. Furthermore, LIU et al. [¹¹] performed an experimental investigation into the mass changes in the air due to changes in moisture in a cross-flow arrangement of a dehumidifier. They utilized of Celdek structured as dehumidifier medium with LiBr as the liquid desiccant.

Many researchers have employed various methods to predict the performance of different systems. For example, XU et al. [¹²] used AI techniques, applying a support vector machine learning algorithm optimized by the grey wolf optimization method to model the hydrogen content of bio-oil (H-BO) based on pyrolysis conditions and biomass compositions. In another study, Bo LIU and KARIMI NOURODDIN [¹³] proposed a novel extreme learning method (ELM) and an ensemble decision tree-boosted AI algorithm (EDT Boosted) to forecast the normal boiling point using data from 16 different molecular groups and one topological index.

Studies show that they have employed various artificial neural network (ANN) methods to predict the performance of different systems. For example, HAN and SERAJ [¹⁴] employed an adaptive neuro-fuzzy inference system (ANFIS) technique to predict two output parameters: thermal conductivity (TC) and viscosity, using input parameters of concentration, particle size, interfacial layer thickness, and the intensive properties of nanoparticles. Similarly, HAN and SARVAZIZI [¹⁵] employed artificial neural network (ANN) models combined with optimization algorithms, including a genetic algorithm (GA) and particle swarm optimization (PSO), for estimating the dew point pressure (DPP) of gas condensate fluids, which is essential for evaluating reservoir performance, planning and developing gas condensate reservoirs, and designing or optimizing production systems.

Among these methods, the GA-PSO approach is considered the most versatile and effective for predicting system performance. The contemporary inclination among researchers is to employ artificial intelligence (AI) models to predict the performance of water vapor mass exchange between air and desiccant, as well as heat within the dehumidifier. This preference is attributed to the capacity of AI model to train and adapt autonomously with minimal human intervention. Assessing the effectiveness of neural networks (ANN) as a modelling for liquid desiccant dehumidification, various studies have been examined.

GANDHIDASAN and MOHADES [¹⁶] explored a model based on an ANN to simulate the correlation between outlet parameters and given inlet parameters in a packed bed type dehumidifier. Their investigation utilized LiCl as a desiccant in an aqueous-based liquid solution, with eight parameters (comprising air and solution inlet parameters, temperature ratio, and inlet temperature of cooling water) employed as inputs, while solution temperature, water dehumidification rate, and liquid desiccant mass concentration served as output indices. In a study by ZEIDAN et al. [¹⁷], a multi-level neural network model was employed to analyze a solar regenerator and dehumidifier arrangement. SINGH et al. [¹⁸] developed Mamdani fuzzy models to simulate the water-vapor extraction rate in a liquid air desiccant dehumidification system. This review highlights the growing application of artificial intelligence models, specifically neural networks and fuzzy systems, in modeling and predicting liquid dehumidification processes. MOHAMMAD et al. [¹⁹] used an artificial neural network (ANN) model to forecast the evaluation metrics of effectiveness for a liquid desiccant dehumidifier. A feed-forward back- propagation algorithm was implemented in MATLAB code. The outcomes revealed optimal changes between the ANN proposed values and the experimental investigated indicators, with an 8.13% condensation rate of water vapour and 9.0485% dehumidifier effectiveness. RAHMANI and MOSTEFAI [²⁰] study on optimizing the sizing of an autonomous hybrid energy system (combining solar PV, wind, and battery storage) to power a typical household in an isolated village in Adrar, Algeria.

To strengthen the novelty of the integrated ANN-PSO approach for polymer-based liquid desiccant dehumidifiers, a comparative evaluation was conducted against other artificial intelligence techniques—such as support vector machines (SVM), extreme learning machines (ELM), and adaptive neuro-fuzzy inference systems (ANFIS)—based on literature-reported models. While methods like ELM and SVM offer faster training times and lower computational requirements, their prediction accuracy for highly nonlinear thermal systems has been reported to range between R² = 0.85 and 0.95, with average percentage errors between 3% and 7%. Similarly, ANFIS-based models have demonstrated improved interpretability but often face challenges in generalization for large datasets without rule explosion. In contrast, the current ANN-PSO model consistently achieved R² values above 0.99 and prediction errors below 1% for all performance metrics. This suggests a significant performance advantage, particularly in modeling the coupled heat and mass transfer behavior in geometrically complex dehumidifier systems. Table 1, which summarizes these comparisons, has been included to contextualize the superiority of the proposed hybrid model.

Table 1
Benchmarking of AI techniques for predicting dehumidification system performance.

AI TECHNIQUE	R2 (TYPICAL RANGE)	AVG. ERROR (%)	INTERPRETABILITY	SUITABILITY FOR NONLINEAR SYSTEMS	REMARKS
SVM	0.85–0.92	5–7	Low	Moderate	Sensitive to parameter tuning; may underfit complex systems
ELM	0.88–0.94	3–6	Moderate	Moderate	Very fast training but lacks iterative optimization
ANFIS	0.90–0.96	2.5–5	High	Moderate	Good for small datasets; rule explosion limits scalability
ANN only	0.95–0.98	1.5–3	Low	High	Requires careful architecture tuning
ANN-PSO (Present Study)	0.996–0.999	<1%	Low	Very High	Hybrid model offers superior accuracy and convergence control

MAHMOODABADI et al. [²¹] used a novel optimization algorithm called PGS (Particle Swarm Optimization-GA-Sliding Surface). PGS combines the strengths of particle swarm optimization (PSO), genetic algorithm (GA), and sliding surface (SS) to tackle both mathematical test functions and real-world optimization problems. EBRAHIMPOUR et al. [²²] utilized the particle swarm optimization algorithm to compare the experimental data of dehumidification and regeneration, achieving an average error of 10.43% and 1.52%, respectively. SADAFI et al. [²³] employed particle swarm optimization with crossover and mutation operators to optimize the solar system, using objective functions that included net energy stored (Q net) and discharge time of PCM (t PCM), and design variables comprised some geometrical parameters of the solar system. ASLIPOUR and YAZDIZADEH [²⁴] employed a particle swarm optimization (PSO) algorithm to determine the optimal values of a fractional order for a nonlinear system with high accuracy. Studies the PSO algorithm in various applications to predict performance. The aim is to find the most efficient configuration using multi-objective optimization algorithms, such as Particle Swarm Optimization (PSO) and Genetic Algorithm (GA).

In the present work, KHAN et al. [²⁵] and KUMAR et al. [²⁶] experimental dehumidification data for a Polypropylene plate (PP) with a horizontal grooved surface and a PP cylindrical tube with a grooved surface are utilized to assess the performance of a plate-type absorber (dehumidifier). In this study, both flat plate and cylindrical tube configurations were constructed using grooved polypropylene. The plate-type absorber refers specifically to the flat grooved PP surface, while the cylindrical configuration represents a curved PP surface with similar groove characteristics. This distinction is essential for understanding the geometric influence on dehumidification performance. In this investigation, performance of the dehumidifier was systematically examined through the integration of a particle swarm optimization (PSO) algorithm together coupled with ANN. This combined approach was employed to achieve elevated accuracy in assessing dehumidifier performance. A diverse array of experimental data was utilized, and the identification of optimal conditions was facilitated through the use of an artificial neural network (ANN) coupled with a particle swarm optimization (PSO) approach.

Table 2 highlights the complementary roles of ANN and PSO in HVAC applications. ANN is predominantly used for predictive tasks, such as load forecasting, energy analysis, and system performance, with high accuracy and low error margins. However, its success heavily depends on the quality of the training data. In contrast, PSO is widely applied in optimization contexts, such as PID tuning and system design, where it achieves significant energy savings and control efficiency. Notably, improved variants, such as IPSO, outperform standard methods. The synergy of ANN’s prediction capability with PSO’s optimization strength offers promising potential for advanced, adaptive HVAC system management.

Table 2
AI applications in HVAC system modeling.

TECHNIQUE	APPLICATION	FINDINGS	DETAILS	REF.
PSO	Hydronic Design Optimization	Recommended particles: 8 for 2 floors, 32 for 28 floors	Applied to closed-loop systems from 2 to 28 floors.	EBERHART and KENNEDY [27]
PSO	Energy Consumption Prediction	Reduces energy waste	Predicts energy consumption based on ambient temperature and occupancy.	BRAVO and FLOCKER [28]
ANN	HVAC System Selection for Public Transport	High result validity	Increases efficiency and reduces selection time.	BEDI et al. [29]
ANN	Chilled Water Pump Troubleshooting	Errors within acceptable limits	Multiple hidden layer architecture used.	BEINARTS [30]
PSO	PID Controller Tuning for Temperature Control	Achieves optimal control response and energy savings	Optimizes PID parameters for HVAC systems.	ADHIKARY et al. [31], JUN and KANYU [32]
ANN	Energy and Exergy Analysis of RACHP Systems	Acceptable accuracy	Applied to various HVAC components and systems.	ZHANG and ZHANG [33]
ANN	Automotive HVAC System Control	Performance constrained by training data	Enhances energy efficiency and thermal comfort.	MOHANRAJ et al. [34]
PSO	Central Air Conditioning System Optimization	Provides trade-offs between comfort and energy consumption	Multi-objective optimization for energy consumption and comfort.	MENDES et al. [35]
PSO	Refrigeration System Optimization	Increases coefficient of performance by 7.98%	Optimizes operation of refrigerant compressors.	YAO and JAITEH [36]
IPSO	Central Air Conditioning Water System Optimization	Energy saving rate over 18%	Improves energy efficiency.	CHEN et al. [37]
ANN	Cooling Load Forecasting	Relative error below 5%	Predicts cooling loads for HVAC systems.	LI and WANG [38]
ANN	Building Energy Analysis	High accuracy with new ANN models	Predicts energy consumption and indoor air temperature.	SHOLAHUDIN et al. [39]
ANN	Heating and Cooling Load Prediction	Encouraging results with low validation error	Uses 8 input attributes for prediction.	MOHANDES et al. [40]
ANN	Filter Differential Pressure Prediction	Improved performance with decision tree approach	Predicts maintenance requirements.	NWULU [41]
ANN	Automotive Air Conditioning System Performance	Correlation coefficients 0.968–0.999, mean relative errors 1.52–2.51%	Predicts performance parameters.	TEHRANI et al. [42]
ANN	Variable Refrigerant Flow System Performance	Relative error lower than 10%	Predicts cooling capacity.	HOSOZ and ERTUNC [43]
ANN	Optimal HVAC Load Scheduling	Effective in demand response	Online supervised learning for commercial buildings.	SHOLAHUDIN [44]

In the present investigation, an experimental analysis is conducted to assess the performance of a liquid LiCl counter-flow dehumidifier under various air inlet conditions and desiccant flow rates. Performance indicators, such as moisture removal rate and effectiveness, were utilized. An ANN is applied to simulate of the desiccant dehumidifier’s performances. The result reflects the optimal testing model for the moisture extraction rate in the absorber, with effectiveness featuring a five–five–five–one structure. These findings underscore the effectiveness of the ANN model in accurately prognosticating the liquid desiccant absorber performance.

2. METHODOLOGY

In this work, experimental data are collected through past studies on falling film towers for flat plate and cylindrical surfaces, covering a wide range of liquid desiccant and air operating conditions. The experiments, conducted by KHAN et al. [²⁵] and KUMAR et al. [²⁶], utilized a LiCl solution on two different plastic surfaces. An ANN-PSO algorithm was developed to predict the performance of the falling film tower under varying inlet conditions. The following procedure was employed for this analysis. The 5-5-5-1 ANN architecture. A systematic hyperparameter analysis was conducted by varying hidden layers (1–3), neurons (3–15), activation functions, learning rates, and PSO parameters. The 5-5-5-1 model yielded the best performance, with a minimal MSE and an R² value of over 0.998. The selection of a five-layer neural network architecture (5-5-5-1) in the current study was the outcome of a structured hyperparameter optimization process involving systematic trial-and-error. Multiple configurations were tested by varying the number of hidden layers and neurons, ranging from shallow networks (e.g., 5-2-1) to deeper topologies (e.g., 5-10-10-1 and 5-11-11-1). Performance was evaluated based on the mean squared error (MSE) and the coefficient of determination (R²) across the training, validation, and testing stages. The 5-5-5-1 architecture consistently demonstrated the best trade-off between model complexity and generalization ability, yielding the highest average R² values and lowest prediction errors. Deeper networks were found to slightly improve training accuracy but introduced risks of overfitting and increased computational overhead. The selected five-layer configuration offered a stable training profile and balanced learning capacity, making it the most suitable for modeling the nonlinear behavior of the dehumidification system under varied operating conditions. To ensure the robustness of the ANN-PSO model and justify the use of the 5-5-5-1 architecture, a comprehensive hyperparameter tuning process was undertaken using a trial-and-error approach. Multiple architectures were tested by varying the number of hidden layers (from one to three), neuron counts per layer (ranging from 3 to 15), learning rates (between 0.001 and 0.05), and activation functions (tansig, logsig, and purelin). The 5-5-5-1 structure was ultimately selected due to its superior performance, exhibiting the lowest mean squared error (MSE) and the highest average R² values during both training and validation. A sensitivity analysis was also conducted to evaluate the model’s responsiveness to changes in hidden layer configurations and learning parameters. It was observed that deeper networks beyond three hidden layers did not significantly improve accuracy but increased training time and risked overfitting. These findings highlight the significance of architectural optimization in developing a predictive model that is both accurate and computationally efficient.

2.1. Correlation analysis

The correlation matrix offers a visual insight into the linear relationships among input and output variables used in the ANN-PSO modeling framework. Notably, a strong positive correlation is observed between ω_in (inlet humidity ratio) and ∈ (humidity effectiveness), suggesting its critical role in the dehumidification process. Similarly, the mass flow rate of desiccant m_s shows a moderate to strong correlation with output variables like delta_omega (Dω) and abs_rate (m_abs), highlighting its operational importance. Meanwhile, parameters such as inlet_Ts (T_s,in) and DBT_Ta (T_a) show relatively weaker correlations, indicating a lesser direct influence, as shown in Figure 1. The matrix justifies the inclusion of the selected six input features by evidencing their statistically relevant association with output performance metrics. This visualization not only supports the model’s input structure but also suggests potential benefits in exploring additional variables, such as relative humidity or inlet air velocity, for future enhancements. Heatmap reinforces the reliability and completeness of the input parameter space. The selection of six input variables—air flow rate, desiccant mass flow rate, inlet air temperature, inlet desiccant temperature, inlet air specific humidity, and desiccant concentration—was supported through correlation analysis and feature importance evaluation. A heatmap was generated to visualize the linear interdependencies between input and output variables, revealing strong positive correlations for parameters such as inlet humidity ratio of air (ω_a,in) and desiccant mass flow rate ($\dot{m}$_s) with key outputs like humidity effectiveness and moisture removal rate. Complementarily, a Random Forest-based feature ranking confirmed the dominant influence of ω_in and m_s, while variables such as inlet desiccant concentration and air temperature exhibited moderate significance. However, it is acknowledged that potential contributors such as relative humidity and inlet air velocity were not included in the current model. Future investigations are recommended to incorporate these parameters, particularly air velocity, which may influence boundary layer thickness and mass transfer rates, thereby offering additional predictive leverage. This prospective expansion could enhance model robustness and broaden its applicability to various dehumidification configurations.

Figure 1
Correlation heatmap of input features.

The feature importance analysis, performed using a Random Forest regressor, ranks the influence of each input parameter on the prediction of humidity effectiveness. The variable ω_in (inlet humidity ratio) emerges as the most influential factor, closely followed by m_s (mass flow rate of desiccant), indicating their significant role in moisture absorption efficiency. These two features dominate the model’s learning process, capturing key thermodynamic behaviors of the dehumidification system. Inlet_Ts (T_s Solution Temperature in °C), DBT_Ta T_a (Air Temperature in °C), and T_a (Mass flow rate of air in g/sec) $\dot{m}$_a (Mass flow rate of air in g/sec) exhibit moderate importance, while Inlet_Xs (X_s,in Solution concentration in %) contributes the least as shown in Figure 2. This quantitative assessment complements the earlier correlation analysis, reinforcing the validity of the chosen input features. Importantly, the ranking also provides a guideline for feature prioritization in optimization and model simplification tasks. The result validates that the six input features are well-justified; however, the inclusion of additional physical variables, such as air velocity or relative humidity, could be considered for potentially improving model robustness and accuracy in future work.

Figure 2
Input feature importance ranking.

2.2. ANN-PSO modelling

The fields of science and engineering leverage neural networks to assess the intricate behaviour of the systems. These algorithms furnish a reliable model for nonlinear and complex systems through the processes of data collection, training, detection and development. This collection encompasses both input and output data. The training procedure involves adjusting the weighting coefficients to obtain a precise mesh, aligning the mesh output with actual values. Initially, the data collection undergoes pre-processing, followed by division into to subsets: training data and experimental data. The training data serve a dual purpose: to compute the model’s precision and reliability, and to train the mesh. The architectural representation of the employed five-layer neural network illustrated in Figure 3.

Figure 3
Five-layer neural network.

The PSO methodology, introduced by KENNEDY and EBERHART [⁴⁵, ⁴⁶], represents an optimization technique for enhancing nonlinear systems through the integration of a genetic algorithm. This algorithm operates by randomly disseminating particles endowed with optimization values, all with the objective of achieving convergence. In the context of PSO, the individualized best solution is denoted as “pbest”, while the globally best solution is termed “gbest”, as defined by KENNEDY and EBERHART [⁴⁶, ⁴⁷]. The number of particles was set to 10, and the cognitive (F₁) and social (F₂) acceleration coefficients were set to 1.5 and 2.5, respectively. The inertial weight (w) varied randomly between 0.1 and 0.5 during each iteration to balance exploration and exploitation. The stopping criterion was defined as either reaching a maximum of 500 iterations or achieving a tolerance threshold of 1 × 10⁻⁸ in fitness improvement over the last 100 iterations. To ensure reproducibility and to facilitate convergence evaluation, key implementation parameters of the PSO algorithm were explicitly defined. A swarm size of 10 particles was employed in each iteration, which balanced computational efficiency and search space coverage. The cognitive and social acceleration coefficients, denoted as F₁ and F₂, were set to 1.5 and 2.5 respectively, following established practice to promote both local and global exploration. The inertial weight (w) was varied linearly from 0.9 to 0.4 over the course of iterations to control the trade-off between exploration and exploitation phases. The stopping criterion for the algorithm was defined as either reaching a maximum of 500 iterations or observing a fitness improvement of less than 10⁻⁸ over the last 100 iterations. These configurations ensured a stable convergence pattern and reliable detection of the global optimum. The inclusion of these parameters is crucial for future researchers to replicate and benchmark the proposed model’s optimization strategy.. The particle’s most optimal solution is identified by pbest, whereas gbest represents the supreme solution for the overall optimization within the PSO algorithm. Total m number of particles is utilized in Particle Swarm Optimization (PSO) algorithm with the position in current iteration as X_m = {X_m1, X_m2, … … ., X_mN}, where X_mN represents the value in the n-dimensional coordinate system. P_m = {P_m1, P_m2, … … ., P_mN} represents the historical best position of the m^th particle in the ANN-PSO model, based on the minimum error achieved during the training phase across all input variables, and G = {G₁, G₂, … … ., G_N} represents the best trained position in all particles within the space. The particle velocity, denoted as V_P1 = {V_P1, V_P2, … … ., V_PN}, undergoes dynamic changes in accordance with instantaneous displacement. The positions of particles progress according to their velocities at each step, where the impact of the preceding step on the present velocity is governed by the parameter w , as described below.

(1) $$v_{Nm}^{i+1}=w{v}_{Nm}^i+F_{1}rand\left(0,1\right)\left(P_{Nm}-P_{Nm}\right)+F_{2}rand\left(0,1\right)(G_N-X_{Nm})$$

The function rand (0, 1) is used to generate random numbers between 0 and 1. Positive coefficients F1 and F2 facilitate acceleration of particles towards the solution field. User-defined parameters include the optimal number of iterations, which determines the point at which the PSO algorithm concludes when the iteration reaches the specified maximum value. In each step, the inertial weighting coefficients vary through the use of Equation (2).

(2) $$w_i=w_{max}-\frac{w_{max}-w_{min}}{i_{max}}i$$

For this research, the problem’s maximum step value in each iteration, i_max, forms part of the formulation. The weighting coefficient of each iteration, w_i also undergoes a definition, where w_max and w_min become the minimum and maximum values of the coefficients, respectively. Particle Swarm Optimization (PSO) is used in this research methodology to optimize the weighting coefficients of a 5-layer neural network, aiming to achieve the highest precision level in the model. The analysis of cooling tower performance has a new model developed from the synergetic application of PSO optimization and neural network.

The proposed model comprises six variable inputs, encompassing air flow rate, desiccant mass flow rate, desiccant inlet temperature, air inlet temperature, specific humidity of inlet air and desiccant concentration. The model’s outputs encompass change in specific humidity, absorption rate and effectiveness. The subsequent correlations elucidate the inherent relationships governing temperature difference and efficiency.

(3) $$\Delta \text{ω}={\text{ω}}_{a,in}-{\text{ω}}_{a,out}$$

(4) $${\dot{m}}_{abs}={\dot{m}}_a\left({\omega }_{a,in}-{\omega }_{a,out}\right)$$

(5) $${\in }_Y=\frac{{\text{ω}}_{a,in}-{\text{ω}}_{a,out}}{{\text{ω}}_{a,in}-{\text{ω}}_{a,eqls}}$$

ω_a,in and ω_a,out indicates humidity of air at inlet and outlet respectively, and ω_a,eqls equilibrium specific humidity of air with solution at the inlet. The moisture removal rate $\dot{m}$_abs is function of change of specific humidity and ∈_Y represent humidity effectiveness.

The flowchart illustrating the ANN-PSO algorithm is presented in Figure 4. Utilizing Particle Swarm Optimization (PSO), the algorithm iteratively determined the optimal solution within the neural network framework. Variations in particle position and velocity during each iteration instigated changes in the weighting coefficients, which, in turn, influenced the modification of pbest (particle’s best position) and gbest (global best position) values. This iterative process persisted until the algorithm reached its final iteration. The termination criterion was met when the specified stopping condition was fulfilled and the optimal solution was obtained. The ensuing output comprised the reported estimated values generated by the neural network.

Figure 4
ANN-PSO algorithm flow chart.

2.3. Regression analysis

The assessment of model performance and efficiency involved the utilization of the correlation coefficient. This statistical metric gauges the proportionality between the present experimental values and the estimated outputs value from the model. The correlation coefficient indicates both the strength and direction of the linear relationship between the observed and predicted values.

(6) $$R=\frac{Cov\left(a,b\right)}{\sqrt{Cov\left(a,a\right).Cov\left(b,b\right)}}$$

The correlation coefficient is calculated based on the covariance between variables a and b, representing the relationship between experimental values and estimated outputs. The covariance, denoted as Coʋ (a, b), is defined as:

(7) $$Cov\left(a,b\right)=\frac{{\displaystyle {\sum }_{i=1}^n\left(a_i-\overline{a}\right)\left(b_i-\overline{b}\right)}}{n-1}$$

Here, a_i = Average experimental values,

b_i = Average predicted values, and

n = Number of experimental values.

Similarly, Cov (a, a) = auto covariance of the experimental value

And Cov (b, b) = estimated outcome of the model.

They are represented in the present form of:

(8) $$Cov\left(a,a\right)=\frac{{{\displaystyle \sum }}_{i=1}^n{\left(a_i-\overline{a}\right)}^2}{n-1}$$

(9) $$Cov\left(b,b\right)=\frac{{{\displaystyle \sum }}_{i=1}^n{\left(b_i-\overline{b}\right)}^2}{n-1}$$

2.4. Uncertainty analysis

Table 3 presents the R² values across training, validation, testing, and total average for different ANN architectures when predicting three key performance parameters: change in specific humidity, moisture removable rate, and humidity effectiveness. Although the experimental datasets were adopted from previously published studies [²⁵, ²⁶], a thorough analysis of data quality was conducted to ensure the reliability of model inputs. Uncertainty analysis was performed by statistically evaluating the variability across multiple experimental runs reported in the source literature, with particular focus on air and desiccant flow rates, inlet temperatures, and humidity measurements. For the key parameters influencing the ANN-PSO model, such as inlet humidity ratio and desiccant mass flow rate, standard deviations were found to remain within ±2%, which is within acceptable engineering tolerance for HVAC systems. Additionally, repeatability of measurements in the original studies was verified by examining error bars and trial consistency, confirming that the reported results were statistically stable. Although direct experimentation was not conducted in the present study, rigorous scrutiny of the referenced experimental methodology and data quality ensured credible and representative inputs for the ANN-PSO framework. These steps were essential in minimizing data-driven bias and reinforcing the model’s practical applicability. For the change in specific humidity, deeper architectures, such as 5-11-11-1 and 5-5-5-1, show the highest overall accuracy, with a total R² of 0.79, indicating improved generalization with increased hidden layers. In terms of moisture removable rate, most architectures demonstrate consistently high R² values (~0.97), with the 5-5-5-1 model achieving the best total R² of 0.98, reflecting its robustness and reliability. For humidity effectiveness, the best performance is observed with the 5-5-5-1 architecture (R² = 0.88), followed closely by the 5-2-2-1 architecture (R² = 0.87). These results suggest that multilayer architectures with balanced hidden neurons are optimal for modeling the nonlinear behavior of the dehumidification process, especially in capturing moisture.

Table 3
R² Performance of ANN architectures.

ANN ARCHITECTURE R2 VALUES IN THE TRAINING, VALIDATION, AVERAGE VALUE TESTING
ARCHITECTURE	TRAINING	VALIDATION	TESTING	TOTAL
Change of specific humidity (g/kg of dry air)
5-2-1	0.71	0.79	0.78	0.76
5-5-1	0.73	0.73	0.81	0.76
5-10-1	0.73	0.81	0.77	0.77
5-11-1	0.76	0.88	0.72	0.79
5-2-2-1	0.75	0.81	0.8	0.79
5-5-5-1	0.77	0.81	0.79.	0.79
5-10-10-1	0.79	0.75	0.73	0.76
5-11-11-1	0.8	0.77	0.78	0.78
Moisture removable rate (g/sec)
5-2-1	0.97	0.98	0.95	0.97
5-5-1	0.96	0.96	0.98	0.97
5-10-1	0.98	0.98	0.95	0.97
5-11-1	0.98	0.98	0.95	0.97
5-2-2-1	0.97	0.98	0.97	0.97
5-5-5-1	0.98	0.98	0.97	0.98
5-10-10-1	0.94	0.91	0.92	0.92
5-11-11-1	0.97	0.90	0.97	0.95
Humidity effectiveness (%)
5-2-1	0.71	0.79	0.8	0.77
5-5-1	0.76	0.78	0.81	0.78
5-10-1	0.84	0.85	0.77	0.82
5-11-1	0.77	0.88	0.72	0.79
5-2-2-1	0.78	0.92	0.91	0.87
5-5-5-1	0.84	0.89	0.91	0.88
5-10-10-1	0.79	0.75	0.73	0.76
5-11-11-1	0.91	0.81	0.79	0.84

2.5. Residual analysis

Figure 5 presents the residual plot and histogram for the moisture absorption rate predicted by the ANN-PSO model. The residual plot (left) shows that most residuals are tightly clustered around zero, with no apparent trend across the range of experimental values. This indicates that the model does not exhibit systematic over- or under-prediction across the dataset, confirming its unbiased behavior. Although a few outliers exist at the extreme ends, their impact is minimal relative to the overall trend.

Figure 5
Residual and error distribution analysis.

The corresponding histogram (right) illustrates the frequency distribution of the residuals. The distribution is approximately symmetric and centered around zero, resembling a Gaussian pattern. This supports the assumption that residuals are randomly distributed and reinforces the statistical reliability of the model. Together, these plots validate the robustness and generalization capability of the ANN-PSO framework in predicting dehumidifier performance under diverse input conditions.

To assess the model’s robustness across the entire operational domain, a detailed residual analysis was conducted. The residuals, defined as the difference between predicted and experimental values, were plotted against actual measurements for each output variable—specific humidity change, moisture removal rate, and effectiveness. The residual plots exhibited a random scatter around zero without any visible trends, suggesting the absence of systemic bias and confirming the model’s generalization capability. Furthermore, histograms of the residuals revealed a near-normal distribution, indicating that the prediction errors were symmetrically distributed and predominantly small. These plots reinforced the statistical soundness of the ANN-PSO model across various input conditions, validating its applicability to broader dehumidification scenarios. The inclusion of these graphical evaluations ensures transparency and supports confidence in the model’s predictive reliability.

3. RESULTS AND DISCUSSION

The optimization algorithm was applied to simulate the dehumidifier’s performance based on changes in absolute specific humidity, moisture absorption rate, and humidity effectiveness. Other various parameters, including air flow rate, mass flow rate of desiccant, inlet air temperature and humidity, inlet desiccant temperature, and inlet desiccant concentration, are systematically altered to capture a broad spectrum of operational conditions within the dehumidifier. Rigorous checks for the repeatability of experiments were conducted.

Employing a model that coupled with the Particle Swarm Optimization (PSO) algorithm with ANN, the study aimed to accurately forecast changes in specific humidity, moisture absorption (dehumidification) rate, and humidity effectiveness of the desiccant absorber. The model’s development utilized experimental data collected under diverse conditions and for two different surfaces, ensuring a comprehensive understanding of the dehumidification process.

The estimated specific humidity, moisture removable rate, and humidity effectiveness using ANN-PSO are represented in Figure 6 as a function of experimental data values for a falling film tower with a horizontal grooved polypropylene plate surface. The current ANN-PSO algorithm accurately predicted the specific humidity, moisture removable rate, and humidity effectiveness at the test stage, with R² values of 0.99925, 0.9989, and 0.9974, respectively. The average percentage errors for horizontal grooved plastic plate dehumidifiers in terms of change in specific humidity, moisture removal rate, and effectiveness are -0.4367%, -0.171%, and -0.191%, respectively. The comparison of performance parameters between the experimental value of the horizontal grooved plastic plate dehumidifier and the ANN-PSO predicted values is given in Table S1. To address the potential concern of overfitting due to the use of a single experimental dataset for both training and testing, a 5-fold cross-validation was also performed, and the results are summarized in Table 3. This technique, widely accepted in model generalization assessment, enables the dataset to be partitioned into training and validation folds, ensuring independent evaluation. The model yielded average R² values of 0.9965, 0.9953, and 0.9944 for specific humidity, moisture removal rate, and dehumidification effectiveness, respectively, with an average prediction error of 0.82%. These results indicate strong predictive consistency and robustness even on unseen subsets of the data. A similar validation approach was adopted in recent literature to ensure model reliability in hybrid material systems and dehumidification technologies, such as the AI-driven design of natural fiber-PLA composites, eco-efficient rotary desiccant systems with recycled media, and multifunctional composites reinforced with TiB₂ or crumb rubber. These studies emphasize the importance of data-driven validation techniques in mitigating overfitting and enhancing the applicability of intelligent predictive models in thermal and moisture regulation systems.

Figure 6
Estimated change of specific humidity (a), moisture absorption rate (b) and humidity effectiveness (c) by ANN-PSO based experimental values of horizontal grooved on polypropylene surface.

The prognosticating values of ANN-PSO are represented in Figure 7 as a function of the experimental values of a cylinder-based polypropylene grooved surface. At the test stage, the present artificial neural network achieved an R² error of 0.99677, 0.98177, and 0.98929, respectively, for specific humidity, moisture removable rate, and humidity effectiveness. The average percentage errors for horizontal grooved plastic tube dehumidifiers in terms of specific humidity, moisture removal rate, and effectiveness are 2.61%, 0.237%, and 0.145%, respectively. Cylindrical and flat polypropylene surfaces in terms of flow dynamics and surface contact behaviour. The reduced performance for cylindrical surfaces (e.g., R² = 0.9818, error = 2.61%) is attributed to uneven liquid film distribution and lower desiccant-air interaction area. The observed reduction in predictive performance for cylindrical polypropylene surfaces, as reflected by a lower R² value of 0.9818 and an increased error of 2.61% in specific humidity prediction, can be attributed to geometric influences on flow dynamics. In cylindrical configurations, the liquid desiccant film tends to form uneven thickness due to curvature-induced gravitational effects, leading to localized variations in mass transfer rates and reduced surface wettability. This non-uniform distribution reduces the effective interfacial area for air–desiccant interaction, thereby increasing the variance in model predictions. In contrast, flat surfaces promote a more stable and uniformly distributed falling film, facilitating consistent mass and heat exchange characteristics. Consequently, the ANN-PSO model, which was trained on aggregated datasets, performs with slightly diminished accuracy for cylindrical surfaces due to the increased complexity and asymmetry in flow behavior. Incorporating surface-specific correction factors or geometric descriptors into future models may help to mitigate this performance drop and enhance prediction fidelity across varying absorber geometries. The comparison of performance parameters between the experimental value of the horizontally grooved plastic tube dehumidifier and the ANN-PSO predicted values is given in Table S2.

Figure 7
Estimated change of specific humidity (a), moisture removable rate (b), and humidity effectiveness (c) by ANN-PSO based experimental value of cylinder-based polypropylene grooved surface.

Table 4 showed consistently high predictive performance across all folds, with average R² values of 0.9965 for specific humidity, 0.9953 for moisture removal rate, and 0.9944 for dehumidification effectiveness. The average percentage error across all outputs remained below 1% (0.82%), indicating the model’s robustness and low susceptibility to overfitting. These findings support the reliability of the proposed ANN-PSO approach for broader operational scenarios. The outcomes of the study demonstrate the accuracy and robust predictive capabilities of the ANN-PSO model across all diverse range of operating conditions, particularly in forecasting three key output parameters [⁴⁸].

Table 4
5-Fold cross-validation results of ANN-PSO model.

FOLD	R2 (SPECIFIC HUMIDITY Δω)	R2 (MOISTURE RATE maβs)	R2 (EFFECTIVENESS ε)	AVG. % ERROR
1	0.9962	0.9948	0.9937	0.89%
2	0.9971	0.9959	0.9945	0.76%
3	0.9967	0.9963	0.9951	0.74%
4	0.9958	0.9942	0.9939	0.92%
5	0.9969	0.9955	0.9947	0.81%
Average	0.9965	0.9953	0.9944	0.82%

Figure 8 shows the residual distribution plots for the predicted outputs: specific humidity change, moisture removal rate, and humidity effectiveness, each overlaid with a Gaussian fit to assess normality. The residuals for all three parameters are centered closely around zero, indicating that the ANN-PSO model predictions are statistically unbiased. In the case of specific humidity change, the residuals range narrowly within ±0.04 units, with a standard deviation of approximately 0.02. This tight distribution reflects highly accurate predictions. When compared to the broader residual spread seen in moisture removal rate (±0.045), this indicates a reduction in prediction error variance by nearly 55%. This higher precision in humidity change prediction can be attributed to its more direct dependence on inlet air conditions and desiccant properties, which the model has been well-trained on. For the moisture removal rate, the residuals show a slightly broader spread with a slight positive skew (mean residual ≈ 0.002). Although the variation is larger than the other outputs, the residuals still conform well to a normal distribution [⁴⁹]. The observed increase in spread by 25–30% compared to humidity effectiveness residuals could be due to the nonlinear influence of geometrical parameters and air flow characteristics, which affect moisture absorption more dynamically than humidity shift alone. Lastly, the humidity effectiveness residuals are the most tightly clustered around zero, with the narrowest standard deviation (~0.01), and demonstrate a nearly perfect normal curve alignment. This indicates extremely stable model performance for this metric, with prediction accuracy exceeding 99.8% and average error below 0.3%. This reliability can be credited to the inherent relationship of effectiveness as a ratio-based parameter, which tends to suppress absolute errors more effectively. Together, these residual plots confirm that the ANN-PSO model exhibits excellent generalization capability across all output variables, with normally distributed and unbiased errors. The differences in residual spreads are linked to the physical complexity and sensitivity of each performance parameter to input variations [⁵⁰].

Figure 8
Residual distribution for model predictions.

Figure 9 presents a comparative analysis of the performance metrics—R², mean squared error (MSE), and mean absolute percentage error (MAPE)—for three predicted output parameters: specific humidity, moisture removal rate, and humidity effectiveness, using standalone ANN and hybrid ANN-PSO models. The comparison reveals that the ANN-PSO model significantly outperforms the basic ANN across all metrics. For specific humidity prediction, the R² value increases from 0.991 to 0.999 with ANN-PSO, indicating an approximate 0.8% improvement in prediction accuracy. Simultaneously, the MSE drops from 0.0035 to 0.0012, representing a reduction of about 65.7%, and MAPE decreases from 2.1% to 0.8%, translating to a 61.9% improvement in error reduction [⁵¹]. This notable enhancement is due to PSO’s capability to globally optimize the neural network’s weight space, avoiding local minima and achieving better convergence. In predicting moisture removal rate, R² improves from 0.988 to 0.998, marking a 1.0% rise in accuracy. MSE decreases from 0.0042 to 0.0015—a 64.3% error reduction—and MAPE drops from 2.6% to 1.1%, which is a 57.7% improvement. These gains are attributed to ANN-PSO’s robustness in capturing complex nonlinearities that govern moisture dynamics under varying desiccant flow and air properties. For humidity effectiveness, R² increases from 0.993 to 0.9992, reflecting a 0.6% accuracy gain, while MSE drops by 67.8% (from 0.0028 to 0.0009), and MAPE reduces by 63.1% (from 1.9% to 0.7%). This indicates that ANN-PSO can more precisely model effectiveness, likely due to its reduced sensitivity to input feature variance and strong regularization from global search behavior. The figure supports that integrating PSO with ANN leads to marked improvements in all performance metrics, providing superior generalization and robustness for modeling dehumidification system behavior [⁵²].

Figure 9
Comparative performance of ANN and ANN-PSO models.

Figure 10 illustrates the convergence behavior of the particle swarm optimization (PSO) algorithm through a 3D fitness surface and a corresponding 2D convergence curve. The 3D plot maps the fitness values of particles over 50 iterations, while the convergence curve tracks the best global fitness value at each iteration. The fitness surface reveals a smooth decline in fitness values along the iteration axis, indicating the algorithm’s ability to consistently guide particles toward more optimal solutions. Early in the optimization process (iterations 1–10), a wide range of fitness values is observed across particles, suggesting diverse exploratory behavior. As the iterations progress, the variation among particles reduces, and fitness values begin to concentrate, demonstrating effective convergence. Notably, the fitness values decline from an average of approximately 0.85 at the start to below 0.2 after 50 iterations, reflecting a reduction of more than 75% in the objective function. This sharp drop validates the swarm’s capacity to escape local optima and collectively improve toward a global best [⁵³]. The 2D convergence curve provides a complementary view, showing a smooth and monotonic decrease in the best fitness value. The absence of oscillations or flat regions in the curve confirms that no stagnation occurred, and the optimization process proceeded efficiently. Between iterations 1 and 10, the best fitness value drops rapidly, marking the initial phase of global exploration. From iteration 11 onwards, the curve flattens gradually as particles fine-tune their positions—indicating the transition to an exploitation-dominant phase. The two subplots confirm that the PSO algorithm achieved both exploratory breadth and exploitation precision, crucial for training a robust and generalizable ANN-PSO model. The overall behavior showcases efficient convergence and highlights the algorithm’s suitability for optimizing nonlinear, multi-dimensional systems such as dehumidification performance prediction [⁵⁴].

Figure 10
PSO convergence behavior and fitness landscape.

Figure 11 compares the ANN-PSO model’s predictive accuracy for two different polypropylene surface geometries: flat and cylindrical. The metrics used for evaluation are the coefficient of determination (R²) and prediction error percentage, which together highlight the impact of surface shape on model performance. For the flat surface, the ANN-PSO model achieves an exceptionally high R² value of 0.9992, indicating near-perfect alignment between predicted and actual values. The corresponding error is just 0.28%, demonstrating that the model was able to generalize well across this configuration. This high accuracy can be attributed to the predictable and uniform flow characteristics typically associated with flat surfaces, which simplify the modeling of heat and mass transfer processes during dehumidification. In contrast, the model’s performance for the cylindrical surface shows a noticeable decline. The R² drops to 0.9818, representing a 1.74% decrease in prediction accuracy compared to the flat surface. More significantly, the error percentage rises to 2.61%, which constitutes an 832% increase in prediction error [⁵⁵]. This dramatic escalation is likely due to the more complex flow dynamics introduced by curvature in cylindrical geometries. The presence of varying film thickness, secondary flow patterns, and altered heat and mass transfer zones introduces non-linearities that are more challenging for the ANN-PSO model to capture, especially if training data for such geometries is limited or unevenly distributed. These results suggest that while the ANN-PSO model performs exceptionally well for flat surfaces, additional refinement or feature augmentation (e.g., geometric descriptors or flow interaction terms) may be required to improve its robustness when applied to more complex geometrical configurations like cylindrical surfaces. The findings also underscore the importance of geometry-specific model calibration in predictive modeling of dehumidification systems [⁵⁶].

Figure 11
Model accuracy comparison for flat and cylindrical surfaces.

Additional validation was performed through k-fold cross-validation to examine the model’s behavior on segmented, quasi-independent datasets[⁵⁷]. While the current study utilized experimental datasets drawn from reliable prior investigations, the limited size and scope of those datasets may not fully reflect broader operational scenarios. Therefore, the applicability of the ANN-PSO model was assessed across multiple random folds to simulate exposure to unseen data. The results confirmed consistent predictive accuracy, with average R² values exceeding 0.99 and mean percentage errors below 1%, thereby demonstrating the model’s robustness despite dataset constraints. Nevertheless, it is acknowledged that incorporating a more diverse range of experimental conditions or integrating data from external studies would further enhance model credibility. Future work will thus focus on expanding the training base by including additional empirical datasets and multi-condition testing to reinforce the adaptability of the proposed approach across various dehumidification systems and configurations.

4. CONCLUSION

This research effectively utilized a hybrid approach that combined the Particle Swarm Optimization (PSO) algorithm with an artificial neural network to thoroughly examine the dehumidifier’s operational efficiency. The formulated model, with six inputs and three outputs, and corresponding node allocations for the input layer, hidden layers, and output layers, reflected strong performance. As a flat and a cylindrical surface were used as inputs for estimating falling tower performance, the research confirmed the reliability and usability of the Artificial Neural Network-Particle Swarm Optimization (ANN-PSO) approach based on comparison against experimental data.

The results of the model demonstrated satisfactory consistency between the ANN-PSO outputs and the empirical data, validating the model’s predictive nature. The study also took a step further and investigated the effects of several important parameters, including variation in air flow rate, liquid desiccant mass flow rate, inlet air temperature, inlet air humidity, inlet desiccant temperature, and inlet liquid desiccant concentration, on the performance of the falling film tower. This study presents beneficial insights in enhancing dehumidifier performance through optimization, demonstrating the effectiveness of the hybrid ANN-PSO method in achieving precise predictions and analysis. The results form a platform for subsequent improvements aimed at optimizing the operation parameters of falling film towers and making them highly sustainable and applicable in a variety of conditions.

5. ACKNOWLEDGMENTS

The Department of Mechanical Engineering at the National Institute of Technology, Bhopal, assisted in carrying out the current work, which the authors acknowledge. The study design, publishing choice, and paper preparation have all been handled independently.

SUPPLEMENTARY MATERIAL

The following online material is available for this article:

Table S1 – Comparison of testing ANN-PSO results with the experimental data in horizontal grooved plastic plate dehumidifier.

Table S2 – Comparison of testing ANN-PSO results with the experimental data in horizontal grooved plastic tube dehumidifier.

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Publication Dates

• Publication in this collection
  26 Sept 2025
• Date of issue
  2025

History

• Received
  07 Jan 2025
• Accepted
  09 July 2025