Introduction

Global energy demand raised by 2.2% in 2024 which is meaningfully faster than the average development of 1.3%, seen between in 2013 to 2023. Fossil fuels are still dominating the source of global energy demand. Approximately 12% of global energy demand is fulfilled by diesel fuel only1. Diesel engine is a powerful and effective source of energy that plays a vital role in the growth of any modern society or country. It is widely used across various key sectors such as transportation, agriculture, and industry2. Their efficiency, robustness, and high torque make them indispensable for societal growth. Global diesel fuel market was valued at approximately USD 225.62 billion in 2022 and is projected to grow at a compound annual growth rate (CAGR) of 3.96% from 2023 to 20303. Despite world oil demand continuing to grow, the energy crisis has a more significant effect on global community and commercial growth. Due to increasing usage of diesel fuel also contributes to regional and worldwide environmental complications. Therefore, the search for alternate resources of good and sustainable energy has become critical4,5,6. It resolves societal troubles such as the raising fuel oil values and environmental concerns like global warming and contamination in air suggested by the burning of common fuels. Lots of efforts were also conducted by many researchers for the sustainable development and push work on renewable energy, such as biofuels, solar, wind energy, etc.7,8. For the internal combustion engine new alternative fuels are required which have reduced the environment pollution and meet the fuel necessity of coming years. There are various technologies which are carrying out to decrease the dangerous gases releases by the diesel engines such as exhaust gas recirculation, implementation of after treatment, use of alternative fuels etc9. Extensive research has focused on reducing both NOx and smoke emissions.10,11. However, governing these impurities concurrently remain exciting job for the scientific community12.

Water-Diesel Emulsified Fuel (WDEF) has recognised to be an effective technique for diminish both NOx and smoke emissions in compression ignition (CI) engine13,14. This is mainly due to the micro-explosion phenomenon, where water quickly vaporizes, breaking fuel into finer droplets and refining air-fuel mixing15. Oliveira P and Brójo F16 had investigated the performance and emission features of diesel engine with water in diesel emulsion (WiDE) and it was found that thermal efficiency is significantly improved and reduce the NO and smoke emissions at specific engine working situations as compared to diesel. Badran O et al.17 had carried out an experimental investigation in a diesel engine with stable emulsion of 10–30% water by volume in diesel fuel under different operating conditions. The results showed that the addition of water to diesel enhance the combustion efficiency. The brake thermal efficiency increased by 5% for 30% water emulsion as compared of diesel fuel. The smoke and NOx emissions were simultaneous decrease as the percentage of water in the emulsion increased to 30%. Wang et al.18 studied WDEF (W10), neat diesel, and diesel-ethanol (E10) in a diesel engine. Their results showed that a soot reduction for E10 and W10 was 21% and 39% respectively. Mondal and Mandal19 had reviewed the various studies on water- diesel emulsified and it was found that it improves thermal and combustion efficiency however reducing the NOx, smoke, and HC emissions. Vellaiyan S20 conducted an analysis on water emulsification in biodiesel-fueled diesel engines, importance its possible for attaining efficient and cleaner combustion without requiring engine modifications or incurring additional costs. Jhalani et al.,21 applied exceptional method of consuming (15%) cow-urine with emulsified diesel for diesel engine. They discovered 24.8% raise in BTE with decrease of 31.8% in NOX emissions, and 36.9% in smoke emissions. Also, they described that no substantial variation in HC was observed. As a result, soot formation decreases. Kumar Patidar and Raheman22 utilized water-emulsion biodisel (B20) blends for the diesel engine with 10% water concentration. The lowest NOX emissions up to 13.80% was observed.

However, a key disadvantage of WDEF is its tendency to growth carbon monoxide (CO) and unburnt hydrocarbon (UHC) emissions. This occurs because of a longer ignition delay, leading to incomplete combustion23. Some latest investigations demonstrated that the nanoparticles when utilized as additives, further enhanced the combustion qualities. This is credited to the higher surface area-to-volume ratio, which enhances fuel dispersion. The mixture of WDEF incorporated with nanoparticles act as the developing alternative fuel as this combination possess the features which will reduce the emissions including NOx, smoke, CO, and HC as well24,25. These refinements are due to the happening of “micro-explosion”, which is the vaporization of small-sized droplets of water in the diesel, stimulating “secondary-atomization” phenomenon for the droplets of emulsified fuel26. Khidr M et al.27 studied the effect of several alumina nano additives and water-emulsion biodiesel dosages on diesel engine. Results are revealed that 10% of biodiesel blend with 1% water emulsion and 150 mg/l alumina nanoparticles (B10A150W1) gave optimum fuel blend and illustrated a 9.1% enhancement of BTE compared to diesel and reduction of CO, smoke and NOx by 40%, 26% and 22% respectively. Pullagura G et al.28 studied the performance, emission and combustion features of a diesel engine with graphene nanoplatelets and 10% v/v dimethyl carbonate as fuel additives in a 30% biodiesel and 70% diesel blend. It was observed that the cylinder pressure and heat release rate, improved by about 15.45% and 9.63%, respectively, for B30GNP60DMC10 blend than diesel at maximum engine loads. Similarly, brake thermal efficiency enhanced by 8.98% compared to diesel. While the emissions (such as hydrocarbons and carbon monoxide) were found to be reduced by 22.87% and 25.67%, respectively, the nitrous oxide and smoke opacity were also reduced by 9.57% and 12.4%, respectively, for the B30GNP60DMC10 sample. Khujamberdiev R and Cho H M29 had conducted a study which explored the impact of TiO2 nanoparticles on the performance and emission characteristics in diesel engine. The fuels analyzed include diesel, 20% of soybean biodiesel blend, and 20% of soybean biodiesel blend with different dosage of TiO2 nanoparticles, 20% of palm biodiesel, and 20% of palm biodiesel with different dosage of TiO2 nanoparticles. Results showed that with the addition of TiO2 nanoparticles the exhaust gas temperature were reduced, indicating improve the performance parameters. Results also exhibit that TiO2 nanoparticles lead to a reduction in CO and HC emissions by up to 30% & 21.5% respectively. Three sizes of CeO2 nanoparticles (i.e., 10, 30, and 80 nm) at a constant volume fraction of 80 ppm were added to a 20% blend of waste cooking oil biodiesel and diesel (B20) by Dinesha P et a30. It was found that 30 nm nanoparticles of CeO2 reduced brake specific fuel consumption (BSFC) by 2.5%, smoke by 34.7% and NOx emission by 15.7%, compared to the additive-free B20.

Hence, lot of study successfully conducted to determine the effect of water diesel emulsified fuel with and without nanoparticles under various operating conditions to attain highest engine performance and lowest exhaust emissions. But these experiment studies are time consuming and expensive. So, more effective methods are required. Using optimization techniques to reduce the requirement for extensive experimental testing is a valuable approach31. Numerous investigators used a wide range of optimization methodologies in design analysis, such as response surface methodology (RSM), Taguchi optimization, genetic algorithm optimization, grey wolf optimization (GWO), particle swarm optimization (PSO), whale optimization algorithm (WOA), artificial neural network (ANN), and intelligent grey wolf optimization (IGWO)31. Mostafa A. et al.32 had investigated the collective effect of water–diesel emulsion and Al2O3 nanoparticles on the diesel engine for performance and emissions characteristics via the design of experiment. A response surface methodology (RSM) based on a central composite design (CCD) was applied to simulate the design of the experiment. A Robust and modern optimization of the sea-horse optimizer (SHO) was run through the support vector regression (SVR) model to find the optimal water addition and engine speed for improving the brake torque and lowering exhaust emissions. Furthermore, the SVR model was compared to the artificial neural network (ANN) model. Bora et al.33 employed a RSM to investigates the usage of biodiesel-based emulsified fuel as pilot fuel and waste-derivative biogas as main fuel to run dual fuel engines at different compression ratios (17, 17.5, 18), injection timing (23°, 26°, 29°, 32° BTDCs), and engine loads (20%, 40%, 60% 80%, 100%). Kumar et al.34 had conducted a study with artificial neural network (ANN)-particle swarm optimization (PSO) technique to find the optimal parameters to produce water–diesel emulsion for engine testing. The projected optimal limits were found as 20% water to diesel ratio, 0.9% surfactant and 2200 rpm of stirrer for a water separation of 14.33% in one day with a variation of 6.54% against the actual value of water separation. Vellaiyan et al.35 developed a Taguchi method coupled with gray relational analysis for water–biodiesel emulsion fuel with nano additives. The findings showed that the quantity of water in the emulsion has maximum impact on overall performance and emission of diesel engine followed by alumina nano additive and soybean biodiesel (SB) concentrations36. conducted an experimental and statistical analysis to optimize the stability aspects of WDEF through response surface methodology (RSM) approach. The quadratic model was established and confirmed for analysis of variance (ANOVA). The predictable optimum values of water concentration, surfactant concentration, and duration of ultrasonication were found to be 4.486% vol., 1.237% vol., and 30.0 min, respectively.

Based on the previous studies, it can be understood that water diesel emulsified fuel (WDEF) with nanoparticles has showed substantial developments in diesel engine performance and emission profiles. Collectively, the interactive effects of water-induced micro-explosions and nanoparticle catalysis in WDEF formulations suggest a favourable method to improving diesel engine efficiency while modifying harmful emissions. It is very tedious and costly to study the combined effect of certain engine parameters such as injection timing (IT), injection pressure (IP), load (%), and speed while estimating the performance and emissions characteristics for nanoparticles with WDEF. Therefore, an effort has been made through this study and evaluating the performance and emission features of WDEF engine at different load, injection pressure and timings of WDEF with SiO2 nanoparticles by using both experimentally and numerical study. The author has conducted an experimental study23 and found that the fuel blend D94W5S1-Si50, comprising of 94% diesel, 5% water, 1% SPAN 80, and 50 ppm silicon nanoparticles (SiNPs), carried higher performance (Brake thermal efficiency) and lower emissions compared to standard diesel fuel. The current study can be considered as an extension of previous work with utilization of D94W5S1-Si50 as the test fuel, and the simultaneous effects of different input parameters such as injection pressure, injection timing, and engine load on engine performance and emission attributes, which are efficiently analysed exercising soft computing approach. The study aims to identify the synergistic effects of fuel formulation and operating conditions, which is essential for optimizing engine performance and reducing emissions incorporating advanced combustion strategies. To the best of the author’s knowledge, such a comprehensive investigation involving this specific fuel composition and combined parameter analysis using multiple soft computing approaches has not been reported in the existing literature. Therefore, three main input parameters which selected for the optimization analysis were: injection pressure, injection timing and load. The Taguchi design approach L9 array was applied and subsequently an ANFIS model has been developed for analysing and prediction of WDEF engine’s performance and emission characteristics through determination of interactions effects and adequate settings of optimized input parameters. Furthermore, the current study has optimized the input variables of a diesel engine for improved performance and emission responses from water–diesel emulsions with the addition of SiO2 nanoparticles according to ANFIS approach and multi-objective prairie dog optimization algorithm (MOPDO).

Materials and methods

Materials

In this work, diesel fuel was utilised as a continuous phase and distilled water considered as dispersed phase while preparing emulsified fuel. Diesel fuel was purchased from the locally situated HP fuel station and distilled water arranged from the chemistry lab of Manipal University Jaipur. The silicon dioxide nanoparticles (SiNP) were procured from Ultra nanotech Pvt. Ltd., Karnataka, (India) with the size of particle: 30–50 nm, powered-white in colour with a density of 2.2 g/cm3. Sorbitan-monooleate (Span 80) surfactant was used to stabilize the water diesel emulsions and was purchased from The Scientific Chemicals, India.

Preparation of test fuel

The process for forming of fuel sample includes two stages. In the first stage the diesel fuel was taken in a measured quantity of 94% (by vol.), distilled water as 5% (by vol), and surfactant SPAN 80 taken as 1% (by vol). In this solution, 50 ppm of silicon dioxide nanoparticles were weighed and added. After that the magnetic stirrer technique was employed for 25 min at 1000 RPM. In the second stage, the process of ultrasonication was regulated by using a probe-type soundproof ultra sonicator. The specification of ultra sonicator is as: Make: LABMAN, Power: 500 Watts, model No. PRO 500 with titanium alloy probe. Ultrasonication process was employed for 30 min duration with the frequency of 20 kHz. The test fuel was prepared and identified as D94W5S1-Si50 (94% diesel, 5% water, 1% SPAN 80, and 50 ppm of SiNP). It can be detected that the presence of the sample fuel was milky-white in colour. The ready fuel D94W5S1-Si50 was also tried for stability study. It was stable for about 6 days (144 h: when kept motionless) without any visible separation of the water layer with the remaining solution. Further, it was tested for fuel properties which are tabulated in Table 1.

Table 1 Fuel specifications of D94W5S1-Si50.
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Experimental set up and methods

A single-cylinder, four-stroke diesel engine with a bore of 87.5 mm, a rated power capacity of 3.5 kW, and an eddy current dynamometer of the Apex Innovation model number 240-PE was used for the trials. Figure 1 illustrates how the experimental setup is done. Figure 2 describes the experimental setup’s photographic location. The AVL 437 C smoke meter was used to quantify the amount of smoke. An AVL DIGAS 444 N exhaust-gas analyzer was utilized to detect NOX emissions. Before the readings were recorded, the engine was allowed to run for about 15 min to stabilise. To maintain the precision in the measured values, every experimentation was taken thrice, and the mean values are used for the relative assessment. For the conduction of experiments, performance and emission analysis for D94W5S1-Si50 fuel was examined at constant engine speed 1500 RPM and fixed compression ratio i.e.18. The load of the engine was changed from 25%, 50% and 75%. The injection pressure (IP) of the engine was varied from 180, 190 &200 bar. The IP was varied by the regulation of the spring tension of the fuel injector by using a setting screw. Injection timing was varied from 190, 210, 230 bTDC. The maximum limit of injection pressure was set as 200 bar because, by raising the injection pressure above this limit, the research engine experienced extreme vibrations. The principle of root mean square method was used for uncertainty analysis and the wide uncertainty connected with the searches comes out to be \(\:\pm\:\)2.28%23 and is listed in Table 2.

Fig. 1
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Experimental layout line diagram.

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Fig. 2
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Actual visualization of experimental setup.

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Table 2 Percentage uncertainty detailing23.
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Experimental planning using Taguchi based design

The current work analyses the influence of three prevalent control variables such as load, injection pressure and injection timing on performance and emission characteristics considering their different settings as displayed in Table 3. The output variables examined are brake thermal efficiency (BTE), NOx and smoke, which are further optimized by analysing different control variables. The current study employed Taguchi L9 orthogonal array for planning of experiments on Minitab statistical software. The Taguchi orthogonal array provides an environment for establishing mathematical and statistical templates to determine optimized response variables. The important of Taguchi design have been realized in several literature owing to efficient reduction of experimental trials than other design like full factorial and response surface methodology, which significantly saves the cost, time and resources37. The L9 array consists of three columns for input process variables along with different levels, which combines to form nine parametric combinations. These nine combinations assist in performing minimum experimental trials and utilized in analysing the relationship between input parameters and response variables as shown in Table 4. Based on recorded response variables, signal-to-noise (S/N) ratio is calculated. The S/N ratio is considered as a performance measure of response variables, which is based on three qualitative properties such as lower-is-better, nominal-is-best and higher-is-better. The current study primarily aims to improve the performance characteristics such as BTE, while it aims to minimize the emission characteristics like NOx and smoke. Therefore, the lower-is-better and higher-is-better mathematical models are utilized to characterize response variables behaviour as shown in Eqs. (1–2).

$$\:S/N=-10*log\left(\sum\:_{i=1}^{m}\frac{{x}_{i}^{2}}{m}\right)$$
(1)
$$\:S/N=-10*log\left(\sum\:_{i=1}^{m}\frac{{(1/x}_{i}^{2})}{m}\right)$$
(2)

where \(\:{x}_{i}\) represents the response variables and \(\:m\) denotes the number of experiments. From experimental results in Table 4, it is evident that maximum value of BTE is found as 28.43%, while minimum values of Nox and smoke are 145 PPM and 26.8 HSU, found on different combinations of input variables. However, it is imperative to realize a perfect trade-off among their values, so that efficient engine performance and emission characteristics can be achieved with optimal input settings.

Table 3 Different engine parameters and their levels.
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Table 4 Experimental outcome of responses with L9 array.
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Adaptive neuro fuzzy inference system

In literature, several authors have exercised ANFIS network for modelling and examining the response characteristics. The concept of ANFIS was first coined by Jang in 1993, which typically described the combination of fuzzy logic (FL) scheme and artificial neural network (ANN) concepts to overcome their weaknesses when applied individually38. In ANN, the prime advantage is its efficient learning rate, conversely, challenging to deduce the information and intelligence developed by it. In contrast, the theory of FL makes troublesome learning experience, however the fuzzy variables are transformed to logical crisp set values for ease of understanding instead of numerical interpretation. ANFIS structure is categorized in five diverse layers as depicted in Fig. 3. Initially, the input parameters data were fed to the network were appropriate fuzzy membership functions applied unique rules for converting numeric data to fuzzified values. The fuzzified values are fed to ANN network for optimizing the parameters and If-Then rules. Furthermore, the appropriate rules are applied for finding the fuzzified output values in the neural network block. Finally, the fuzzified output is converted to crisp or numeric values using de-fuzzifier block.

Fig. 3
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ANFIS architecture.

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Results and discussions

Taguchi based analysis

The S/N ratio is evaluated for all experimental trials based on diverse settings of input parameters considering their relevant mathematical models. Table 5 shows the combined response table for signal-to-noise ratio of all performance variables. It is clearly illustrated that engine load (L) have most significant influence on all the performance characteristics i.e., BTE, NOx and smoke. The second most influential input parameter is injection pressure (IP) followed by injection timing (IT) as calculated by difference in maximum and minimum values of S/N ratio, known as delta. Furthermore, for achieving maximum BTE value individually, the best input parameters combination is L3, IP3 and IT2. Similarly, for achieving minimum NOx and smoke emission, it is established that the best input parameters settings are L1, IP1 and IT3, and L1, IP1 and IT3, respectively.

Table 5 Response table for S/N ratio of all response variables.
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Furthermore, statistical confirmation of the above results and the correlation of input control factors on engine characteristics are evaluated employing ANOVA analysis. Tables 6, 7 and 8 displayed the results of ANOVA analysis for a level of significance of 5%, thus confirming confidence level up to 95%, for response variables BTE, NOx and smoke, respectively. The p-value shown in each ANOVA table are lower than 0.05, validating the level of significance for all response variables. It also demonstrates that more than 95% of results are explained by these models and can be utilized for further analysis. For BTE and NOx, the most influential parameter is load followed by injection pressure, while for smoke most influential parameter is established as injection pressure followed by engine load. It is worth noting that injection timing is least influential parameters in changing response variables. In addition, the competence of obtained regression model was attained through critical evaluation metrics. The value of coefficient of determination (R2) nearer to 1 demonstrates adequate fit of the model. For all the three regression models, the value of R2 is 0.9876, 0.9912 and 0.9667, which is closer to 1, thus confirming its precision in predicting response variables. The regression models for BTE, NOx and smoke are developed based on ANOVA analysis as shown in Eqs. (3–5).

Table 6 ANOVA analysis for BTE.
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Table 7 ANOVA analysis for NOx.
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Table 8 ANOVA analysis for Smoke.
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$$\begin{aligned} BTE\left( \% \right) = & - 283.5\: + \:1.102{\text{*L}}\: + \:1.078{\text{*IP}}\: + \:14.65{\text{*IT}} - \:0.003672{\text{*L}}^{2} - \:0.002133{\text{*IP}}^{2} \\ & - \:0.3379{\text{*IT}}^{2} \: - \:0.001773{\text{*L*IP}} - \:0.007867{\text{*L*IT}} + 0.000123{\text{*IT*IP}} \\ \end{aligned}$$
(3)
$$\begin{aligned} No_{x} \left( {PPM} \right) = & 4209\: + \:1.300{\text{*L}}\: - \:65.17{\text{*IP}} + 165.0{\text{*IT}} - 0.08267{\text{*L}}^{2} \: + \:0.1667{\text{*IP}}^{2} \\ & - 3.542{\text{*IT}}^{2} + 0.1200{\text{*L*IP}} - 0.2333{\text{*L*IT}} - 0.000010{\text{*IT*IP}} \\ \end{aligned}$$
(4)
$$\begin{aligned} Smoke\:\left( {HSU} \right) = & - 249.4 - 0.5898{\text{*L}} + 2.866{\text{*IP}} - 2.422{\text{*IT}} + 0.004595{\text{*L}}^{2} - 0.005850{\text{*IP}}^{2} \\ & - 0.01625{\text{*IT}}^{2} - 0.002653{\text{*L*IP}} + 0.05387{\text{*L*IT}} - 0.000141{\text{*IT*IP}} \\ \end{aligned}$$
(5)

Figure 4 demonstrated the main effect of individual engine input parameters with varying level on three output response characteristics. It is clear that with increase in engine load, all three responses i.e., BTE, Nox and smoke, have shown direct relationship as they also increased, however, the values are lower than experimental values. Such trend can be attributed to more fuel burning per cycle, and with minimum thermal losses, allowing more efficient combustion, producing higher BTE at higher loads. Nox emission is also increasing with the increasing of load due to the higher cylinder temperature during combustion. At high load, sometimes air-fuel ratio decreases which lead to incomplete combustion and cause of higher soot or smoke. Similar trend can be seen for injection pressure, which cause positive impact on BTE, however, the emission characteristics like NOx and smoke seems to have deteriorated. The probable reason being production of finer fuel droplets at higher injection pressure, attaining shorter combustion duration, lower peak cylinder temperature and reduced diffusion phase with the increasing of injection pressure. Finally, with increase in injection timing till 21 bTDC, the BTE increases more, while NOx emission also increases, and smoke remains constant. However, with injection timing peaking at 23 bTDC, the BTE decreases reaching slightly higher from initial level. The NOx and smoke decreased and showed positive response with maximizing the value of injection timing. Increasing timing improves efficiency up to a certain point, but too premature injection indicates to work loss and lower temperatures, triggering BTE and NOx to decrease, while smoke reduces due to improved premixing. The enhancements in BTE and the reductions in NOx and smoke emissions observed in this study are in agreement with the literature recommendations39,40.The optimal combination of input parameters for achieving maximum BTE, minimum NOx and smoke based on these plots are found to be L3IP3IT2, L1IP1IT3, L1IP1IT3, thus realizing perfect trade-off among response variables and optimizing engine performance metrics.

Fig. 4
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Mean response plot for engine output characteristics.

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Although, the individual input parameter effects have seen significant changes among engine performance and emission characteristics, however for detailed investigation it is imperative to examine the interaction influence of two parameters simultaneously on response variables. To this end, Fig. 5 illustrated the interaction effects of input variables such as L and IT, L and IP, IT and IP on BTE, Nox and smoke, respectively. Figure 5a-c shows the contour plots for BTE. Figure 5a showed that with load % and injection timing have positive impact on brake thermal efficiency. With increase in interaction values there is significant improvement in BTE peaking to more than 28%. It is notable that load % seems to have more influence on BTE as with low injection timing of 19bTDC, because higher load improves combustion and energy conversion, leading to better efficiency. Injection timing impact is to a lesser extent significant at high load due to the combustion duration is inherently shorter due to rapid fuel burn and higher in-cylinder pressure. Figure 5b showed that higher injection pressure of 200 bar and load percentage of even 50 can shows significant rise in BTE values because high injection pressure improves combustion superiority, and moderate to high load provides the exact in-cylinder situations to maximize energy translation resultant in a substantial improvement in BTE. Figure 5c depicts a contradiction between interaction parameters injection pressure and injection timing for attaining higher BTE percentage. The higher injection pressure and lower value of injection timing depicted to a have obtained higher thermal efficiency and vice-versa. In contrast, higher values of both parameters simultaneously realized lower brake thermal efficiency. Excessive injection pressure is helpful only when combined with optimized (not too early) injection timing. Otherwise, the benefits of pressure are invalid by poor burning phasing and extreme pre-TDC losses. Figure 5d-f shows the contour plots for NOx emission. Figure 5d show that with increasing load (%) the NOx emission value will also increase. With increasing of injection pressure from 180 bar to 190 bar, NOx emission will increase but after the increasing of IP from 190 bar to 200 bar NOx emission will decrease at maximum load condition. The main reason is that at higher injection pressure it leads to better atomization, shorter ignition delay, and lower peak temperatures. Figure 5e indicates the contradiction between interaction parameters injection timing and load for NOx emission. It is clearly shown that with the increasing of load NOX emission will increase but for advanced timing, NOx emission will decrease. Similarly, Fig. 5f shows the contradiction between interaction parameters such as injection pressure & injection timing for NOx emission which indicate that NOx emission increases at higher injection pressure and timing due to too early of atomization. Figure 5g-i shows the contour plots for smoke emission. Figure 5g depicts the contradiction between load (%) and injection pressure (bar) for smoke emission which indicate that smoke will increase with the increasing of both injection pressure and load. Figure 5h shows contradiction between load (%) and injection timing for smoke emission. Figure clearly show that with increasing of load at low timing smoke emission will increase and with the advanced timing or increasing the injection timing smoke emission will decrease. Figure 5i exhibits the contradiction between injection pressure & injection timing for smoke emission. High injection pressure reduces smoke emission due to better spray quality and advanced injection timing also reduces smoke by improving air-fuel mixing.

Fig. 5
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Contour interaction plots for (a-c) BTE (d-f) NOx (g-i) Smoke.

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The probability plots in Fig. 6 revealed that all predicted values are within the range of 95% confidence interval and follows a straight line for all three engine variables viz. BTE, NOx and Smoke. Therefore, these plots indicate to have no outliers, non-normality and prediction follows normal distribution with no unknown variables.

Fig. 6
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Probability plots for (a) BTE (b) Nox (c) Smoke.

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Modelling of engine performance characteristics using ANFIS

After analysing the experimental outcomes for various engine performance and emission characteristics, this section assesses the ANFIS modelling and validation of the experimental trials. For training and testing of ANFIS models, experimental trials data were considered. The current work considers three inputs with single output scheme for each of the engine’s performance characteristics. Figure 7a depicts an example of sugeno ANFIS architecture for evaluating BTE considering three given input variables. Similarly, the ANFIS architecture was established for NOx and smoke evaluation considering gaussian membership functions as shown in Fig. 7b-d. The gaussian membership functions were selected for input parameters based on minimum root mean square error (RMSE) value in training the ANFIS model. Table 9 displayed the comparison between RMSE values for different membership functions, which reveals that gaussian membership functions have lowest root mean square error values i.e. 2.2334E-05, 6.0230E-04, 4.8670E-05 for BTE, Nox and smoke responses, respectively, thus considered for modelling their interaction with input parameters. The linguistic variable employed for defining the membership functions are three i.e., low (L), medium (M) and high (H), and having 27 rules. The numeric values as an input to ANFIS model converted in fuzzy set values exercising the gaussian membership functions. The training error convergence curves for these three ANFIS models are shown in Fig. 8 for 200 epochs. The training was not extended after 200 epochs owing to stagnation in error values. The training of developed ANFIS model were performed utilizing hybrid method combining the advantages of least square method and back propagation techniques. Figure 9 shows the real ANFIS architecture with different layers for prediction of engine performance and emission characteristics.

Fig. 7
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ANFIS structure with membership functions.

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Table 9 RMSE values for different membership functions.
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Fig. 8
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Training error of ANFIS model for (a) BTE (b) Nox (c) smoke.

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Fig. 9
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ANFIS final structure.

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The comparative results of ANFIS predicted models with experimental trials for three response variables are displayed in Fig. 10. Furthermore, the regression analysis has also been introduced for validating the normal distribution of predicted data with experimental trials. The results suggested that the response variables are predicted by developed ANFIS models are in accordance with the experimental outcomes. Furthermore, the percentage error in ANFIS prediction values for different responses are also illustrated in Fig. 10a, c and e. In BTE prediction, the maximum absolute error percentage is observed to be nearly 7.5%, while for NOx, the maximum percentage of absolute error is approximately 7%. At last, the maximum absolute percentage of error for smoke prediction is nearly 9%, which confirms that the developed ANFIS model have successfully modelled and predicted the response variables. The efficacy of developed model and predicted response variables are validated with normal distribution plots as shown in Fig. 10b, d and f. The distribution of predicted response variables depicted that they are in accordance with the experimental values owing to falling near or on straight line. In addition, the coefficient of correlation (R2) is an excellent parameter typically considered for determining the perfectness of predicted values with experimental trials. The R2 values of 0.9896, 0.9948 and 0.9528 for BTE, NOx and smoke demonstrated that ANFIS predicted values have higher precision, accuracy and a good correlation with experimental values.

Fig. 10
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Experimental and ANFIS predicted responses with normal distribution plot.

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Figure 11 depicted ANFIS predicted surface plots showing interaction effects of input parameters on water diesel emulsified engine’ emission and performance characteristics. Figure 11a-c showed enhanced brake thermal efficiency with higher load and injection pressure, while low injection temperature with higher load is also favourable interaction providing positive response to BTE. The probable reason being higher combustion and energy conversion owing to higher load application, thus revealing better efficiency. Similarly, with higher injection pressure and moderate injection temperature the brake thermal efficiency is higher, otherwise the high and low values provide significant lower BTE. Figure 11d-f illustrated the interaction influence of input parameters on NOx, it is evident that with lower to moderate load percentage and all values of injection pressure reveals lower emission of NOx. The primary reason being better atomization, shorter ignition delay, and lower peak temperatures at moderate to higher injection pressure. Similar trend is explained in interaction of load and injection timing, however moderate of injection pressure with lower injection timing reveals better emission characteristics. Figure 11g-i shows smoke emission properties variation with changing input parameters simultaneously. It is worth noting that lower load percentage and injection pressure exposes minimum smoke emission. The injection temperature with its lower and higher values along with lower load percentage have significantly lowered the smoke emission. The moderated to high value of injection pressure with lower injection time have substantially decreased the smoke emission characteristics. The high injection pressure reduces smoke emission due to better spray condition and also reduces smoke by improving air-fuel mixing.

Fig. 11
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Surface interaction plot for (a-c) BTE (d-f) NOx (g-i) Smoke.

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Engine performance characteristics optimization exercising multi-objective prairie dog optimization (MOPDO) algorithm

This section demonstrated the working procedure of prairie dog optimization (PDO) algorithm for further optimizing the engine performance and emission characteristics, thus enhancing the efficacy and sustainability of emulsified engine. The prairie dog optimization (PDO) algorithm is a recently introduced metaheuristic algorithm, inspired from four exceptional strategies covering burrow construction, foraging technique, anti-predatory skills and communication strategy41. The flowchart of classical PDO algorithm is shown in Fig. 12. The PDO algorithm starts with generating random prairie dogs and coteries position. The diverse mechanisms employed by prairie dogs are utilized for efficient swapping of diversification and intensification phases in PDO algorithm. In first half of iterations, prairie dog search for food and perform burrow building activities, thus assist in diversification. The latter half of iterations govern intensification of solution space through communication mechanism. Then, the present coteries positions are updated based on their fitness solutions. The minimum fitness provides best food fitness, and the best possible solutions in current iterations and global best position of prairie dog is updated. At last, the PDO algorithms stops its working as soon as the iterations are maxed out or with attaining global optimal solution. The PDO algorithm is applied here for engine performance and emission characteristics optimization viz. BTE, Nox, smoke, and determining optimal engine settings in terms of input parameters. For solving such multi-objective problems, MOPDO algorithm42 is employed in the current study incorporating the concepts of archive for storing the solutions, concept of grid and non-dominance for storing diverse and pareto front solutions for multiple objectives in classical PDO algorithm. In past literature43, it is demonstrated that the MODPO has higher convergence speed and reached to stable pareto front in comparison to different competitive multi-objective optimization algorithm. In addition, the other noteworthy advantages are enhanced exploration and exploitation behaviour, variety of populations, scalability, etc., thus making the search behaviour efficient and converges to accurate global optimal fronts. The MOPDO begins with initialization of prairie dogs and coterie positions with their fitness functions. The next phase is determining non-dominated pareto fronts and updating old solutions, which are stored in archive. The concept of grid is utilized for clearing most crowded regions and merging of new solutions to archive is performed. In current study, MOPDO is exercised for multi-objective optimization of engine performance and emission characteristics considering regression Eqs. (3–5) for maximizing BTE and minimizing NOx, smoke, simultaneously. These response variables are described in terms of engine input parameters in regression equations for improving its efficiency and sustainability. The population of prairie dog and coteries taken for current study are 100, while 200 iterations are considered for finding optimal solutions using MOPDO algorithm. The lower bound and upper bound values for design variables are considered as load % (25–75), injection pressure (180–200 bar) and injection timing (19–23 bTDC), respectively. The MOPDO algorithm obtained results for two objectives through showing forty optimal pareto fronts values, which is shown in Fig. 13a-c. Figure 13a shows the x-axis as BTE (%) and y-axis as Nox (PPM). The optimal pareto fronts depicts variation in BTE in range of 28–30%., while the NOx having range of 138 ppm to 146 ppm. The optimal response value with corresponding engine input parameters is tabulated in Table 10. In Fig. 13b, the optimal fronts of BTE are in the range of 26.5–28%., while for smoke having range of 24.5 HSU to 27 HSU. Similarly, Fig. 13c showed optimal fronts variation of smoke in range of 20 to 32 HSU while Nox as 140 ppm to 200 ppm. The pareto front curves also described the conflicting nature of considered objectives. It was found that best optimal solutions are obtained as: BTE as 29.6674%, Nox as 139.11 ppm and 26.32 HSU for corresponding engine parameters as shown in Table 10. It is clearly evident that higher BTE % and minimum Nox (ppm) and smoke (HSU) characteristics can be obtained when mid to higher engine load is applied with higher injection pressure, while lower injection timing is recommended. The validation experimental trials were performed on these settings of input parameters, and it was revealed that the values of BTE% and emission features are in accordance with optimized results. These results for enhancing BTE and minimizing Nox and smoke are in line with the literature recommendations of44,45.

Fig. 12
figure 12

PDO algorithm flowchart41.

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Fig. 13
figure 13

Pareto fronts for (a) BTE vs. Nox (b) BTE vs. Smoke (c) Smoke vs. Nox.

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Table 10 Pareto optimal solutions.
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Conclusions

This study analyses the influence of water diesel emulsified fuel with SiO2 nanoparticles on the performance and emission attributes of diesel engines, involving the engine load percentage, injection pressure (bar) and injection timing (bTDC). The acclaimed Taguchi orthogonal array was implemented for designing of minimum experimental trials followed by ANFIS modelling of engine’s performance and emission attributes. In addition to the analysis of individual parameters and their interactions on output responses, a multi-objective PDO algorithm was implemented for investigating and optimizing both engine performance and emissions parameters, simultaneously. Furthermore, the research results of present work can be summarized as follows:

  1. 1.

    Based on ANOVA analysis for BTE and NOx, the most influential parameter is engine load followed by injection pressure, while for smoke most influential parameter is established as injection pressure followed by engine load. It is worth noting that injection timing is least influential parameters in affecting response variables. The regression models for BTE, NOx and smoke are developed based on ANOVA analysis and the value of coefficient of determination (R2) is 0.9876, 0.9912 and 0.9667 respectively which is close to 1. Thus, confirming its precision in predicting response variables.

  2. 2.

    The optimal combination of input parameters for achieving maximum BTE, minimum NOx and smoke are found to be 50% load, 200 bar injection pressure and 210bTDC, 25% load, 180 bar injection pressure and 230bTDC, 25% load, 180 bar injection pressure and 230bTDC respectively. Thus, realizing perfect trade-off among response variables and optimizing engine performance metrics.

  3. 3.

    The ANFIS model validated experimental outcomes for various engine performance and emission characteristics. The maximum absolute error percentage for BTE, NOx and smoke were observed, and it was found that the value of maximum absolute error percentage is to be nearly 7.5%, 7% and 9% respectively which confirms that the developed ANFIS model have successfully modelled and predicted the response variables.

  4. 4.

    The coefficient of correlation (R2) is an excellent parameter typically considered for determining the perfectness of predicted values with experimental trials. The R2 values of 0.9896, 0.9948 and 0.9528 for BTE, NOx and smoke respectively and it is demonstrated that ANFIS predicted values have higher precision, accuracy and a good correlation with experimental values.

  5. 5.

    For enhancing the efficacy and sustainability of emulsified engine, the multi-objective Prairie Dog Optimization (MOPDO) algorithm was used for optimizing the engine performance and emission characteristics. The optimal response value for BTE is in the range of 26.5–28%., while for smoke having range of 24.5 HSU to 27 HSU and NOx as 140 ppm to 200 ppm, thus revealing that higher BTE % and minimum NOx (ppm) and smoke (HSU) characteristics can be obtained when mid to higher engine load is applied with higher injection pressure, while lower injection timing is recommended.

Future recommendation

It is advised that future research in this area go in the following directions:

  1. 1.

    Long-Term Testing and Transient Engine Conditions: Only steady-state engine running is included in this study. To assess fuel stability, deposit formation, and wear characteristics, more research should investigate how nanoparticle-enhanced WDEF behaves in both long-duration testing and transient engine circumstances (such as acceleration and deceleration).

  2. 2.

    Incorporation of Other Nanoparticles and Concentrations: To find more efficient additives for improving combustion efficiency and lowering emissions, future research may examine the impacts of additional nanoparticles (such as AlO₃, TiO2, and ZnO) and different concentrations on fuels that are emulsified with water and diesel.

  3. 3.

    Extension to Other Engine Types and Sizes: To assess scalability and practical viability, the methodology can be extended to multicylinder engines or engines utilized in various applications, such as the heavy-duty transportation, agricultural, or marine industries.

  4. 4.

    Advanced Control Strategies and RealTime Implementation: To dynamically optimize injection parameters and guarantee better engine performance and reduced emissions during actual driving cycles, it may be possible to integrate soft computing models such as ANFIS with real-time engine control systems.

  5. 5.

    To evaluate the overall sustainability, a lifecycle assessment (LCA) of SiO2based WDEF should be carried out, considering the effects of post combustion emission impact.

  6. 6.

    For better global convergence and more reliable multi-objective solutions, future research may examine on hybrid metaheuristic algorithms that combine MOPDO with additional strategies (such as GA, PSO and NSGA-II).