Open access peer-reviewed chapter - ONLINE FIRST
Summary of ANFIS and hybrid ANFIS-based applications in the energy sector.
Abstract
Accurate and computationally efficient prediction of electrical power output is essential for the operational optimization of combined-cycle power plants (CCPPs). Although data-driven models such as artificial neural networks have been widely applied, their performance often relies on high-dimensional input spaces and extensive hyperparameter tuning, which may limit robustness and interpretability. This study proposes a reduced-order adaptive neuro-fuzzy inference system (ANFIS) framework for predicting the net electrical power output of a 420 MW gas-fired CCPP using a minimized set of thermodynamic input variables. A publicly available dataset comprising 9568 hourly operational records collected over 6 years was utilized. Based on sensitivity analysis, ambient temperature, exhaust vacuum, and ambient pressure were selected as the sole input variables. The ANFIS model was trained using a hybrid learning algorithm that combines least-squares estimation with gradient descent within a first-order Sugeno-type fuzzy inference structure. A systematic parametric investigation involving nine membership function types was conducted. The results indicate that three generalized bell-shaped membership functions per input provide optimal predictive performance, yielding root-mean-square errors (RMSE) of 4.0926 and 4.0481 MW for the training and test datasets, respectively. The close agreement between training and validation errors confirms strong generalization capability and negligible overfitting, despite the reduced input dimensionality. Compared with higher-dimensional and hybrid optimization-based models reported in the literature, the proposed reduced-order ANFIS framework achieves competitive accuracy while maintaining substantially lower computational complexity. These findings demonstrate that reliable power output forecasting in CCPPs can be achieved using a compact and interpretable neuro-fuzzy structure, making the proposed approach well-suited for real-time monitoring and decision-support applications in thermal power plant operations.
Keywords
- artificial intelligence
- machine learning
- fuzzy logic
- power plant
- energy sector reliability
1. Introduction
Electric power generation can be advantageous, contributing to a better quality of life for the entire society. The ongoing and emerging global needs have driven the adoption of effective energy sources, including thermal power plants and renewable energy technologies such as wind and solar [1]. Thermal power plants have substantially met the energy sector’s needs, but they have disadvantages in terms of electricity efficiency. This gap is filled by the introduction of CCPPs, which are more prominent due to their 60% improved performance and reduced environmental impact [2].
Technological evolution over the last few years has enabled novel methods to predict energy system performance, even in the power sector [3]. These methodologies include a range of modern machine learning techniques, including artificial intelligence and artificial neural networks [4, 5, 6, 7]. They also incorporate soft-computing techniques, such as fuzzy logic and ANFIS, which excel at addressing complex problems and demonstrate superior robustness with enhanced computational capabilities. Other state-of-the-art methods, such as genetic algorithms and particle swarm optimization (PSO), further enhance the model’s performance [8]. Among these techniques, ANFIS is widely used and implemented by potential investigators in various real-world applications, such as energy prediction in the building sector, control of a stepping motor drive, time-series prediction, wind-speed prediction, and membrane separation [9, 10, 11, 12, 13]. ANFIS is part of the machine learning domain, combining artificial intelligence tools such as artificial neural networks and fuzzy logic rules within an adaptive network structure. This framework establishes correlations between the study’s various thermodynamic inputs and output parameters, with explicit focus on estimating the EP. Adopting the novel toolbox [14] and its MFs are calibrated through a back-propagation or least squares approach. ANFIS is developed via the trained and learned input data structure, and its methodology, which illustrates the inputs and outputs, will be outlined in a different section of this research.
The paper addresses gaps in understanding the impact of sensitivity on network performance when reducing the number of four-input parameters (AP, AT, V, and RH) from the entire dataset (9658) to three inputs ((AP, V, and AT) and (P1, P2, and P3)). It demonstrates robust forecasting performance for the EP. Further reduction to two or a single input parameter is not considered, as the inclusion of the RH feature yielded meaningless outcomes and was therefore omitted. The novelty is that the proposed approach in the CCPP field has not been investigated or reported in the literature; thus, it makes a significant contribution to knowledge. The overfitting issues in the massive amount of data did not affect the entire network’s performance, resulting in reliable, accurate solutions. An extensive literature review of ANFIS implementation in real-world engineering applications is presented in the following section.
2. Literature review
Various machine learning techniques have been implemented in the energy sector to predict output quantities, including work done and system performance. The capabilities and qualities of the ANFIS have led in this direction and have attracted several investigators. Therefore, in the wind energy field, a novel study on output power forecasting based on turbine speed and the wind turbine’s operational characteristics, using ANFIS and multi-source data fusion within a moving window, is highlighted, resulting in better operational control [15, 16]. An integrated approach combining an ANFIS and a genetic algorithm to optimize the power output of a solar PV system via a standard control boost converter under various weather conditions is presented in [17].
Three different hybrid models, the ANFIS-PSO, ANFIS-GA, and ANFIS-DE with ANFIS, are adapted and compared for the prediction of the wind power density on a weekly and monthly basis, highlighting the advocacy of ANFIS-PSO and ANFIS-GA coupled models [18]. A prediction method for the capacity of a 60 MW PV system using the soft-computing tools ANFIS and the coupled ANFIS-PSO algorithm is proposed, demonstrating the superiority of the integrated approach. In the buildings sector, accurate forecasting of very short-term energy consumption using ANFIS that replicates energy meter measurements is identified [19, 20]. In the thermal power plant sector, an adaptation of the machine learning tool (ANFIS) demonstrated an ability to predict the failure time of its equipment, contributing to predictive maintenance planning. The ANFIS method is proposed for accurate load forecasting of energy systems, compared to other methods [21, 22].
A soft-computing model, specifically ANFIS, is used in nuclear power plants to accurately estimate turbine output and generator energy. This underscores its superiority over other established thermodynamic cycle tools in terms of reliability [23]. Novel outcomes of gas emissions and global temperature in the energy sector are demonstrated using various statistical tools, including ANFIS, artificial neural networks, and fuzzy time series models [24]. The evaluation of the Tennessee Valley Authority power station models using ANFIS improves reliability over time [25]. A hybrid model consisting of an adaptive neuro-fuzzy inference model and a genetic algorithm is compared with another hybrid artificial neural network fuzzy c-means algorithm towards the performance assessment of traditional power plants with outstanding advantages [26].
The temperature forecasting of PV systems involves six environmental variables, and the output power is also predicted using the ANFIS toolbox with different MFs, thereby ensuring robustness [27]. A novel technique for multi-carrier energy systems to fulfill power demand, coupling an ANFIS with a genetic algorithm, is also proposed. A daily global solar radiation prediction is proposed using an ANFIS that identifies essential parameters with accurate results [28, 29]. In ship technology, the coupling between the energy management systems and the intelligent system (ANFIS) that emulates the ship’s output power is also identified [30]. In the CCPP field, effective control of NOx emissions and reduction of their environmental impact are achieved through the integration of ANFIS and a genetic algorithm. Various ANFIS models (ANFIS1, ANFIS2, ANFIS3, and ANFIS4) are compared to estimate the performance of a CCPP plant, demonstrating the superiority of ANFIS4 using the existing input-space fuzzy c-means clustering method [31, 32].
An adaptation of the effective neuro-fuzzy method, coupled with a Firefly algorithm, is proposed for engine torque and emissions, accounting for fuel consumption and engine speed [33]. A reliable method of predicting the power output of a CCPP under full loading conditions, implementing a hybrid model consisting of an ANFIS model, a random forest, and a random tree method, is highlighted [34]. A regularized particle filtering toolbox, coupled with an ANFIS model of the impact of humidity on gas turbine engine performance deterioration, yielded encouraging results [35].
ANFIS adoption in the solar PV section of a maximum power point tracker to optimize a solar PV system is proposed. An innovative study on the fault detection of a rearranged PV system with high-performance, effective outcomes is provided [36, 37]. PV power forecasting using ANFIS resulted in fewer errors (6.14%) than regression analysis (16%). A comparison of the electricity performance feature between ANFIS, a time-series model, and a first-order fuzzy time series highlights ANFIS’s superiority in terms of reduced mean absolute percentage error [38, 39]. A study using short-term forecasting data with an adaptive neuro-fuzzy model in the wind energy field accurately predicted wind power [40, 41]. An application of ground vibration prediction from blasting to the structures of three power plants and dams is estimated.
The integration of ANFIS with various optimization algorithms has also been explored in power generation forecasting, particularly considering wind speed and direction. A hybrid coupling between ANFIS and a genetic algorithm optimizing NOx emissions and the dual-fuel engine’s performance is also proposed [42, 43]. In conventional thermal power plants, the coupling of ANFIS with a genetic algorithm for performance assessment and improvement is depicted. Introducing an improved hybrid model that combines ANFIS with a genetic algorithm to optimize the power extraction capability of a fuel cell-connected system achieves a performance of 98% [26]. The incorporation of hybrid algorithms with statistical techniques to meet industrial demands has also been investigated in various studies. An interesting study comparing the mean least-squares techniques with the hybrid PSO-ANFIS and ANFIS shows the superiority of the PSO-ANFIS energy demand prediction technique [44, 45].
Integration of the adaptive neuro-fuzzy inference model with an equilibrium optimizer for the efficiency prediction of a solar parabolic dish collector is also presented [46]. In the solar sector, an identical study coupling the ANFIS with a wavelet transform is investigated [47]. A hybrid singular spectrum analysis with ANFIS for wind speed forecasting is proposed, yielding outstandingly stable outcomes [48]. The prediction of solar radiation based on various meteorological data, such as monthly mean minimum and maximum temperatures, is also achieved [49]. In the wind power sector, ANFIS accurately matches the output of a regional climate model and a low-wind-potential model. Furthermore, the optimum wind power coefficient value is predicted. A hybrid singular spectrum analysis with an ANFIS model for wind speed forecasting is investigated [48, 50, 51].
Moreover, the coefficient of performance of a refrigeration system using R134a/LPG is evaluated statistically using ANFIS. A study on implementing ANFIS to predict the thermal performance and resistance of a two-phase closed thermosiphon and achieve optimal results is proposed in [52, 53]. Another survey on predicting output power for a grid-connected PV system highlights an ANFIS-based controller coupled with Taguchi’s optimization method, yielding optimal solutions [54].
In this study, ANFIS was employed to predict the electrical power of a CCPP. The dataset comprised 9568 observations from a CCPP plant in Turkey that operated over 5 years (2006–2011). As a primary parameter, electric power was predicted from several input thermodynamic variables, including AT, AP, RH, and V. The paper uses a design process of decreasing the input parameters into three parts: AT, V, and AP. The paper focuses on AT, V, and AP to streamline the input parameters. The ANFIS network was implemented in MATLAB, leveraging its graphical user interface and command-line functionality [14, 18]. Further details will be expounded upon in subsequent sections, while the following section outlines the materials and methods employed in this investigation.
Given the breadth and diversity of ANFIS-based applications reported in the literature, a structured synthesis is necessary to facilitate comparative evaluation and to highlight prevailing research directions. Therefore, the principal studies reviewed above are systematically consolidated in Table 1. The table categorizes applications by energy domain, modeling configuration (standalone ANFIS or hybridized frameworks), optimization strategy, input variables, and primary performance objectives. This consolidated presentation enables a clearer assessment of methodological trends, hybridization strategies, and forecasting performance, while underscoring the increasing adoption of ANFIS-based models as reliable tools for prediction, optimization, control, and performance enhancement across the energy sector.
| Model approach | Sector(s) | Main applications | Key findings |
|---|---|---|---|
| ANFIS (standalone) | Wind power Solar power Nuclear power Thermal power Refrigeration Ship energy Buildings | Power forecasting Load prediction Turbine output estimation Radiation prediction COP evaluation Environmental and emissions Modeling | High prediction accuracy Reliability improvement Reduced forecasting errors |
| ANFIS + GA | Buildings | Power optimization NOx control Performance enhancement | Optimization improvement Maximum performance |
| ANFIS + PSO | Wind energy Energy demand | Wind power density Demand forecasting | Superior accuracy |
| ANFIS + DE | Wind energy | Wind power density Prediction | Improved convergence |
| ANFIS + Firefly | Engine systems | Torque and emissions modeling | Enhanced fuel and emission prediction |
| ANFIS + RF / RT | CCPP | Full-load power output prediction | Reliable hybrid forecasting |
| ANFIS + Particle Filtering | Gas turbines | Humidity-related performance deterioration | High predictive capability |
| ANFIS + Taguchi | Grid-connected PV | Controller optimization | Optimal parameter tuning |
| ANFIS + EO / WT / SSA | Solar and wind | Efficiency and wind speed forecasting | Stable High-precision outcomes |
Table 1.
3. Layout and dataset description
A CCPP integrates two thermodynamic cycles, the Brayton cycle (gas turbine) and the Rankine cycle (steam turbine), to enhance overall energy conversion efficiency. The plant primarily consists of a gas turbine unit, a heat recovery steam generator (HRSG), and a steam turbine generator.
In the first stage, compressed air is mixed with fuel and combusted within the gas turbine combustor. The high-temperature, high-pressure combustion gases expand through the turbine blades, producing mechanical work that drives an electrical generator. However, a significant portion of thermal energy remains in the turbine exhaust gases, typically at temperatures between 450 and 600°C. Instead of being released directly into the atmosphere, these exhaust gases are directed to the HRSG, where their residual heat is recovered through a series of heat exchangers (economizer, evaporator, and superheater sections). This process generates high-pressure steam without additional fuel consumption. The produced steam is then expanded in a steam turbine connected to a second electrical generator, thereby generating additional power. By recovering and utilizing waste heat from the gas turbine, the CCPP achieves substantially higher overall thermal efficiency—typically exceeding 55–60%—compared to single-cycle gas turbine plants, which generally operate at 33–40%. This dual-cycle configuration enables improved fuel utilization, reduced specific fuel consumption, and lower emissions per unit of generated electricity.
Figure 1 presents a simplified schematic illustrating the integrated operation of the gas turbine, HRSG, and steam turbine subsystems within the combined-cycle configuration.
Figure 1.
Combined cycle power plant diagram [4].
The performance of the CCPP under full working conditions depends on various thermodynamic design variables, such as AT, AP, RH, and exhaust steam pressure; however, the present study’s sensitivity analysis demonstrated that RH did not significantly improve predictive accuracy and was therefore excluded from the final reduced-order model [55, 56, 57]. The CCPP dataset consists of time-series data collected from a gas-fired power plant with a capacity of 420 MW over 6 years, from 2006 to 2011. This dataset contains 9568 samples of hourly measurements of various parameters, such as AT, AP, V, and RH, as well as the net hourly predicted electrical energy output. The original dataset comprised 674 daily datasheets in .
| Group parameter | Symbol | Type | MATLABNotation |
|---|---|---|---|
| Ambient temperature | AT | Input | P1 |
| Exhaust vacuum | V | Input | P2 |
| Ambient pressure | AP | Input | P3 |
| Three input parameters | AT, V, AP | Input | P1 + P2 + P3 |
Table 2.
Features of the three input independent variables (P1, P2, P3).
The prediction of electrical power output (EP) is performed using ANFIS, a hybrid soft-computing technique that combines the learning capabilities of artificial neural networks with the linguistic reasoning of fuzzy logic. ANFIS has demonstrated strong predictive performance across numerous real-world engineering applications, thanks to its ability to model complex nonlinear relationships while maintaining interpretability through rule-based structures.
In the proposed framework, the selected input variables are mapped to the output variable (EP) through a structured fuzzy rule base. Membership functions are assigned to each input variable to define fuzzy sets, which map crisp numerical input values to degrees of membership ranging from 0 to 1. This fuzzification process allows the system to represent gradual transitions between operating conditions rather than relying on binary true/false logic, as in classical Boolean systems. The inference mechanism evaluates a set of IF-THEN rules that capture the nonlinear interactions between the input variables and the output power. Through this rule-based structure, the system aggregates the contributions of different operating regions and generates a unified output response.
There are two principal types of fuzzy inference systems: Mamdani and Sugeno. The primary distinction lies in the formulation of the output function. In Mamdani systems, the output is expressed as a fuzzy set, requiring a separate defuzzification stage. In contrast, Sugeno-type systems define the output as either a constant (zero-order Sugeno model) or a linear combination of the input variables (first-order Sugeno model). Due to its computational efficiency and suitability for parameter optimization, the first-order Sugeno model is adopted in this study. The ANFIS training procedure employs a hybrid learning algorithm that combines least-squares estimation (to optimize the consequent parameters) with gradient descent (to update the premise parameters). This approach minimizes prediction error between the estimated and actual outputs while ensuring stable convergence.
The detailed ANFIS design methodology for the reduced three-input dataset (AT, V, and AP) is presented in the following section.
4. Methodology
The architecture of the ANFIS model employed in this study consists of three input variables – ambient temperature (AT), exhaust vacuum (V), and ambient pressure (AP) – denoted as
Figure 2.
ANFIS sample geometry with three input parameters and five layers [4].
Figure 3.
Block diagram of ANFIS toolbox [6].
In this study, ANFIS is applied to predict the electrical power output (EP) of a CCPP. The dataset comprises 9568 observations collected from a combined gas power plant in Turkey over 5 years (2006–2011). The EP, the primary output variable, is initially examined against several thermodynamic input parameters, including ambient temperature (AT), ambient pressure (AP), relative humidity (RH), and exhaust vacuum (V); however, the final reduced-order ANFIS model employs only AT, V, and AP as input variables. To streamline the model, the analysis focuses on three input variables, AT, V, and AP. The ANFIS network is implemented in MATLAB using both the graphical user interface and command-line functionalities [18, 19]. Further methodological details are provided in subsequent sections, while the following section describes the materials and methods employed in this investigation.
5. Results
The application of reducing the initial dataset from four input parameters (AT, V, AP, and RH) to three (AT, V, and AP) for predicting the output parameter (EP) was investigated, yielding the following outcomes. Figures 4 and 5 illustrate the checking data after loading 30% and 70% of the entire training dataset into the toolbox, respectively, before commencing training, with each design variable configured to have three MFs.
Figure 4.
Checking of the 30% of the entire dataset.
Figure 5.
Training of the 70% of the entire dataset.
The fuzzy inference system (FIS) constructed for the reduced three-input configuration (AT, V, and AP) is illustrated in Figure 6. This figure presents the complete rule-based architecture of the ANFIS model, showing how the three input variables are connected to the output variable (EP) through a structured set of IF-THEN fuzzy rules. It visually represents the mapping mechanism between the input space and the predicted electrical power output.
Figure 6.
Fuzzy inference system with three input variables (P1 + P2 + P3).
Figure 7 depicts the initial triangular membership functions (trimf) assigned to each of the three input variables prior to the training process. These membership functions partition the input space into fuzzy regions and define the degree to which each input value belongs to a specific linguistic category (e.g., low, medium, and high). They establish the initial fuzzification boundaries and serve as the initial parameter set, which is subsequently adjusted during the ANFIS training procedure to minimize prediction error.
Figure 7.
Triangular MFs (trimfs) of three input parameters (P1 + P2 + P3)).
Triangular membership functions (MFs) are employed in the fuzzification stage for the three input parameters, defined by the parameters.
Figure 8.
Network structure of the training process interaction between the five layers.
Figure 9 presents the RMSE trends obtained during the training and testing phases of the ANFIS model. The results demonstrate stable, acceptable convergence, as evidenced by a continuous reduction in RMSE with increasing iterations. After 100 training epochs, the RMSE for the training dataset decreases to 4.13995, while the RMSE for the testing dataset reaches 4.09731. The close agreement between the training and testing errors indicates good generalization capability of the proposed ANFIS model and suggests that overfitting is effectively minimized.
Figure 9.
Convergence error (RMSE) history of the training (*) and the checking data (+).
Figures 10 and 11 illustrate the performance of the trained fuzzy inference system during testing on both the training and test datasets. The results demonstrate an agreement between the predicted and actual output values across the entire dataset, indicating a high-quality model fit. The close alignment observed in these figures confirms the robustness of the ANFIS model, its strong predictive capability, and its effectiveness in capturing the underlying nonlinear relationships between the input variables and the output power (EP).
Figure 10.
Testing of the training data of the fuzzy interference system model with three design variables.
Figure 11.
Testing of the checking data of the fuzzy interference system model with three design variables.
Figure 12 presents a representative view of the ANFIS rules editor, illustrating the structure of the fuzzy rule base used in the proposed model. The figure highlights the IF–THEN logic applied to each of the three input design variables and the corresponding output variable across the complete set of 27 fuzzy rules. Each rule defines a specific combination of input membership functions and their associated consequent parameters, collectively forming the decision-making framework of the fuzzy inference system. This rule configuration enables the model to effectively capture the complex interactions between the input variables and the electrical power output (EP).
Figure 12.
Rule’s editor with the 27 cases of the IF and THEN options between the input and the output variable.
Figure 13 presents the rule viewer corresponding to the full set of 27 fuzzy IF–THEN rules implemented in the reduced three-input ANFIS model. The rule viewer provides a dynamic visualization of how the three input variables, ambient temperature (AT), exhaust vacuum (V), and ambient pressure (AP), are partitioned into their respective membership functions and how these fuzzy regions interact within the inference mechanism.
Figure 13.
Rule structure of the ANFIS model with three inputs and one output.
Each input variable is associated with three membership functions, resulting in
The graphical interface allows visualization of the rule-firing levels and the corresponding output surface in real time, thereby clarifying how the nonlinear relationships among the inputs are captured. It demonstrates how the weighted contributions of all activated rules are combined to generate the predicted electrical power output (EP). This visualization confirms that the model effectively integrates the interactions among AT, V, and AP, highlighting the collective influence of environmental and operational conditions on plant performance.
Figures 14–16 present the three-dimensional surface response plots generated by the trained ANFIS model, showing how the electrical power output (EP) varies with pairwise combinations of the three input variables. Each surface plot shows the predicted EP as two input variables vary within their operational ranges, with the third input held constant at its nominal or mean value.
Figure 14.
Surface response prediction of the EP vs. AT (P1) and V (P2) design variables.
Figure 15.
Surface response prediction of the EP vs. AT (P1) and AP (P3) design variables.
Figure 16.
Surface response prediction of the EP vs. V (P2) and AP (P3) design variables.
Specifically, Figure 14 depicts the relationship between ambient temperature (AT) and exhaust vacuum (V) on EP, Figure 15 illustrates the combined effect of ambient temperature (AT) and ambient pressure (AP), and Figure 16 shows the interaction between exhaust vacuum (V) and ambient pressure (AP). These surfaces provide a continuous visualization of the nonlinear relationship between power output and environmental and operational conditions.
The color gradients on the surfaces represent the magnitude of the predicted electrical power output. Warmer colors (green to yellow regions) correspond to higher predicted EP values, indicating more favorable operating conditions, whereas cooler tones represent lower power output levels. The distribution of these color regions highlights the operating domains where optimal power generation is achieved under different combinations of AT, V, and AP.
The validation process of the adaptive neuro-fuzzy logic toolbox is marked by its successful handling of the reduced three-input parameters, showcasing its robustness. The performance measure for this network is the RMSE across nine different MFs applied to the three input design variables. The generalized bell-shaped MFs (
| MFs | Types of MFs | Training | Checking |
|---|---|---|---|
| Error | Error | ||
| 3–3-3 | trimf | 4.1399 | 4.0971 |
| trapmf | 4.1573 | 4.1072 | |
| gbellmf | 4.0926 | 4.0481 | |
| gaussmf | 4.1013 | 4.0631 | |
| gauss2mf | 4.1331 | 4.0716 | |
| pimf | 4.1913 | 4.1371 | |
| dsigmf | 4.1059 | 4.0554 | |
| psigmf | 4.1061 | 4.0555 |
Table 3.
Training and checking data error (RMSE) for three input variables for different MFs calculation.
6. Discussion
The results demonstrate that accurate prediction of electrical power output in CCPPs can be achieved using a reduced-order ANFIS architecture without sacrificing predictive reliability. By limiting the input space to three thermodynamic variables, ambient temperature, exhaust vacuum, and ambient pressure, the proposed model preserves strong generalization capability while significantly reducing model complexity. This finding is particularly relevant for real-world power plant applications, where excessive input dimensionality often leads to higher computational costs, reduced interpretability, and increased susceptibility to overfitting.
The convergence behavior observed during training and validation confirms the robustness of the hybrid learning strategy. The proximity of the training and validation RMSE values (4.0926 and 4.0481 MW, respectively) indicates that the model effectively captures the nonlinear relationships between the selected environmental parameters and power output while avoiding overfitting to the training data. This behavior contrasts with many high-capacity machine learning models, such as deep neural networks, which typically require extensive regularization and large datasets to achieve similar generalization performance.
The comparative analysis of MF types reveals that generalized bell-shaped membership functions (
The observed RMSE reduction, although numerically modest, is significant from an operational perspective, as even minor improvements in prediction accuracy can translate into better dispatch planning and more efficient plant-level optimization. Although the achieved RMSE values (4.0926 MW for training and 4.0481 MW for testing) may appear numerically small relative to the plant’s nominal capacity of 420 MW, their operational implications are substantial. The prediction deviation is approximately 0.96% of the rated capacity, indicating that the proposed reduced-order ANFIS model forecasts electrical output with near 1% accuracy.
Assuming an annual operating duration of 7500 hours, a 420 MW combined-cycle power plant produces approximately 3.15 TWh of electricity per year. A conservative 0.5% improvement in dispatch optimization enabled by enhanced forecasting accuracy corresponds to nearly 15,750 MWh of optimized energy management annually. At a representative wholesale electricity value of 60 USD/MWh, this translates to an estimated economic impact approaching 0.9–1.0 million USD per year. These savings may arise from improved fuel scheduling, reduced imbalance penalties, and optimized reserve allocation.
In addition to economic gains, the reduced-input ANFIS structure lowers computational complexity by limiting the rule base to 27 fuzzy rules, representing a 66% reduction compared with a four-input configuration employing equivalent membership functions. This reduction enhances real-time applicability, decreases retraining time, and facilitates integration into supervisory control and decision-support systems. Furthermore, improved predictive stability contributes to better management of thermal stresses across varying ambient temperatures, potentially extending turbine component life and reducing maintenance frequency.
The three-dimensional surface response analyses provide additional physical insight into the model’s behavior. The results confirm that ambient temperature exerts a more substantial influence on electrical power output, consistent with established thermodynamic theory regarding gas turbine inlet conditions. Increased ambient temperature reduces air density and mass flow rate, thereby decreasing power output. Exhaust vacuum and ambient pressure also exhibit clear nonlinear interactions with power output, reinforcing the necessity of nonlinear modeling approaches such as ANFIS. The reduced-order ANFIS model’s ability to reproduce these physically meaningful trends enhances confidence in its applicability beyond purely data-driven fitting.
Compared with existing ANFIS-based CCPP studies reported in the literature, the present work achieves comparable or superior prediction accuracy with fewer input parameters and without relying on external optimization algorithms, such as genetic algorithms or particle swarm optimization. While hybrid optimization techniques can marginally improve accuracy, they often introduce substantial computational overhead and reduce transparency. The proposed approach demonstrates that careful input selection and MF tuning can yield competitive performance with a simpler, more interpretable model structure.
From a practical standpoint, the reduced-order ANFIS framework offers several advantages for deployment in operational environments. The limited number of inputs simplifies sensor requirements and data acquisition, while the compact rule base facilitates real-time implementation and maintenance. Furthermore, the transparent rule-based structure of ANFIS enables plant operators to interpret model behavior and relate predictions to underlying physical conditions, an advantage over black-box learning models.
Overall, the discussion highlights that reduced-input ANFIS models are not merely computationally efficient alternatives but robust predictive tools capable of delivering physically consistent and operationally valuable insights for combined-cycle power plant performance analysis.
7. Conclusion
This study developed and validated a reduced-order ANFIS-based modeling framework for predicting the electrical power output of a combined cycle power plant using a minimal set of thermodynamic inputs. By restricting the input space to ambient temperature, exhaust vacuum, and ambient pressure, the proposed model maintains high predictive accuracy while significantly reducing model complexity. A hybrid learning strategy combining least-squares estimation and gradient descent was employed within a first-order Sugeno fuzzy inference structure. Extensive parametric analysis demonstrated that three membership functions per input variable provide the best trade-off between accuracy and computational efficiency. Among the nine tested membership function types, the generalized bell-shaped membership function consistently outperformed the alternatives, yielding RMSE values of 4.0926 MW for the training data and 4.0481 MW for the unseen validation data. The slight discrepancy between training and test errors confirms strong generalization and indicates that overfitting is effectively avoided, even with a reduced input set. The three-dimensional response surfaces further reveal physically consistent relationships between environmental conditions and power output, highlighting the dominant influence of ambient temperature and exhaust vacuum on CCPP performance. These findings reinforce the suitability of ANFIS as an interpretable and reliable surrogate model for nonlinear thermodynamic systems. In contrast to many existing studies that rely on high-dimensional inputs or computationally intensive hybrid optimization schemes, the proposed reduced-order ANFIS framework achieves comparable accuracy with lower computational cost and improved transparency. This makes the approach particularly attractive for real-time performance monitoring, operational optimization, and decision-support systems in thermal power plants. Future work will extend the present analysis by investigating two-parameter input combinations and aggregated feature representations, and by benchmarking the reduced-order ANFIS model against deep learning architectures under identical data and operating conditions.
Conflict of interest
The authors declare that they have no conflicts of interest, whereas no scientific funding is involved.
Data availability
Data availability does not apply to this article as no new data were created or analyzed in this study.
Use of artificial intelligence (AI)
The authors declare that the generative artificial intelligence (AI) tool
Nomenclature
adaptive neuro-fuzzy inference system | |
combined-cycle power plants | |
differential evolution | |
genetic algorithm | |
graphical user interface | |
heat recovery steam generator | |
liquefied petroleum gas | |
least square error | |
membership function | |
particle swarm optimization | |
photovoltaic | |
root mean square error | |
ambient pressure | |
ambient temperature | |
electric power | |
input for ambient temperature | |
input for exhaust vacuum | |
input for ambient pressure | |
relative humidity | |
exhaust vacuum |
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