Implementation and Possibilities of Fuzzy Logic for Optimal Operation and Maintenance of Marine Diesel Engines

: This paper explores the implementation and possibilities of utilizing fuzzy logic theory for optimal operation and early fault detection in marine diesel engines. It emphasizes its role in managing the complexity and ambiguity inherent in engine performance and preventive maintenance. Preventive maintenance is crucial for ensuring the reliability and longevity of marine diesel engines. Implementing fuzzy logic control (FLC) systems can enhance the preventive maintenance strategies for these engines, leading to reduced downtime, lower maintenance costs, and improved overall performance. Through a comprehensive literature review and analysis of a case study, this paper demonstrates the adaptability, effectiveness, and transformative potential of fuzzy logic systems. Focusing on applications such as engine speed control, performance improvements, and early fault detection, the paper highlights the implementation of fuzzy logic for enhanced predictive capabilities. The study aims to offer a flexible approach to engine management through fuzzy logic, laying the way for significant improvement in optimal marine diesel engine operation.


Introduction
Fuzzy logic theory is a sophisticated approach to handling the complexity and ambiguity that often exists in real-case situations.Unlike traditional systems that rely on binary logic (true or false, on or off), fuzzy logic introduces gradations and nuances, making it more similar to human reasoning.This approach is especially useful in systems where the processes or the relations between variables are not precisely known or are too complex for conventional strategies, such as marine diesel engines.The primary advantages of the fuzzy logic system include simplicity and more straightforward system design and development, reduced operational and maintenance costs, and enhanced ease of maintenance.
There is a lot of diversity in the literature addressing the implementation and possibilities of fuzzy logic theory for diesel engine applications.
Tran et al. discussed a fuzzy diesel engine speed controller [1].This system contains decision-making logic that appropriately uses "if" and "then" rules to decide the main diesel engine speed.The results clarified the advantages of the fuzzy logic control method in determining the stability of marine diesel engine speed.The results also show that each marine diesel engine's operation condition will respond to a specific speed position.The proposed method is very convenient and valuable for users since it does not need to establish the mathematical algorithm precisely compared to other methods.The controller platform was carried out for specific diesel engines with the speed setting value as the reference input signal to evaluate this fuzzy diesel engine speed controller.The marine diesel engine of MAN B&W 7S 80MC-C with seven cylinders was used in the research.This diesel engine was installed on a bulk carrier by a VINIC shipping transportation company in Vietnam.In order to validate the diesel engine speed controller appropriately using the fuzzy logic theory method, a comparison between this model and the diesel engine speed controller using the PID elements (proportional, integral, derivate) control theory method is needed.Furthermore, the diesel engine speed controller using the fuzzy logic control theory method seems more stable than the PID theory control method [1].
Nguyen detailed an overview paper about fuzzy control systems (past, present, and future) [2].The study demonstrates the key features of the three types of fuzzy systems.First, if-then rules associated with linguistic variables define Mamdani's fuzzy systems [2][3][4].Second, Takagi-Sugeno's fuzzy systems (T-S) are determined by functional consequences [2].Third, Singleton fuzzy systems, or piecewise multi-affine (PMA) systems, are a special case of both previous types [2].Nguyen mentioned that Mamdani performed the first application of fuzzy logic control on a laboratory steam engine, which significantly impacted the fuzzy control research.All three types of fuzzy systems are known to have general approximation capability for any nonlinear functions [2].
Sakthivel et al. described the principal application of fuzzy logic for predicting an internal combustion engine's performance [3].The experimental study was conducted on a single-cylinder, constant-speed, direct-injection diesel engine operating under varying load conditions.
The performance characteristics that were considered include combustion and emissions characteristics such as thermal efficiency, exhaust gas temperature, ignition delay, and combustion delay.The collected data were used to develop a multiple inputs and multiple outputs fuzzy logic model.The model presented was created using the graphical user interface of the FIS (fuzzy inference system) editor in the fuzzy logic toolbox and integrated into the LabVIEW ® V11.0 framework [3].

Year
Authors Fuzzy Logic-Based Application Engin, O. et al. [8] Engine valve manufacturing process Ghaffari, A. et al. [9] Fuzzy control system to examine the air-fuel ratio of the spark ignition engine García-Nieto, S. et al. [10] Fuzzy controller for air management in diesel engines Kekez, M. and Radziszewski, L. [11] Measurement and modeling of cylinder pressure in diesel engines Piltan, F. et al. [13] Fuzzy estimator variable structure control Rai, A. et al. [15] Prediction of performance and emissions parameters of an LPG diesel dual-fuel engine Namitha, S. and Shantharama, R. [16] Speed control of the IC engine Sakthivel, G. et al. [3] Predicting the internal combustion engine's performance Cheng, L. et al. [17] Optimizing the performance and emissions of diesel engines Tran, T. A. et al. [1] Speed controller by fuzzy logic control theory Nguyen, A.T. et al. [2] Fuzzy control systems Ceylan, B. [4] Risk assessment of turbocharger fouling using the fuzzy FMEA method Yucesan, M. et al. [6] Evaluation of ship diesel generator failures using fuzzy logic Ceylan, B. [7] Risk analysis of shipboard compressor systems using fuzzy FMEA Tran, T. A. [12] Effect of ship loading on fuel consumption using fuzzy clustering Babichev, S. et al. [5] Fuzzy inference model for the management of a marine engine Gaonkar, R.S. et al. [14] Fuzzy failure mode for the air system of a marine diesel engine Tavana et al. [18] offered a practical and comprehensive review of the methods and applications of fuzzy expert systems.The primary objective of fuzzy expert systems is to utilize human knowledge to process uncertain and ambiguous data.This paper's two interesting points are the most common applications for fuzzy expert systems and the most common tools to create these systems.
First, the most common use of fuzzy expert systems is in the medical field, at 21%, and then in the field of fault diagnosis, at 7%.The remaining fields vary for control systems, performance evaluation, risk prediction, and power load forecasting.
Second, the most frequently used tools to design fuzzy expert systems are Matlab, Java, and Visual Studio [18].MATLAB has been widely adopted for this purpose, starting with MATLAB R13, which introduced the early version of the Fuzzy Logic Toolbox, and continuing to the latest version, MATLAB R2024a.Java has also been a popular choice, beginning with Java SE 6, the earliest version supporting fuzzy logic libraries, and extending to Java SE 17.Similarly, Visual Studio has been a key tool, starting with Visual Studio 2008 following the introduction of LINQ, which is useful for data handling in fuzzy logic systems, and progressing to Visual Studio 2022.Matlab's and Java's popularity can be linked to their fuzzy logic toolbox and efficient and straightforward end-user interface.In addition to this information, the new fuzzy expert package in Python 3.9 for building Mamdani fuzzy inference systems offers advantages in terms of flexibility, ease of use, adaptability to mixed data types, and the ability to provide clear and interpretable results, particularly in the context of Mamdani Fuzzy Inference Systems.
Cheng et al. proposed a novel fuzzy logic control system to determine the appropriate positions of the variable geometry turbocharger vanes and exhaust gas recirculation valves in real time [17].The proposed fuzzy logic control system improved the turbocharger efficiency, while NOx and emissions were significantly reduced.The fuzzy logic control strategy determines the positions of the VGT (variable geometry turbocharger) vanes and EGR (exhaust gas recirculation) valve in real-time to optimize the engine's efficiency and emissions output.Unlike conventional control systems that rely on predefined set points, the fuzzy logic controller adapts to changing engine conditions in real time, providing more dynamic and responsive control.The authors developed a Sugeno-type fuzzy logic controller with rules based on understanding interactions among VGT, EGR, and engine dynamics.Control rules are derived for adjusting VGT vanes and EGR valve positions in real time considering engine speed, load, inlet pressure, opacity (smoke levels), NOx emissions, and EGR position [17].
Markiewicz et al. used fuzzy logic techniques to predict combustion engines' performance and emissions parameters powered by diesel oil and fatty acid methyl esters [19].The study cases were motor vehicles equipped with an 81 kW self-ignition engine and a common rail injection system.The unique aspect of this research is the application of fuzzy logic techniques to assess the performance and emissions of diesel engines using these alternative fuels.This approach provides a more nuanced and comprehensive analysis compared to traditional methods.The study is divided into initial tests (analyzing physical-chemical characteristics of fuel mixtures) and main tests (measuring performance parameters of the engines).The part that is related to our investigation is the main test, which involves measuring ten performance parameters of the engines, including power, torque, noise emissions, solid particle content in exhaust, and composition of exhaust gases (like oxygen, carbon monoxide, hydrocarbons, nitric oxides, and air excess coefficient).The model is verified using fuzzy logic, which allows for a more flexible and realistic interpretation of data, considering the variability and uncertainty inherent in realworld engine performance.The study specifically assesses how different compositions of fuel mixtures impact various performance criteria, including oxygen and carbon dioxide emissions, as well as particulate emissions, with a specific focus on the applications of fuzzy logic techniques [19].
Berber et al. investigated the characteristics of a four-stroke internal combustion diesel engine using artificial neural networks (ANNs) and adaptive neuro-fuzzy inference system (ANFIS) modeling techniques [20].The research introduces ANNs and ANFIS as alternative modeling approaches to predict diesel engine performance parameters, aiming to reduce the cost and number of experiments.The authors found that both ANN and ANFIS models effectively predicted diesel engine performance, with the ANFIS model performing slightly better.According to the results, the fuzzy logic approach had more predictive ability than ANN.The results demonstrate the close correlation between computational models and experimental data, suggesting a strong potential for these techniques to become industry standards [20].
Xia et al. explored optimizing a diesel engine's performance at high altitudes using a multi-parameter fuzzy optimization approach [21].The research focuses on adjusting fuel injection mass, fuel injection advance angle, and bypass valve opening of a high-pressure turbine to enhance engine performance, considering diesel engines' nonlinear and complex nature.The optimization method proposed is based on a fuzzy logic controller and is applied in a Matlab/Simulink R2014a environment.The research findings indicate significant engine torque, power improvements, and reductions in brake-specific fuel consumption (BSFC) at high altitudes.High altitude presents unique challenges for diesel engines, and the research addresses the need for improved engine performance in such conditions.The simulation results show that all performance values improved when the fuzzy logic optimization method was implemented.At the full load point of 2100 r/min, engine power increased from 256.6 to 319.6 kW, and BSFC decreased from 243.1 to 222.3 g/(kWh).Maximum torque also increased from 1944.8 to 2173.2 Nm [21].
In recent years, several advanced control methods have been developed to address the challenges associated with high-order uncertain nonlinear systems, which are relevant to the performance optimization of marine diesel engines.Among these methods, multilayer neurocontrol and asymptotic tracking with integral robust schemes have gained significant attention.
Multilayer neurocontrol, which employs neural network-based strategies, is effective in managing high-order nonlinear systems with active disturbance rejection.This method can dynamically adapt to uncertainties and disturbances in the system, ensuring robust performance.Similarly, asymptotic tracking with novel integral robust schemes provides precise control for mismatched uncertain nonlinear systems.These schemes are designed to handle discrepancies between the model and the actual system, ensuring reliable tracking and performance optimization [22,23].
Based on the synthesis of the literature, the following facts can be concluded: 1. Fuzzy logic is highly adaptable and effective in handling the complexity and ambiguity of diesel engine systems.2. Fuzzy logic in marine diesel engines could extend beyond diagnostics to include performance improvements, offering a dual-purpose tool for engine management.3. Various studies have demonstrated the effectiveness of fuzzy logic in real-world applications, including engine speed control, performance prediction, and emissions management.4.There is a growing trend towards integrating fuzzy logic with other computational techniques like ANNs and ANFIS for enhanced predictive capabilities.5. Fuzzy logic provides a more nuanced and flexible approach than traditional binary systems, making it particularly suitable for marine diesel engine operations' dynamic and complex nature.
The literature demonstrates fuzzy logic's potential as a transformative tool in marine diesel engine diagnostics and performance enhancements.Its ability to handle complexity and uncertainty, combined with its adaptability for various applications, positions it as a valuable asset in the field of marine engineering.
This article aims to investigate and illustrate the potential of fuzzy logic theory in enhancing the management and performance of marine diesel engines using engine performance curves.This also includes examining its role in managing engine speed, performance optimization, and emissions control.The article aims to demonstrate how fuzzy logic can address the inherent complexity and ambiguity of engine operation.It is a pivotal technology for improving efficiency and reliability in marine diesel engine applications.
The structure of the article is organized into four main sections.Following the introduction and the literature review in Section 1, we illustrate the adjustable and non-adjustable parameters in marine diesel engines in Section 2. After that, Section 3 presents an overview of the investigated case study.The discussion of fuzzy logic implementation is in Section 4.Then, Section 5 presents the paper's findings and conclusions.
The article's main research contribution is a demonstration of how fuzzy logic can be utilized to enhance the management and performance of marine diesel engines.It provides an extensive demonstration of how fuzzy logic can significantly improve the control systems of marine diesel engines.It addresses the complexity and variability inherent in the operational environments of these engines.The primary objectives of this study are to explore the application of fuzzy logic in optimizing marine diesel engine performance by managing key parameters such as fuel injection timing, air-to-fuel ratio (AFR), exhaust gas recirculation (EGR) rate, and turbocharger boost pressure.This involves developing a conceptual framework for a Mamdani-type fuzzy logic controller (FLC) tailored for marine diesel engines, detailing the fuzzy sets, membership functions, and rules.The study aims to theoretically evaluate the expected improvements in engine performance.Additionally, it identifies research gaps and proposes a structured approach for future experimental validation to quantify the benefits of FLC in real-world marine engineering scenarios.

Adjustable and Non-Adjustable Parameters in Marine Diesel Engines
In marine diesel engines, adjustable parameters typically include fuel injection timing, fuel pressure, air intake temperature, turbocharger boost pressure, and exhaust gas recirculation rates.These parameters can be tuned to adjust the engine's performance, efficiency, and emissions output.
Non-adjustable parameters are inherent to the engine's design and cannot be changed once the engine is built.These include the engine bore and stroke, compression ratio, piston displacement, and fixed geometry of the engine's airways and structure.These parameters are set during the design and manufacturing process and define the fundamental characteristics and capabilities of the engine.
Adjustable parameters can be modified in marine diesel engines to enhance performance.These include: 1. Fuel Injection Timing/Quantity: Adjusting the timing or quantity of fuel injection is crucial for optimizing combustion efficiency and emissions.Precise control over when and how much fuel is injected into the engine allows for better combustion management, directly impacting engine performance and environmental compliance.2. Fuel Injection Rate: This parameter determines the rate at which fuel is delivered to the combustion chamber.Modifying the fuel injection rate influences the atomization and mixing of the fuel with air, essential for efficient combustion and power output.3. Air-to-Fuel Ratio (AFR): Managing the ratio of air to fuel is vital for optimal engine performance.Adjusting the AFR can enhance combustion efficiency and reduce emissions.A well-balanced AFR ensures enough air is available for complete fuel combustion, maximizing efficiency and reducing harmful emissions.4. EGR Rate: The exhaust gas recirculation (EGR) rate affects how much exhaust gas is reintroduced into the engine.Adjusting the EGR rate can help control nitrogen oxide emissions but may also impact overall engine efficiency.This trade-off is crucial for meeting environmental standards while maintaining engine performance.5. Turbocharger Boost Pressure: This parameter adjusts the pressure of air the turbocharger compresses before entering the engine.Changing the turbocharger boost pressure can significantly affect the engine's power output and efficiency by altering the density of the intake air.
While these are the primary adjustable parameters focused on for the FLC inputs, we would like to highlight that marine diesel engines have other adjustable factors.However, for the purposes of our fuzzy logic implementation, these specific parameters re selected due to their direct impact on optimizing engine performance and emissions.
Non-adjustable parameters, typically fixed in design, include: 1. Engine Bore and Stroke: the cylinders' diameter and the pistons' travel distance.
2. Compression Ratio: the ratio of the volume inside the cylinder when the piston is at the bottom of its stroke compared to when it is at the top.3. Piston Displacement: the total volume displaced by the pistons within an engine's cylinders, commonly known as the engine displacement.
While non-adjustable parameters set the fundamental capabilities and limitations of the engine, adjustable parameters can be fine-tuned using a fuzzy logic system to enhance the engine's performance under varying operating conditions.By implementing a fuzzy system, we could achieve a more adaptive and responsive engine control strategy, leveraging the adjustable parameters to compensate for the limitations created by the non-adjustable ones.

Predictive Maintenance Using Fuzzy Logic
Predictive maintenance involves forecasting and addressing potential failures before they occur [24].Fuzzy logic, which can handle imprecise and uncertain data, is well-suited for predictive maintenance applications.The FLC system can analyze real-time data from various sensors and predict the likelihood of component failures based on trends and patterns [24].FLC can also optimize preventive maintenance schedules by considering multiple operational parameters and their interactions.Traditional maintenance schedules are often based on fixed intervals, which may not reflect the actual condition of the engine.In contrast, FLC-based scheduling is dynamic and adapts to the real-time state of the engine [24][25][26][27].
The integration of fuzzy logic control systems into marine diesel engines can significantly enhance preventive maintenance strategies.Utilizing real-time data and continuous simulation allows for the proactive prediction and addressing of potential failures [27].This approach not only reduces downtime and maintenance costs but also improves the overall reliability and performance of the engines.The importance of adaptive maintenance scheduling based on actual engine conditions rather than fixed intervals ensures that maintenance activities are performed precisely when needed, optimizing engine performance and longevity.Additionally, the approach significantly reduces maintenance costs by focusing on actual needs and preventing unnecessary interventions.Regular and timely maintenance, driven by accurate data analysis through FLC, also enhances engine performance.It ensures that the engine operates at optimal levels, which helps in reducing fuel consumption and minimizing emissions.Moreover, FLC-driven preventive maintenance increases engine reliability by proactively identifying and addressing potential issues before they develop into significant failures, extending the engine's operational lifespan and enhancing its overall reliability.

The Investigated Marine Diesel Engine
In this section, we will present an overview of the case study.In general, marine diesel engine technology advancements have continually pushed the boundaries of innovation and efficiency in the maritime industry.These advancements have significantly impacted the sector by offering more reliable, efficient, and environmentally friendly propulsion solutions.The investigated engine represents an example of an engine technology.The new industries' commitments to reducing fuel consumption and emissions aligns with global efforts toward environmental sustainability.The versatility and reliability of the engine make it an ideal choice for a wide range of marine applications, from leisure crafts to commercial vessels, emphasizing their contribution to enhancing maritime operations.
Table 2 summarizes the key specifications of a high-performance marine diesel engine, showcasing its robust 324 kW rated output at 3300 rpm, optimized for marine applications.The engine features a 5.813 L displacement across six cylinders, ensuring efficient fuel combustion through direct injection.It has a turbocharged and intercooled aspiration system for durability and performance.Notably, the overall dimensions are 1440 mm in length, 748.5 mm in width, and 773.8 mm in height.Electronic controls enhance operational precision, while compliance with RCD 2, IMO Tier 2, EPA Tier 3 and 3C, BSO II, EMC, and SOLAS certifications confirms its adherence to strict environmental and safety standards.This combination of advanced features and certifications makes it an excellent choice for marine vessels requiring high power, reliability, and environmental compliance.Table 2. Technical specifications for the investigated marine diesel engine [28].This engine is considered a high-performance marine diesel engine.The performance curves would illustrate its efficiency, power output, fuel consumption, and other vital metrics under these or similar conditions.These curves are crucial for vessel designers, operators, and engineers to understand how the engine will perform in real-world situations and select the appropriate engine model for their needs.

Fuzzy Logic Control for Performance Monitoring of the Investigated Marine Diesel Engine
For the purpose of implementing our perspective to develop a fuzzy controller, we would like to start by incorporating the performance curves of the engine into a fuzzy logic control system, which involves using these curves as a reference to define the system's rules and membership functions.The goal is to optimize engine performance, fuel efficiency, and emissions by dynamically adjusting control parameters based on the engine's operating conditions.To integrate our findings into a fuzzy system for enhancing marine diesel engine performance, we must establish a set of rules and linguistic variables corresponding to the engine's inputs and outputs.Fuzzy logic systems excel at dealing with imprecise inputs and formulating outputs based on a set of rules, making them ideal for optimizing engine parameters like fuel consumption, power output, and efficiency.
The optimal operation of the engine is a specific state or range that is determined based on the desired balance between three factors, considering the operational goals: 1. Fuel Efficiency: operating the engine at a speed and load where the fuel consumption is minimized for the required power.2. Performance Requirements: running the engine within a range that meets a particular task's power or torque requirements.3. Emission Standards: adjusting the engine's operating conditions to reduce emissions while maintaining performance and efficiency.It aims for fuel efficiency and performance and strictly adheres to emission standards, which might require dynamic adjustments based on regulatory changes or operational areas.
For the purpose of implementing our perspective to develop a fuzzy controller, we would like to start our analyses by incorporating the performance curves of the investigated engine; the performance curves are based on a propeller load exponent of 2.5.The propeller load exponent is a key parameter in the equation that describes how the power required by the propeller changes with the vessel's speed.

Define Fuzzy Inputs and Outputs
In a fuzzy logic control system, inputs and outputs are crucial elements that define the system's behavior and its ability to optimize performance.Inputs refer to the measurable variables that the system receives, which are used to determine the appropriate control actions.These inputs are essential for assessing the system's current state and providing the necessary data to the fuzzy logic controller for decision-making.On the other hand, outputs are the actions or responses produced by the fuzzy logic controller based on the processed input data.They represent the system's adjustments to achieve desired performance outcomes.
I. Inputs The power the propeller requires to propel the vessel, derived from the engine's power output.

Digital Analysis of the Performance Curves
Following the digitization of the performance curves, a comprehensive analysis was conducted to determine the operational characteristics of the marine diesel engine under consideration.This analysis revealed key insights into the engine's performance metrics, particularly in efficiency, power output, and fuel consumption.

Crankshaft Torque Efficiency Analysis
Figure 1 illustrates the relationship between the engine speed [rpm] and the engine's torque output [Nm].As engine speed increases, the torque increases to a peak before gradually decreasing.The curve highlights the engine's optimal performance range and helps identify the most efficient fuel consumption and power delivery operating point.The curve indicates how the engine responds to increased demand and maintains high torque levels over various speeds.
The analysis identified the peak efficiency of the crankshaft torque at 1219 [Nm].This peak efficiency was observed within an engine speed range of 2109.69 to 2524.41 [rpm].This insight is critical for optimizing engine performance, as it delineates the operational range where the engine operates with maximal efficiency.The FLC (fuzzy logic controller) would adjust the fuel injection timing or quantity to maintain engine operation within the optimal speed range (2109.69 to 2524.41 [rpm]) to maximize torque efficiency because the torque output is at its peak efficiency at a specific engine speed range, indicating an optimal balance between fuel consumption and power delivery.The engine can be kept within this optimal range by adjusting the fuel injection, enhancing overall efficiency.

Fuel Injection Timing Impact on Engine Performance
Fuel injection timing refers to the precise point at which fuel is introduced into the combustion chamber relative to the engine's cycle, typically measured in degrees of crankshaft rotation before the piston reaches the top dead center (TDC).Optimal fuel injection timing is crucial for efficient combustion, affecting the engine's efficiency and power output.
Advanced Timing: Injecting fuel earlier (before TDC) can increase the time available for fuel-air mixture combustion, potentially increasing the engine's torque and power output at lower engine speeds.However, overly advanced timing may lead to incomplete combustion, increased emissions (such as NOx), and engine knock, which can damage the engine.
Retarded Timing: Injecting fuel closer to or at the TDC can result in a more rapid combustion process, functional at higher engine speeds where the window for combustion is shorter.However, excessively retarded timing may cause lower peak cylinder pressures, reducing torque and efficiency and increasing unburnt fuel emissions.
From a thermodynamic standpoint, adjusting fuel injection timing aims to align the combustion process's peak pressure with the optimal crank angle for power production, maximizing the work done on the piston.The timing adjustment seeks to optimize the tradeoff between maximizing cylinder pressure (and thus torque) and minimizing heat losses and emissions production within the constraints of mechanical and emissions regulations.

Fuel Injection Quantity Impact on Engine Performance
Fuel injection quantity refers to the amount of fuel injected into the combustion chamber during each injection event.This parameter directly influences the engine's power output and efficiency, as it determines the fuel-air ratio, which is critical for combustion dynamics.
Increased quantity: Injecting more fuel increases the fuel-air ratio, leading to higher combustion energy and, consequently, higher torque and power output.This approach is typically beneficial when higher engine performance is required, such as under load or acceleration conditions.However, it can lead to increased fuel consumption and higher emissions, especially if the combustion becomes too rich (excess fuel relative to air).
Decreased quantity: Reducing the fuel injected leads to leaner combustion, which can improve fuel efficiency and reduce emissions.However, it may also reduce engine power and torque, making it challenging to meet performance requirements under certain conditions.
The control of fuel injection quantity balances achieving desired power levels and maintaining fuel efficiency and emissions standards.The stoichiometric ratio (the ideal ratio of air to fuel for complete combustion) plays a central role in this context.Deviations from this ratio can significantly impact combustion efficiency, engine performance, and emissions.Precise control over the fuel injection quantity allows for dynamic adjustments to engine operation, optimizing performance across different operating conditions.

Propeller Power Output Characteristics
Figure 2 shows the relation between the output power and engine speed.Two curves represent the power at the crankshaft and the power available at the propeller shaft, which is considered a typical load exponent.This comparison is crucial for vessel operators to understand the actual power delivered to the propulsion system compared to the engine's maximum capability.
The maximum output at the crankshaft curve shows the theoretical maximum power the engine can produce at the crankshaft with a typical load.Conversely, the propeller power curve (load exp.2.5) shows how much power is available to the propeller, considering the load with an exponent of 2.5. it is typically lower than the crankshaft power because of the additional effort required to move the propeller through water, which increases rapidly with speed.
The load exponent helps plan for the appropriate engine size and propeller design to ensure efficient operation of the vessel under typical working conditions.
Further examination disclosed that the maximum value for propeller power, considering a load exponent of 2.5, occurs at the point [308.33-3233.94].Additionally, the maximum output at the crankshaft is approximated at point 335.This maximum output's corresponding engine speed zone extends from 2682.31 to 3299.01 [rpm].This range is particularly relevant for scenarios requiring maximum power delivery, such as navigating through adverse sea conditions or achieving high-speed transit.This component of the FLC aims to optimize power delivery to the propeller, especially ensuring that the engine operates within the speed range of 2682.31 to 3299.01 [rpm] for maximum power output.
Turbocharger Boosts Pressure Impact on Engine Performance A turbocharger enhances an engine's efficiency and power output by forcing extra compressed air into the combustion chamber, allowing more fuel to be burned and thus increasing power output.Turbocharger control, therefore, involves adjusting the amount of air compressed and fed into the engine.This adjustment is usually achieved by varying the turbocharger's boost pressure, which can be carried out through various means such as variable geometry of turbochargers (VGTs), wastegates, or electronic control of the turbocharger's components.
Increasing the turbocharger's boost pressure delivers more air to the combustion chamber, significantly enhancing combustion efficiency and increasing power output, which is useful under high-load conditions or when additional power is required.However, excessive boost can lead to engine knock, higher thermal stress on engine components, and increased NOx emissions due to higher combustion temperatures.
Reducing the boost pressure decreases the air supply to the combustion chamber, potentially lowering power output and reducing the risk of engine knock and high combustion temperatures, which can be beneficial in reducing NOx emissions and managing engine stress under certain conditions.

Fuel Injection Rate Impact on Engine Performance
The fuel injection rate refers to the quantity of fuel delivered to the combustion chamber over a specific period.It is a crucial parameter that directly influences the combustion process and, subsequently, the engine's performance.
An increased fuel injection rate delivers more fuel into the combustion chamber, increasing the energy released during combustion.This additional energy can accelerate the engine, leading to a higher engine speed [rpm] and power output.However, this is conditional upon the engine load and operating state.In a fixed-load situation, such as with a propeller curve, increasing the fuel rate may not significantly increase [rpm] but will increase the torque and, thus, the power output.
A decreased fuel injection rate reduces the fuel injected into the engine and decreases the energy available for combustion.This reduction can decrease engine speed, mainly if the engine is not operating under a heavy load.In operational terms, this means lower fuel consumption and reduced power output, which might be desirable when fuel efficiency is prioritized over performance.However, it is crucial to manage reductions in power output carefully to ensure they align with operational needs and do not compromise the vessel's performance.

Synchronizing Fuel Injection Rate Control with Turbocharger Adjustments
In a comprehensive engine management system, particularly one utilizing fuzzy logic control, adjustments to the fuel injection rate are often made in concert with turbocharger control modifications.Increasing the fuel injection rate while adjusting the turbocharger to provide more air can enhance combustion efficiency and power output without significantly increasing emissions or fuel consumption per unit of power produced.Conversely, reducing the fuel injection rate and appropriately lowering the turbocharger boost can help maintain fuel efficiency and reduce emissions during lower power demand periods.

Optimization of Fuel Consumption
Fuel efficiency is presented in this curve, showing fuel consumption (in liters per hour, L/h) with engine speed (Figure 3).This curve is useful for operational cost assessment, calculating fuel expenses at different speeds, and planning efficient voyages.It is beneficial when evaluating the engine's performance for extended operations, ensuring that its power does not come at the expense of fuel efficiency.These findings are essential to developing advanced control strategies to enhance the performance of marine diesel engines.By integrating these insights into a fuzzy logic control system, it is possible to dynamically adjust engine parameters to optimize efficiency, power output, and fuel consumption.This approach contributes to the operational excellence of marine propulsion systems and aligns with sustainability objectives by minimizing fuel consumption and reducing emissions.
It is important to emphasize that the performance curves represent the characteristic behavior of the engine across different operating conditions.These curves provide detailed information about the engine's performance regarding torque, power output, and fuel consumption at various engine speeds.

Fuzzy Logic Control Application in the Tested Marine Engines
The study uses a Mamdani-type fuzzy logic controller (FLC) for the implementation.This type is chosen due to its intuitive rule-based structure, which is well suited for the complexity and non-linearity of marine diesel engine operations.
The fuzzy sets for each input and output parameter are defined using triangular membership functions (Figure 4).These are selected for their simplicity and effectiveness in modeling the uncertainty and variability in engine parameters.For example: If the fuel injection rate is high and the AFR is rich, then the turbocharger boost pressure is high.3.If the EGR rate is medium and the engine load is high, then the fuel injection timing is advanced.4. Inference Engine: Apply the fuzzy rules to the fuzzified inputs to generate fuzzy outputs.The Mamdani inference method is used, which involves the min-max composition technique.5. Defuzzification: Convert the fuzzy outputs back into crisp values.The centroid method is used for defuzzification, which calculates the center of the area under the fuzzy set curve.
In a fuzzy logic control system for engine management, output variables such as engine speed [rpm] and power output [kW] can be determined by optimal adjustment to the fuel injection rate and the turbocharger's boost pressure.The goal is to maintain optimal engine performance while considering fuel efficiency and emissions standards.
For high engine speed and demand for high power output: The system might increase fuel injection and turbocharger boost pressure to meet the power demand, ensuring the engine operates efficiently and effectively.
For low engine speed or lower power demand: The control system might reduce the turbocharger boost pressure and adjust the fuel injection accordingly to maintain efficiency, reduce wear on the engine, and control emissions.
Figure 5 illustrates the relationship between the key input parameters, the fuzzy logic controller, and the resulting outputs.This implementation is crucial for optimizing the performance and efficiency of marine diesel engines.The inputs include fuel injection timing/quantity, fuel injection rate, air-to-fuel ratio, EGR rate, and turbocharger boost pressure.The FLC processes these inputs to produce controlled outputs, which include engine speed, crankshaft torque, and propeller power demand.The ultimate goal is to optimize fuel consumption and overall engine performance.Figure 5 visually represents these relationships and the flow of information from the inputs through the FLC to the outputs and optimization goals.We can dynamically adjust the engine parameters to achieve optimal performance and fuel efficiency by utilizing a fuzzy logic control system.This approach enhances the operational effectiveness of marine diesel engines and contributes to sustainability by minimizing fuel consumption and adhering to emissions standards.

Conclusions
The exploration of fuzzy logic theory within the field of marine diesel engines, as detailed in this paper, discloses a promising direction for improving engine operation.The application of fuzzy logic offers a robust method for managing the intricate dynamics of engine performance and emissions control, addressing the inherent complexity and uncertainty that conventional systems struggle to handle.
This study highlights the significant potential of fuzzy logic control (FLC) in enhancing the performance and efficiency of marine diesel engines.The key findings of our research are summarized as follows: 1. Enhanced Control and Optimization: FLC provides a flexible and adaptive approach to engine management, allowing for precise adjustments to key parameters such as fuel injection timing, air-to-fuel ratio, EGR rate, and turbocharger boost pressure.This adaptability leads to smoother engine operations and better performance.

Improved Fuel Efficiency and Reduced Emissions:
The study establishes that FLC can theoretically improve fuel efficiency and reduce emissions.By managing the inherent complexity and variability in engine operations, FLC offers a robust solution for optimizing engine performance.

Early Fault Detection:
FLC's ability to continuously monitor and adjust engine parameters contributes to early fault detection, which can prevent severe malfunctions and extend engine life.This proactive approach enhances the reliability and operational safety of marine diesel engines.

Establishing Empirical Foundations:
An empirical validation through long-term experiments will be applied.Future studies will focus on collecting performance metrics before and after FLC implementation to quantify the benefits, including fuel consumption, emission levels, and engine speed optimization.

Time and Operation Cost Savings:
Implementing FLC in marine diesel engines can lead to significant time and cost savings by reducing maintenance needs and improving operational efficiency.The study suggests that adopting FLC could be a transformative step towards more sustainable and efficient marine engine management.
These findings emphasize the importance of further research to fully realize and empirically validate the potential of FLC in marine diesel engines.
The added value of this research lies in its demonstration of how fuzzy logic can be effectively applied to marine diesel engines to improve performance and efficiency.By implementing fuzzy logic control systems, marine engines can achieve better adaptability and precision in managing various operational parameters, leading to enhanced fuel efficiency, reduced emissions, and overall improved engine performance.This research provides a robust framework for future advancements in marine diesel technology, offering significant potential for innovation in engine management and contributing to the broader goals of environmental sustainability and operational excellence in the maritime industry.

Figure 4 .
Figure 4. Different membership functions for the fuzzy sets.The implementation involves the following steps: 1. Fuzzification: Convert the crisp input values (e.g., fuel injection timing, AFR) into fuzzy values using the defined membership functions.2. Rule Base: Develop a set of if-then rules based on expert knowledge and literature.For example: If the fuel injection rate is high and the AFR is rich, then the turbocharger boost pressure is high.3.If the EGR rate is medium and the engine load is high, then the fuel injection timing is advanced.4. Inference Engine: Apply the fuzzy rules to the fuzzified inputs to generate fuzzy outputs.The Mamdani inference method is used, which involves the min-max composition technique.5. Defuzzification: Convert the fuzzy outputs back into crisp values.The centroid method is used for defuzzification, which calculates the center of the area under the fuzzy set curve.

Figure 5 .
Figure 5. Flow diagram of inputs and outputs in a fuzzy logic controlled marine diesel engine.
1. Fuel Injection Timing [° crank angle]/Quantity [mg/stroke]: Fuel injection timing is the precise point in the engine cycle at which fuel is injected into the combustion chamber.Fuel injection quantity is the amount of fuel delivered to the combustion chamber per injection cycle.2. Fuel Injection Rate [mg/ms]: the speed at which fuel is injected into the combustion chamber.3. Air-to-Fuel Ratio (AFR) [ratio]: the air mass ratio to the fuel mass entering the combustion chamber.4. EGR Rate [%]: The exhaust gas recirculation (EGR) rate represents the proportion of exhaust gas recirculated back into the engine's intake air. 5. Turbocharger Boost Pressure [kPa]: indicates the pressure of the air supplied to the engine by the turbocharger.