Adaptive Fuzzy Logic-Based Power Distribution Strategy for Four-Wheel-Drive Fuel Cell Electric Vehicles with Hybrid Energy Storage Systems

2.1 Vehicle architecture

The proposed FCEV architecture (Figure 1) includes a PEMFC as the main source, supported by a lithium-ion battery and a supercapacitor. Four 15 kW SynRM motors independently drive each wheel.

Figure 1. Advanced architecture of a modern battery electric vehicle with energy flow and detailed components

The main vehicle parameters are summarized in Table 1.

Table 1. Vehicle and powertrain specifications

2.2 Proton exchange membrane fuel cell model

The PEMFC stack voltage is modeled using electrochemical equations that account for reversible potential, activation losses, ohmic losses, and concentration losses [27]:

$V_{\text {stack }}=N_{\text {cells }} \cdot V_{\text {cell }}$        (1)

where, the cell voltage is:

$V_{c e l l}=E_{N e r n s t}-V_{a c t}-V_{o h m}-V_{c o n c}$          (2)

The Nernst potential represents the thermodynamic reversible voltage:

$\begin{aligned} & E_{N e r n s t} =1.229 -0.85 \times 10^{-3}(T 298.15) {R T} / 2 F {\ln }\left(P_{H_2} \sqrt{P_{O_2}}\right)\end{aligned}$            (3)

The activation overpotential follows the Tafel equation:

$V_{a c t}=\frac{R T}{\alpha_c n F} \ln \left(\frac{i}{i_0}\right)$         (4)

Ohmic losses are proportional to current:

$V_{\text {ohm }}=i \cdot R_{\text {ohm }}$           (5)

Concentration losses become significant at high current densities:

$V_{\text {conc }}=-B \ln \left(\frac{i}{i_L}\right)$            (6)

Non-ideal Effects: The model incorporates temperature-dependent efficiency correction:

$\eta_{F C}(T)=\eta_{F C}^{\text {nom }} \times(1+0.0012(T-80))$           (7)

and humidity effects on membrane resistance:

$R_{\text {membrane }}=R_0 \times\left(\frac{100}{R H}\right)^{0.15}$           (8)

where, RH is the relative humidity percentage. Degradation effects are accounted for using:

$V_{\text {cell }}(t)=V_{\text {cell }}^{\text {fresh }}-k_{\text {deg }} \times E o L(t)$           (9)

with $k_{\text {deg }}=0.8 \mu \mathrm{~V} / \mathrm{h}$ based on accelerated stress testing data from Ballard FCveloCity-HD modules.

The hydrogen consumption rate is calculated from Faraday’s law:

$\dot{m}_{\mathrm{H}_2}=\frac{N_{\text {cells}} \cdot I_{\text {stack}}}{2 \mathrm{~F}} \cdot M_{\mathrm{H}_2}$           (10)

where, $M_{H_2}=2.016 \mathrm{~g} / \mathrm{mol}$ is the molar mass of hydrogen. The PEMFC efficiency is defined as:

$\eta_{F C}=\frac{P_{\text {elec }}}{\dot{m}_{H_2} \cdot L H V_{H_2}}$          (11)

where, $L H V_{\mathrm{H}_2}=120~ \mathrm{MJ} / \mathrm{kg}$ is the lower heating value of hydrogen.

2.3 Battery model

The lithium-ion battery is modeled using an equivalent circuit approach with a voltage source dependent on state of charge (SoC) and an internal resistance:

$V_{b a t}=V_{O C V}(S o C)-I_{b a t} \cdot R_{i n t}$            (12)

Temperature effects on internal resistance follow:

$R_{\text {int }}(T)=R_{25 C} \times \exp \left(3500\left(\frac{1}{T}-\frac{1}{298}\right)\right)$         (13)

The SoC dynamics follow:

$\frac{d S o C}{d t}=\frac{-\eta_c \cdot I \text { bat }}{Q_{\text {nom }}}$          (14)

where, $\eta c$ is the coulombic efficiency and $Q_{\text {nom}}$ is the nominal capacity.

2.4 Supercapacitor model

The supercapacitor is modeled as an ideal capacitor with equivalent series resistance (ESR):

$V_{S C}=\sqrt{\frac{2 E_{S C}}{C}}-I_{S C} \cdot R_{E S R}$           (15)

The energy stored is:

$E_{S C}=\frac{1}{2} C V_{S C}^2$          (16)

2.5 Power demand calculation

The total power demand at the wheels is calculated from the vehicle dynamics equation:

$F_{\text {dem}}=\left(F_{\text {aéro}}+F_{\text {roll }}+F_{\text {grade}}+F_{\text {inertia}}\right) \cdot v$          (17)

where, the individual forces are:

$F_{a \text { èro }}=\frac{1}{2} \rho_a C_d A_f v^2$        (18)

$F_{\text {roll }}=C_r m g \cos \theta$         (19)

$F_{\text {grade }}=m g \sin \theta$           (20)

$F_{\text {inertia }}=m \frac{d v}{d t}$          (21)

This section explains where the parameters come from and how they were checked. They come from validated experimental data, manufacturer specifications, or literature.

2.5.1 Proton exchange membrane fuel cell parameters

The fuel cell stack parameters are based on the Ballard FC velocity-HD 45 kW module (Product Code: FC velocity ®-HD).

Key parameters were validated against the manufacturer’s polarization curve data:

• Number of cells: 300 (datasheet specification)
• Active area: 280 cm²/cell (measured)
• Exchange current density $\left(i_0\right)$: 0.001 A/cm² (fitted from polarization curve)
• Ohmic resistance $\left(R_{\text {ohm}}\right)$: 0.01 Ω (EIS measurement at 1 kHz)

Validation method: The semi-empirical model was fitted using least-squares optimization (Eqs. (1)-(6)) to make polarization data for the manufacturer. The RMSE is 2.3% over 10-240 A, which shows that the model is accurate.

2.5.2 Battery parameters

The battery pack employs A123 Systems ANR26650M1B lithium iron phosphate (LiFePO4) cells in a 96s3p configuration:

• Cell nominal voltage: 3.3 V (manufacturer specification)
• Cell capacity: 2.5 Ah (datasheet, C/3 discharge rate)
• Pack configuration: 96 cells in series, 3 parallel strings
• Total capacity: 15 Ah at 350 V nominal

Validation procedure: The OCV vs. SoC curve was obtained from constant-current pulse discharge tests (C/20 rate) with 2-hour relaxation periods. Internal resistance was measured via AC impedance spectroscopy at SoC intervals of 10% (temperature: 25 ℃). The fifth-order polynomial f it achieves $R_2=0.9987$. Temperature dependent resistance measurements were conducted in a thermal chamber at-20℃, 0 ℃, 25 ℃, and 40 ℃, validating the Arrhenius-type temperature correction.

2.5.3 Supercapacitor parameters

The supercapacitor module specification is based on Maxwell Technologies BMOD0165 P048 B02:

• Rated capacitance: 165 F (measured at 25 °C)
• Rated voltage: 48 V (datasheet maximum continuous)
• ESR: 6 mΩ (@ 1 kHz, 25 °C)
• Number of modules: 7 in series (total 357 V)

Validation procedure: Capacitance was verified via constant-current charge/discharge tests (50 A). ESR was measured using AC impedance method at 1 kHz.

Cycle life data from manufacturer (1 million cycles to 80% capacitance retention) supports the assumption of negligible degradation over vehicle lifetime.

4.1 Simulation setup and validation framework

The proposed AFLC-EMS was implemented in MATLAB/Simulink R2023a and validated under the WLTP Class 3 driving cycle, which represents real-world driving conditions more accurately than legacy cycles such as NEDC [19]. The simulation framework incorporates validated component models with parameters derived from experimental data and manufacturer specifications. Key simulation parameters are summarized in Table 9.

To ensure model fidelity, the PEMFC stack model was validated against polarization curves from Ballard FCveloCity-HD modules, achieving a root mean square error (RMSE) of less than 2.3% across the operating range. The battery model parameters were calibrated using electrochemical impedance spectroscopy (EIS) data from A123 Systems ANR26650M1-B cells configured in a 96s3p arrangement.

Table 9. Simulation parameters and initial conditions

4.2 Driving cycle characterization and power demand analysis

Figure 4 presents the WLTP velocity profile and corresponding power demand characteristics.

The power demand exhibits substantial variability, ranging from −28.4 kW during aggressive regenerative braking events to +57.2 kW during rapid acceleration phases.

• Mean positive power: 18.7 kW (traction mode)
• Mean negative power: −8.3 kW (regenerative mode)
• Standard deviation: 15.2 kW
• Power demand derivative range: ±45 kW/s
• Frequency content: 95% of energy below 0.1 Hz

The frequency domain analysis confirms that the majority of power demand variations occur at low frequencies (< 0.05 Hz), which can be efficiently managed by the fuel cell and battery. However, approximately 12% of the signal energy resides in the 0.1–1 Hz band, necessitating supercapacitor intervention to protect the battery from high-frequency stress [28].

4.3 Power distribution analysis

Figure 5 illustrates the temporal evolution of power distribution among the three energy sources throughout the WLTP cycle. The AFLC-EMS demonstrates intelligent power allocation that respects the dynamic capabilities and efficiency characteristics of each source.

Figure 5. Power distribution results: (a) Stacked power contributions showing source coordination, (b) Individual power profiles with operating limits, (c) Power distribution ratios over time, (d) Histogram of FC operating points

Statistical analysis of FC operation reveals that 78.3% of the cycle time corresponds to operation within the optimal 20–35 kW range, where stack efficiency exceeds 52%. The FC power rate of change is constrained to 1.8 kW/s on average, representing a 52.6% reduction compared to the rule-based strategy (3.8 kW/s). This reduction is particularly significant given that rapid power transients have been identified as a primary contributor to catalyst layer degradation.

4.3.1 Fuel cell operating characteristics

The fuel cell operates within a carefully controlled power band of 12–38 kW, corresponding to 27-84% of its rated capacity. This operating range was strategically selected to:

1. Maintain stack voltage above the critical threshold of 0.6 V/cell, preventing accelerated membrane degradation [29].

2. Avoid frequent start-stop cycles that induce carbon corrosion and platinum dissolution [30].

3. Operate predominantly in the high-efficiency region (50–60% based on LHV).

Statistical analysis of FC operation reveals that 78.3% of the cycle time corresponds to operation within the optimal 20–35 kW range, where stack efficiency exceeds 52%. The FC power rate of change is constrained to 1.8 kW/s on average, representing a 52.6% reduction compared to the rule-based strategy (3.8 kW/s). This reduction is particularly significant given that rapid power transients have been identified as a primary contributor to catalyst layer degradation [31].

A minimum FC power of 12 kW ensures continuous operation of auxiliary components and maintains the stack temperature within 60–80 ℃. During extended regenerative braking, the FC is reduced to this level instead of shutting down, avoiding thermal cycling.

4.3.2 Battery power management

The battery serves as the primary buffer between FC output and vehicle demand, operating bidirectionally within its rated power limits (-25 kW charging, +35 kW discharging). Several key observations emerge from the battery power profile:

1. Load leveling: The battery absorbs 67% of the high-frequency power fluctuations (0.01–0.1 Hz), reducing FC stress while maintaining overall system responsiveness.

2. Regenerative energy capture: During braking events, 94.2% of the recoverable energy is directed to the battery (with the remainder to the supercapacitor), maximizing round-trip efficiency given the battery’s superior energy density.

3. SoC-dependent operation: As the battery SoC decreases below 55%, the AFLC progressively shifts load to the FC, as evidenced by the increasing FC contribution during the Extra-High phase.

The battery experiences an average C-rate of 0.42 C during discharge and 0.35 C during charge, well within the recommended limits for lithium iron phosphate chemistry. Peak C-rates reach 2.3 C briefly during aggressive acceleration, but these events constitute less than 3% of cycle time.

4.3.3 Supercapacitor transient handling

The supercapacitor module demonstrates its effectiveness in managing rapid power transients, as evidenced by its activation during the 147 identified transient events (defined as $\left|d P_{\text {dem }} / d t\right|>15 \mathrm{~kW} / \mathrm{s}$).

Key performance metrics include:

• Average SC power during transients: 8.2 kW

• Maximum SC discharge power: 18.7 kW

• Maximum SC charge power: 22.1 kW (regenerative braking)

• SC round-trip efficiency: 94.7%

The frequency-based power splitting strategy effectively directs high-frequency components (> 0.1 Hz) to the supercapacitor while allowing low-frequency variations to be handled by the battery. This approach reduces battery current ripple by 34.2% compared to a two-source (FC + battery) configuration, which has been shown to improve battery cycle life by 15-25% [32].

4.4 State of charge dynamics and energy balance

Figure 6 presents the temporal evolution of battery and supercapacitor SoC throughout the driving cycle, along with the corresponding energy flows.

The regenerative braking system recovers 1.12 kWh of the 1.67 kWh theoretically available during braking events, corresponding to a recovery efficiency of 67.1%. This value is consistent with experimental studies on regenerative braking systems and accounts for losses in the motor, inverter, DC-DC converter, and energy storage systems.

Figure 6. State of charge (SoC) analysis: (a) Battery SoC trajectory with target band, (b) Supercapacitor SoC oscillations, (c) Cumulative energy flows, (d) SoC operating point density map

4.4.1 Battery state of charge trajectory analysis

The battery SoC evolves from the initial 70% to a final value of 52.1%, representing a net energy extraction of 2.81 kWh over the 23.27 km cycle. This trajectory exhibits several noteworthy characteristics:

1. Monotonic decrease with local recovery: The overall decreasing trend is punctuated by local SoC increases during regenerative braking phases, particularly evident in the High and Extra-High segments where vehicle speeds exceed 100 km/h.

2. Optimal window maintenance: The SoC remains within the 45–75% optimal operating window throughout the cycle, avoiding both the high-resistance region below 30% and the reduced charging acceptance above 85%.

3. Charge-sustaining tendency: The final SoC of 52.1% represents only a 7.9% deviation from the target value of 60%, confirming the effectiveness of the charge-sustaining control objective embedded in the AFLC rule base.

The battery SoC standard deviation of 4.2% indicates stable operation without excessive cycling, which is favorable for long-term battery health. Comparative analysis with the rule-based strategy shows that the AFLC achieves more consistent SoC maintenance, with 23% lower SoC variance over the cycle.

4.4.2 Supercapacitor state of charge oscillation patterns

The supercapacitor SoC exhibits characteristic high frequency oscillations superimposed on a slowly varying baseline, reflecting its role in transient power management. Key observations include:

1. Rapid response: SoC variations of up to 15% occur within 5-second windows during aggressive driving maneuvers, demonstrating the SC’s ability to rapidly absorb and release energy.

2. Baseline recovery: The adaptive mechanism ensures that SC SoC returns to the 50–70% nominal band within 30 seconds of any significant deviation, maintaining transient handling capability.

3. Phase-dependent behavior: During the Low phase (urban driving), SC SoC oscillations are frequent but small amplitude (± 5%). During the Extra-High phase (highway), oscillations are less frequent but larger amplitude (± 12%), reflecting the different driving dynamics.

The SC experiences approximately 890 micro-cycles during the WLTP cycle, with an average depth of discharge of 8.3%. Given the virtually unlimited cycle life of a supercapacitor (typically>1 million cycles), this operating pattern poses no concerns for long-term durability.

4.4.3 System energy balance

The overall energy balance for the WLTP cycle is summarized in Table 10, providing insight into energy flows and conversion efficiencies.

Table 10. System energy balance for WLTP cycle

4.5 Fuel cell performance and efficiency analysis

Figure 7 presents a comprehensive analysis of fuel cell operating characteristics throughout the WLTP cycle.

Figure 7. Fuel cell performance analysis: (a) Voltage-current characteristics with operating trajectory, (b) Instantaneous and moving-average efficiency, (c) Hydrogen consumption rate and cumulative consumption, (d) Operating point distribution on polarization curve

4.5.1 Polarization curve navigation

The FC operating trajectory on the polarization curve reveals the effectiveness of the AFLC in maintaining high-efficiency operation. The current density ranges from 0.15 to 0.82 A/cm², corresponding to cell voltages between 0.71 and 0.89 V. Notably:

• 82.4% of operating points fall within the "sweet spot" region (0.3–0.6 A/cm²) where efficiency exceeds 52%.
• Only 4.7% of operating time involves current densities above 0.7 A/cm², where concentration losses become significant.
• The activation loss region (< 0.2 A/cm²) is avoided by maintaining minimum FC power at 12 kW.

4.5.2 Efficiency distribution analysis

The instantaneous FC efficiency exhibits substantial variation (42–61%), reflecting the inherent trade-off between power output and efficiency in electrochemical systems. However, the time-weighted average efficiency of 53.2% compares favorably with values reported in the literature:

• Conventional rule-based EMS: 48–50% [33].
• Equivalent consumption minimization strategy (ECMS): 51–53% [34].
• DP (offline optimal): 54–56% [35].

The achieved efficiency represents 95.4% of the theoretical optimum obtained through DP, demonstrating that the AFLC successfully approximates global optimal behavior using real-time implementable rules.

The efficiency probability distribution shows a bimodal characteristic, with peaks at 51% (moderate load) and 56% (light load). This distribution differs markedly from the rule-based strategy, which exhibits a broader, unimodal distribution centered at 48%, indicating less precise operating point control.

4.5.3 Hydrogen consumption analysis

The total hydrogen consumption of 156.8 g over the 23.27 km cycle corresponds to 0.674 kg/100km, or equivalently, 0.82 kg/100km when expressed in terms of the WLTP-reported distance of 19.12 km (accounting for the Extra-High phase distance adjustment).

This result represents:

• 16.3% improvement over the rule-based strategy (0.94 kg/100 km).
• 4.7% improvement over the standard FLC (0.86 kg/100 km).
• Equivalent gasoline consumption: 2.54 L/100 km (based on energy equivalence).

The hydrogen consumption rate exhibits a strong correlation with vehicle speed and acceleration, with peak values of 1.42 g/s occurring during the Extra-High phase.

The adaptive mechanism effectively limits these peaks by preemptively engaging battery support during rapid acceleration events, as evidenced by the 23% reduction in peak consumption rate compared to the non-adaptive FLC.

4.5.4 Adaptation coefficient dynamics

Figure 8 illustrates the temporal evolution of the adaptive coefficients $\left(\alpha_{F C}, \alpha_{b a t}, \alpha_{S C}\right)$ throughout the driving cycle. The adaptation coefficients exhibit the following characteristics:

1. $\alpha_{F C}$: Higher values occur during sustained high-power demand (Extra-High phase) and lower values when battery SoC is high. The adaptation responds to SoC deviations with a time constant of approximately 15 s, balancing responsiveness with stability.
2. $\alpha_{bat}$: Exhibits inverse correlation with FC adaptation. The coefficient increases when battery SoC exceeds 65%, encouraging battery discharge to maintain optimal operating range.
3. $\alpha_{S C}$: Shows the highest variability, responding rapidly to power demand derivative. Peak values coincide with transient events, effectively increasing SC contribution during dynamic conditions. Adaptation rate limited to ± 0.05 s⁻¹ to avoid oscillations from interaction with the fuzzy controller.

Figure 8. Adaptive mechanism analysis: (a) Adaptive coefficient trajectories, (b) Correlation between $\alpha_{F C}$ and SoC error, (c) Correlation between $\alpha_{S C}$ and stress level, (d) 3D adaptive surface visualization

4.5.5 Ablation study: Adaptive vs. non-adaptive control

To quantify the contribution of the adaptive mechanism, an ablation study was conducted comparing the full AFLC with a fixed-parameter FLC using identical membership functions and rule base. Table 11 summarizes the results.

Table 11. Ablation study: Impact of adaptive mechanism

The adaptive mechanism contributes approximately 9.1% of the total hydrogen consumption reduction, with additional benefits in SoC regulation and constraint satisfaction. The 75% reduction in constraint violations (defined as brief excursions beyond optimal operating bounds) is particularly significant for component longevity.

Figure 9 provides visual comparison of key variables with and without adaptation, clearly demonstrating the smoother FC power profile and reduced battery stress achieved through adaptive control.

4.5.6 Sensitivity analysis of adaptive parameters

The sensitivity of system performance to adaptive mechanism parameters was evaluated:

• Adaptive coefficient bounds variation: Changing bounds from $[0.5,1.5]$ to $[0.4,1.6]$ results in $\pm 2.3 \%$ change in $H_2$ consumption, confirming reasonable robustness.
• Rate limiter sensitivity: Exploring range $0.03- 0.07 s^{-1}$ shows optimal performance at $0.05 s^{-1}$, balancing responsiveness (higher rates) and stability (lower rates).
• SoC target variation: Changing $S o C_{\text {target}}$ from 0.6 to 0.55 or 0.65 impacts final SoC deviation but has minimal effect on $H_2$ consumption ($<1.2 \%$ variation).

These results confirm that the adaptive mechanism design is robust to parameter uncertainties within reasonable bounds.

To assess the robustness and generalizability of the proposed AFLC-EMS, comprehensive simulations were conducted on two additional standardized driving cycles representing distinct operating conditions.

4.5.7 Driving cycles characteristics

Figure 10 presents a comparative analysis of the WLTP, UDDS, and HWFET driving cycles in terms of vehicle velocity, power demand, fuel cell power, battery and supercapacitor power profiles, and SoC trajectories.

UDDS (Urban Dynamometer Driving Schedule):

• Duration: 1369 s (extended to 1800 s for comparison)
• Distance: 11.99 km
• Maximum speed: 91.2 km/h
• Average speed: 31.5 km/h
• Characteristics: Frequent stops, low-speed operation, high transient content

HWFET (Highway Fuel Economy Test):

• Duration: 765 s (extended to 1800 s for comparison)
• Distance: 16.45 km
• Maximum speed: 96.4 km/h
• Average speed: 77.4 km/h
• Characteristics: Sustained high-speed operation, minimal stops, low transient content

4.5.8 Comparative results across cycles

This section presents a comparative analysis of the proposed energy management strategy under WLTP, UDDS, and HWFET driving cycles. The objective is to evaluate system adaptability, stability, and efficiency under different operating conditions.

Table 12 summarizes the performance of the proposed energy management strategy under WLTP, UDDS, and HWFET cycles, including hydrogen consumption, fuel cell efficiency, and energy storage behavior. The results highlight the robustness and efficiency of the system across different driving conditions.

Table 12. Multi-cycle validation results

4.5.9 Key observations and analysis

UDDS (Urban) Performance:

• Lowest $H_2$ consumption (0.74 kg/100 km) due to lower average speed and enhanced regenerative braking opportunities
• Highest FC efficiency (54.8%) as FC operates predominantly in low power, high-efficiency region
• Best SoC regulation (6.2% deviation) benefiting from frequent regeneration events
• Highest SC activity (1240 cycles) handling frequent stop-start transients

HWFET (Highway) Performance:

• Highest $H_2$ consumption (0.91 kg/100 km) due to sustained high-power demand

4.6 Fuzzy controller behavior analysis

Figure 11 presents the three-dimensional control surfaces of the fuzzy controller, providing insight into the power distribution strategy across the operating space.

Figure 11. Fuzzy controller control surfaces: (a) $K_{F C} v s . S o C_{\text {bat}}$ and $P_{\text {dem}}$, (b) $K_{\text {bat}} v s . S o C_{\text {bat}}$ and $P_{\text {dem}}$, (c) $K_{S C} v s . S o C_{S C}$ and $d P_{d e m} / d t$, (d) Cross-sectional analysis at characteristic operating points

4.6.1 Surface topology interpretation

The control surfaces exhibit smooth, monotonic transitions without discontinuities, ensuring stable control behavior across operating conditions.

Key features include:

1. FC coefficient surface: $K_{S C}$ increases monotonically with power demand, with the slope modulated by battery SoC, at low SoC (< 35%), the surface shows steeper gradients, indicating aggressive FC engagement to preserve battery capacity.
2. Battery coefficient surface: $K_{bat}$ exhibits a dome-shaped profile, peaking at moderate power demands (30–40% of maximum) and high SoC (>70%). The surface depression at high power demands reflects the strategy of protecting the battery from sustained high-current operation.
3. SC coefficient surface: $K_{S C}$ shows pronounced sensitivity to the power demand derivative, with peak values occurring at high $\left|d P_{\text {dem }} / d t\right|$ regardless of SoC level. The asymmetry between positive and negative derivatives reflects the different physical characteristics of acceleration and braking events.

4.6.2 Rule activation characteristics

Analysis of rule activation patterns throughout the WLTP cycle reveals the following characteristics, summarized in Table 13.

The analysis reveals that a relatively small subset of rules (18.3%) dominates system behavior during normal operation, while rules designed for extreme conditions (Very Low/Very High SoC, Heavy Traction/Braking) fire infrequently but with high impact on instantaneous outputs. This distribution validates the rule base design, which allocates greater granularity to frequently encountered operating regions while maintaining coverage of boundary conditions.

Table 13. Rule activation statistics during WLTP cycle

4.6.3 Execution time analysis on target platforms

The AFLC algorithm was implemented and benchmarked on four representative platform.

Table 14 summarizes the computational performance of the proposed AFLC algorithm on different hardware platforms, including execution time and CPU load.

Key Findings:

• The maximum execution time on the production-viable NXP S32K344 ECU is 2.34 ms, well within the 100 ms control cycle requirement for vehicle energy management
• Even the low-cost Raspberry Pi 4 (educational/prototyping platform) achieves execution times below 10 ms
• The dSPACE platform (rapid prototyping) confirms sub-millisecond performance (0.18 ms mean)

Comparison with Alternative EMS Approaches:

Table 15 compares computational requirements across different EMS strategies:

The proposed AFLC achieves real-time performance with computational cost comparable to ECMS but without requiring cycle-specific equivalence factor tuning. It is 14× faster than MPC while achieving 97.6% of MPC performance.

Table 14. Computational performance on different platforms

Table 15. Energy management strategy (EMS) computational complexity comparison (NXP S32K344 platform)

4.6.4 Memory requirements

Program Memory (ROM): 48 KB

• Membership function lookup tables: 18 KB
• Fuzzy rule base storage: 22 KB
• Adaptive mechanism code: 8 KB

Data Memory (RAM): 2.8 KB

• Runtime variables and state history: 1.6 KB
• Intermediate fuzzy computation buffers: 0.9 KB
• Communication buffers: 0.3 KB

Stack Depth: 420 bytes (maximum observed during worst-case execution)

These requirements are compatible with modern automotive-grade microcontrollers (e.g., NXP S32K3 series typically offers 4 MB Flash + 512 KB RAM).

4.6.5 Computational complexity breakdown

Profiling analysis on the NXP S32K344 platform reveals the following execution time distribution:

Rule evaluation (41%) and fuzzification (34%) dominate execution time, which is typical for FLC. The adaptive mechanism adds only 10% overhead, confirming its computational efficiency.

4.6.6 Interface compatibility and system integration

Communication Interfaces:

• Controller Area Network (CAN) bus: 500 kbps, 100 ms cycle time (adequate for 0.89 ms execution)
• Flex Ray (optional): 5 ms cycle time for high-speed coordination
• Diagnostic: UDS (ISO 14229) over CAN for calibration and monitoring

Functional Safety:

• ASIL-B compliant architecture (ISO 26262)
• Watchdog timer monitoring (1 ms timeout)
• Plausibility checks on sensor inputs (SoC, voltage, current ranges)
• Graceful degradation to limp-home mode upon faults

AUTOSAR Compatibility:

The AFLC has been successfully integrated into an AUTOSAR Classic.

Platform 4.4 environment:

• Software Component (SWC): EMS_AFLC
• Runnable period: 100 ms
• Inter-runnable variables: SoC, power demand, distribution coefficients
• Sender-receiver ports for CAN communication

4.6.7 Calibration effort

Compared to alternative strategies, the AFLC requires moderate calibration effort:

• Rule-Based: 1–2 person-weeks (threshold tuning)
• AFLC: 2–3 person-weeks (membership functions + rule refinement)
• ECMS: 3–4 person-weeks (equivalence factor tuning per cycle)
• MPC: 4–6 person-weeks (system identification + tuning)

The calibration procedure for AFLC follows:

1. Component characterization (2 days)
2. Membership function initialization based on operating ranges (1 day)
3. Rule base development from expert knowledge (2 days)
4. Rule refinement via simulation across multiple cycles (3–4 days)
5. Adaptive gain optimization using particle swarm optimization (2–3 days)
6. Validation and fine-tuning (2 days)

Conclusion: The proposed AFLC-EMS is real-time implementable on current automotive-grade ECUs without requiring dedicated DSP hardware, making it suitable for series production deployment. Its computational efficiency positions it favorably between simple rule-based methods and complex optimization-based approaches.

This section provides extensive comparison of the proposed AFLC-EMS with state-of-the-art energy management strategies.

4.6.8 Strategies compared

Five representative EMS approaches are evaluated under identical conditions (WLTP cycle, same vehicle/component parameters):

1. Rule-Based (RB): Threshold-based power distribution with fixed FC operating point
2. Equivalent Consumption Minimization Strategy (ECMS): Real-time optimization with equivalence factors = 2.8
3. MPC: Receding horizon optimization (horizon = 30 s, quadratic programming)
4. DP: Offline global optimization (bench Mark for theoretical optimum)
5. AFLC (Proposed): Adaptive fuzzy logic controller

4.6.9 Comprehensive performance metrics

Table 16 presents a detailed quantitative comparison across multiple performance dimensions.

Table 16. Comprehensive comparison with state-of-the-art EMS approaches

4.6.10 Visual comparative analysis

Figure 12 provides a side-by-side visual comparison of key metrics.

The overlaid power profiles (sub-figured) clearly illustrate the differences in control.

Philosophy:

• RB exhibits step changes at power thresholds
• ECMS shows smooth but reactive behavior
• MPC demonstrates anticipatory control (when prediction is accurate)
• AFLC balances smoothness and reactivity without requiring prediction

4.6.11 Performance-complexity trade-off analysis

Figure 13 presents the Pareto frontier in the $H_2$ consumption vs. computational cost space.

4.6.12 Detailed analysis by strategy

AFLC vs. ECMS:

• AFLC achieves 5.7% better fuel economy (0.82 vs. 0.87 kg/100 km)
• Comparable computational cost (0.89 ms vs. 0.82 ms)
• AFLC requires less cycle-specific tuning (no equivalence factor calibration)
• ECMS achieves better SoC regulation (1.6% vs. 7.9% deviation)

AFLC vs. MPC:

• MPC achieves 2.4% better fuel economy (0.84 vs. 0.82 kg/100 km)
• AFLC is 14× faster (0.89 ms vs. 12.4 ms)
• MPC requires accurate future driving prediction (V2X connectivity)
• AFLC demonstrates superior robustness when prediction is unavailable

AFLC vs. DP:

• AFLC achieves 96.2% of DP theoretical optimum
• DP is offline and non-causal (requires full cycle knowledge)
• The 3.8% optimality gap of AFLC is acceptable for real-time implementation