Random Road Profile Research Articles

Evaluation of the unsprung mass effect on ride comfort of in-wheel motor driving vehicles

As an innovative powertrain configuration for electric vehicles, in-wheel motor drive has tremendous potentials. However, the influence of excessive unsprung mass related to the in-wheel motor drive on vehicle performance remains ambiguous or even controversial. This paper tries to address the issue based on a full-vehicle model, taking into consideration different road profiles, body positions and vehicle speeds. A full-vehicle model is established for an in-wheel motor driving vehicle, and a centralized driving vehicle with lighter unsprung mass is taken as the baseline vehicle. Simulation studies are carried out for both vehicle configurations at various speeds on random and bumpy road profiles, respectively. Various observations about the effects of the increased unsprung mass are obtained and clarified, including those mentioned in the literature and some new ones. The results indicate that, for random roads, the increased unsprung mass enlarges the wheel dynamic load and suspension travel, and thus deteriorates the road holding and suspension performances. Interestingly, the effects of the increased unsprung mass on body vertical acceleration vary with body position due to the wheelbase filtering property. Front and rear body accelerations are magnified with the increased unsprung mass at all speeds, whereas the body centroid acceleration exhibits an alternating pattern of increase and decrease throughout the speed range. Moreover, the increased unsprung mass reduces the body roll acceleration at all speeds. For bump roads on the other hand, the increased unsprung mass deteriorates all metrics at low speeds, but improves them at high speeds.

Adaptive neural network backstepping control for the magnetorheological semi-active air suspension system with uncertain mass and time-varying input delay

Aiming at rejecting external disturbance induced by the random road profile, this paper proposes an adaptive robust control strategy to address the control problem of semi-active air suspension system installed with magnetorheological dampers (MRD) for enhancing ride comfort and handling performance. To effectively depict the inherent nonlinear dynamics of the adjustable air spring, a radial basis function neural network (RBFNN) model is trained by the experimental data offline, and an adaptive learning algorithm is introduced to maintain the modeling accuracy. Moreover, to handle the prevalent sensitive parameter variation (such as sprung mass), a nonlinear estimator is designed to estimate the uncertain sprung mass. Furthermore, a delay compensator is integrated into the control law to mitigate the impact of the time-varying input delay caused by the actuator of MRD to restrain the chattering phenomena. Additionally, the stability of the closed-loop system is rigorously proven by employing a Lyapunov–Krasovskii functional, guaranteeing the boundedness of both tracking error and estimation error. Simulation results are displayed and analyzed, illustrating the feasibility and efficiency of the proposed control strategy in depressing the sprung mass acceleration and tire deflection, showing its significance in both control performance enhancement and chattering elimination.

Semi-active control implementation in aircraft landing gear systems using hardware-in-the-loop test bench

In small-sized aircraft landing gear systems, magnetorheological (MR) dampers offer an innovative approach to adjusting damping levels under wide range of operating situations in order to achieve competing control objectives such as ride comfort, suspension travel, and energy consumption. Also, MR dampers have nonlinear dynamics and exhibit hysteresis. In this context, this paper aims to present a Hardware-In-the-Loop (HIL) technique for the implementation of backstepping control and linear quadratic regulator (LQR) control. Experimental results highlight that, compared to passive suspension (Passive Off), backstepping control and LQR control approaches reduce the fuselage vertical acceleration by 29.13% and 24.95%, respectively. Moreover, the ISO 2631 standard was adopted to evaluate ride comfort. LQR control can able to minimize the fuselage roll acceleration under a random road profile. Also, LQR control provides the highest performance in terms of fuselage roll acceleration, achieving a 6.2% improvement with lower energy consumption. By utilizing HIL, semi-active control methods can be tested and developed without the need for the aircraft, while keeping the characteristics that the physical aircraft would bring.

Real-time estimation of vehicle inertia parameters based on Kalman-bucy filter

Vehicle inertial parameters such as mass and moments of inertia are required for most vehicle dynamic control systems. Due to the wide range variation of these parameters during vehicle operation, accurate estimation of their values in real-time plays an important role in improving the efficiency of vehicle control systems. In this article, the vehicle sprung mass and moments of inertia are estimated in real-time based on a Kalman-Bucy filter algorithm designed for a spatial vibration model of a two-axle truck. This proposed method requires measuring only the vertical, roll, and pitch velocity of the sprung mass and, therefore can reduce the sensor cost significantly. The simulation results for a random roughness road profile according to ISO 8608 class C with step variations in sprung mass and moments of inertia showed that the designed estimator rejected the process and measurement noises and tracked the real vehicle parameters effectively with acceptable errors

The modified in-plane rigid-elastic-coupled tire modal model: dynamic response to short wavelength road profiles

ABSTRACT The 400-degree-of-freedom deformed in-plane rigid-elastic-coupled tire model was enhanced by incorporating the vertical movement of the wheel as a rigid body. This refined model was then utilised to build the tire modal model. The tire modal model was developed to derive the transfer function (TF) covering a range of 0–300 Hz, which connects road irregularities as input to the contact patch and the wheel's vertical motion as output. The TF was operated under a quasi-static condition to obtain the tire's enveloping characteristics rolling over short wavelength obstacles as a direct function of vertical wheel displacement under varying contact patch length constraints. The tire modal model was combined with the quarter car model to analyse the vehicle's response when passing through short wavelength obstacles and random road profiles. This analysis was performed under varying load conditions represented by the contact patch length. The model and methodology demonstrated their effectiveness in handling rolling tires over short-wavelength obstacles and random road profiles.

Virtual testing ground mathematical model design and it’s software realization in Simcenter AMESim

The object of the development is a virtual testing ground mathematical model with the road random profile irregularities for conducting simulation tests of vehicle dynamics. The work aim is to create a virtual testing ground mathematical model in the form of 3D-fields of irregularities and its software implementation in the Simcenter AMESim. To create a 3D-polygon model, the well-known theoretical knowledge for modeling various categories irregularities of ground surface are considered, differential equations for modeling profile realizations are compiled, profile realizations are simulated and 3D-fields of irregularities integrated into the Simcenter AMESim environment are created with the help of the obtained implementations. As a work result, a 3D-field random profile road irregularities mathematical model with a modeling technology description was obtained. A universal unit for modeling a virtual testing field with the ability to simulate roads of various irregularities categories was software implemented in the Simcenter AMESim. The created model is universal. It was designed for conducting virtual tests of various vehicles types when driving on various roads types. Due to a simulation modeling of vehicle dynamics when driving through irregularities fields, it becomes possible to measure, compare, control and regulate a large number of different cars parameters. The created block can be included in cars simulation models of any complexity level realized in Simcenter AMESim to conduct virtual tests of vehicle dynamics in conditions close to reality. Keywords mathematical model, virtual testing ground, unevenness 3D-field, random road profile, Simcenter AMESim

Improvement of ride quality for a wheel loader with semi-active cab isolation system via fuzzy self tuning of PID controller

Improving driver ride comfort of a wheel loader is important to avoid potential health hazards from the whole-body vibration. A fuzzy self-tuning of PID controller is designed to control the damping coefficient of Semi-active cab isolation system (SCIS) for a wheel loader. A dynamic model of a wheel loader is establish under survey conditions for analysis and evaluation. The r.m.s acceleration responses of the vertical driver's seat and pitch angle of vehicle body according to ISO2631-1 (1997-E) are chosen as objective functions. The effectiveness of the proposed control strategy is analyzed through simulations involving excitations for a random road profile in time domain. The proposed SCIS is simulated and analyzed by Matlab/Simulink software in comparison with a passive cab isolation system (PCIS) under survey conditions. The achieved results indicate that ride comfort effectiveness of a wheel loader with SCIS is better than PCIS under survey conditions. In addition, the study results are the initial basis for optimizing controller parameters.

Ride comfort analysis of vehicle seat suspension systems: A co-simulation study

In this study, the vehicle seat suspension system installed with a semi-active magnetorheological (MR) damper is excited by the power spectral density (PSD) and its vibration control performance is evaluated using finite element analysis (FEA). The control system receives the velocity of the sprung and unsprung mass from the seat mounting locations and calculates the desired controllable damping forces available from MR damper. The effectiveness of the control systems is demonstrated by adopting ride quality evaluation method. To predict a better ride comfort and ride quality, co-simulation methodology is utilized considering the dynamic behavior of the real-world seat system. In this case, the multi-body dynamics and control system are coupled by solving the mechanical equations and the control logic. Then, the computed damping force is exchanged between the dynamics and controller in an iterative manner by passing state variables. The simulation results achieved from co-simulation methodology associated with the controller are analyzed by comparing with ISO 2631-1. The co-simulation results studied using vibration dose value (VDV), crest factor (CF) and seat effective amplitude transmissibility (SEAT) in terms of percentage improvement were found to be 44.33%, 26.66% and 17.65% respectively which were better than that for the passive suspension for a random rough road profile. Modified skyhook controller delivers superior performance for vibration suppression of the vehicle seat suspension as compared to other control policies. The application of co-simulation methodology can reduce time and cost for the development of a semi-active seat suspension system.

Superposition of populations in multi-objective evolutionary optimization of car suspensions

The design of the suspension model of road cars is extremely important for both driver comfort and safety. Road traffic injuries are currently the eighth leading cause of death worldwide and are predicted to become the seventh leading cause of death by 2030, according to the World Health Organization (WHO). Among other factors, road infrastructure is one of the most important factors to consider when designing the suspension model, especially as autonomous driving becomes more popular. In addition, there is a growing need to test and study the impact of road roughness and pavement type on autonomous vehicles (AVs). This work provides the following contributions: a platform for suspension system optimization–flexible, highly parameterizable and rich in applications. Our solution implements, tests and optimises the 2, 3 and 4 degrees of freedom (DOF) quarter-car models (QCM) with linear seat suspension and the 5 DOF half-car model (HCM), respectively, based on random road profiles generated according to ISO 8608 standards. In addition, many multi-objective optimization (MOO) algorithms have been implemented and applied in isolation to see their comparative performance (in terms of Pareto fronts, hypervolume, coverage, spread, and epsilon), but most importantly we have also introduced a meta-optimization technique by super-positioning Non-dominated Sorting Genetic Algorithm II and Strength Pareto Evolutionary Algorithm 2, where each of the algorithms, running concurrently, produces a percentage of the total number of individuals in a generation, percentage that is calculated according to the solution quality of the individuals in the previous generation. The experimental results were obtained by simulating the optimal configurations generated by the MOO heuristic algorithms on different categories of cars (small/medium). Finally, the Taguchi method and regression analysis were used to evaluate the effects of specific parameters on system responses such as sprung mass acceleration and displacement. The Taguchi simulation was performed to experimentally validate the results obtained by metaheuristic optimization methods.

Analyzing the effect of vehicle speed and class of random road profile on a 4-axle truck vehicle vibration

The vehicle will generate vibration due to the impact of road surface, wind, steering, accelerating, braking...as it moves on road surfaces. These vibrations directly affect people and goods. A 14 DOF full vehicle dynamic model of the 4-axle truck vehicle with the torsion of the chassis and the “Walking Beam” tandem suspension is developed to analyze the effect of vehicle speed and a class of random road profile conditions on the vibration of the 4-axle truck vehicle which is developed based on Newton Euler equations and solved via Matlab/Simulink software. The study results have shown that the road surface and vehicle speed conditions have a great effect on vehicle vibrations. In addition, the results of this study could provide useful analysis results for proposing solutions to optimize the structure of the suspension system to improve the ride comfort of the vehicle and reduce the dynamic load of multi-axle truck vehicles.

Two-Layer Parallel Fuzzy Logic Controller Design for Semiactive Suspension System with a Full Car Model

This paper presents research results on semiactive suspension using a fuzzy logic controller. Firstly, a full car model is built with 7 degrees of freedom using a semiactive suspension system at all four wheels. The dynamic equations are converted to the state space representation to facilitate control design and improve accuracy in simulation design. Then, a two-layer parallel fuzzy logic controller is designed with 49 and 25 rules for two fuzzy inference systems. In this way, the fuzzy logic controller is able to respond to a wide operating range of the system and the output force is smoother. Finally, the evaluation results are performed in the frequency and time domains with a real random road profile, and they showed that the root mean square value of the signals when using a semiactive suspension system with the proposed fuzzy logic controller decreased by over 25% compared to the passive suspension system. This clearly demonstrates the effectiveness of the proposed controller in improving the ride comfort, the road holding and ensuring the suspension travel of cars.

Can a nonlinear quasi-zero-stiffness spring improve the ride quality of a vehicle?

The paper examines the possibility of using a nonlinear Quasi-Zero-Stiffness (QZS) spring in a vehicle suspension. The response of a Single Degree of Freedom (SDOF) model to harmonic base excitations is obtained which may be unstable and unbounded depending on the excitation level and the damping ratio. This is followed by obtaining the response of the SDOF model to harmonic base excitation with an amplitude that is varying according to a road profile spectrum. Such dependency of the excitation amplitude to the frequency changes the qualitative behaviour of the nonlinear system and the responses would be always bounded. The QZS spring also improves the isolation of the system. Transient responses of a quarter car model with a QZS suspension to a road hump and random road profile are investigated. The maximum acceleration of the vehicle with the QZS suspension passing over the speed hump is considerably lower than a vehicle with a conventional linear suspension. Wb weighted RMS of acceleration (BS 6841-1987) is also lower by as much as 14% for a vehicle with the QZS suspension travelling at 30 km/h on a class E road compared to its linear counterpart.

An investigation of a bus’s ride comfort by using the quarter car model with linear asymmetric damper

The linear asymmetric damper’s effects on the ride comfort, safety, and handling control were investigated to get full understanding of the suspension system design processes of an inner-city bus. The dynamic responses were analyzed for both two cases of linear symmetric and linear asymmetric dampers using the quarter car model with two degrees of freedom (2 DOFs) subjected to random road profiles and single bump cases of triangular and sine-squared bumps. The obtained results show that the linear symmetric damper performs the same as that of the linear asymmetric one in terms of comprehensive performance when the vehicle is subjected to a random road profile. The ride comfort, the working space have been significantly improved in specific range of velocity in case of the linear asymmetric damper. However, in general, slightly better performance has been obtained in the linear symmetric damper case.

An interval-based multi-objective robust design optimization for vehicle dynamics

This study presents an Interval-based Multi-objective Robust Design Optimization (IB-MORDO) algorithm applied to a vehicle dynamic problem. The proposed algorithm optimizes a full 15 degrees-of-freedom (15-DOF) vehicle model, subjected to a double-lane change (DLC) maneuver under random road profiles, to attain driver comfort and safety. This study does not make assumptions about uncertain parameter statistics; instead, the uncertainties are quantified using a non-probabilistic α-cut level interval analysis. These uncertainties are applied to the system parameters and design variables to ensure robust results. After the optimization process, the root mean square (RMS) vertical acceleration at the driver’s seat resulted in a robust solution of 1.041 m/s2 and a parameter interval radius (IR) equals to 0.631 m/s2, whereas the RMS lateral acceleration at the driver’s seat resulted in a solution of 1.908 m/s2 with an interval radius of 0.168 m/s2. Unlike the Robust Optimization, the algorithm proposed herein considers uncertainties at system parameters and design variables without assuming any statistical data. HIGHLIGHTS An Interval-based Robust Multi-objective Optimization procedure is proposed and tested on a 15-DOF vehicle model. Αn α-cut level methodology is used to deal with the uncertainty propagation. Resulted optimal suspension parameters minimize center and interval radius of driver’s vertical and lateral accelerations.

Saturated PD-SMC method for suspension systems by exploiting beneficial nonlinearities for improved vibration reduction and energy-saving performance

In this paper, through purposely employing beneficial nonlinear stiffness and damping with a constructed bioinspired reference model, a novel saturated PD with sliding mode control method (referred to as saturated PD-SMC method), is designed for active suspension systems under saturated control input constraints. The designed control method has several distinct benefits, including the simple structure of PD control method, strong robustness of SMC method with respect to model uncertainties and external disturbances, without requirements of exact system parameters associated with traditional SMC method, as well as taking input constraints into consideration. In the designed control method, the PD part is employed to stabilize the controlled active suspension system, the SMC part is applied to provide strong robustness, and the saturation functions are introduced to prevent the violation of control input constraints. The corresponding stability analysis is provided by Lyapunov techniques. Several experimental results show that, the proposed control method dramatically improves transient performance in comparison with some existing methods, including significantly decreasing control energy by 30% for sinusoidal road profile, and decreasing control energy up to 66% for random road profile, which achieve a satisfactory trade-off between costs and results for suspension system control. As far as we know, it is the first time to combine PD control, SMC method, and saturation structures together, to achieve obvious performance improvements for suspension systems, and simultaneously, complete stability analysis is given.

Tube-based Model Reference Adaptive Control for Vibration Suppression of Active Suspension Systems

With the developments of industrial automation in recent years, vehicle suspension systems have received a great deal of attention in industry and academia due to their critical role in the chassis performance of vehicles [1]. The suspension system is expected to guarantee the vehicle's maneuverability and provide satisfactory ride comfort by absorbing the vibrations arising from the road surface excitations and ensuring road-holding capability and suspension safety. Motivated by the desirable performance of the model reference adaptive control (MRAC) approach, various literature studies have investigated its performance in diverse linear and nonlinear practical systems [2], [3] (for more background review, see Supplementary material-Appendix A). Aiming to improve the conventional MRAC in terms of closed-loop stability, asymptotical tracking, and robustness against uncertainties and external disturbances, authors in [4] developed the tube-based MRAC (T-MRAC) approach. To simultaneously achieve the desired objectives, the developed scheme split the control signal into two main terms; an adaptive part and another part that corrects the control objective. In addition, an optimization problem is formulated to find the newly determined correction control component. However, although the method's performance was verified using some simple single-input single-output unstable systems [5], more extensive investigations on complex practical systems are needed to validate its performance. The main contributions of this paper are to develop a novel tube-based MRAC approach for multi-input multi-output active suspension systems; a realistic design that guarantees ride comfort and suspension safety and achieves better control performance with reduced control effort in the presence of external disturbances compared to conventional methods. Moreover, to validate the method's applicability in practical applications, three different road profiles are conducted to simulate distinct practical road situations, as the bump-dip road, random road, and sinusoidal profiles. Furthermore, the vibration suppression performance of the developed adaptive control scheme is investigated, and superior simultaneous ride comfort, road handling, and suspension safety are guaranteed compared to conventional MRAC [6] and SMC [7] approaches.

Intelligent PID Controller with Cuckoo Search Algorithm and Particle Swarm Optimisation for Semi-Active Suspension System Using Magneto-Rheological Damper

This article presents the employment of Cuckoo Search (CS) Algorithm to tune a Proportional Integral Derivative (PID) controller for a semi-active suspension system in order to improve and enhance ride comfort and stability in a vehicle. In the meantime, the Cuckoo Search Algorithm has been compared between existing intelligent approaches such as Particle Swarm Optimisation (PSO) and passive system. The performances of the Proportional Integral Derivative controller have been optimised via Cuckoo Search Algorithm and Particle Swarm Optimisation, respectively. The mean square error for the suspension system has been determined as an objective function for the proposed controller's optimisation. The performance of the proposed PID-CS controller has been compared to existing PID-PSO controller and passive system in terms of body acceleration and body displacement. The bump and hole together with random road profile have been set as the source of disturbance for the system. The simulated results have demonstrated that the PID-CS controller has been able to improve significantly ride comfort between 14-16% in terms of mean square error for both body displacement and body acceleration.

Optimal selection for an air suspension system on buses through a unique high level parameter in genetic algorithms

Air suspension systems are being widely used on ground vehicles in general and buses in particular. The element that makes the superiority of this system is air spring. This paper introduces the application of genetic algorithms method to optimize the parameters of the air spring element. A full model of a bus using air suspension system with air spring element, which is modeled based on the Gensys model. From the real experiments, the bounds of seven optimized parameters of the air spring are determined. In which, by using a single α value, it is possible to determine the optimal parameters according to each desired criteria between the road safety and the ride comfort. Optimal results are verified in the time domain simulations with random road profile according to the ISO standard 8608. The results show that by using the optimal parameters of the air spring when α = 0.5, the ride comfort is improved about 15% while the road safety is still guaranteed.

A Mathematical Approach Towards Random Road Profile Generation Based on Chaotic Signals of Chua's Circuit

In response to application demands in vehicle dynamics and control, traffic engineering, urban planning, and logistics, the generation of an adequate artificial road profile in terms of the diversity of geometric scenarios has been addressed in the current manuscript. The underlying mathematical principles for generating a geometrically comprehensive, yet logically meaningful, 3D road profile have been taken from high and unbiased sweeping factors of random number sequences over their domain of interest. And to generate such random number sequences, the mathematically manipulated output signal of a well-established chaotic system has been utilized, namely that of the Chua's circuit. Having defined the target road profile mathematically with all its geometrical complexities, a suitable scheme derived from the mentioned chaotic signal has been used to generate the required random number sequences as defining parameters of the road profile. The scheme has been otherwise tested and proven to show the demanded level of randomness in literature. Several attempts have been made to create a diverse range of road profiles, considering the constraints imposed by vehicle dynamics. To generate the road geometries, the limitations imposed by the vehicle's motion, such as the limitations on corresponding curvatures, slopes, and banking angles are negotiated, in terms of vehicle dynamics and available tire-road friction forces, by evaluating how close a vehicle will be to its tire force capacity limits as it travels on sections of the generated road.

Multi-Objective Optimisation of the Electric Wheelchair Ride Comfort and Road Holding Based on Jourdain’s Principle Model and Genetic Algorithm

Abstract The paper addresses the multi-body modelling of an electric wheelchair using Jourdain’s principle. First, a description of the adopted approach was presented. Next, the mathematical equations were developed to obtain the dynamic behaviour of the concerned system. The numerical computation was performed with MATLAB (matrix laboratory: a high performance language of technical computing) and validated by MBD (Multi-Body Dynamics) for Ansys, a professional multi-body dynamics simulation software powered by RecurDyn. Afterwards, the model was treated as an objective function included in genetic algorithm. The goal was to improve the ride quality and the road holding as well as the suspension workspace. The multi-objective optimisation aimed to reduce the Root-Mean-Square (RMS) of the seat’s vertical acceleration, the wheels load and the workspace modulus by varying the bodies’ masses, the spring-damper coefficients and the characteristics of the tires. Acceptable solutions were captured on the Pareto fronts, in contrast to the relatively considerable processing time involved in the use of a random road profile generated by the power spectral density (PSD). During the process, the compatibility and the efficiency of Jourdain’s equations were inspected.