Random Excitation Research Articles

Magnetic-Control Variable Stiffness and Damping Tail Support for a Wind-Tunnel Aircraft Model

To suppress random vibration of aircraft models during wind tunnel tests, a novel magnetorheological elastomer (MRE)-based device with variable stiffness and variable damping (VSVD) is proposed, which is installed on the tail support system. Firstly, the dynamic characteristics of the tail support system are established using finite element model simulation to obtain the vibration mode and stress distribution. Next, the vibration reduction mechanism of the MRE-based tail support system is analyzed by solving a finite element model. Then, the magnetic-controlled VSVD device with an annular sandwich structure is proposed, and the decisive rheology material and structural parameters in relation to the tail support system’s dynamics are determined. Subsequently, the magnetically generated element with multicoils is designed to guarantee a large enough magnetic field, and the optimal structure parameters are obtained. Finally, random wind flow experiments in the wind tunnel and frequency sweep tests in the ground laboratory for the tail support system equipped on the VSVD device are conducted to verify the effectiveness of the proposed device, respectively. The results under 15–200 Hz random excitation indicate the root mean square of acceleration at the centroid of the aircraft model with the VSVD device can be decreased by 46.8% compared to the system without the VSVD device.

Investigation on fatigue life of push-the-bit rotary steerable bottom hole assembly with random bit-rock interaction

Rotary steerable systems are critical for challenging boreholes in deep-sea oil and gas drilling, where fatigue failure is the normal form of damage. A procedure with deterministic excitation and random excitation is presented in this paper to reliably predict the fatigue life of the bottom hole assembly. The initial defects, the Coulomb friction model, frictional contact between the drill bit and rock, and the stochastic rock-cutting process are included in the model. Monte Carlo approach is used to obtain the Statistical characteristics of the stochastic model. Based on the program mentioned above, influences of some parameters, such as rotational speed, weight on bit, steering force, and random excitation on torsional vibration characteristics, are investigated. Moreover, the rain-flow counting method is applied to reveal the dependency relationship between fatigue life and torsional vibration. It is found that random excitation can exacerbate the torsional vibration phenomenon and even significantly reduce the fatigue life. Finally, compared with the deterministic system, the sensitivity index coefficient of the fatigue life in the random excitation model is about 0.8 % - 2.2 % higher. The research results can provide a theoretical basis for reducing tool failure in on-site deep-sea oil and gas drilling.

Application of covariance statistical method for damage identification on railway truss bridge using acceleration response: experimental and numerical validation

This paper presents a novel statistical analysis-based approach to non-parametric damage detection in truss bridges. The method utilizes the normalized acceleration response time histories (NARTHs) of a bridge under random excitation. The coefficients of variation matrices are calculated using NARTHs for the truss bridge in both its baseline and damaged states. The results are shown as the difference in covariance matrices (DCMs) between the two conditions (pristine and damaged). The row or column-wise summation of the DCM matrix yields a summation of the difference in covariance matrix (SDCM) bar plot having one distinct peak for the damaged member. The location and relative severity of the damage can be determined by examining the DCM matrix and the SDCM bar plot. The variation in magnitude of the coefficients demonstrates the relative severity of damage. Experimental investigation of the proposed method for detecting damage on the truss bridge shows promising results. The approach is then numerically validated using a finite element model of a truss bridge. The proposed method effectively identified, located, and evaluated damage, even when the acceleration time histories are contaminated with noise. The case of multiple-member damage detection in the truss structure is further investigated in the study. The early detection of damage and monitoring of its progression through this method can assist in creating efficient maintenance strategies for truss bridge infrastructure.

Sequential simulated annealing for life-cycle optimization of nonlinear stochastic systems via arbitrary polynomial chaos expansion

Quantifying the uncertainties of engineering systems modeled as nonlinear oscillators subject to random excitation is a theoretically complex and computationally demanding task. Consequently, finding an optimal design of such systems considering their life-cycle performance is prohibitive with Monte Carlo simulation methods. In this paper, an efficient performance-based design optimization approach is developed for finding the optimal parameters of engineering systems modeled as nonlinear/hysteretic oscillators subject to stationary and non-stationary excitation. This novel approach utilizes an arbitrary polynomial chaos expansion to estimate the expected cost of failure without performing a computationally expensive integration over the hazard levels. Moreover, we introduce a novel sequential heuristic optimization scheme based on simulated annealing to minimize the total expected cost over the structure life-cycle. Three examples are included in the paper to assess the developed optimization scheme. First, we use the developed framework to optimize a linear single-degree-of-freedom oscillator subject to broadband excitation. Second, a multi-degree-of-freedom oscillator with cubic nonlinearity in damping and stiffness, subject to stationary broadband excitation, is optimized to show the influence of the problem dimensionality in the optimization process. In the last example, a multi-story reinforced concrete shear building modeled as a multi-degree-of-freedom Bouc-Wen oscillator with stiffness and strength degradation and subject to multi-hazards modeled as stationary (wind excitation) and non-stationary (earthquake) stochastic processes, is optimized.

Modeling of electromagnetic propagation inside jet engine environment using statistical electromagnetic approach

In this paper, the distribution of the electromagnetic field inside a complex jet engine environment is analyzed using statistical electromagnetics. The jet engine environment is an extremely complex geometry and exhibits random behavior due to the presence of moving metallic parts. This renders traditional analytical and simulation modeling techniques highly inefficient. To address this issue, two different approaches are proposed to model the propagation characteristics of the jet engine environment. The first is an innovative dynamic system approach based on dynamic system simulation which is inspired by the analysis of mechanically stirred reverberation chambers. In the dynamic system simulation the dynamic system, which is characterized by the rotation of a distinct set of blades, is primarily studied through the simulation program. A dimension scaling method is also introduced along with the dynamic system simulation to solve the complex jet engine environment. In the second approach, a novel statistical excitation method is applied to develop an equivalent model for the dynamic jet engine system. The studied jet engine is considered as a static jet engine system without blade rotation (static blades), but with a random excitation.A small signal analysis method is used to integrate the static and dynamic system parameters to generate random excitation characteristics of the static system. The extracted electric field values from the dynamic jet engine simulation environment and the static system field values from the small signal analysis have been analyzed statistically to prove the statistical equality between the two systems. The numerical results of the static system model are presented and verified through comparison with finite element method simulation packages.

Proportional-retarded control of a quasi-zero-stiffness vibration isolator

This paper explores the control design and performance analysis of an active quasi-zero-stiffness vibration isolator utilizing the proportional-retarded (PR) control architecture. The PR architecture replaces the conventional “derivative” term in the proportional-derivative (or displacement-velocity) controller with the novel “retarded (time-delayed)” term, which is a new and effective way of active vibration suppression. Comprehensive gain-delay conjoint regulation strategies are developed for the strengthened isolation performance. For impact excitations, a complete stability analysis is conducted near the equilibrium position. Furthermore, a parameterized dominant pole placement algorithm is proposed to optimize the transient response of the PR-actuated isolator. Focusing on the rectangular pulse and long-duration step impacts, the algorithm adjusts the dominant poles to optimize the transient performance metrics, including the maximum displacement overshoot, steady-state displacement overshoot, and settling time. Regarding harmonic excitations, the delay-coupled effect is scrutinized for better low-frequency isolation performance, including the resonance frequency, nonlinear steady-state amplitude, multiple steady-state bands and nonlinearity elimination, equivalent active damping and stiffness, and absolute displacement transmissibility. In the case of random excitations, we demonstrate the superiority of the PR structure over the passive system.

Response analysis of the vibro-impact system under fractional-order joint random excitation

As a kind of good damping material, viscoelastic material is widely used in machinery, civil engineering, and other fields. In this paper, the viscoelasticity of the system is described by fractional differentiation. The dynamic response of a unilateral vibro-impact system with a viscoelastic oscillator under joint random excitation is studied, in which joint random excitation is composed of additive and multiplicative white noise. The fractional-order derivative was calculated based on Caputo’s definition, and the fractional derivative was equivalent to the corresponding linear damping force and linear restoring force. As a result, a new random system without fractional-order terms was obtained. A non-smooth transformation was introduced, which was equivalent to the original system to a new system without a velocity jump. The steady-state probability density functions of fractional-order vibro-impact systems under joint random excitation are solved by using the random average method and non-smooth transformation. In addition, the effects of parameters on the steady-state response of the system are analyzed.

Dynamic Characteristics of Bistable Vibration Energy Harvester Incorporating Electromagnetic Generator

Although various vibration energy harvesters have been designed over the past few decades, efforts to develop efficient, broadband energy harvesters continue. This work provides a detailed insight into a bistable vibration harvester subjected to correlated Gaussian white noise, with the friction between the rack and pinion described by the slip-stick model. Using the harmonic balance method, the frequency response curve of the amplitude under different mass ratios is discussed. The system response will be enhanced with an increased mass ratio for sinusoidal excitation, but not in the case of random excitation. By employing the stochastic average of the energy envelope, the dynamical governing equation of the harvester is solved, and the probability density functions (PDFs) under different damping coefficients, nonlinear stiffness of the restoring force, and excitation intensities are derived. The results are compared with those from Monte Carlo simulations (MCS) and show good accuracy. The results reveal the presence of P-bifurcations. When the nonlinear stiffness and damping coefficient vary, the number of peaks in the PDFs of system displacement and velocity changes. By adjusting the system parameters, the motion of the system can be significantly enhanced.

Design and analysis of magnetostrictive two-dimensional kinetic energy harvester

Conventional energy harvesters often require high ambient vibration frequencies and can only capture vibration energy in a single direction. To address these issues, this paper designs a magnetostrictive two-dimensional kinetic energy harvester placed under the floor and capable of capturing energy in both vertical and horizontal directions. In order to achieve higher electrical power output at low-frequency input forces, a two-stage force amplification mechanism is designed to amplify the walking kinetic energy of pedestrians and the main parameters of this structure are analyzed and optimized. On the other hand, by constructing different forms of bias magnetic field, the influence of bias magnetic field on the deflection and motion of the internal magnetic domain of Terfenol-D is systematically studied, and the best bias form that can make the material shows the strongest magnetization characteristics is determined. Next, a prototype harvester was built, and an experimental vibration system was set up to test and analyze the output characteristics of the harvester comprehensively. The experimental results show that the harvester produces 21.2 mW of peak output power under sinusoidal excitation at an operating frequency of 4 Hz. Under random excitation, a peak output voltage of 2.64 V and 170 mW peak power was obtained. Under actual pedestrian walking tests, 17.62 mW peak output power is obtained to power low-power devices. The study’s results provide preliminary evidence that the designed magnetostrictive energy harvester can stably harvest kinetic energy from pedestrian walking.

Local modeling for FRF estimation with noisy input measurements

The frequency response function (FRF) is an essential means by which dynamic systems are qualified. In recent years, local modeling approaches have been extensively researched and shown to significantly outperform traditional FRF estimators. However, the standard local modeling approach assumes a perfectly-known system input, which results in biased FRF estimates in the presence of input noise. This paper derives a simple adjustment that can be used to improve FRF estimation for systems subjected to random excitation with noisy input data. This improvement can be implemented with little modification to standard local modeling algorithms and with little additional computational burden. The adjustment is coupled with a model selection procedure to avoid underfitting and overfitting. The methods presented in this paper are validated on a simulation, and they are shown to reduce bias due to input noise.

Analysis of random induced dynamic response of rural roads considering friction effect and nonlocal effect under the load of construction vehicles

Abstract The objective of this paper is to propose a novel computational model for solving the problem of accurately evaluating the randomly induced road vibration response of engineering vehicles traveling on rural roads. The computational model, first, focuses on the unique pavement characteristics of rural roads, constructs a tire grounding function model and innovatively introduces a dynamic friction factor, and successfully develops a coupled stochastic excitation system model for the interaction between the dynamic loads of 1/4 vehicle tires and the pavement of rural roads by applying the power spectral density function of the rural roads and combining it with the elastic roller model of the vehicle tires. Second, considering the nonlocal superposition effect of the soil skeleton of the roadbed, a coupled vibration response model of a 1/4 automobile rural road is successfully developed, and a validation method is given. Finally, the coupled vibration response characteristics of engineering vehicles and rural roads under random excitation at different speeds are analyzed. The analysis results show that the model proposed in this paper can well predict the degree and influence the range of rural road vibration caused by random excitation of construction vehicles traveling at any speed.

Dynamic Response Analysis of the Floor Structure under Random Crowd Excitation

The popularity of new structural systems and prestressing technology has led to the widespread use of the large-space floor structures in large buildings such as high-speed rail terminals, conference centers, and sports stadiums. The reduction of nonessential load-bearing elements and the increase in span of the structure result in a reduction in the natural frequency and damping ratio of the floor structure, while the floor is a crowded area with disorderly flow between people, which may lead to human-induced vibration problems. In order to assess the dynamic performance of the large-span floor structure under crowd load, the random crowd-floor vertical interaction equation is derived, and the correctness of the equation is verified by comparing it with the test. For the stochastic nature of walking crowds, a formulation modeling method for random crowd is proposed, including pedestrian-dynamics parameters, formulation model, and response parameters. The model is characterized by considering inter- and intrasubject variability and reflects the vertical interaction between pedestrians and the floor system. According to the random crowd-floor dynamic equation, the variation of modal parameters and acceleration response of the floor during random crowd walking are also analyzed. The research in this paper will help in analyzing the comfort of large-span floor structures under pedestrian excitation and better meet the needs of the development of lightweight large-span structures.

The vibroacoustic characteristic of beam-plate coupled structure in similitude

Similitude theory can be used to extrapolate the experimental data of a small, inexpensive, and easily tested model into design information for a large prototype. Scaling laws provide the relationship between a full-scale structure and its scale models. However, one challenging issue is the similitude of complex structure. To address the problem, an energy similarity method is presented based on the principle of conservation of power flow. The emphasis is to predict the vibroacoustic characteristic of beam-plate coupled structure in an effective and convenient way. The vibration response and radiated sound are investigated on the beam-plate coupled structure under random excitation. Numerical simulation and model test are both implemented, which validate the effectiveness and efficiency of the proposed method. Both aluminum and honeycomb materials are considered in beam-plate coupled structures. In addition, the comparison between the classic similitude method and the presented method (energy similarity) is illustrated. The results show that the energy similarity presented in this study can achieve a better performance in reproducing the vibroacoustic characteristic of beam-plate coupled structure than the classic similarity method.

An Efficient Method for Calculating Hysteretic Dry Friction Response of Dynamic Systems Subjected to Combined Harmonic and Random Excitation.

Many examples of dynamic analysis require modelling of dry friction. Often this is represented by a so-called Jenkins element or multiple Jenkins elements in parallel, which is sometimes termed a parallel-series Iwan element. This study considers the case where a system that includes these representations of dry friction are loaded dynamically with a combination of deterministic harmonic and random excitation. This paper presents a new efficient method for predicting the response of systems subject to combined deterministic and random excitation. The method is based on equivalent linearisation and involves averaging across both an ensemble of random responses as well as over a harmonic excitation period. The key novelty in the approach is the use of an auxiliary harmonic term to facilitate an analytical representation of the nonlinear force. This overcomes the challenge of analysing a discontinuous hysteretic nonlinearity in the presence of random excitation. Analytical solutions are presented and it is shown that the proposed approach can predict the approximate response at a significantly reduced computational cost.

Vibration Control of Base-Excited Rotors Supported by Active Magnetic Bearing Using a Model-Based Compensation Method

Active magnetic bearings (AMBs) are a type of mechatronics product widely used in high-speed rotating machinery. Considerable research has been conducted on the vibration rejection of the AMBs-rotor systems at the base standstill. However, little attention has been paid to the case where the rotor operates under base excitations, such as turbines mounted on ships with wave excitation. The increased rotor vibration caused by base excitations is a great challenge to operational safety. To address this issue, a base acceleration feedforward compensation (BAFC) algorithm was proposed in this paper. Using the online base excitation data and the dynamic model of the rotor system, the proposed model-based algorithm determines the optimal compensation current in real time. Further, to reject the decreased compensation performance due to inaccurate modeling, a method for correcting the compensation error has been presented. Moreover, the effect of controller parameters on system stability was explored to avoid parametric instability during base excitations. By employing the BAFC algorithm in the experiments, the rotor vibration was reduced considerably under both the harmonic and random base excitations with a maximum vibration reduction of 85%, demonstrating the remarkable effectiveness of the BAFC algorithm.

Remora optimization algorithm-based adaptive fusion via ant colony optimization for traveling salesman problem

The traditional ant colony optimization (ACO) is easy to fall into local optimal when solving large-scale traveling salesman problem (TSP), and the convergence speed is slow. In order to enhance the local search ability of ACO, speed up the efficiency of ACO and avoid the premature problem, this paper proposes a novel remora optimization algorithm-based adaptive fusion via ant colony optimization for solving TSP. Firstly, an improved K-means clustering method is used to obtain the best clustering results and the optimal solutions of each class quickly by adaptive clustering strategy based on the maximum and minimum distance and class density. By using an improved Remora optimization algorithm, adjacent classes are fused to effectively improve the accuracy of the initial solution. In addition, the initial solution is optimized by the k-opt strategy. Finally, the random recombination strategy is used to recombine the pheromone and random excitation to make the algorithm jump out of the local optimal as far as possible and improve the accuracy of the algorithm. The experimental results show that the proposed algorithm not only guarantees the accuracy of solution, but also improves the stability when solving large-scale TSP.

Semi-active control for the seat car suspension system using MR elastomer isolator

The suspension system for the car seat is an important part of the vehicle that helps to increase comfort and reduce fatigue. The study of suspension systems using magnetorheological elastomer (MRE) has attracted researchers in recent years. MRE is an elastomer material such as rubber. The modulus of the material can change when a magnetic field is applied. In this study, an MRE-based isolator is first developed for a seat car suspension system. The characteristics of the isolator are investigated under the strength of the magnetic field. Based on Lyapunov theory and constraint force, the semi-active controller is then designed. Numerical simulations for the car seat dynamics system show that the developed isolator can reduce vibrations more when compared with the passive approach in the case of bump and random excitations. The results show significant potential for its application in vehicle seat vibration control.

Analysis of damping multi-mode switching control of semi-active suspension based on digital controlled hydraulic cylinders group

In order to improve the ride comfort of vehicle suspension, this article proposes a damping multi-mode semi-active suspension system and its control method. The semi-active suspension takes a hydraulic electromagnetic shock absorber based on a digital controlled hydraulic cylinders group as the core, and realizes the switching of multiple damping modes by controlling the on-off statuses of three groups of switch solenoid valves, thus making the semi-active suspension have the characteristics of damping multi-mode adjustable. The damping characteristics corresponding to the single damping mode are verified through the prototype bench test of the shock absorber principle. On this basis, the semi-active suspension model of the vehicle is established, and a multi-mode switching control strategy of suspension damping using fuzzy control is designed. The filtered Gaussian white noise is used as the random road excitation for simulation. The simulation results show that compared with the traditional passive suspension and the semi-active suspension based on skyhook control, the damping multi-mode semi-active suspension based on the digital controlled hydraulic cylinders group can realize the switching of multiple damping modes, have good damping performance, and help to improve the vehicle ride comfortable capability.

Neural Network-Based Adaptive Height Tracking Control of Active Air Suspension System with Magnetorheological Fluid Damper Subject to Uncertain Mass and Input Delay.

In this paper, we present a novel robust adaptive neural network-based control framework to address the ride height tracking control problem of active air suspension systems with magnetorheological fluid damper (MRD-AAS) subject to uncertain mass and time-varying input delay. First, a radial basis function neural network (RBFNN) approximator is designed to compensate for unmodeled dynamics of the MRD. Then, a projector-based estimator is developed to estimate uncertain parameter variation (sprung mass). Additionally, to deal with the effect of input delay, a time-delay compensator is integrated in the adaptive control law to enhance the transient response of MRD-AAS system. By introducing a Lyapunov-Krasovskii (LK) functional, both ride height tracking and estimator errors can robustly converge towards the neighborhood of the desired values, achieving uniform ultimate boundness. Finally, comparative simulation results based on a dynamic co-simulator built in AMESim 2021.2 and Matlab/Simulink 2019(b) are given to illustrate the validity of the proposed control framework, showing its effectiveness to operate ride height regulation with MRD-AAS systems accurately and reliably under random road excitations.

A novel non-intrusive ROM for randomly excited linear dynamical systems with high stochastic dimension using ANN

Analyzing large stochastic dynamical systems is computationally very expensive. A statistical simulation framework requires invoking the solver multiple times — ranging from thousands to millions. A non-intrusive reduced order model (ROM) serves as a computationally efficient alternative in this framework. Uncertainties in dynamical systems originate from two sources: system parameters and excitation. However, all the existing ROMs have been developed for uncertainty only in the system parameters. To the best of the authors’ knowledge, no ROM exists for dynamical systems under random excitation. A discretization of the input process increases the stochastic dimensionality, typically by a few hundred or thousand. This leads to a high dimensional interpolation or regression in the ROM, which is practically infeasible. This issue is addressed in this work by proposing a novel non-intrusive ROM that bypasses the need for such discretization. Accordingly, a regression is carried out directly on the random excitation using a neural network-based surrogate model. A principal component-based data compression is used in tandem to reduce the stochastic dimensionality of excitations. Detailed numerical studies are conducted to study the accuracy and efficiency of the proposed ROM using two examples: a mistuned bladed disk problem and a soil–structure interaction. The numerical results show that the proposed ROM is accurate and gains a significant speed-up of more than sixty for both examples. Using the proposed ROM, the cost of uncertainty quantification can be reduced significantly within the framework of Monte Carlo simulation.