Improving Automotive Air Conditioning System Performance Using Composite Nano-Lubricants and Fuzzy Modeling Optimization

Abstract

This study aims to enhance the effectiveness of automobile air conditioning (AAC) systems through the use of composite nano-lubricants and fuzzy modeling optimization techniques. Composite nano-lubricants, which consist of varied metal oxide ingredients and content ratios, are projected to surpass single-component nano-lubricants in terms of improving the performance of AAC systems. Fuzzy modeling is used to simulate the AAC system based on experimental data using three input parameters: volume concentration of nano-lubricants (%), the refrigerant charge (g), and compressor speed (rpm). The output performance of the AAC system is measured using four parameters: cooling capacity (CC) in kW, compressor work (CW) in kJ/kg, coefficient of performance (COP), and power consumption (PC) in kW. Optimization is performed using the marine predators algorithm (MPA) to identify the best values for the input control parameters. The objective function is to minimize CW, COP, and PC while simultaneously maximizing CC and COP. Results showed that the performance of the AAC system improved from 85% to 88% compared to the experimental dataset, highlighting the potential benefits of using composite nano-lubricants and fuzzy modeling optimization for improving the energy efficiency of AAC systems. Furthermore, a comprehensive comparison with ANOVA was performed to demonstrate the superiority of the fuzzy modeling approach. The results indicate that the fuzzy model outperforms ANOVA, as evidenced by a reduced root mean square error (RMSE) for all data, from 0.412 using ANOVA to 0.0572 using fuzzy. Additionally, the coefficient of determination for training increased from 0.9207 with ANOVA to 1.0 with fuzzy, further substantiating the success of the fuzzy modeling phase.

1. Introduction

Automotive air conditioning (AAC) systems are critical components in modern vehicles, providing thermal comfort and safety to passengers in different weather conditions. The efficiency and effectiveness of AAC can significantly impact its performance, energy consumption, and environmental impact, making the optimization of AAC performance an increasingly important area of research in the automotive industry [1]. The change in temperature within a vehicle’s interior can cause discomfort for passengers, making AAC even more crucial in maintaining a comfortable temperature inside the cabin; however, the operation of AAC consumes power either from the vehicle’s engine or its battery, which can have an impact on the fuel economy, cruising range, or overall performance of the automobile [2]. With the extensive application of AAC in residences, industries, and vehicles, the energy consumed is significant; therefore, researchers are prompted to design efficient and green devices with better efficiency to conserve energy and protect the environment. An efficient operation of air conditioning systems (ACSs) can minimize operating costs and negative environmental consequences, which can be achieved by adopting a proper control strategy [3]. Worldwide, pollution and air conditioning requirements in the vehicle industry are becoming increasingly strict. For many years, the vapor compression refrigeration (VCR) approach was extensively employed in AAC. According to reports published by the International Energy Agency (IEA) in 2019 [4], AAC currently accounts for approximately 1.5% of the world’s total oil consumption, equivalent to a volume exceeding 1.8 million barrels of oil/day (Mboe/d). Studies indicate that automobile ACSs consume around 6% of the yearly worldwide energy consumption by vehicles, which can range from 3% to 20% depending on factors such as driving habits, traffic congestion, and climate conditions. In areas with hot climates and heavy traffic, the energy consumption by automobile ACSs can increase significantly, reaching up to 40% [5].

The performance of AAC systems can be affected by factors such as compressor work, power consumption, refrigerant charge, and cooling capacity [6]. Enhancing the functioning of AAC systems is essential to minimize energy consumption and enhance energy efficiency. One promising approach to achieving this goal is through the use of appropriate lubricants, such as composite nano-lubricants. These lubricants, consisting of varying ratios and components of metal oxides, are expected to enhance the performance of the AAC systems beyond what single-component nano-lubricants can achieve. Zawawi et al. [7] examined the performance of the AAC system performance with Al₂O₃-SiO₂/PAG composite nano-lubricants, which had a composition ratio of 60:40 and volume concentrations (vol %) ranging from 0.005% to 0.06%. The results showed that 0.015% volume concentration of Al₂O₃-SiO₂/PAG nano-lubricants was the most efficient, with the highest COP of 9.19 and CC enhancement up to 65.21%, while CW and PC reduced up to 25.26% and 19.70%, respectively. Redhwan et al. [8] examined the performance of Al₂O₃/PAG nano-lubricant in a compact vehicle mobile air conditioning (MAC) system. Results indicated that using a 0.010% volume concentration of the nano-lubricant leads to significant enhancements in COP, CW, and CC. Comparisons with SiO₂/PAG nano-lubricant show that Al₂O₃/PAG nano-lubricant performs better in all categories. As a result, the study recommends using a 0.010% volume concentration of Al₂O₃/PAG nano-lubricant for MAC systems. Hamisa [9] examined the effect of TiO₂/POE nano-lubricant on the rheological properties of AAC systems. The dynamic viscosity of the nano-lubricant at vol % of 0.01% to 0.1% and temperatures varying from 0 to 100 °C was measured. The results showed that the nano-lubricant behaves as a Newtonian fluid, with only a slight increase in dynamic viscosity at high vol % and temperatures. The study concluded that TiO₂/POE nano-lubricant could enhance the rheological characteristics of POE lubricant for use in AAC systems.

There are various technologies available for automobile air conditioning, each with its own set of benefits and drawbacks [10]. One such technology is the absorption refrigeration system, which has been of significant interest owing to its potential to reduce greenhouse gas emissions [11]. This system operates by absorbing the refrigerant into a liquid or solid absorbent, usually lithium bromide or ammonia, which is then heated to release the refrigerant vapor [12]. The refrigerant vapor is subsequently compressed and cooled to generate the desired cooling effect. The absorption refrigeration system is an attractive choice for automotive air conditioning since it eliminates the need for a compressor, reducing the overall energy usage of the system. Rêgo et al. [13] evaluated an absorption refrigeration system by connecting the exhaust system to the generator element to boost the energy efficiency of vehicles. The performance of the system was assessed utilizing a control technique for the mass flow rate of the engine exhaust system. The results showed that adjusting the quantity of input heat based on the temperature of the absorption cycle generator improved the refrigeration system’s performance. Aly et al. [14] analyzed the thermal efficiency of a diffusion absorption refrigerator (DAR) powered by the exhaust gas of the engine. The diesel engine was examined at various torque levels, with the DAR connected to the exhaust pipe through a heat exchanger. The results demonstrated that by regulating the flow of exhaust gas manually, the DAR system could operate efficiently across a broad range of engine loads, achieving a maximum COP of 0.10 at 30 N m torque.

Depending on the engine load, the refrigerator cabin attained a stable temperature of between 10 and 14.5 °C after approximately 3.5 h from the commencement of the system, and the system accomplished almost 10% waste heat recovery. Jadhav et al. [15] studied the feasibility of using vapor absorption refrigeration (VAR) as an alternative to VCR for AAC. The Electrolux VAR setup was used to test the hypothesis, which showed that implementing VARC can lead to up to 10% energy savings, making air conditioning more economical and promoting energy conservation in tropical countries. The experiment also analyzed the performance of the VAR system at different temperatures and the practical implementation of the system in automobiles. Farzadi and Bazargan [16] investigated the use of exhaust waste heat to power VAR for cooling purposes; however, operational limitations arise when the car engine is idling or operating at low speeds. To address this issue, the authors designed and built a new generator that improved the heat transfer to the ARC by more than 19%. The modified system was able to reach the desired temperatures for the evaporator and refrigerator compartment at low engine speeds, resulting in more efficient cooling.

Another innovative technology for automobile air conditioning is the thermoelectric system that utilizes the temperature variation between the interior and exterior of the vehicle to provide cooling [17]. In this system, thermoelectric modules are used to generate electricity from the temperature variation between the module’s hot and cold sides [18]. The electricity generated is then used to power the cooling system, providing efficient and eco-friendly cooling. Attar and Lee [19] focused on optimizing the design of air-to-air thermoelectric air conditioners (TEAC) systems with a counterflow configuration. The authors combined the thermal isolation method with dimensional analysis and an optimal design approach to develop an analytical model. The model was used to optimize two variables concurrently: the electrical current and thermocouple numbers/geometric factor. Junior et al. [20] assessed the feasibility of a thermoelectric system in automobiles by developing a Modelica model of a thermoelectric liquid–gas heat exchanger. The model was used to simulate transient and steady-state behavior in the air conditioning system of a vehicle, demonstrating its potential application in automotive energy management. Ahmed et al. [21] developed a new cooling system that utilized thermoelectric cooling technology and was installed on the roof of a vehicle. A theoretical transient thermal model was developed. The results showed that the thermo-electric cooling system could decrease the in-cabin temperature to approximately 26 °C at 1000 W of the input power, which was significantly lower than the conventional system. Although the coefficient of performance (COP) of the proposed system is lower, it is still competitive due to its advantages, such as lower annual costs compared to the conventional system.

In recent years, fuzzy modeling and optimization techniques have been increasingly applied to improve the performance of different systems, including AAC systems. Fuzzy modeling is a mathematical approach that allows for the creation of a model that incorporates uncertainties and imprecision in the input data [22]. Optimization techniques, such as the grasshopper optimization, particle swarm optimization, whale optimization algorithm, sea-horse optimizer, and marine predators algorithm (MPA) can then be applied to the fuzzy model to identify the best values for the input controlling parameters and maximize the output performance [23,24,25]. Furthermore, Adopting proper control strategies can also boost the performance of air conditioning systems [26]. Improving the design of climate control systems can be a cost-effective solution to reduce the fuel consumption associated with cooling vehicle passenger compartments [27]. In fact, about 30% of the total fuel consumption of a vehicle is attributed to the A/C system’s operation [28]. In the United States, cooling vehicle passenger compartments consumes approximately 26 billion liters of fuel each year, highlighting the potential for significant cost savings through improved climate control system design [29]. The increasing demand for more efficient and energy-saving vehicles, coupled with the staggering quantity of fuel consumed by the HVAC systems for mobile enclosures, has fueled a growing interest in re-evaluating the current approach to the HVAC systems of mobile enclosures. This has led to increased efforts to investigate and analyze the subsystems, control strategies, and overall design of the HVAC systems in order to optimize their performance [30]. Huang et al. [31] proposed a control strategy for an air conditioning system called the multistage constant-compressor speed (MCCS) system, which employed genetic algorithm optimization. The strategy employed the cabin temperature and compressor speed as input and output factors, respectively. The proposed strategy was compared with other control strategies, such as on/off controllers and the engineering-applied (EA) air conditioning control strategy. The MCCS controller was shown to save more energy consumption and improve the coefficient of performance compared to other controllers, making it an efficient choice for electric vehicle AC systems. Farzaneh and Tootoonchi [32] enhanced the performance of ACS by using the predicted mean value (PMV) index as controller feedback instead of temperature. The study designed and compared two fuzzy controllers, one with temperature feedback and the other with PMV index feedback. According to the findings, the PMV feedback controller was more efficient in maintaining thermal human comfort and reducing energy consumption. To optimize the parameters of the PMV controller, a genetic algorithm was utilized, resulting in even better thermal comfort and energy efficiency.

The study aims to boost the energy efficiency and performance of AAC systems using composite nano-lubricants and fuzzy modeling optimization techniques. This paper presents a simulation model of the AAC system depending on experimental data, using the volume concentration of nano-lubricants, refrigerant charge, and compressor speed as input parameters and CC, CW, COP, and PC as output parameters. The optimization of the AAC system is performed using the MPA algorithm to identify the best values for the input control parameters, with the objective of minimizing CW, COP, and PC while simultaneously maximizing CC and COP. The novelty of this study lies in the use of composite nano-lubricants and fuzzy modeling optimization techniques for improving the energy efficiency of AAC systems. To confirm the superiority of the proposed methodology, a comparison with ANOVA has been considered.

2. Data Set

Permission was obtained from Ref. [33] to use an experimental data set consisting of 15 sets, which reflects the effectiveness of the AAC system. The input parameters of the system include the volume concentration (VC) of nano-lubricants (%), the refrigerant charge (RC) in grams, and compressor speed (CS) in revolutions per minute (RPM). The output parameters comprise the cooling capacity (CC) in kW, compressor work (CW) in kJ/kg, coefficient of performance (COP), and power consumption (PC) in kW; however, the data set has some limitations, notably the low number of data points, which consists of only 15 points. To address the potential issue of overfitting and establish a robust model, the authors carefully selected three factors that impact the reliability of the model predictions. These factors include: (1) the choice of the modeling tool, (2) the ratio of training to testing samples, and (3) the number of training epochs. In this study, the fuzzy logic, as a general approximator, was adopted to build the system’s model due to its capability to effectively handle complex and non-linear datasets. Additionally, the subtractive clustering algorithm (SC) was employed to generate the fuzzy rules. The data samples were divided into a ratio of 2:1 for training and testing, respectively. Accordingly, ten data points were allocated for training, while the remaining five points were reserved for testing purposes.

Based on the data presented in

Table 1. Experimental data set.

	VC	CS	RC	CC	CW	COP	PC	Change in CC %	Change in CW %	Change in COP %	Change in PC %	OPI %
1	0.005	900	95	0.665	23.1	8.13	0.61	45.8	85.28	88.76	96.72	79.14
2	0.045	900	95	0.477	24.8	7.65	0.59	32.85	79.44	83.52	100	73.95
3	0.005	2100	95	0.86	39.2	4.72	1.07	59.23	50.26	51.53	55.14	54.04
4	0.045	2100	95	0.568	43.1	4.31	1.06	39.12	45.71	47.05	55.66	46.88
5	0.005	900	155	0.777	19.7	9.16	0.68	53.51	100	100	86.76	85.07
6	0.045	900	155	0.873	20.2	8.66	0.73	60.12	97.52	94.54	80.82	83.25
7	0.005	2100	155	1.452	32.2	5.15	1.42	100	61.18	56.22	41.55	64.74
8	0.045	2100	155	0.954	34.5	4.87	1.34	65.7	57.1	53.17	44.03	55
9	0.005	1500	125	0.956	32.8	6.06	0.94	65.84	60.06	66.16	62.77	63.71
10	0.045	1500	125	0.77	33.3	5.62	0.89	53.03	59.16	61.35	66.29	59.96
11	0.025	900	125	0.797	21.9	8.52	0.6	54.89	89.95	93.01	98.33	84.05
12	0.025	1500	125	0.891	37.35	4.81	1.08	61.36	52.74	52.51	54.63	55.31
13	0.025	1500	95	0.667	33	5.49	0.71	45.94	59.7	59.93	83.1	62.17
14	0.025	1500	155	1.168	26.6	6.27	0.89	80.44	74.06	68.45	66.29	72.31
15	0.025	1500	125	0.832	31	5.85	0.85	57.3	63.55	63.86	69.41	63.53

, the overall performance index (OPI) was found to be 85.07% in experiment number 5, with input parameter values of 0.005% for the volume concentration of nano-lubricants, 900 RPM for the compressor speed, and 155 g for the refrigerant charge. Under these conditions, the CC, CW, COP, and PC were measured to be 0.777 kW, 19.7 kJ/kg, 9.16, and 0.68 kW, respectively. Due to the limited number of experiments, the use of fuzzy logic is suggested to model the performance of the air conditioning system [34]. Additionally, modern optimization techniques can be employed to identify optimal input parameters that improve the overall performance of diverse applications [35], such as the AAC system [36].

3. Modeling and Optimization

The method being proposed consists of two stages: first, a fuzzy modeling stage; and second, a parameter identification stage for the automotive air conditioning system.

3.1. Fuzzy Model

During the fuzzification phase, membership functions (MFs) are used to achieve the nonlinear mapping of inputs. The inference engine phase involves creating fuzzy rules, evaluating the outputs of those rules (product Layer), and aggregating the fired rules (normalized layer) to produce the final fuzzy output [37]. The output is then mapped to a crisp form during the defuzzification phase. In fuzzy modeling, the input–output map is formulated using the IF-THEN rules. An example of such a fuzzy rule is presented below.

IF x is A₁ and y is B₁ then f₁ = g₁(x, y)

(1)

IF x is A₂ and y is B₂ then f₂ = g₂(x, y)

(2)

where the A₁ and B₁ are the MFs of the two inputs x and y.

The estimated final output f is as follows:

$$\mathrm{Output} \mathrm{Layer}: f={\tilde{\omega }}_1{f}_1+{\tilde{\omega }}_2{f}_2$$

(3)

$$\mathrm{Defuzzification} \mathrm{Layer}: \mathrm{Evaluating} {\tilde{\omega }}_1{g}_1\left(x,y\right) \mathrm{and} {\tilde{\omega }}_2{g}_2\left(x,y\right)$$

(4)

$$\mathrm{N} \mathrm{Layer}: {\tilde{\omega }}_1=\frac{{\omega }_1}{{\omega }_1+{\omega }_2} \mathrm{and} {\tilde{\omega }}_2=\frac{{\omega }_2}{{\omega }_1+{\omega }_2}$$

(5)

$$\mathsf{\pi } \mathrm{Layer}: {\omega }_1={\mu }_{A_1}\ast {\mu }_{B_1}\mathrm{and} {\omega }_2={\mu }_{A_2}\ast {\mu }_{B_2}$$

(6)

$$\mathrm{Fuzzification} \mathrm{Layer}: {\mu }_{A_1}, {\mu }_{A_2},{\mu }_{B_1}\mathrm{and}{\mu }_{B_2}\mathrm{are\; the\; MF\; values\; of\; the\; two\; inputs}$$

(7)

3.2. Marine Predators Algorithm (MPA)

The MPA algorithm is a metaheuristic optimization approach that takes inspiration from the foraging behavior and encounter rate policy of marine creatures, developed recently based on this concept. MPA imitates the hunting behavior of aquatic predators in search of food, and involves three distinct phases. The first phase, represented by [38], is utilized when iteration t falls within the first third of t_Max.

$$\begin{gathered} D_i=R_B\otimes \left(Elit{e}_i-R_B\otimes \mathrm{Pr}e{y}_i\right) \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}Pre{y}_{i+1}=Pre{y}_i+0.5\cdot R\otimes D_i \end{gathered}$$

(8)

The step size of the ith predator is denoted by $D_i$, while $R_B$ is a vector produced through the distribution of Brownian motion. The symbol R represents random numbers ranging from 0 to 1. The entry-wise multiplication is represented by the symbol ⨂. When t is in the second third of t_Max, the optimization process enters phase 2, which is divided into two subphases. The first subphase occurs when t is less than half of t_Max and can be expressed as:

$$\begin{gathered} D_i=R_L\otimes \left(Elit{e}_i-R_L\otimes Pre{y}_i\right) \\ Pre{y}_{i+1}=\mathrm{Pr}e{y}_i+0.5\cdot R\otimes D_i \end{gathered}$$

(9)

This refers to a situation where the vector $R_L$ is created by utilizing the distribution of Lévy motion. On the other hand, if t is greater than half of t_Max, the second subphase is initiated and can be represented as:

$$\begin{gathered} D_i=R_B\otimes \left(R_B\otimes Elit{e}_i-Pre{y}_i\right) \\ Pre{y}_{i+1}=Elit{e}_i+0.5\cdot CF\otimes D_i \\ CF={\left[1-\left(\frac{t}{t_{Max}}\right)\right]}^{2t/t_{Max}} \end{gathered}$$

(10)

The final phase can be represented as:

$$\begin{gathered} D_i=R_L\otimes \left(R_L\otimes Elit{e}_i-Pre{y}_i\right) \\ Pre{y}_{i+1}=Elit{e}_i+0.5\cdot CF\otimes D_i \end{gathered}$$

(11)

Figure 1 depicts the flowchart of the MPA algorithm.

4. Results and Discussion

4.1. Modeling Phase

Fifteen data points were measured and used to construct the fuzzy model, which is divided into two sets. The first set, consisting of 10 points, is utilized to train the model, while the remaining data is employed to test the model. A hybrid approach is used to train the model, which employs least square estimation (LSE) in the forward path and backpropagation in the backward path. In this work, ten rules were created using subtractive clustering (SC) to establish the system’s rules. The models were then trained until a smaller root mean square error (RMSE) was obtained. The statistical metrics of the resulting fuzzy model are presented in

Table 2. Statistical metrics of fuzzy model.

RMSE			R2
Train	Test	All	Train	Test	All
model of cooling capacity
0.0002	0.0991	0.0572	1.0	0.9653	0.9645
model of compressor work
1.420	0.9619	1.2855	0.9473	0.9898	0.9662
model of COP
0.2326	0.4261	0.3108	0.9808	0.9005	0.9614
model of power consumption
0.0514	0.0692	0.0580	0.9218	0.9548	0.9471

.

According to Table 2, the fuzzy model for cooling capacity has RMSE values of 0.0002 and 0.0991 for training and testing data, respectively. Compared to ANOVA [33], the RMSE for all data is reduced from 0.412 (using ANOVA) to 0.0572 (fuzzy). The coefficient of determination (R²) values for training and testing are 1.0 and 0.9653, respectively. For training, compared to ANOVA [33], the coefficient of determination is increased from 0.9207 (ANOVA) to 1.0 (fuzzy), indicating a successful modeling phase using fuzzy. Figure 2 depicts the three-input–single-output construction of the fuzzy models, while Figure 3 illustrates the outlines of the Gaussian shape MFs. For the compressor work fuzzy model, the RMSE for all data is reduced from 8.93 (using ANOVA) to 1.2855 (fuzzy), a reduction of about 85.6%. The fuzzy model for COP also exhibits a reduced RMSE for all data from 2.06 (using ANOVA) to 0.3108 (fuzzy). Finally, the fuzzy model for power consumption results in a reduced RMSE for all data from 0.15 (using ANOVA) to 0.058 (fuzzy).

The spatial description from a 3D point of view of the system’s input–output function is shown in Figure 4, with contours depicting the output for every two inputs at a time. The highest output value is represented by dark red, while the lowest value is indicated by dark blue.

The accurate relationship between the input and output parameters of the automobile air conditioning system enables the fuzzy model to effectively predict the output parameters. It can be observed from the plot in Figure 5 that the constructed fuzzy model predicts the output parameters accurately when compared to the experimental data. The good fitting between the estimated and measured data can be observed, obviously. Furthermore, the figure also displays the prediction plots for both the training and testing stages around the one-hundred-percent precision line.

4.2. Optimization Phase

Optimization methods are utilized to tackle a range of challenges, such as harmonic and numeric problems. These methods can be classified into distinct categories based on certain criteria. Firstly, there are population-based algorithms that enhance solutions by combining them. Secondly, iterative algorithms progressively approach the desired outcome through iterations. Thirdly, probabilistic or stochastic algorithms utilize probabilistic rules to improve results [39]. Additionally, another categorization can be established based on the nature of the phenomena emulated by the algorithm [40]. The optimal values for the volume concentration of nano-lubricants, refrigerant charge, and compressor speed, which enhance both CC and COP while minimizing compressor work and power consumption, were determined using reliable fuzzy models and the MPA approach. After constructing reliable fuzzy models, the MPA approach was utilized to determine the optimal values for the three control parameters. The formulation of the optimization problem for the case study can be expressed as follows:

$$max \left(f \left(X\right)\right)$$

(12)

where X represents the three controlling parameters, and f is the objective function defined as COP + CC − CW − PC.

The optimal parameters and their respective output parameters, as determined using experimental data and MPA, are presented in

Table 3. Optimal parameter values using measured data and proposed strategy.

	Volume Concentration (%)	Compressor Speed (rpm)	Refrigerant Charge (g)	CC (kW)	CW (kJ/kg)	COP	PC (kW)	Performance Index
Measured	0.005	900	155	0.777	19.7	9.16	0.68	85.07%
Proposed	0.0054	1337	147.4	1.13	28.85	13.02	0.92	88%

. The integration between fuzzy and MPA resulted in a 44.84% increase in CC from 0.777 kW to 1.1254 kW and a 42% increase in COP from 9.16 to 13.0157; however, the CW and PC increased by 46% and 35.88%, respectively. Overall, the system performance increased from 85% to 88% compared to the experimental dataset. The convergence of particles during parameter identification is shown in Figure 6. The optimal values for the controlling input parameters are 0.0054%, 1336.63 rpm, and 147.3908 g for the volume concentration, compressor speed, and refrigerant charge, respectively.

5. Conclusions

The study aims to specify the optimal values of three input parameters, namely the volume concentration of nano-lubricants, refrigerant charge, and compressor speed, to boost the performance of an AAC system. The performance of the AAC is evaluated using various parameters such as CC, CW, COP, and PC. Fuzzy modeling was used to simulate the performance of the AAC system based on these input parameters. The results show that the fuzzy model significantly outperforms ANOVA, as evidenced by a reduced RMSE for all data, from 0.412 using ANOVA to 0.0572 using fuzzy. Additionally, the coefficient of determination for training is increased from 0.9207 with ANOVA to 1.0 with fuzzy, which provides further evidence of the successful modeling phase using fuzzy. The fuzzy model for compressor work significantly improves the results compared to ANOVA, as indicated by the reduction in RMSE for all data from 8.93 with ANOVA to 1.2855 with fuzzy, representing an improvement of approximately 85.6%. The RMSE for all data in the fuzzy model of COP is reduced from 2.06 using ANOVA to 0.3108 using fuzzy. Similarly, the fuzzy model of power consumption leads to a reduction in RMSE for all data from 0.15 using ANOVA to 0.058 using fuzzy, thanks to the application of fuzzy modeling. The integration of the fuzzy and marine predators algorithm resulted in a significant boost in the CC from 0.777 kW to 1.1254 W, which corresponds to an increase of about 44.84%. Moreover, the COP is improved from 9.16 to 13.0157, which represents an increase of approximately 42%; however, the CW and PC have increased by 46% and 35.88%, respectively. Overall, the performance of the system has increased from 85% to 88% compared to the experimental dataset.

Based on the findings of this study, several recommendations and future works can be suggested. Firstly, the use of composite nano-lubricants shows promise in boosting the performance of AAC systems, and further research can focus on investigating the optimal composition ratios and metal oxide components for maximum efficiency. Additionally, future studies can explore the effect of different nano-lubricants on the performance of AAC systems. Secondly, the fuzzy modeling approach was found to be more effective in simulating the performance of the AAC system than ANOVA; therefore, future studies can focus on further optimizing the fuzzy model parameters and exploring different fuzzy logic approaches for better accuracy and performance. Thirdly, the MPA was used to optimize the input controlling parameters for the AAC system, and further studies can focus on exploring other optimization algorithms for better performance and efficiency. Finally, future studies can also focus on investigating the impact of the improved AAC system performance on overall vehicle energy efficiency and emissions, as well as the potential economic and environmental benefits of using composite nano-lubricants and fuzzy modeling optimization techniques in AAC systems.