Research on Energy Management Strategy for Marine Methanol–Electric Hybrid Propulsion System Based on DP-ANFIS Algorithm

Abstract

To address the challenges of high fuel consumption and emissions in traditional diesel-powered inland law enforcement vessels, this study proposes a methanol–electric hybrid propulsion system retrofitted with a novel energy management strategy (EMS) based on the integration of Dynamic Programming (DP) and Adaptive Neuro-Fuzzy Inference System (ANFIS). The DP-ANFIS algorithm combines the global optimization capability of DP with the real-time adaptability of ANFIS to achieve efficient power distribution. A high-fidelity simulation model of the hybrid system was developed using methanol engine bench test data and integrated with models of other powertrain components. The DP algorithm was used offline to generate an optimal control sequence, which was then learned online by ANFIS to enable real-time energy allocation. Simulation results demonstrate that the DP-ANFIS strategy reduces total energy consumption by 78.53%, increases battery state of charge (SOC) by 3.24%, decreases methanol consumption by 64.95%, and significantly reduces emissions of CO, HC, NOx, and CO₂ compared to a rule-based strategy. Hardware-in-the-loop tests confirm the practical feasibility of the proposed approach, offering a promising solution for intelligent energy management in marine hybrid propulsion systems.

1. Introduction

Under the dual pressures of energy conservation and emission reduction goals, alongside carbon neutrality targets within the global shipping industry [1,2], hybrid-powered vessels have emerged as a pivotal direction for green transformation due to their high efficiency and low emissions [3]. As an integral component of the shipping sector, inland waterway vessels face particularly acute emission challenges, underscoring the urgent need to develop new propulsion systems that harmonize economic viability with environmental sustainability [4,5]. Methanol fuel, recognized for its carbon-neutral potential, safety in storage and transportation, and technological maturity, is considered a promising alternative to conventional fossil fuels. Methanol was chosen over alternatives such as ammonia or hydrogen due to its technological maturity, safety, and infrastructural compatibility [6]. Unlike ammonia, which is toxic and requires careful handling, or hydrogen, which requires energy-intensive liquefaction or high-pressure storage systems, methanol is a liquid at ambient conditions. This allows it to be stored and handled using infrastructure and procedures similar to those for conventional diesel fuel, significantly simplifying the retrofitting process and reducing costs. Furthermore, spark-ignition methanol engine technology is more immediately applicable and commercially mature for marine propulsion compared to hydrogen fuel cells or ammonia combustion systems, which are still under active development for widespread maritime use. These characteristics make methanol an particularly suitable candidate for the decarbonization of existing inland vessels where operational practicality and retrofit feasibility are paramount. Meanwhile, electric propulsion systems, leveraging the synergy between energy storage systems and electric motors, can substantially enhance energy efficiency and reduce pollutant emissions [7].

While the methanol–electric hybrid architecture offers a viable pathway towards greener shipping, its overall efficiency and emission reduction performance are highly dependent on the effectiveness of the Energy Management Strategy (EMS), which governs the real-time power split between the methanol engine and the battery pack. Existing EMS methodologies for marine hybrid systems can be broadly classified into three categories: rule-based, optimization-based, and learning-based strategies [8].

Substantial research efforts have been devoted to developing energy management strategies (EMS) for marine hybrid power systems. Existing studies have predominantly concentrated on diesel-electric hybrids [9], composite power architectures [10], and fuel cell-based systems [11]. For instance, Acanfora et al. [9] designed an electrical energy storage system for a hybrid diesel-electric ship aimed at load leveling in irregular wave conditions. In contrast, methanol–electric hybrid propulsion systems have received comparatively limited attention, with insufficient investigation into the dynamic modeling of methanol engines and the coordinated control strategies for integrated electric propulsion.

Current EMS methodologies can be broadly classified into three categories: rule-based, optimization-based, and learning-based strategies [8]. Rule-based methods (e.g., state machines [12] or fuzzy logic) are widely adopted in industrial applications owing to their simplicity, reliability, and computational efficiency. However, they often depend heavily on expert knowledge and may underperform in complex, multi-objective optimization scenarios [12]. Optimization-based techniques, such as dynamic programming (DP) which is renowned for its global optimality [13,14], and the equivalent consumption minimization strategy (ECMS) which offers a practical online implementation [15], can achieve high theoretical accuracy. For instance, Yuan et al. [16] demonstrated a novel hybrid EMS that combines DP with model predictive control (MPC) for a diesel-electric hybrid ship, leveraging the strengths of both methods. Nevertheless, these methods typically require a priori knowledge of the driving cycle and suffer from high computational cost, limiting them to offline applications or simplified online implementations [15]. Learning-based strategies, including those utilizing deep reinforcement learning [17], have shown promise but still face challenges such as substantial data dependency, limited robustness in real-time operation, and safety concerns, indicating that further development and validation are necessary before they can be reliably deployed [17].

A recent trend involves harnessing the global optimization capability of offline algorithms to inform and enhance online strategies. For example, Gómez-Barroso et al. [18] applied a DP-based ANFIS for fuel cell hybrid electric vehicles, while Yuan et al. [16] combined DP with MPC for ships. However, the application of such a synergistic approach, specifically for the nascent methanol–electric hybrid propulsion systems tailored to the complex and variable profiles of inland waterway vessels, remains largely unexplored.

This literature review reveals a clear research gap: a lack of a dedicated, high-fidelity, and real-time capable energy management framework for methanol–electric hybrid propulsion systems in inland waterway applications. The highly variable operating conditions and stringent emission regulations specific to this context complicate the design of an effective EMS, underscoring the need for an approach that harmonizes global optimization with real-time control performance.

Furthermore, for alternative fuels like methanol, the optimization of the engine itself is crucial to fully exploit its low-carbon emission reduction potential. Beyond energy management strategies, the application of variable systems, such as Variable Compression Ratio (VCR) and variable fuel injection timing, represents a key technological pathway to optimize the combustion process for different fuels while maintaining high efficiency and low emissions. For instance, Milojević et al. [19], in a study on a tribologically optimized diesel engine, demonstrated a significant correlation between the compression ratio, injection timing, and the engine’s emission and combustion characteristics. Although the present study is based on a current technology mature methanol engine with fixed parameters, exploring the coordinated control of advanced variable systems like VCR with global energy management strategies presents a highly promising research direction for future work aimed at achieving deeper emission reductions and multi-fuel adaptive operation.

To address these challenges, this study designs a methanol–electric hybrid propulsion system and proposes a real-time energy management strategy (EMS) combining dynamic programming (DP) and an adaptive neuro-fuzzy inference system (ANFIS). The main contributions are threefold:

A high-fidelity simulation model of the hybrid system is developed, integrating methanol engine characteristics from bench tests and models of other powertrain components. A DP-ANFIS-based EMS is designed to enhance both global optimization and real-time performance. The model accurately simulates energy efficiency and emissions under typical navigation conditions, enabling comparative analysis of rule-based (RB), DP, and DP-ANFIS strategies. Furthermore, a distributed hardware-in-the-loop (HIL) platform based on NI PXIe is established to experimentally validate the real-time performance and robustness of the proposed strategy. Through integrated theoretical modeling, simulation, and experimental verification, this study provides a low-emission, high-efficiency EMS for inland vessels and offers new insights into multi-objective cooperative control in hybrid propulsion systems.

2. Materials and Methods

This study focuses on retrofitting an inland river law enforcement vessel by replacing its conventional diesel propulsion with a methanol–electric hybrid system. The new configuration integrates a methanol engine–generator set (250 kW), a lithium iron phosphate battery pack (200 Ah), a permanent magnet synchronous motor (200 kW peak power), and associated power conversion modules.

A high-fidelity simulation model was developed in MATLAB/Simulink (R2024b), incorporating a MAP-based methanol engine model derived from bench test data of the CHG234V8MPI engine (Henan Diesel Engine Heavy Industry Co., Ltd., located in Luoyang, China) to characterize power, fuel consumption, and emissions. This model was combined with motor efficiency maps and a dynamic battery state-of-charge (SOC) model, enabling comprehensive multi-physics co-simulation of the hybrid propulsion system. Key test equipment specifications are provided in

Table 1. Specifications of the test equipment.

Instrument	Specifications	Accuracies
Methanol Engine	Henan Diesel Engine Heavy Industry Co., Ltd. (Luoyang, China) CHG234V8MPI	-
Electric Dynamometer	AVL ASM 3000 (AVL List GmbH, headquartered in Graz, Austria)	Torque: ±0.2% F.S; Speed: ±2 rpm
Methanol Flow Meter	FC2212L (Hunan Xiangyi Power Test Instrument Co., Ltd., Changsha, China)	±0.12%
Air Flow Meter	AVL FLOWSONIX Air 150 (AVL List GmbH, Graz, Austria)	±1% F.S
Combustion Analyzer	AVL-INDISET ADVANCED PLUS (AVL List GmbH, Graz, Austria)	-
Pressure Sensor	Kistler 6054BR (Kistler Group, Winterthur, Switzerland)	±0.6% F.S
Excess Air Ratio Meter	HORIBA MEXA 730 AFR (HORIBA, Ltd., Kyoto, Japan)	±0.01
Emissions Analyzer	HORIBA MEXA 7100 DEGR (HORIBA, Ltd., Kyoto, Japan)	±0.5% F.S
Intake Air Temperature Sensor	Pt100 (Verder (Shanghai) Instrument Equipment Co., Ltd., Shanghai, China)	±0.15 °C
Coolant Temperature Sensor	Pt100	±0.15 °C
Exhaust Temperature Sensor	K-type thermocouple (FLAMAX WIRE INDUSTRIES, Thane, India)	±1.5 °C

, and the test bench schematic is shown in Figure 1.

To optimize the energy management of the hybrid system, three control strategies were designed: a heuristic RB strategy, a global optimization strategy using dynamic programming (DP), and a collaborative DP-ANFIS strategy that integrates DP with an adaptive neuro-fuzzy inference system.

In the DP approach, the propulsion power demand and battery state of charge (SOC) are used as state variables, with the methanol engine’s output power as the decision variable. The optimal control sequence is computed over a finite horizon of 150 steps (3000 s, with Δt = 20 s per step) using a backward search algorithm. This horizon length was selected through sensitivity analysis to balance optimization performance and computational burden. It covers multiple complete navigation cycles—including acceleration, cruising, and deceleration—enabling effective energy planning. A longer horizon (e.g., 200 steps) offered diminishing optimality improvements at significantly higher computational cost, while a shorter one (e.g., 100 steps) failed to capture long-term energy dynamics, leading to suboptimal fuel economy.

For the DP-ANFIS strategy, the optimized control sequences from DP are used to train a Sugeno-type fuzzy inference system within ANFIS. A hybrid learning algorithm optimizes the membership functions and rule base, facilitating real-time power allocation.

The selection of these two baseline strategies is intentional. The RB strategy represents a widely deployed industrial standard due to its robustness and low computational overhead, serving as a practical benchmark for performance improvement. In contrast, the DP strategy, while non-causal and computationally intensive, provides the globally optimal solution and thus serves as a theoretical benchmark to evaluate the optimality gap of any real-time implementable strategy, such as the proposed DP-ANFIS.

Simulation studies were conducted under typical inland waterway operating conditions to evaluate and compare the performance of the three control strategies in terms of fuel consumption, emission reduction, and battery state of charge (SOC) maintenance. Furthermore, a hardware-in-the-loop (HIL) test platform was established using an NI PXIe dual real-time system. Through a distributed architecture, real-time closed-loop validation of both the control strategies and the plant model was achieved, confirming the feasibility and robustness of the DP-ANFIS algorithm for practical engineering applications.

3. Methanol–Electric Hybrid Propulsion System for Marine Applications

3.1. System Configuration and Key Parameters

The subject of this study is an inland river law enforcement vessel (as shown in Figure 2). Originally equipped with a conventional diesel propulsion system, the vessel exhibited relatively high emissions under typical operating conditions, failing to comply with national emission control zone regulations. To support green navigation objectives, the vessel is retrofitted with a methanol–electric hybrid propulsion system, which integrates a methanol engine and a lithium-ion battery pack. The retrofit aims to maintain the original navigation performance—including speed and range—while introducing an intelligent energy management system. Furthermore, the energy management strategy is optimized for typical operating profiles to reduce fuel consumption and pollutant emissions. The key design parameters of the vessel are summarized in

Table 2. Key design parameters of the inland river law enforcement vessel.

Parameters	Value
Length Overall	25.5 m
Beam	5.2 m
Draft	1.5 m
Displacement	80 t
Propeller Diameter	0.9 m
Maximum Propeller Speed	850 rpm
Maximum Speed	22 km/h

.

3.2. Design of a Marine Methanol–Electric Hybrid Propulsion System

As shown in Figure 3, the methanol–electric hybrid propulsion system employs a modular architecture comprising four functional modules: power generation, energy storage, power conversion, and propulsion execution. The power generation module utilizes a methanol-fueled generator set with an electromagnetic clutch, enabling disconnection for pure electric operation. Energy storage is provided by a LiFePO₄ battery pack connected via a bidirectional DC/DC converter, with SOC managed in real time by a BMS. The power conversion module includes an AC/DC rectifier, a bidirectional DC/DC converter, a DC/AC inverter, and a regenerative braking rectifier. Propulsion is achieved using high-efficiency PMSMs (up to 96% efficiency) capable of four-quadrant operation and regenerative braking. Energy flows through both mechanical and electrical paths, supporting unidirectional and bidirectional transfer, while customized energy management strategies optimize efficiency, reduce emissions, and maintain performance.

The selection and sizing of components for the hybrid propulsion system were based on power and energy requirements derived from typical operating profiles of the inland law enforcement vessel (see Figure 2 and Table 2). A 250 kW methanol-fueled generator set was chosen to supply ample power for high-speed cruising and sustained operations, ensuring frequent operation within its high-efficiency zone. To address peak propulsion demands and enable efficient regenerative braking, a 200 kW permanent magnet synchronous motor (PMSM) was selected for its high torque density and operational efficiency. Additionally, a 200 Ah lithium iron phosphate (LiFePO₄) battery pack was incorporated to support all-electric operation during port maneuvering and low-speed patrols (typically 1–2 h), while also providing peak power shaving during accelerations. The LiFePO₄ chemistry was preferred over other lithium-ion batteries due to its enhanced safety, longer cycle life, and excellent stability, which are particularly critical in marine environments. Based on these typical navigation profiles, the parameters of the methanol–electric hybrid propulsion system were systematically matched, with the resulting key component specifications summarized in

Table 3. Key parameter configuration of the marine methanol–electric hybrid propulsion system.

Power Components	Parameters	Value
Methanol Generator Set	Rated Power	250 kW
	Rated Speed	1500 r/min
	Number of Cylinders	8
	Displacement	14 L
Permanent Magnet Synchronous	Rated Frequency	50 Hz
	Peak Power	200 kW
	Maximum Torque	2400 N·m
	Number of Pole Pairs	4
Lithium Iron Phosphate Battery	Rated Voltage	716.8 V
	Rated Capacity	200 A·h
	Number of Cells	112

.

3.3. Operational Modes of the Marine Methanol–Electric Hybrid Propulsion System

Based on the analysis of daily operational profiles of inland river law enforcement vessels, the hybrid propulsion system designed in this study incorporates the following primary operating modes:

3.3.1. All-Electric Propulsion Mode

The energy flow in all-electric propulsion mode is illustrated in Figure 4. This mode is primarily employed during vessel startup, port maneuvering, and extended low-speed cruising. Its key technical characteristic is the complete shutdown of the methanol engine, enabling true zero-emission operation. Compared to conventional propulsion systems, this mode offers notable advantages including significantly reduced noise, faster dynamic torque response, and improved speed control accuracy.

The overall energy efficiency in this mode (from battery DC terminal to propeller shaft) is primarily determined by the combined efficiency of the motor drive (inverter + PMSM) and the mechanical transmission, typically ranging from 85% to 90%.

3.3.2. Methanol Range-Extended Propulsion Mode

The energy flow in methanol range-extended propulsion mode is illustrated in Figure 5. This mode is primarily used during medium-speed cruising, battery charge-sustaining phases, extended voyages, and port standby charging. Its key technical characteristics include dual energy paths for both propulsion and charging, allowing the methanol engine to operate consistently within its highest efficiency range. Surplus power is utilized for efficient battery charging. This power management approach significantly reduces fuel consumption and pollutant emissions.

This mode involves multiple energy conversions. The overall efficiency (from methanol chemical energy to propeller shaft power) is a product of the methanol engine efficiency (peak ~35–40% for SI methanol engines), generator efficiency (~95%), power electronics efficiency (rectifier ~97%, inverter ~98%), and motor efficiency (~95%). This results in a typical overall efficiency range of 30% to 35% for generating propulsion power. When charging the battery, additional losses occur in the DC/DC converter and battery charging process.

3.3.3. Hybrid Propulsion Mode

The energy flow in hybrid propulsion mode is depicted in Figure 6. This mode is primarily employed during high-speed navigation, emergency collision avoidance, heavy-load operations, and similar high-power demand scenarios. Its key technical feature is a redundant dual-power-source configuration, which enhances system reliability. By leveraging the peak-shaving and valley-filling capability of the battery pack, the system achieves coordinated power distribution between the methanol engine and the energy storage unit, while significantly improving dynamic response performance.

The overall system efficiency in this complex mode is dynamic and depends on the power split. It combines the efficiency paths of both all-electric and range-extended modes. The energy management strategy aims to maximize efficiency by operating the engine near its optimal point and minimizing unnecessary energy conversions.

3.3.4. Regenerative Braking Mode

The energy flow during regenerative braking mode is illustrated in Figure 7. This mode is primarily activated during vessel deceleration, berthing maneuvers, and emergency stops. Its key technical advantages include efficient energy recovery, extended battery service life, and reduced mechanical braking losses, thereby maximizing energy utilization and minimizing emissions.

The efficiency of energy recovery during regenerative braking is determined by the motor/generator efficiency and the efficiency of the bidirectional power converters and battery charging process. Typically, 60% to 70% of the kinetic energy during braking can be recovered and stored in the battery, which is significantly more efficient than dissipating it as heat in mechanical brakes.

Figure 8 illustrates the logic diagram for operational mode transitions of the marine methanol–electric hybrid propulsion system. Transitions among the All-Electric, Range-Extended, Hybrid, and Regenerative Braking modes are determined by the acceleration command $Acc$, battery state of charge (SOC), and propulsion power demand $Preq$, with specific thresholds indicated on the arrows.

Based on the operational characteristics of these modes and the functional parameters of the key power components, the mode switching logic is designed as shown in Figure 8. Here, $Preq$ denotes the total demanded power, ${P_{batt}}_{\_max}$ represents the maximum discharge power of the lithium battery pack, ${P_{eng}}_{\_\min }$ indicates the minimum high-efficiency power of the methanol engine, ${P_{eng}}_{\_\max }$ refers to the maximum output power of the methanol engine, and $Acc$ corresponds to the acceleration command.

4. Modeling of the Marine Methanol–Electric Hybrid Propulsion System

This study developed a high-fidelity simulation model of the marine hybrid propulsion system using the MATLAB/Simulink platform, incorporating experimental data from bench tests of the CHG234V8MPI methanol engine. The modeling effort emphasized detailed characterization of key power components, structured as follows: first, a quasi-steady-state model of the methanol engine was established based on empirical test data; second, a permanent magnet synchronous motor model was developed to balance efficiency and dynamic performance; concurrently, a lithium-ion battery pack model accounting for dynamic state-of-charge (SOC) variations was constructed, and an energy management strategy for power distribution was designed. Throughout the modeling process, special emphasis was placed on capturing the dynamic coupling effects between subsystems. Real-time data interaction interfaces were incorporated to ensure the accuracy of dynamic responses in the overall hybrid propulsion system simulation.

4.1. Modeling Framework and Key Assumptions

The high-fidelity simulation model was developed under the following key assumptions to balance computational efficiency with model accuracy:

Quasi-Static Component Models: The methanol engine, motor, and battery are primarily represented by steady-state efficiency maps (e.g., BSFC, efficiency). Dynamic responses are approximated by first-order transfer functions with delay, as detailed in Section 4.2, Section 4.3 and Section 4.4. Transient effects such as fuel injection dynamics or detailed electrochemical reactions within the battery are neglected.

Ideal Power Electronics: The efficiency of converters (AC/DC, DC/DC, DC/AC) is assumed to be constant. Voltage fluctuations on the DC bus are not modeled.

Simplified Propeller Load: The propeller load is calculated based on a simplified quadratic law (load torque proportional to speed squared), neglecting complex hydrodynamic effects like wake fraction or thrust deduction.

Fixed Auxiliary Load: The power consumption of auxiliary systems (e.g., lighting, navigation) is considered constant and is included in the total power demand.

These assumptions are common in system-level energy management studies [8] and focus the analysis on the high-level power split strategy rather than on transient physical phenomena.

4.2. Quasi-Static Modeling of the Methanol Engine with Dynamic Correction

The core fuel consumption and emission characteristics of the methanol engine are derived from steady-state bench test data and represented as MAPs (Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15 and Figure 16). Although this lookup-table method accurately reflects steady-state performance, it does not capture dynamic transient processes such as intake delay, combustion transients, and turbocharger lag. To better simulate the engine’s dynamic response, a first-order inertia element combined with a transport delay is incorporated into the model.

The study is based on the CHG234V8MPI methanol engine, a V-type 8-cylinder high-speed spark-ignition engine with intake manifold injection. It is an upgraded version of a marine gas engine from the same series. Key performance parameters are listed in

Table 4. Key design parameters of the methanol engine.

Parameters	Value
Engine Type	V8, Turbocharged with Intercooler
Number of Cylinders	8
Bore	128 mm
Stroke	140 mm
Connecting Rod Length	255 mm
Compression Ratio	12
Intake Swirl Ratio	0.4
Combustion Chamber Type	Re-entrant Bowl
Fuel Injection System	Port Fuel Injection

. Bench tests recorded fuel consumption, emissions, and power output under various conditions, providing essential data for building an accurate simulation model.

As shown in Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15 and Figure 16, bench testing was performed to evaluate the performance of the CHG234V8MPI methanol engine. Figure 9 displays the test setup, and the following figures illustrate key metrics across different speeds and torque conditions: power distribution (Figure 10), methanol consumption rate (Figure 11), brake-specific fuel consumption (Figure 12), as well as emissions of CO (Figure 13), CO₂ (Figure 14), HC (Figure 15), and NOx (Figure 16). These results are visualized as three-dimensional MAPs, effectively capturing the engine’s behavior and providing a critical foundation for system simulation and optimization.

The dynamic response between the commanded fuel rack position (or throttle command) and the actual engine output torque is modeled using a first-order transfer function with a delay:

$$G(s)={\displaystyle \frac{P_{\mathrm{e}\mathrm{n}\mathrm{g},\mathrm{a}\mathrm{c}\mathrm{t}}(s)}{P_{\mathrm{e}\mathrm{n}\mathrm{g},\mathrm{c}\mathrm{m}\mathrm{d}}(s)}}={\displaystyle \frac{e^{-{\tau }_{d}s}}{{\tau }_{e}s+1}}$$

(1)

where $P_{eng,act}(s)$ is the actual engine output power (kW), $P_{eng,cmd}(s)$ is the commanded output power (kW), ${\tau }_e$ is the engine time constant (s), characterizing the inertia of the rotating assembly and the response speed of the combustion process, ${\tau }_{\mathrm{d}}$ is the transport delay (s), representing the time delay due to the gas exchange process, compression stroke, and combustion duration.

The parameters ${\tau }_e$ and ${\tau }_{\mathrm{d}}$ were identified by comparing the model’s response to step changes in power command with experimental transient data recorded during bench tests. This calibration ensures that the model’s dynamic behavior closely approximates that of the physical methanol engine.

4.3. Permanent Magnet Synchronous Motor Modeling

4.3.1. Analysis of Dynamic Torque Characteristics

The dynamic torque response of the reversible motor is modeled using a first-order inertial element, represented by the following transfer function:

$$\mathrm{G}\left(\mathrm{s}\right)={\displaystyle \frac{T_{m,act}\left(s\right)}{T_{m,req}\left(\mathrm{s}\right)}}={\displaystyle \frac{1}{\tau s+1}}$$

(2)

where $T_{m,act}$ denotes the actual output torque ($N·m$), $T_{\mathrm{m},\mathrm{r}\mathrm{e}\mathrm{q}}$ represents the torque command value ($N·m$), and $\tau$ is the electromechanical time constant, typically set to 0.01 s. This transfer function captures the lag inherent in the motor’s torque response, with $\tau$ characterizing the electromagnetic inertia of the motor system.

4.3.2. Efficiency Modeling

An efficiency MAP model is established using two-dimensional interpolation:

$${\eta }_m=\mathsf{\Phi }(n_m,T_m)$$

(3)

where ${\eta }_m$ denotes the overall efficiency (%), $n_m$ represents the rotational speed (r/min), and $T_m$ is the load torque ($N·m$). The full operating-condition efficiency data are obtained through bench testing, and a lookup table is constructed to enable rapid data retrieval during simulation.

4.4. Electro-Mechanical Energy Conversion

A bidirectional energy flow model is employed to calculate the power transfer:

$$P_{shaft}=\left\{\begin{array}{c}{P}_{batt}·{\eta }_m (\mathrm{P}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{u}\mathrm{l}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e})\\ {\displaystyle \frac{P_{batt}}{{\eta }_m}} (\mathrm{G}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e})\end{array}\right.$$

(4)

where $P_{shaft}$ denotes the mechanical power at the shaft, and $P_{batt}$ represents the electrical power on the DC bus. This model accurately describes the motor’s power conversion behavior during both propulsion and regenerative braking, forming a computational basis for energy management in hybrid power systems.

4.5. Lithium-Ion Battery Model

A standard lithium-ion battery model from the Simulink library was adopted in this study. This equivalent circuit model (ECM) was selected for its computational efficiency and adequacy in capturing the primary State of Charge (SOC) dynamics and terminal voltage behavior, which are the most critical factors for energy management strategy development at the system level. The model parameters were configured based on the manufacturer’s datasheet for the LiFePO₄ battery pack to meet the power requirements of the marine methanol–electric hybrid propulsion system:

The open-circuit voltage is modeled as a function of SOC, ranging from approximately 560 V (at 0% SOC, 2.5 V/cell) to 817.6 V (at 100% SOC, 3.65 V/cell).

The internal resistance is set to ≤50 mΩ (AC, 1 kHz) for the entire pack, accounting for the cumulative resistance of 112 cells in series and interconnections.

The polarization resistance and associated time constant were estimated from Hybrid Pulse Power Characterization (HPPC) test data, with a typical value around 30 mΩ for the pack, reflecting the dynamic voltage response under load.

The nominal capacity is 200 Ah, corresponding to a 0.2C discharge rate from the fully charged state to the cut-off voltage.

It is acknowledged that this model does not inherently account for thermal and aging effects; the implications of these simplifications are discussed in the following paragraphs.

The operational behavior of the battery is characterized as follows:

Charge/Discharge Characteristics: The battery terminal voltage is modeled using a piecewise function.

Under discharge condition ($i^{*}>0$):

$$V_{dis}=[E_0-{\displaystyle \frac{KQ}{Q-i_t}}{i}^{*}-{\displaystyle \frac{KQ}{Q-i_t}}{i}_t+A] ·e^{-Bit}$$

(5)

Under charging condition ($i^{*}<0$):

$$V_{chg}=[E_0-{\displaystyle \frac{KQ}{0.1Q+i_t}}{i}^{*}-{\displaystyle \frac{KQ}{Q-i_t}}{i}_t+A]·e^{-Bit}$$

(6)

where $i^{*}$ is the operating current (A), $E_0$ denotes the open-circuit voltage (V), K represents the polarization resistance (Ω), Q is the nominal capacity (Ah), $i_t$ indicates the extracted capacity (Ah), and A and B are empirical coefficients. The inclusion of the 0.1Q compensation term in the charging condition accurately captures the polarization effects during the charging process.

The state of charge (SOC) is dynamically updated in real time using the current integration method:

$$SOC(\tau )={\displaystyle \frac{Q_0-{\int }_0^{\tau }i(t)dt}{Q}}$$

(7)

where $Q_0$ is the initial charge capacity (Ah), $i\left(t\right)$ denotes the instantaneous current (A)—defined as positive during discharge and negative during charging—and Q represents the nominal capacity (Ah).

The above lithium-ion battery model dynamically tracks the accumulated energy, providing an accurate representation of the actual energy state of the battery.

The implemented battery model operates under the assumption of a constant, ideal temperature (typically 25 °C). In reality, battery internal resistance, capacity, and dynamics are strongly influenced by temperature. Similarly, the efficiency and emissions of the methanol engine are also temperature-dependent. For this study, which focuses on the validation of the energy management strategy under nominal conditions over a single voyage, these thermal effects were not modeled. This is a common simplification in the initial stages of EMS research to reduce model complexity. It is recognized that for lifecycle analysis or operation in extreme climates, a coupled thermal-management model would be necessary. The sensitivity of the results to battery degradation modeling is explored in the following section.

4.6. Integrated Modeling of the Marine Methanol–Electric Hybrid Propulsion System

By integrating simulation models of core power components—including the methanol engine, permanent magnet synchronous motor, and lithium-ion battery pack—along with key subsystems such as the energy management system and transmission system, a comprehensive co-simulation platform for the marine methanol–electric hybrid propulsion system has been developed. The overall architecture of the platform is illustrated in Figure 17. The integrated model explicitly captures the energy coupling relationship between the methanol engine and the lithium-ion battery pack. It enables detailed simulation and analysis of the dynamic performance of the hybrid propulsion system across various operational profiles.

4.7. Validation of the Marine Methanol–Electric Hybrid Propulsion System Model

To evaluate the accuracy of the developed simulation model, the output speed profile was compared against a predefined target speed curve, as depicted in Figure 18. Over the 3000 s simulation period, the overall trend of the simulated speed aligned well with the reference. Quantitative assessment using the Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) yielded values of 0.45 m/s and 0.62 m/s, respectively. The maximum error of 1.2 m/s occurred during a high-power transient around 2800 s.

The following characteristics were observed regarding tracking performance:

• Dynamic Response Characteristics:

During acceleration and deceleration phases, the simulated speed exhibited smoother transitions compared to the reference, with an average tracking lag of approximately 0.5 m/s. This is mainly attributed to the dynamic delay of the internal combustion engine and the inherent inertia of the propulsion system.

2.

Performance Across Operating Conditions:

The model demonstrated strong tracking capability during low-speed steady-state and cruising segments. However, between 2700 and 3000 s, the hybrid propulsion system did not provide immediate deceleration support, leading to a reliance on fluid resistance for speed reduction and a noticeable deviation from the reference.

3.

System Response Mechanisms:

The electric drive system—comprising the motor and battery pack—delivered high responsiveness and accuracy under low-speed operations. In contrast, the methanol generator set introduced dynamic delays during transients, contributing to the observed discrepancies.

Despite these errors, the deviations remain within acceptable limits for system-level analysis. The simplified dynamic models of the methanol engine and propeller load were identified as the primary sources of error, yet their use was deemed appropriate for this study’s focus on energy management strategy design and validation. The results confirm that the simulation model is sufficiently accurate for further performance evaluation and control strategy verification.

5. RB Energy Management Strategy

A rule-based energy management strategy (RB-EMS) is developed for the marine methanol–electric hybrid propulsion system, based on the mode-switching logic illustrated in Figure 8. The strategy dynamically determines operational modes and allocates power between energy sources using real-time inputs including acceleration command ($Acc$∈ [−1, 1]), battery state of charge ($SOC$), propulsion power demand ($P_{req}$), and maximum battery discharge power ($Bat{t}_{dischgPwr}$).

The primary objectives of the RB-EMS are to maintain $SOC$ within a safe range, minimize fuel consumption by operating the methanol engine near its high-efficiency zone, and meet propulsion demands under all conditions. Rule thresholds are designed based on component specifications (Table 3) and typical profiles of inland law enforcement vessels.

The operational modes are defined as follows:

All-Electric Mode ($Acc$ > 0, $P_{req}$ ≤ $P_{motor\_max}$, $SOC$ > 55%): Activated for low power demands to prioritize zero-emission operation, while maintaining a high state of charge and reducing engine cycling.

Range-Extended Mode ($P_{req}$ > 75 kW, $SOC$ > 35%): Engaged when power demand exceeds the engine’s minimum efficient output. The engine operates near its peak efficiency (~90 kW), with excess power charging the battery if $SOC$ < 50%.

Hybrid Mode ($P_{req}$ > $P_{engine\_max}$ or $SOC$ < 35%): Triggered during high power demand or low $SOC$ to prevent overload. The engine operates at maximum power (250 kW), supplemented by the battery.

Regenerative Braking Mode ($Acc$ < 0): Activated during deceleration to recover kinetic energy, improving overall efficiency.

Mode transitions are controlled in real time through continuous monitoring of $Acc$, $SOC$, and $P_{req}$, enabling adaptive and efficient power management.

In the preceding text, $Acc$ represents acceleration signal, $P_{req}$ represents demand power, $Bat{t}_{dischgPwr}$ represents lithium battery pack discharge power, $P_{motor\_max}$ represents maximum output power of the lithium battery pack, $P_{engine\_max}$ represents maximum output power of the methanol engine. Flowchart of the RB energy management strategy is illustrated in Figure 19.

6. Dynamic Programming-Based Energy Management Strategy

Dynamic programming (DP) is a multi-stage decision optimization method founded on Bellman’s principle, widely applied to problems such as shortest-path search and energy management in hybrid power systems [13]. The DP algorithm decomposes the problem into multiple stages, each characterized by discrete states and feasible decisions. By evaluating the transition cost between states, it determines the globally optimal control sequence [14]. In the context of hybrid propulsion system energy management, the DP approach utilizes time as the stage variable and incorporates key parameters such as the battery state of charge (SOC) and propulsion power demand. It optimizes the power split between the methanol generator set and the battery pack to minimize fuel consumption while maintaining system constraints [16].

The advantage of the dynamic programming (DP) algorithm in energy management for hybrid propulsion systems lies in its predictive capability [20]. By comparing the preset ship speed with the simulated speed and incorporating a ship dynamics model, the DP algorithm pre-calculates the required propulsion power, thereby generating a predictive demand power input. As illustrated in Figure 20, the DP-based energy management controller uses the demanded propulsion power and the battery state of charge (SOC) as inputs. Through optimization, it determines and transmits the output power of the methanol generator set, the propulsion motor speed, and the battery pack output power to the hybrid propulsion system model. This predictive power allocation mechanism allows the energy management strategy to achieve near-optimal control performance.

Based on the principles of dynamic programming (DP) and the operational characteristics of the marine methanol–electric hybrid propulsion system, a DP-based energy management algorithm was designed in this study. The specific design procedure is outlined as follows:

• State Variables

In the marine methanol–electric hybrid propulsion system, the state of charge (SOC) of the battery pack is selected as the state variable, as it effectively reflects the overall operational characteristics of the hybrid system while satisfying the requirements of non-aftereffect and observability. The SOC variation range is constrained between 30% and 60% with a discretization step of 0.1% to prevent overcharging or over-discharging. The dynamic behavior of the SOC can be described by Equation (8):

$$s_k=SOC(k)$$

(8)

In the equation, $s_k$ represents the state variable of the k-th stage.

2.

Decision Variable

In the marine methanol–electric hybrid propulsion system, the output power $P_{eng}$ of the methanol engine–generator set is chosen as the decision variable, as expressed in Equation (9):

$$u_k\left(s_k\right)=P_{eng}(k)$$

(9)

where $u_k\left(s_k\right)$ represents the decision variable at the k-th stage. This selection is motivated by the objective of operating the methanol engine at its minimum fuel consumption point, thereby ensuring optimal fuel economy.

• Stage Division

Although dynamic programming can yield globally optimal solutions, it is necessary to avoid the curse of dimensionality that arises from an excessive number of stages. To balance computational accuracy and complexity, the navigation profile in this study is divided chronologically into 150 stages, each with a duration of 20 s. The stage variable $k$ thus takes values in the set $k$= 1, 2, …, 150.

The optimal control sequence is computed over a finite horizon of 150 steps (equivalent to 3000 s, given a 20 s step time Δt). This horizon length was selected through a sensitivity analysis to provide a sufficiently long look-ahead for effective optimization of the battery SOC depletion/recharge cycles, while maintaining computational tractability for the backward DP algorithm. A longer horizon showed diminishing returns in solution quality at a greatly increased computational cost.

2.

State Transition Equation

The state transition equation defines how the current state $s_k$ and the decision variable $u_k\left(s_k\right)$ collectively determine the subsequent state $s_{k+1}$. It is mathematically expressed as:

$$s_{k+1}=T(s_k,u_k)$$

(10)

Given the complex relationship between the methanol engine power $P_{eng}$ and the battery state of charge (SOC), this study utilizes the MATLAB System Identification Toolbox to develop a nonlinear model that captures the dynamic characteristics of the system. A state-space model was identified and validated against experimental data, achieving a fitting accuracy of 95.75% with a 96% confidence interval. The errors were maintained within 5%, confirming that the state-space model accurately represents the system dynamics. The functional expression of the state-space model is given by Equation (11).

$$\left\{\begin{array}{c}x\left(t+∆t\right)=Ax\left(t\right)+B{u}_k\left(t\right)\\ y\left(t\right)=Cx\left(t\right)+D{u}_k\left(t\right)\\ x\left(1\right)=x_0\end{array}\right.$$

(11)

In the state-space model described above, $t$ denotes the current time (in seconds), and $∆t$ represents the sampling interval (in seconds). Mathematically, $x\left(t\right)$ is defined as the differential form of the state variable $y\left(t\right)$, which characterizes the real-time state of the system at time $t$. The input $u_k\left(t\right)$ is expressed in matrix form, specifically comprising the output power of the methanol generator set $P_{eng}$ and the motor output power $P_{mot}$, i.e., ${[P}_{eng},P_{mot}]$. The model parameters include the initial state $x_0$ and the four coefficient matrices A, B, C, and D, which are identified through systematic parameter estimation. These coefficients comprehensively capture the dynamic relationships among the variables in the state-space representation.

3.

Cost Function

The cost function serves to evaluate the quality of decisions made by the energy management strategy. In this study, with the objective of optimizing fuel economy, the cost function is defined as follows in Equation (12):

$$L\left(s_k,u_k\right)=m_{BSFC}(s_k,u_k)$$

(12)

where $m_{BSFC}$ denotes the brake-specific fuel consumption rate, measured in $\mathrm{g}/\mathrm{k}\mathrm{W}\mathrm{h}$.

The optimal cost function is designed to minimize the total fuel consumption, as expressed in Equation (13):

$$J=min\left\{{\sum }_{k=1}^{N}L(s_k,u_k)\right\}$$

(13)

4.

Constraints

To ensure safe and stable operation of the system, the following constraints are imposed (Equations (14)–(16)):

Battery SOC limits:

$${SOC}_{min}\le SOC\left(k\right)\le {SOC}_{max}$$

(14)

Battery power range constraints:

$$P_{batt\_chg}\le P_{batt}\le P_{batt\_dischg}$$

(15)

Methanol engine power limits:

$$P_{engmin}\le P_{eng}\le P_{engmax}$$

(16)

In summary, the DP algorithm achieves optimal fuel economy for the marine methanol–electric hybrid propulsion system through stage-wise decomposition, state transition optimization, and constraint enforcement.

This study employs a backward-solving approach to address the dynamic programming problem. The detailed computational procedure is illustrated in Figure 21.

While the DP strategy provides a globally optimal benchmark when the future driving cycle is perfectly known, its performance is inherently sensitive to uncertainties in real-world applications. The primary source of uncertainty is the deviation between the pre-defined speed profile used for optimization and the actual future speed profile encountered by the vessel. Factors such as changing weather conditions, traffic, or altered mission profiles can lead to this deviation.

If the actual power demand is consistently higher than predicted, the DP solution may deplete the battery SOC too early, forcing the engine to operate inefficiently at high loads to compensate. Conversely, if the actual demand is lower, the battery may not be sufficiently utilized, missing opportunities for fuel savings. This lack of robustness to forecast errors is a fundamental limitation of deterministic DP approaches.

Therefore, the DP strategy itself is not suitable for direct online implementation. Its key role in this work is to serve as an offline benchmark to reveal the theoretical fuel economy upper limit and, more importantly, to generate optimal training data for the DP-ANFIS controller. The ANFIS strategy is then designed to learn the underlying optimal mapping from system states to control actions, enabling it to adapt in real-time to actual conditions, thus overcoming the robustness limitation of the pure DP approach.

7. Energy Management Strategy Based on DP-ANFIS Algorithm

7.1. The Establishment Process of the DP-ANFIS Algorithm

The optimal control sequence derived from the dynamic programming (DP) algorithm for energy management of the marine methanol–electric hybrid propulsion system is utilized as training data for the Adaptive Neuro-Fuzzy Inference System (ANFIS). An adaptive modeling approach is employed to construct the fuzzy inference system. The hybrid learning algorithm—particularly suitable for controlling complex systems with nonlinear and time-varying dynamics—is applied to optimize both the fuzzy rules and the parameters of the membership functions [18].

The DP-ANFIS algorithm operates as follows: the optimal control sequence from DP is used as training data, the required power of the marine methanol–electric hybrid propulsion system and the battery SOC are chosen as input variables, while the output power of the methanol engine is set as the output target. To enhance training accuracy, the min–max normalization method is applied to scale the data to the interval [0, 1]. Subsequently, the ANFIS toolbox (anfisedit) within the MATLAB environment is employed to construct a Sugeno-type fuzzy inference system with two inputs and one output. Key parameter configurations include: the AND operator is set to algebraic product (prod), the OR operator to probabilistic OR (probor), and the defuzzification method to weighted average (wtaver). After configuration, the normalized data is imported into the toolbox for model training [21,22].

In this study, the subtractive clustering method is employed to construct the fuzzy inference system (FIS), with all parameters maintained at their default settings [23]. The resulting ANFIS control system architecture is illustrated in Figure 22.

As shown in Figure 22, the adaptive neuro-fuzzy inference system (ANFIS) in this study adopts a five-layer feedforward structure. The layers perform: input reception (two variables), fuzzification via five Gaussian membership functions, automatic generation of five fuzzy rules, linear inference output, and defuzzification. Inputs are normalized to [0, 1], and membership parameters are adaptively optimized during training.

The system is trained using a hybrid backpropagation and least squares algorithm over 35 epochs with zero error threshold. Training results (Figure 23) show error stabilization near 30 iterations and final convergence to 0.0030689, validating the training configuration.

Each input variable was mapped using five Gaussian membership functions, the number of which was automatically determined via subtractive clustering during the initial Fuzzy Inference System (FIS) generation. This data-driven approach identified five clusters as optimal for capturing the input-output relationships, balancing model complexity and accuracy. Fewer functions (e.g., three) failed to represent system nonlinearities adequately, while more (e.g., seven) led to overfitting without error reduction. Gaussian functions were chosen for their smoothness, differentiability—supporting gradient-based learning in ANFIS—and strong performance as universal approximators.

As shown in Figure 24 and Figure 25, the ANFIS demonstrated high adaptability by autonomously generating five mutually consistent fuzzy rules. The non-uniform distribution of membership functions and their flexible shapes exceed the capability of fixed rule-based systems, enabling self-adjustment of parameter boundaries according to training-derived optima. Furthermore, Figure 26 illustrates that the trained methanol engine output power surface is smooth and well-regulated, confirming operation within the optimal range and contributing to reduced fuel consumption and emissions.

7.2. Sensitivity Analysis of Key Parameters in the DP-ANFIS Algorithm

To evaluate the robustness of the proposed DP-ANFIS algorithm, a sensitivity analysis on key parameters was conducted. The aim is to investigate the impact of these parameters on the algorithm’s performance and to verify the rationality of our selected values.

ANFIS Training Parameters: The hybrid learning algorithm’s performance is influenced by the number of training epochs and the error goal. As shown in Figure 23, the training error converges after approximately 30 epochs. Setting the epoch number to 35 ensures sufficient training while avoiding potential overfitting. The error goal was set to 0 to achieve the highest possible precision. Tests showed that a looser error goal (e.g., 0.01) led to a noticeable degradation in the controller’s performance, confirming the necessity of our strict setting.

DP State Discretization Step: The discretization step of the state variable (SOC) is crucial for the DP algorithm, as it balances computational burden and optimization accuracy. We compared the performance and computation time using different SOC steps: 0.1% (original), 0.5%, and 1.0%.

The results are summarized in

Table 5. Performance and computation time under different SOC discretization steps.

SOC Step Size	Total Methanol Consumption (kg)	Computation Time (s)	Relative Increase in Fuel Use
1.0%	28.5	125	+7.5%
0.5%	27.3	415	+3.0%
0.1%	26.5	2580	0.0%

below. A finer step (0.1%) yielded marginally better fuel economy but required considerably longer computation time. A coarser step (1.0%) significantly reduced computation time but resulted in a suboptimal SOC trajectory and increased fuel consumption.

The chosen step of 0.1% provides an excellent compromise, offering high-quality optimization results acceptable for offline training purposes without excessive computational cost.

The analysis confirms that the performance of the DP-ANFIS strategy is not overly sensitive to the chosen parameters within a reasonable range, demonstrating the robustness of our algorithm design and parameter selection.

Sensitivity to Battery Degradation: The impact of battery aging on the DP-ANFIS strategy’s performance was investigated by simulating the system with a degraded battery capacity, reduced to 90% of its original value (180 Ah instead of 200 Ah). The results indicated a marginal increase in ~2.1% in total methanol consumption compared to the baseline scenario. The SOC trajectory was slightly lower but maintained within the safe operating bounds. This demonstrates that the proposed strategy is robust to moderate battery capacity fade. The primary reason is that the ANFIS controller, trained on the DP’s global optimization results, inherently learns to adapt power distribution based on the SOC state, which indirectly compensates for the reduced energy buffer. For long-term operations, however, incorporating an explicit health-aware mechanism into the EMS would be beneficial to further mitigate degradation effects.

7.3. Computational Performance Metrics

To quantitatively substantiate the real-time capability of the DP-ANFIS controller, its computational performance was evaluated. The trained ANFIS network was deployed on the NI PXIe-8861 real-time controller. The average inference time for a single control decision was measured to be 45 μs. This is orders of magnitude faster than the offline DP optimization, which required approximately 2580 s for the same voyage profile on a high-performance desktop computer. Furthermore, during HIL testing, the DP-ANFIS strategy consumed less than 1% of the CPU’s resources. These metrics conclusively demonstrate that the proposed strategy imposes negligible computational overhead and is fully capable of high-frequency real-time implementation.

8. Simulation Results and Analysis

The performance of the proposed DP-ANFIS strategy is evaluated through a comparative analysis against two baseline strategies: a Rule-Based (RB) strategy and a Dynamic Programming (DP) strategy. This dual-baseline approach provides a comprehensive assessment: comparison with the RB strategy demonstrates the practical advantage over a conventional method, while comparison with the DP benchmark reveals how closely the proposed real-time strategy approximates the global optimum.

To evaluate the performance of the DP-ANFIS-based energy management strategy for the marine methanol–electric hybrid propulsion system, this study integrated three control strategies—rule-based, DP-based, and DP-ANFIS-based energy management controllers—into the simulation model illustrated in Figure 17. Simulations were conducted under typical navigation conditions, as depicted in Figure 18. The following performance metrics were collected and analyzed: methanol consumption, brake-specific fuel consumption (BSFC), battery state of charge (SOC), and emissions of CO, CO₂, HC, and NOx.

To facilitate a clearer comparison of algorithmic performance, the output results of the marine methanol–electric hybrid propulsion system under the three energy management strategies are categorized and presented in Figure 27, Figure 28, Figure 29, Figure 30, Figure 31, Figure 32 and Figure 33.

Qualitative analysis of Figure 27, Figure 28, Figure 29, Figure 30, Figure 31, Figure 32 and Figure 33 shows that the DP-based energy management strategy successfully kept the methanol engine in its optimal operating range and reduced its runtime by utilizing the electric drive system’s peak-shaving and valley-filling capabilities. Compared to the RB strategy, the DP approach exhibited clear advantages in fuel economy, emission reduction, and battery SOC stabilization.

The DP-ANFIS strategy, incorporating pre-optimized DP results, closely follows the performance trends of the DP strategy and significantly outperforms the RB method. Although slightly inferior to pure DP due to learning errors, it achieves markedly better optimization than RB and—unlike offline DP—enables real-time online optimization, making it highly suitable for practical applications.

Quantitative results in Figure 34, Figure 35, Figure 36, Figure 37, Figure 38, Figure 39 and Figure 40 confirm that both DP and DP-ANFIS lead to notably lower fuel consumption and emissions compared to RB, while DP-ANFIS also maintains higher battery SOC levels. Its performance approaches that of pure DP, aligning with qualitative conclusions and underscoring its strengths in near-optimal optimization and real-time applicability.

The total energy consumption W of the marine methanol–electric hybrid propulsion system across all operational conditions is calculated using the energy superposition method, as expressed in Equation (17):

$$W=F_c+E_c$$

(17)

where $F_c$ denotes the energy equivalent of methanol consumption (in $\mathrm{k}\mathrm{W}\mathrm{h}$), and $E_c$ represents the energy consumed by the battery pack (in $\mathrm{k}\mathrm{W}\mathrm{h}$).

The methanol-related energy component is computed using the integral form given in Equation (18):

$$F_c={\int }_0^t{\displaystyle \frac{m_{fuel}·Q_{fuel}}{3600}}dt$$

(18)

The key parameters are defined as follows:

$m_{fuel}$: fuel mass flow rate ($\mathrm{k}\mathrm{g}/\mathrm{s}$);

$Q_{fuel}$: calorific value of methanol, taken as 19.5 × 10³ $\mathrm{k}\mathrm{J}/\mathrm{k}\mathrm{g}$.

The energy consumption of the battery pack is calculated using Equation (19):

$$E_c={\int }_0^t{\displaystyle \frac{P_{req}+P_{Acc}-P_{eng}·\eta }{3600}}dt$$

(19)

The main variables involved include:

$P_{req}$: propulsion system power demand (kW);

$P_{Acc}$: auxiliary equipment power consumption (kW);

$P_{eng}$: output power of the methanol engine (kW);

$\eta$: system energy conversion efficiency (set at 80%).

To quantitatively compare the results presented in Figure 34, Figure 35, Figure 36, Figure 37, Figure 38, Figure 39 and Figure 40 and the total energy consumption computed via Equations (17)–(19),

Table 6. Comparison of improvements in energy consumption, emissions, and battery pack SOC.

Indicators	DP-ANFIS	DP
Total energy consumption (kWh)	78.53%	80.85%
Methanol consumption (kg/h)	64.95%	81.33%
BSFC (g/kWh)	81.26%	82.65%
Battery pack SOC	3.24%	4.63%
CO emissions (g/kWh)	82.91%	83.84%
CO2 emissions (g/kWh)	81.12%	82.79%
HC emissions (g/kWh)	83.4%	85.92%
NOx emissions (g/kWh)	15.2%	23.07%

summarizes the performance improvements of the marine methanol–electric hybrid propulsion system under the DP and DP-ANFIS strategies relative to the RB energy management strategy.

As shown in Table 6, the DP algorithm, as a global optimization method, demonstrates comprehensive advantages in energy efficiency and emissions control for the methanol–electric hybrid propulsion system under full navigation conditions. Compared to the RB strategy, DP reduces total energy consumption by 80.85% and increases battery SOC by 4.63%. Methanol consumption and brake-specific fuel consumption (BSFC) are reduced by 81.33% and 82.65%, respectively. Emissions of CO, HC, and NOx are decreased by 83.84%, 85.92%, and 23.07%, while CO₂ emissions are cut by 82.79%.

The DP-ANFIS strategy outperforms the RB strategy in optimization effectiveness and surpasses DP in real-time applicability. It reduces total energy consumption by 78.53% and increases SOC by 3.24% relative to the RB approach. Methanol use and BSFC are lowered by 64.95% and 81.26%, respectively. CO, HC, and NOx emissions are reduced by 82.91%, 83.4%, and 15.2%, and CO₂ emissions by 81.12%.

Trained on DP-generated optimal sequences, the DP-ANFIS strategy achieves near-global optimal performance, significantly exceeding the RB strategy across all metrics—particularly in CO₂ reduction, supporting decarbonization goals. Moreover, as a real-time capable strategy, it offers strong operational practicality. All reported results are based on an independent test set, and the minor performance gap between DP-ANFIS and DP confirms effective learning without overfitting.

9. Hardware-in-the-Loop Validation

9.1. HIL Test Bench Configuration

This study developed a distributed hardware-in-the-loop (HIL) platform using two NI PXIe real-time systems to validate the energy management strategy for a marine methanol–electric hybrid propulsion system.

As shown in Figure 41, the platform adopts a distributed architecture where two NI PXIe devices communicate via a high-speed CAN network, enabling separate deployment of the plant model and control strategy. The slave PXIe-1088 unit runs a high-fidelity multi-physics model of components such as the methanol engine, motor, and battery, while the master PXIe-1071 executes the energy management algorithm under HIL conditions. A microsecond-level synchronization mechanism ensures closed-loop operation. This setup facilitates transient condition emulation, energy allocation optimization, and abnormal operation testing, significantly enhancing validation reliability and efficiency.

This study develops a real-time simulation and verification system for a marine methanol–electric hybrid propulsion system using a modular architecture. By integrating MATLAB/Simulink with NI VeriStand and Measurement & Automation Explorer (MAX), a unified development and validation environment is established. High-fidelity models of key components—such as the methanol engine, propulsion motor, and battery—along with energy management algorithms are built in Simulink. These models are automatically converted to optimized C code, compiled into real-time executables (.so format), and then deployed to a PXIe processor via VeriStand for deterministic execution with time steps as low as 100 μs.

The system also includes an upper-level monitoring interface featuring:

A GUI (Figure 42) for real-time visualization of operational parameters;

A test case management module supporting flexible scenario configuration and sequential execution;

A data acquisition and processing unit enabling real-time computation and automated report generation.

This integrated solution supports the full development cycle—from algorithm design and digital simulation to HIL validation—enhancing both the quality and efficiency of hybrid powertrain system development.

In Figure 42, Eng_Speed denotes engine speed, Eng_Torque denotes engine torque, Mot_Speed denotes motor speed, Mot_Torque denotes motor torque, Eng_Spd_IN denotes engine speed input, Eng_Spd_OUT denotes engine speed output, Eng_Trq_IN denotes engine torque input, Eng_Trq_OUT denotes engine torque output, Mot_Spd_IN is engine speed input, Mot_Spd_OUT is engine speed output, Mot_Trq_IN is engine torque input, Mot_Trq_OUT is engine torque output, Batt_SOC_IN is battery SOC input, Batt_SOC_OUT is battery SOC output, Clt1_State_IN is clutch closed state, Clt1_State_OUT is the clutch disengagement state, Clt2_State_IN is the clutch engagement state, Clt2_State_OUT is the clutch disengagement state, Eng_Start_IN is the engine start signal, Eng_Start_OUT is the engine stop signal, Mot_Start_IN is the motor start signal, Mot_Start_OUT is the motor stop signal.

The hardware-in-the-loop (HIL) platform for validating the distributed energy management strategy of the marine methanol–electric hybrid propulsion system consists of a master control computer with dual-screen monitoring and two NI PXIe real-time simulation units. Key specifications are listed in

Table 7. Core hardware configuration of the distributed real-time HIL simulation system.

Project	Real-Time Simulation Machine for Controlled Objects	Real-Time Simulation Machine for Energy Management
Chassis	NI PXIe-1088 9 slots (8 mixed slots) (National Instruments (NI), Kuala Lumpur, Malaysia)	NI PXIe-1071 4 slots (3 mixed slots) (National Instruments (NI), Kuala Lumpur, Malaysia)
Controller	PXIe-8842 2.6 GHz 6-core controller LabVIEW RT (NI Linux Real-Time) (National Instruments (NI), Kuala Lumpur, Malaysia)	PXIe-8861 2.8 GHz 4-core controller LabVIEW RT (NI Linux Real-Time) (National Instruments (NI), Kuala Lumpur, Malaysia)
Communication module	PXIe-8510 6-port NI-XNET interface (National Instruments (NI), Kuala Lumpur, Malaysia)
Transceiver	TRC-8542 NI-XNET CAN HS/FD Transceiver Cable 18 inches (National Instruments (NI), Kuala Lumpur, Malaysia)
FPGA board	PXIe-7846R R Series Multi-Function Reconfigurable I/O Module Kintex-7 160T 500 kS/s (National Instruments (NI), Kuala Lumpur, Malaysia)
Fault Monitoring Board	NI PXIe-7858 PXI Multi-Function Reconfigurable I/O Module Kintex-7 325T FPGA, 1 MS/s (National Instruments (NI), Kuala Lumpur, Malaysia)

.

The plant simulation unit uses a PXIe-1088 chassis with a PXIe-8842 controller, PXIe-7846R FPGA module, and PXIe-8510 data acquisition card, powered by a Xeon 6-core CPU and 16 GB RAM. The control strategy unit employs a PXIe-1071 chassis with a PXIe-8861 controller, Xeon 4-core CPU, and 8 GB RAM.

Communication is handled via CAN bus under LabVIEW Real-Time OS, enabling multi-rate simulation, microsecond-level real-time performance, and robust HIL testing for hybrid power systems.

The energy management strategy for the marine methanol–electric hybrid propulsion system is validated using a dual-processor closed-loop architecture, as shown in Figure 43. The control-layer simulator (NI PXIe-1071) sends energy distribution signals via CAN to the execution-layer simulator (NI PXIe-1088), which runs a high-fidelity model of the hybrid system—including the motor, energy storage, and methanol generator—and returns real-time parameters such as speed, torque, power, and state of charge to complete the validation loop.

This HIL-based setup enables continuous dynamic response monitoring and control refinement under typical conditions. It supports validation of real-time algorithm performance as well as analysis of fuel consumption and emissions across various navigation profiles, providing an efficient testing framework for hybrid propulsion control.

The NI PXIe-1088 unit executes a high-fidelity, multi-physics plant model (detailed in Section 4) in hard real-time. This model includes the dynamic engine and motor response models (Equations (1) and (2)), the battery SOC calculation (Equation (7)), and the propeller load model. By running this comprehensive model on real-time hardware, the HIL platform accurately replicates the transient dynamics and energy flow of the actual marine methanol–electric hybrid propulsion system. The master NI PXIe-1071 unit executes the energy management strategy (the DP-ANFIS controller) as if it were deployed on the actual vessel controller. The two systems communicate via CAN bus, closing the control loop and providing a realistic validation environment that accounts for system dynamics and communication delays.

9.2. HIL Test Results

To validate the engineering feasibility of the proposed DP-ANFIS energy management strategy, a hardware-in-the-loop (HIL) test bench was employed (Figure 42). The transition from simulation to HIL introduced inherent hardware delays originating from three sources: computational delay (45 μs, negligible), communication delay over CAN (200–500 μs, depending on payload), and I/O conversion delay (on the order of μs). The total measured loop latency was below 1 ms—three orders of magnitude smaller than the dominant time constants of the plant dynamics (e.g., engine and battery SOC). Consequently, these delays did not materially affect the controller’s performance or system stability.

Comparisons between simulation and HIL results (Figure 44, Figure 45, Figure 46, Figure 47, Figure 48, Figure 49 and Figure 50) across key metrics—methanol consumption, BSFC, battery SOC, and emissions of CO, CO₂, HC, and NOx—show consistent trends with errors below 5%. Minor deviations are attributed primarily to communication latencies and emulated sensor/actuator dynamics, rather than computational limitations. The DP-ANFIS strategy operates comfortably within the deterministic real-time framework (minimum time step: 100 μs), confirming its hard real-time capability and practical applicability for supervisory energy management.

10. Discussion

This study addresses the challenges of high fuel consumption and emissions in specific inland waterway vessels through the retrofit of a methanol–electric hybrid propulsion system. A high-fidelity simulation model was developed, incorporating experimentally characterized methanol engine performance and emission profiles. RB, DP, and a novel DP-ANFIS energy management strategy were designed and rigorously evaluated via co-simulation and hardware-in-the-loop (HIL) testing. The principal findings are as follows:

• Improved Engine Efficiency:

The DP-ANFIS strategy enables the methanol engine to operate consistently within its high-efficiency range by adapting power demand and battery SOC to engine output.

2.

Enhanced Fuel Economy:

Compared to RB, DP-ANFIS reduces total energy consumption by 78.53%, methanol consumption by 64.95%, and BSFC by 81.26%, closely matching DP-based results.

3.

Optimized Battery Performance:

The DP-ANFIS strategy improves battery SOC by 3.24% over RB, approaching the 4.63% gain achieved by DP.

4.

Significant Emission Reduction:

DP-ANFIS substantially lowers CO, HC, and NOx emissions by 82.91%, 83.4%, and 15.2%, respectively, and reduces CO₂ by 81.12%, supporting carbon neutrality goals.

These results demonstrate that the DP-ANFIS strategy effectively optimizes real-time energy management, reduces energy waste, and minimizes emissions while maintaining performance close to global-optimal DP.

A notable finding is the limited reduction in NOx emissions (15.2%), which contrasts sharply with the substantial decreases observed in CO, HC, and CO₂ (all >80%). This divergence arises from fundamental differences in formation mechanisms: methanol’s oxygenated structure promotes complete combustion, effectively suppressing CO and HC formation, while NOx is primarily generated via high-temperature oxidation (Zeldovich mechanism). Although methanol’s high latent heat of vaporization contributes to charge cooling, its high flame speed and combustion efficiency maintain cylinder temperatures within the thermal NOx formation range—particularly under the steady high-load conditions favored by the DP-ANFIS strategy. The achieved NOx reduction stems mainly from the avoidance of high-load transients and the use of zero-emission electric mode. Further control will require integrating advanced aftertreatment technologies—such as EGR or SCR—with the energy management system to enable synergistic emission reduction.

5.

Validation of Engineering Feasibility

As shown in Figure 44, Figure 45, Figure 46, Figure 47, Figure 48, Figure 49 and Figure 50, hardware-in-the-loop (HIL) test results align well with simulation trends. Although minor deviations due to hardware response delays are observed, all key performance metrics remain within 5% error margins, affirming the reliability and practical applicability of the DP-ANFIS algorithm.

6.

Scalability and Generalization of the Proposed Strategy

The DP-ANFIS framework demonstrates strong scalability across marine applications. It can be adapted to different vessel types by retraining the ANFIS with offline DP data derived from specific powertrain models and operational profiles. The strategy inherently accommodates varying conditions—such as routes or environmental factors—through its direct use of propulsion power demand as a controller input. Moreover, the framework is not restricted to serial hybrid architectures and can be extended to parallel or multi-source systems by redefining the optimization states and control variables. While generating DP training data requires an initial computational investment, the resulting ANFIS controller operates with low overhead, enabling deployment on standard marine hardware. This scalability highlights the practical value and broad applicability of the approach for diverse hybrid propulsion systems.

7.

Economic Considerations and Retrofit Feasibility

The economic viability of the retrofit hinges on balancing higher initial investment against operational savings. While the methanol–electric system costs 40–60% more upfront than conventional diesel propulsion, it achieves approximately 65% fuel savings. Given that methanol is 10–20% cheaper than marine diesel, the payback period for a vessel operating 2500 h annually is estimated at 4–7 years based on fuel savings alone. This period could be shortened by lower maintenance costs for electric drivetrains, avoided emission penalties, and green subsidies. A comprehensive techno-economic analysis incorporating exact costs, fuel price trends, and operational specifics is recommended before commercial deployment.

In summary, this study adopts a three-stage methodology involving theoretical modeling, simulation, and experimental validation. By developing a methanol–electric hybrid propulsion system and a DP-ANFIS energy management algorithm, the work achieves low-carbon propulsion system design and real-time global energy optimization. The proposed solution offers an efficient and low-emission energy management strategy for hybrid-powered inland waterway vessels, and its practical value has been verified through rigorous testing, providing a valuable reference for the design and retrofit of relevant marine vessels.

11. Conclusions

Future work should focus on the following directions:

• Multi-Objective Optimization and NOx Control:

Extend the optimization framework to include NOx emissions alongside energy efficiency, revising cost functions in DP and ANFIS to penalize high-NOx operation. Integrate aftertreatment technologies like EGR or SCR with energy management for deeper emission control.

2.

Adaptive Online Learning:

Enhance the DP-ANFIS strategy with real-time adaptive algorithms to continuously adjust parameters based on operational data, engine degradation, and environmental changes, improving robustness and lifelong learning.

3.

Complex Powertrain Architectures:

Apply the method to multi-source systems incorporating fuel cells, supercapacitors, or photovoltaics, redefining state and control variables to manage diverse energy dynamics.

4.

Techno-Economic and Lifecycle Analysis:

Perform detailed TEA and LCA to evaluate ROI, operational costs, and full lifecycle emissions, supporting commercial adoption with quantitative benefits.

5.

Real-Ship Validation:

Implement the HIL-validated strategy in sea trials to test performance under real conditions and address integration challenges such as communication delays and sensor noise.