An optimal control method for time-delay feedback control of 1/4 vehicle active suspension under random excitation

Time-delay feedback control can effectively broaden the damping frequency band and improve the damping efficiency. However, the existing time-delay feedback control strategy has no obvious effect on multi-frequency random excitation vibration reduction control. That is, when the frequency of external excitation is more complicated, there is no better way to obtain the best time-delay feedback control parameters. To overcome this issue, this paper is the first work of proposing an optimal calculation method that introduces stochastic excitation into the process of solving the delay feedback control parameters. It is a time-delay control parameter with a better damping effect for random excitation. In this paper, a 2 DOF one-quarter vehicle suspension model with time-delay is studied. First, the stability interval of time-delay feedback control parameters is solved by using the Lyapunov stability theory. Second, the optimal control parameters of the time-delay feedback control under random excitation are solved by particle swarm optimization (PSO). Finally, the simulation models of a one-quarter vehicle suspension simulation model are established. Random excitation and harmonic excitation are used as inputs. The response of the vehicle body under the frequency domain damping control method and the proposed control method is compared and simulated. To make the control precision higher and the solution speed faster, this paper simulates the model by using the precise integration method of transient history. The simulation results show that the acceleration of the vehicle body in the proposed control method is 13.05% less than the passive vibration absorber under random excitation. Compared with the time-delay feedback control optimized by frequency response function, the damping effect is 12.99%. The results show that the vibration displacement, vibration velocity, and vibration acceleration of the vehicle body are better than the frequency domain function optimization method, whether it is harmonic excitation or random excitation. The ride comfort of the vehicle is improved obviously. It provides a valuable tool for time-delay vibration reduction control under random excitation.

Dynamic modeling and damping performance improvement of two stage ISD suspension system

In this paper, the dynamics of the vehicle suspension system under the random excitation and the periodic excitation are investigated. To improve the damping performance of the vehicle suspension system, a two stage ISD suspension with “Inerter-Spring-Damper” in each stage is proposed based on electromechanical similarity theory. A vehicle dynamic model with two stage ISD suspension is established in this paper. The dynamic equation is solved by the Runge-Kutta method and the dynamic response of the whole vehicle system is obtained. Taking the traditional suspension as the comparison object, the dynamic characteristics of the system under random excitation and periodic excitation are studied in the time domain, and the suppression effect of the suspension designed in this paper on the resonance peak is verified in the frequency domain. The influence of the inertia coefficient on the damping performance of the vehicle suspension system is analyzed. The effects of excitation amplitude and vehicle speed on ride comfort improvement of vehicle system with two stage ISD suspension are discussed respectively. The results show that, the resonance peak values of body acceleration, dynamic travel of rear suspension and rear tire dynamic load frequency response are reduced by 59.1%, 21.6%, and 60.3% respectively. With the increase of excitation amplitude in the range of 0.02–0.04 m, the ride comfort improvement of two stage ISD suspension system is always more than 61%. With the increase of vehicle speed in the range of 10–25m/s, the performance improvement rate of two stage ISD suspension system can reach more than 34.1%.

Bayesian Uncertainty Identification of Model Parameters for the Jointed Structures with Nonlinearity

Jointed structures in engineering naturally perform with some of nonlinearity and uncertainty, which significantly affect the dynamic characteristics of the structural system. In this paper, the method of Bayesian uncertainty identification of model parameters for the jointed structures with local nonlinearity is proposed. Firstly, the nonlinear stiffness and damping of the joints under the random excitation are represented with functions of excitation magnitude in terms of the equivalent linearization. The process of uncertainty identification is separated from the representation of local nonlinearity. In this way, the dynamic behavior of the joints is penetratingly characterized instead of ascribing the nonlinearity to uncertainty. Secondly, a variable-expanded Bayesian (VEB) method is originally proposed to identify the mixed of aleatory and epistemic uncertainties of model parameters. Different from traditional Bayesian identification, the aleatory uncertainties of model parameters are identified as one of the most important parts rather than only measurement noise of output. Notablely, a series of intermediate variables are introduced to expand the parameter with aleatory uncertainty in order to overcome the difficulty of establishing the likelihood function. Moreover, a 3-DOF numerical example is illustrated with case studies to verify the proposed method. The influence of observed sample size and prior distribution selection on the identification results is tested. Furthermore, an engineering example of the jointed structure with rubber isolators is performed to show the practicability of the proposed method. It is indicated that the computational model updated with the accurately identified parameters with both nonlinearity and uncertainty has shown the excellent predictive capability.

Aspects about bouncing of plough caused by random

In this paper the author deals aspects about the vertical motion (named bouncing) of a tractor with plough mounted on the rear frame, during displacement over the random excitation surface of the agricultural land. Final results of the simulation process, performed on the model of tractor-plough with 3 degree of freedoms, show the difference between digging depth function as velocity motion and longitudinal profile of the terrain. Thus, the deviation of the plough depth from the reference depth is evaluated.

Numerical study of the vertical vibration of a vehicle model with variable speed

The paper deals with the numerical analysis of the general model of vehicle oscillations considering the non-stationarity of random excitation. The model parameters of the applied railway vehicle are deterministic functions. The non-stationary random function will be modelled by the variable speed of the vehicle and the vertical unevenness of the track. The so-called evolutionary Gaussian random process will be considering. The proposed comparative study of the dynamics of the vertical motion of the analysed railway vehicle will be realized using Monte Carlo simulation and a numerical procedure based on the theory of Markov processes. The originality of the article can be found in the implementation and algorithmization of the principles of solving non-stationary oscillation problems of machines. A universal methodology applicable in the dynamics of machines of various purposes is presented.

Response Statistics of a Shape Memory Alloy Oscillator with Random Excitation

This paper aimed to explore analytically the influences of random excitation on a shape memory alloy (SMA) oscillator. Firstly, on the basis of the deterministic SMA model under a harmonic excitation, we introduce a stochastic SMA model with a narrow-band random excitation. Subsequently, a theoretical analysis for the proposed SMA model was achieved through a multiple-scale method coupled with a perturbation technique. All of the obtained approximate analytical solutions were verified by numerical simulation results, and good agreements were observed. Then, effects of the random excitation and the temperature value on the system responses were investigated in detail. Finally, we found that stochastic switch and bifurcation can be induced by the random fluctuation, which were further illustrated through time history and steady-state probability density function. These results indicate that the random excitation has a significant impact on dynamics of the SMA model. This research provides a certain theoretical basis for the design and vibration control of the SMA oscillator in practical application.