Article citation information:

Nguyen, A.N., Nguyen, X.H., Pham, T.Q., Vu, H.Q. Enhancing ride comfort for the driver and passengers in a five-seat vehicle using regression modeling, TOPSIS, and PID control. Scientific Journal of Silesian University of Technology. Series Transport. 2026, 132, 243-265. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2026.132.13

 

 

Anh Ngoc NGUYEN[1], Xuan Hien NGUYEN[2], Tuan Quang PHAM[3], Hai Quan VU[4]

 

 

 

ENHANCING RIDE COMFORT FOR THE DRIVER AND PASSENGERS IN A FIVE-SEAT VEHICLE USING REGRESSION MODELING, TOPSIS, AND PID CONTROL

 

Summary. This paper examines the effects of realistic and randomly varying loading conditions – including variations in driver mass, longitudinal seat position, and the number and seating positions of passengers – on the ride comfort of both the driver and passengers in a five-seat passenger vehicle. A thirteen-degree-of-freedom full-vehicle dynamic model is developed, incorporating an actively controlled driver seat suspension governed by a Proportional-Integral-Derivative (PID) controller. Regression analysis is employed to characterize the combined influence of loading and seat position variations on the root-mean-square (RMS) acceleration and RMS displacement of the driver seat. Subsequently, a multi-criteria decision-making method is applied to determine the optimal driver seat position. Three PID tuning methods – Ziegler-Nichols, Auto-Tune, and Particle Swarm Optimization (PSO) – are evaluated and compared. To improve computational efficiency, Ziegler-Nichols and Auto-Tune are used to constrain the PSO search space. Simulation results indicate that the integrated application of regression analysis, TOPSIS, and PID control can achieve up to a 78% reduction in RMS seat acceleration while maintaining floor vibration levels within the comfort limits specified by ISO 2631. In addition, the proposed PSO search-space optimization strategy demonstrates a notable improvement in computational time.

Keywords: ride comfort, PSO-based optimization, multi-criteria decision making, Polynomial regression

 

 

1. INTRODUCTION

 

Ride comfort is a key factor influencing driver performance, passenger satisfaction, and overall safety, particularly in five-seater passenger vehicles operating under variable loads and road conditions. Excessive road-induced vibrations can lead to discomfort, fatigue, and long-term musculoskeletal disorders, as defined in ISO 2631-1 [1]. The vibration behavior of such vehicles is inherently nonlinear due to variations in seat properties, asymmetric passenger distribution, and luggage placement.

Conventional passive suspension systems (PSS) are simple and economical but fail to adapt to changing road excitations and payloads, thus limiting vibration isolation [2, 3]. Although parameter optimization improves their performance, effectiveness remains limited under dynamic conditions. Active and semi-active suspensions (ASS, SASS) overcome these limitations by adjusting damping and stiffness in real time. Modern control strategies, such as model predictive control (MPC), fuzzy logic control (FLC), and hybrid GA-LQR optimization, have improved both ride comfort and handling [4-6]. Furthermore, intelligent control methods, including deep learning, genetic-based PID tuning, and hybrid fuzzy-genetic algorithms, show strong potential for vibration mitigation [7, 8], while machine learning (ML) introduces adaptive self-optimization capabilities [9]. However, issues of data reliability, interpretability, and safety remain open challenges.

Despite these advancements, most studies rely on simplified quarter- or half-vehicle models that neglect coupling between full-vehicle dynamics, seat suspension, and load distribution. Influences such as seat cushioning and luggage position are often overlooked. Classical PID controllers remain prevalent in practice, yet few works have systematically compared different tuning techniques – Ziegler-Nichols, Auto-Tune, and PSO – within a full-vehicle context [10-13]. Moreover, multi-criteria decision-making (MCDM) and regression-based prediction models are rarely employed to comprehensively assess ride comfort [14, 15].

To address these gaps, this study proposes an integrated framework for optimizing ride comfort in five-seater vehicles by: Developing a 13-DOF full-vehicle vibration model incorporating seat suspension and load distribution; deriving analytical formulations for adaptive suspension tuning; comparing three PID tuning approaches; implementing a regression-based vibration prediction model; and applying a TOPSIS-based MCDM method to evaluate ride comfort under diverse operating conditions.

 

2. METHODS AND MATERIAL

 

2.1. Vibration Modeling

 

Based on Newton's second law, D'Alembert's principle, and the principle of conservation of energy, a dynamic model of the full suspension system for a five-passenger vehicle with one luggage compartment is constructed in Fig. 1.

 

 

 

Fig. 1. Physical model

 

2.1.1.   Full-vehicle Model

 

The full-vehicle model consists of thirteen degrees of freedom (DOF), representing the vertical and angular motions of a five-seat passenger vehicle under varying load conditions. The model includes the front unsprung mass mu1, a rear unsprung mass mu2 with rotational inertia Iu2, the two-stage driver-seat subsystem comprising the seat frame mass mse and the driver mass mDr, four lumped passenger-seat masses mP1–P4, and the luggage mass mlug. These DOFs collectively describe the primary pathways through which tire-road excitations propagate toward the driver and occupants.

 

2.1.2. Sprung Mass and Body Coordinates

 

The vehicle body is modeled as a rigid mass m_scapable of heave, pitch, and roll motions, governed respectively by the inertial properties Iy (pitch) and Ix (roll). All subsystem coordinates are referenced to the geometric center of gravity (CG).

The longitudinal distances from the CG to the front and rear axles are denoted by a and b, while the lateral offsets of the suspension mounting points are given by d1 and d2. The driver-seat and passenger-row longitudinal locations are specified by C1 and C2. The driver's seat and passengers also exhibit a lateral offset d. The front and rear tire positions relative to the roll axis are defined by dp1 and dp2. These geometric parameters determine the transformation between local vertical displacements and the resulting pitch-roll motions.

2.1.3. Unsprung Masses, Tire, and Suspension Assemblies

 

Each front wheel is modeled as an independent unsprung mass mu1 connected to the sprung mass through suspension stiffness Ks1 and damping Cs1. The corresponding tire dynamics are described using Kelvin-Voigt elements with parameters Kt1 and Ct1.

The rear axle is represented by a single rigid unsprung body mu2 linked to the chassis via suspension parameters Ks2 and Cs2. Its tire-road interaction is characterized by Kt2 and Ct2.

 

2.1.4. Driver-Seat Subsystem with Active PID Actuation

 

The driver seat adopts a two-stage isolation structure consisting of the seat frame mass mse supported by a seat suspension with stiffness Kse and damping Cse, and the driver mass mDr interacting through a viscoelastic cushion characterized by KDr and CDr.

An electromechanical actuator is mounted in parallel with the seat suspension to generate an active control force Fa. A PID controller modulates Fa based on the deviation between the driver’s measured acceleration and the desired value (0) to suppress vertical vibration.

 

2.1.5. Passenger-Seat Masses

 

Four additional DOFs represent the vertical motions of the passenger-seat masses. Each mass is mounted directly on its cushion without auxiliary suspension elements, reflecting typical middle- and rear-row seating structures. These DOFs introduce additional loading on the car body and affect how vibration energy propagates across the cabin.

 

2.1.6. Luggage Mass Representation

 

The luggage is modeled as a lumped mass mlug located at horizontal and vertical offsets: f and e from the CG. Luggage is placed on the vehicle floor via rigid bumpers, represented as Klug and Clug. Its presence alters axle load distribution, shifts the effective CG location, and modifies pitch-related vibration transmission.

 

2.1.7. Integrated Multi-Subsystem Dynamics

 

All subsystems are coupled through suspension forces, tire-road interactions, geometric offsets, and distributed masses. The vertical forces arise from tire deflections (Kt1, Kt2), suspension compression (Ks1, Ks2), and seat-human interactions (Kse, Cse, KDr, CDr). The parameters a, b, d1, d2, dp1, and dp2 dictate the pitch-roll coupling of these forces. The force analysis diagram for the entire system is illustrated in Fig. 2.

 

2.1.8.   Differential Equations

 

Driver vertical displacement

 

(1)

 

 

Fig. 2. Free body and force analysis diagram

 

Driver’s seat vertical displacement:

 

(2)

 

Passenger seat  motion (for ):

 

(3)

 

Vehicle’s floor vertical displacement:

 

(4)

 

Floor angular displacement (pitch, longitudinal axis):

 

(5)

 

Floor angular displacement (roll, lateral axis):

 

(6)

 

Front unsprung mass displacement :

 

(7)

 

Rear unsprung mass displacement (dependent axle):

 

(8)

 

Angular displacement of the rear unsprung mass:

 

(9)

 

2.1.9.   Determination of Technical Parameters of the Seat Suspension System

 

According to ISO 2631 [1] and numerous experimental studies, ride comfort for occupants in passenger vehicles is most sensitive within the vibration frequency range of 1-2 Hz. Therefore, the design objective is to select the seat suspension stiffness (K) and damping coefficient (C) such that the natural frequency of the driver’s seat suspension system falls within this optimal range, while maintaining adaptability to varying driver body masses and loading conditions. Accordingly, the key parameters are determined as:

 

(10)

 

where fn is the desired natural frequency (Hz); m is the combined seat-driver mass (kg); and ζ is the damping ratio (typically 0.2-0.8, with ζ = 0.8 adopted in this study) [16].

 

2.2       Apply Methodologies

 

2.2.1.   Polynomial Regression Model

 

A second-order polynomial regression model was established to predict the RMS acceleration and displacement responses at the driver’s seat and vehicle floor. The general quadratic form is expressed as in Equation 11 [17].

 

(11)

 

In this study, the regression model is formulated as Equation 12:

 

(12)

 

where mDr is the driver’s body mass (kg), C1 is the longitudinal seat coordinate (m), and βi is the regression coefficients are estimated via least squares.

The model performance is evaluated using statistical indices, including the coefficient of determination R2, root mean square error (RMSE), as defined in Equation 13, 14.

 

(13)

 

(14)

 

These metrics collectively assess model accuracy, robustness, and generalization capability [17, 18].

 

Tab. 1

Regression model evaluation

 

Metric

Good Threshold

Interpretation

R2

> 0.95

Indicates an excellent model fit

RMSE

< 0.01-0.03 m/s²

Reflects high prediction accuracy

 

2.2.2.   TOPSIS Method

 

According to the eight-step procedure for calculating the Ci* index presented in [19], the performance indicators, including the RMS acceleration, RMS displacement, and the driver’s settling time, were determined using the assigned weighting factors of 0.35, 0.35, and 0.3, respectively.

 

2.2.3.   PID Control Method

 

A PID controller is implemented to regulate the hydraulic actuator for attenuating road-induced vibrations at the driver’s seat. Three tuning approaches are considered:

Ziegler-Nichols Method [20]

PID gains are determined as:

 

Tab. 2

Ziegler-Nichols tuning rule for PID

 

Controls

or

or

P

–

–

PI

–

PID

 

MATLAB PID Tuner

Provides automatic PID tuning via linearization at the operating point; requires user expertise.

 

PSO-Based PID Optimization

The Particle Swarm Optimization (PSO) algorithm was employed to optimize the proportional-integral-derivative (PID) controller gains Kp, Ki, Kd for the active driver-seat suspension system. In this study, an electromechanical actuator mounted beneath the driver seat generates an active control force Fa to reduce seat vibration and improve ride comfort.

In the PSO framework, each particle represents a candidate PID parameter set:

 

                                                     (15)

 

The velocity and position of each particle are updated iteratively according to:

 

    (16)

 

where w is the inertia weight, c1 and c2 are the acceleration coefficients, and r1, r2  [0,1]are random numbers. The inertia weight was dynamically updated to improve convergence performance:

 

                                                    (17)

 

The fitness evaluation was implemented in the MATLAB Simulink environment. The optimization objective was to minimize the weighted RMS value of the vertical driver-seat acceleration (aw) while constraining the actuator force within the allowable limit of 500 N. The fitness function is defined as:

 

                                              (18)

 

with the penalty function expressed as:

 

 

The optimization process continued until the maximum number of iterations was reached, and the optimal PID parameters were obtained from the global best solution.

 

2.3.      Ride Comfort Evaluation Standard

 

The ride comfort evaluation in this study follows the ISO 2631-1:1997 standard [1], in which the root mean square (RMS) acceleration in the vertical direction is employed as the primary indicator of whole-body vibration (WBV). The RMS acceleration is computed as:

 

(19)

 

The ride comfort is classified based on the magnitude of whole-body vibration (WBV) exposure, with predefined thresholds corresponding to different comfort levels.

 

 

Fig. 3. Flowchart of the PSO algorithm and the values of its variables

 

Tab. 3

RMS acceleration assessment standard

 

Vibration Emission

Comfort Scale Rating

<0.315 m/s²

Not uncomfortable

0.315 m/s² - 0.63 m/s²

A little uncomfortable

0.5 m/s² - 1 m/s²

Fairly uncomfortable

0.8 m/s² - 1.6 m/s²

Uncomfortable

1.25 m/s² - 2.5 m/s²

Very uncomfortable

>2.5 m/s²

Extremely uncomfortable

 

2.4.      Simulation

 

CD Road Profile Modeling: The road surface was modeled following ISO 8608:1995[23], using a Class C-D Power Spectral Density (PSD) profile at reference spatial frequency  cycle/m with  m³ and slope exponent . The spatial PSD was converted to the time domain using  (vehicle velocity  m/s). The road elevation signal  was synthesized as:

 

(20)

 

 

where  is a random phase and  is the spatial frequency increment. The synthesized profile (band  cycle/m, ) was sampled at 1000 Hz for 10 s and implemented in Simulink via a From Workspace block to excite the vehicle model. The CD Road profile is described in Fig. 4.

 

 

Fig. 4. Standard CD Road profile

 

The simulation block diagram developed in Simulink software is presented in Figure 5. The simulation data used in Table 4 are referenced from document [24]. In addition, the seat displacement parameter C1 was directly measured on a 2021 Mitsubishi XPander car.

Refer to the simulation parameter table reported in [24] as the simulation data.

 

Tab. 4

Simulation parameters

 

Symbol

Value

Unit

Symbol

Value

Unit

1.011

m

2460

Kg.

1.803

m

460

Kg.

0.3-0.5

m

250

Kg.

0.25

m

40; 85

Kg

0.65

m

35

Kg

0.761; 0.711

m

1460

Kg

0.761; 0.761

m

50

Kg

31000

N/m

V

16.67

m/s

830

N.s/m

g

9.8

m/

19960; 17500

N/m

f

0

m

1290; 1620

N.s/m

e

1.2

m

175500

N/m

KDr

18000

N/m

20

N.s/m

CDr

200

N.s/m

 

 

Fig. 5. Full-vehicle simulation model

 

 

 

3. RESULTS AND DISCUSSION

 

3.1.      Effects of Driver Mass and Seat Position on Ride Comfort of Driver and Vehicle Floor

 

The regression analysis was conducted to predict the vibration responses at the driver’s seat and vehicle floor under varying load and seating conditions. Numerical simulations were performed by varying the driver’s body mass (40-100 kg) and longitudinal seat position (0.20-0.60 m) on a Mitsubishi Xpander 2021, yielding 117 cases.

RMS Acceleration at the Vehicle Floor (Floor aRMS)

As the driver’s mass increases from 40 to 100 kg, the floor RMS acceleration slightly decreases from 0.411 to 0.391 m/s², indicating greater dynamic stability under higher loads. This trend agrees with the forced vibration relation a = F/m.

Seat position has a negligible influence, with variations below 0.002 m/s² across all masses. The high stiffness and uniform load distribution through the vehicle body ensure that the floor vibration remains largely unaffected by driver configuration. Overall, the fluctuation of less than 5% confirms that the floor maintains stable dynamic behavior under CD-type road excitation

 

Fig. 5. The regression of RMS acceleration and displacement

 

RMS Displacement at the Vehicle Floor (Floor dRMS)

The floor RMS displacement remains nearly constant at 0.0240 ± 0.0001 m, showing that its motion primarily reflects the vehicle body’s global vibration, governed by suspension and road input rather than seat-specific effects.

RMS Acceleration at the Driver’s Seat (Seat aRMS)

Unlike the floor, seat RMS acceleration increases significantly with driver mass. As rises from 40 to 100 kg,  grows by approximately 43% (0.444 → 0.636 m/s² at m). This occurs due to resonance coupling: increasing mass reduces the seat’s natural frequency . When  approaches (≈ 2.3 Hz), resonance amplifies seat acceleration. Seat position causes only secondary effects – RMS acceleration slightly decreases at front positions (0.2-0.4 m) and stabilizes toward the rear, with overall variation within ±5%. This is mainly due to changes in excitation energy related to the vehicle’s center-of-gravity distance.

RMS Displacement at the Driver’s Seat (Seat dRMS)

Seat displacement varies slightly between 0.02445 and 0.0255 m, increasing by about 4% with driver mass but remaining insensitive to seat position. The seat structure thus maintains stiffness and small oscillations around equilibrium without excessive deflection.

Regression Model Performance

RMS acceleration at the floor:

 

(21)

 

 

RMS displacement at the floor:

 

(22)

 

RMS acceleration at the driver’s seat:

 

(23)

 

RMS displacement at the driver’s seat:

 

(24)

 

The second-order polynomial regression accurately characterizes the nonlinear relationship between driver mass, seat position, and vehicle vibration responses. The coefficients of determination demonstrate high predictive accuracy, with R² = 0.9787 for seat acceleration, 0.9572 for floor acceleration, and 0.9228 for seat displacement. In contrast, the floor displacement exhibits a very low coefficient of determination (R² = 0.0392), indicating minimal sensitivity to driver mass and seat position. This suggests that floor displacement remains nearly constant and is primarily governed by global vehicle body motion rather than local seat – occupant dynamics, making polynomial regression ineffective for predicting this response based on these variables alone. The corresponding root-mean-square errors (RMSE = 0.0055 m/s² for seat acceleration, 0.00135 m/s² for floor acceleration, and 7.48×10⁻⁵ m and 5.42×10⁻⁵ m for seat and floor displacements, respectively) confirm the regression model’s strong interpolation capability and physical consistency. These results validate the model as a reliable surrogate for numerical simulation, enabling a substantial reduction in computational cost while maintaining high predictive precision. Extrapolation remains applicable for small variations in driver mass within fixed seat position limits. For instance, at mDr = 120 kg and C₁ = 0.3 m, the model predicts RMS accelerations of 0.695 m/s² (seat) and 0.393 m/s² (floor), both consistent with the observed nonlinear trend.

 

3.2.      Integrated Evaluation Using Polynomial Regression and TOPSIS

 

Polynomial regression results were integrated into a multi-criteria decision-making (MCDM) framework to identify the optimal seat position balancing comfort and dynamic stability.

The analysis identifies the most comfortable configuration at mDr = 40 kg and C₁ = 0.35 m (  = 0.989), while the least comfortable configuration occurs at mDr = 100 kg and C₁ = 0.20 m (  = 0.003). These results provide a quantitative basis for seat position optimization under varying driver loads.

The analysis indicates that the optimal seat position (C₁) generally increases with driver mass from 40 kg to approximately 90 kg (0.35-0.60 m) and slightly decreases at 100 kg. This trend reflects the shifting center of mass of the driver-seat system and its influence on vibration transmission, allowing improved comfort for moderate loads.

 

 

Fig. 6. The ride comfort index based on TOPSIS

 

3.3.      Evaluation of Passenger and Luggage Effects on Driver Ride Comfort

 

Simulation Conditions: Passenger count varies randomly from 0 to 4, each weighing 60 kg, with seating positions randomly assigned (P1-P4). One luggage item of 50 kg is placed randomly in the trunk.

 

Tab. 5

Driver vibration under varying passenger and luggage configurations

 

Passengers &Luggage

Min

Position

Interpretation

Max

Position

Interpretation

0 passenger

–

No passengers or luggage, due to light floor load.

–

-

1 passenger

P2

The load is biased to the right

P1

Load uniform on the front axle

2 passengers

P2, P3

The load is biased to the right

P2, P4

Load uniform on the rear axle

3 passengers

P2, P3, P4

The load is biased to the right and rear

P1, P2, P4

Load uniform between front and rear

4 passengers & luggage

–

Heavy, uniform load

All positions + luggage

The absolute minimum occurs with a heavy, uniform load.

 

Tab. 5 indicates the randomly distributed passenger positions that result in the most uncomfortable and the most comfortable ride conditions for the driver, based on the evaluation of displacement and acceleration criteria using the TOPSIS.

The driver’s RMS acceleration increases significantly under asymmetric loading, particularly when the mass is biased toward the right or rear positions (P2-P4). The lowest acceleration occurs when the vehicle carries four passengers and luggage, where the load is heavy but evenly distributed; however, such loading also increases the seat and floor displacements, which, if excessive, may cause bump-stop contact and directly affect the driver’s comfort and safety.

 

Tab. 6

Most and least comfortable passenger positions on the vehicle

 

Passengers

Max

Position

Min

Position

Ride comfort in descending order

1 passenger

P1

P2

P1>P4>P3>P2

2 passengers

P1_P2

P2_P3

P1_P2>P1_P3>P1_P4>P4_P2>P4_P3>P2_P3

3 passengers

P1_ P2_P4

P2_P3_P4

P1_P2_P4>P1_P2_P3>P1_P3_P4>P2_P3_P4

4 passengers & luggage

P1

P2

P1>P4>P3>P2

 

Tab. 6 confirms that passenger seat selection directly affects individual ride comfort. Central positions, particularly P1, are subjected to lower vibration levels because they are closer to the vehicle’s longitudinal centerline, where dynamic load transfer remains more balanced. In contrast, peripheral seats such as P2 experience higher accelerations due to asymmetric loading and increased lateral vibration. This variation is explained by the manner in which oscillatory forces are transmitted through the suspension and vehicle body, depending on seat location. In practical terms, passengers seated in less favorable positions are more susceptible to motion-related discomfort such as motion sickness, headaches, or nausea. This influence becomes even more critical in multi-passenger vehicles, where the choice of seating arrangement plays a decisive role in overall ride comfort.

 

3.4.      Solutions for Improving Ride Comfort of Vehicle Occupants

 

3.4.1    Adjustment of Seat Suspension Parameters

 

Equation 10 was applied to recalculate the seat suspension parameters based on the data in Tab. 4. Subsequently, a comparison was carried out to evaluate the improvement achieved by adjusting the seat suspension characteristics to match the occupant’s weight and the vehicle’s ride comfort frequency, in comparison with the conventional passive seat suspension system. The calculation results indicate that the seat suspension stiffness was recalculated to  and the damping coefficient to . The calculated parameters of the seat suspension system under different loading conditions were compared with the results reported in the literature [26, 27] to assess the validity of the numerical results.

The results in Figure 8 indicate that the comfort level of the seat suspension system strongly depends on the accurate tuning of the spring and damper parameters. In the non-optimized case (aZDrdd-none), the driver’s RMS acceleration reached 0.5 m/s², which is 19.6% higher than the floor acceleration: aZsdd (0.402 m/s²), corresponding to a “quite uncomfortable” condition. After optimization, this value decreased to 0.33 m/s² (aZDrdd_CT), which is 17.9% lower than the floor acceleration (0.436 m/s²) and 34% lower than that of the passive suspension system, demonstrating a significant improvement in ride comfort.

 

 

Fig. 8. Floor and driver acceleration graph

 

3.4.2    Implementation and Evaluation of PID Tuning Strategies

 

The PID controller tuned using the Ziegler-Nichols method reduced the RMS acceleration to approximately 0.35 m/s2, corresponding to a reduction of nearly 30%. According to ISO 2631 ride comfort evaluation criteria, this improvement changes the driver’s perception from fairly uncomfortable to a little uncomfortable. (Kp = 600; Ki = 10909; Kd = 8.25).

The PID controller optimized using the Particle Swarm Optimization (PSO) algorithm further reduced the RMS acceleration to approximately 0.30 m/s2, equivalent to a 40% reduction (Kp = 1927.4690; Ki = 8776.4448; Kd = 6.6063).

 Meanwhile, the MATLAB PID Tuner achieved the minimum RMS value of approximately 0.29 m/s2, corresponding to a 42% reduction, resulting in a ride condition classified as not uncomfortable (Kp = 2683; Ki = 2738; Kd = 0).

 

 

Fig. 9. Seat Acceleration when applying 3 PID turning methods

 

At approximately t 0.5s, the vehicle encountered a sudden downward road disturbance immediately after the start of motion. This excitation generated the largest negative acceleration peak in the passive suspension response, exceeding -1 m/s2. To counteract this rapid downward motion, the active controllers generated compensating actuator forces. In particular, the PSO-based PID controller produced a large positive actuator force of approximately 430 N, which effectively lifted the seat upward and mitigated the “free-fall” effect induced by the road profile.

 

 

Fig. 10. Force generated by actuator

 

The PSD analysis indicates that the ISO Class C-D road profile contains most of its energy concentration within the low-frequency range. Consequently, the dominant PSD peaks of the driver-seat acceleration also appeared mainly in the frequency band of 0.5-1.5 Hz, which is highly sensitive to human body vibration. The active suspension controllers, especially the PSO-PID strategy, significantly attenuated these PSD peaks, demonstrating strong effectiveness in suppressing large and long-wavelength road irregularities associated with Class C-D road conditions.

 

 

Fig. 11. PSD of seat acceleration

The PSD curves also reveal an important trade-off characteristic of the passive suspension system. After the major excitation peak occurring around 0.5s, the PSD magnitude of the passive system decreased rapidly and eventually became lower than the three active PID controllers after approximately 4s. This behavior reflects the inherent compromise of passive suspension systems, where high damping characteristics help the vehicle return more quickly to equilibrium following severe disturbances, albeit at the expense of transmitting larger initial accelerations to the driver.

 

3.4.3.   The Multi-Method Integration

 

The Multi-Method Control Framework was developed based on the decision-making process of a fundamental Artificial Intelligence algorithm.

As illustrated in Fig. 8, the procedure begins with the real-time acquisition of key parameters, including driver and passenger loads, seat positions, and vehicle velocity ( ), along with road excitations assumed as Step, SW, and CD profiles. After calibration and signal filtering, a regression model combined with a multi-criteria decision-making (MCDM) approach is applied to determine the most comfortable seat position for both passengers and luggage.

Once the load conditions are established, Equation 10 is employed to compute and adjust the suspension stiffness and damping coefficients (  and ) before vehicle departure. During operation, when the vehicle encounters uneven road surfaces and external disturbances, the Hybrid-PSO algorithm is activated to suppress real-time vibrations transmitted to the driver.

Finally, the measured vehicle responses are compared with predicted values, ISO reference limits, and the observed deviations are used to update model parameters continuously. This closed-loop learning mechanism enables the controller and prediction model to self-adapt and progressively enhance ride comfort performance through successive driving cycles.

 

 

Fig. 12. Multi-method integration process

 

 

As illustrated in Fig. 12, polynomial regression is first employed to capture the characteristics of driver acceleration and displacement as functions of mass distribution and the longitudinal distance between the seat and the vehicle center of gravity. These results are then evaluated using the TOPSIS method to identify the optimal seating position. Subsequently, Equation 10 is employed to compute and adjust the suspension stiffness and damping coefficients (kse and Cse) before vehicle departure. Finally, a PSO-PID controller is applied to attenuate vibration during vehicle operation

The evaluation scenario assumes a driver with a body mass of 56 kg accompanied by a passenger weighing 60 kg, both randomly positioned within the vehicle cabin. An additional luggage load of 50 kg is placed randomly in the trunk compartment. The vehicle is simulated on an ISO Class CD Road surface under a constant forward velocity of 16.67 m/s. The results of applying the multimethod calculation procedure are shown in Fig. 13 and 14.

 

 

Fig. 13. Driver’s acceleration

 

 

Fig. 14. Driver’s displacement

 

The passenger seat position that provided the greatest comfort for both the driver and passenger was identified as P1, with a₍RMSP1₎ = 0.401 m/s², corresponding to a “slightly uncomfortable” level according to ISO 2631-1, yet still within the acceptable range for short-term exposure. The optimal luggage position was determined at the center of the luggage compartment, aligned with the longitudinal axis of the vehicle.

The driver seat position that provided the greatest comfort was identified as C1 = 0.35m, the effective acceleration (a₍RMS₎) was reduced by approximately 78%, from 0.50 m/s² to 0.11 m/s², indicating a substantial attenuation of transmitted vibration and a significant improvement in the physiological perception of whole-body vibration.

The effective seat displacement (d₍RMS₎) decreased by 76% (from 0.025 m to 0.006 m), reflecting enhanced postural stability, improved biomechanical coupling between the body and the seat, and reduced fatigue accumulation during prolonged driving. The obtained RMS acceleration and displacement values are consistent with previously reported results for vehicle suspension systems under similar operating conditions [15, 25].

The force generated by the actuator controlled by the PID controller using the PSO algorithm now only needs to reach a maximum value of 150 N (a reduction of 62.5%) while still ensuring high ride comfort for the driver. This improvement is achieved because the seat suspension stiffness has been adjusted appropriately according to the driver’s weight instead of using the default parameters listed in Table 4 (yellow dashed line in Fig. 10).

In particular, the PSO seat acceleration curve (yellow dashed line in Fig. 11) becomes smoother at low frequencies (0.5-2 Hz) and approaches zero, demonstrating the effectiveness of combining multiple optimization methods.

The ride comfort position is defined as C1 = 0.35 m. The seat suspension parameters are Kse = 2803 N/m and Cse = 714 N.s/m. The passenger seating position is P1, and the luggage position is at the center of gravity of the trunk (f = 0 m).

 

 

4.  CONCLUSIONS

 

This study demonstrates that ride comfort in a five-seat vehicle can be significantly improved through an integrated framework combining seat suspension stiffness tuning, PSO-PID control, regression-based prediction, and TOPSIS decision-making. The proposed approach reduced seat RMS acceleration by 78% and seat RMS displacement by 76%, while decreasing actuator force demand by 62.5% compared with the conventional PSO-PID strategy. These improvements effectively reduce vibration exposure, driver fatigue, and actuator workload, thereby enhancing both ride comfort and control efficiency.

The main novelty of this work lies in integrating seat-level suspension control with predictive passenger-load analysis and multi-criteria optimization. The results confirm that passenger seating position and luggage distribution strongly affect ride comfort, where the P₁ seating configuration and centrally located luggage provide the best vibration performance. Unlike conventional full-vehicle suspension optimization, the proposed method improves local ride comfort at the driver seat without modifying the primary suspension system.

The proposed framework offers a scalable and intelligent solution for adaptive ride comfort optimization under varying occupancy and loading conditions. Future work will focus on experimental validation using magnetic or pneumatic seat suspension systems and the development of AI-based adaptive controllers for real-time vibration mitigation in multi-occupant vehicles.

 

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Received 20.04.2026; accepted in revised form 11.07.2020

 

 

Scientific Journal of Silesian University of Technology. Series Transport is licensed under a Creative Commons Attribution 4.0 International License


[1] School of Mechanical and Engineering, Hanoi University of Industry (HaUI), 298 Cau Dien street, Hanoi, Vietnam. Email: ngocnguyencnoto@haui.edu.vn. ORCID: https://orcid.org/0000-0003-4899-1694

[2] School of Mechanical and Engineering, Hanoi University of Industry (HaUI), 298 Cau Dien street, Hanoi, Vietnam. Email: hien.nguyen15@haui.edu.vn. ORCID: https://orcid.org/0000-0002-1552-1867

[3] School of Mechanical and Engineering, Hanoi University of Industry (HaUI), 298 Cau Dien street, Hanoi, Vietnam. Email: tuanquangpham2003@gmail.com. ORCID: https://orcid.org/0009-0005-9705-9862

[4] School of Mechanical and Engineering, Hanoi University of Industry (HaUI), 298 Cau Dien street, Hanoi, Vietnam. Email: quanvh@haui.edu.vn. ORCID: https://orcid.org/0000-0002-9560-8662