Linear random vibration by stochastic reduced‐order models

A practical method is developed for calculating statistics of the states of linear dynamic systems with deterministic properties subjected to non‐Gaussian noise and systems with uncertain properties subjected to Gaussian and non‐Gaussian noise. These classes of problems are relevant as most systems have uncertain properties, physical noise is rarely Gaussian, and the classical theory of linear random vibration applies to deterministic systems and can only deliver the first two moments of a system state if the noise is non‐Gaussian. The method (1) is based on approximate representations of all or some of the random elements in the definition of linear random vibration problems by stochastic reduced‐order models (SROMs), that is, simple random elements having a finite number of outcomes of unequal probabilities, (2) can be used to calculate statistics of a system state beyond its first two moments, and (3) establishes bounds on the discrepancy between exact and SROM‐based solutions of linear random vibration problems. The implementation of the method has required to integrate existing and new numerical algorithms. Examples are presented to illustrate the application of the proposed method and assess its accuracy. Copyright © 2009 John Wiley & Sons, Ltd.     

Synthesizing nonstationary,non‐Gaussian random vibrations

This paper presents a novel technique by which non‐Gaussian vibrations are synthesized by generating a sequence of random Gaussian processes of varying root mean square (rms) levels and durations. The technique makes use of previous research by the authors which shows that non‐Gaussian vibrations can be decomposed into a sequence of Gaussian processes. Synthesis is achieved by first computing a modulation function which is produced from the rms and the segment length distribution functions, both of which were developed in previous research. This is achieved by first generating a sequence of uniformly distributed random numbers scaled to the range of segment length, which itself is a function of the desired total duration of the synthesized process. In order to transform a uniformly distributed random variable into any arbitrary non‐uniform distribution, the cumulative distribution function is established and used as a transfer function applied to the uniformly distributed random variable. This modulation function is applied to a Gaussian random signal itself generated by a standard laboratory random vibration controller (RVC) by means of a purposed‐designed variable gain amplifier system. In order to counteract the feedback function of the RVC, a second variable gain amplifier is introduced into the system in order to attenuate the feedback signal in inverse proportion to the gain applied to the command signal. This result is a nonstationary, non‐Gaussian random signal that statistically conforms to the desired PSD as well as the RMS distribution function. Copyright © 2010 John Wiley & Sons, Ltd.     

Inverse Sub‐Structuring Method for Multi‐Coordinate Coupled Product Transport System

A new high‐accuracy transfer function is selected, and an inverse sub‐structuring method is developed for the analysis of the dynamic characteristics of a three‐sub‐structure coupled product transport system. The closed‐form analytical solution to inverse sub‐structuring analysis of multi‐coordinate coupled multi‐ sub‐structure product transport system is derived. The proposed method is validated by a lumped mass spring damper model; the predicted frequency response functions (FRFs) of sub‐structures and the coupling stiffness, in addition to the most concerned system‐level FRF, are compared with the direct computations, showing exact agreement. Then, FRF tests of a physical prototype of the multi‐coordinate coupled product transport system with three sub‐structures are performed to further check the accuracy of the suggested method. The method developed offers an approach to predict the unknown sub‐structure‐level FRFs and coupling stiffness purely from system‐level FRFs. The suggested method may help obtain the main controlling factors and contributions from the various structure‐borne paths for the product transport system, which may certainly facilitate the cushioning packaging design. Copyright © 2013 John Wiley & Sons, Ltd.     

Inverse Sub‐structuring Method for Multi‐coordinate Rigidly Coupled Product Transport System based on a Novel Shearing Probe Technique

The inverse sub‐structuring method can predict the component‐level frequency response functions (FRFs) of product (critical component) for product transport system from only measured system‐level FRFs, facilitating the cushioning packaging design. However, the FRFs of the coupling interface between product and vehicle are usually of extreme difficulty to be measured due to the limited accessible space. To overcome this difficulty, the authors suggested a so‐called FRF probe technique method in the previous study, which may be more suitable for the single‐coordinate coupled system. In practice, most of the product transport systems should be treated as multi‐coordinate coupled system. The aim of this paper is to derive a new FRF‐based inverse sub‐structuring method for multi‐coordinate rigidly coupled product transport system and develop a new shearing probe technique to obtain the difficult‐to‐monitor FRFs at the coupling interface, which will be validated by a lumped mass model and finite element models, respectively, showing perfect agreement. Finally, the experiment on a physical prototype of multi‐coordinate rigidly coupled product transport system is performed to further check the feasibility of the application prospect of the shearing probe technique for inverse analysis of product transport system. The method proposed in this study will provide the packaging designers an alternative method to monitor the integrity of product transport system. Copyright © 2017 John Wiley & Sons, Ltd.     

A contact detection algorithm for multi‐sphere particles by means of two‐level‐grid‐searching in DEM simulations

In discrete element method simulations, multi‐sphere particle is extensively employed for modeling the geometry shape of non‐spherical particle. A contact detection algorithm for multi‐sphere particles has been developed through two‐level‐grid‐searching. In the first‐level‐grid‐searching, each multi‐sphere particle is represented by a bounding sphere, and global space is partitioned into identical square or cubic cells of size D, the diameter of the greatest bounding sphere. The bounding spheres are mapped into the cells in global space. The candidate particles can be picked out by searching the bounding spheres in the neighbor cells of the bounding sphere for the target particle. In the second‐level‐grid‐searching, a square or cubic local space of size (D + d) is partitioned into identical cells of size d, the diameter of the greatest element sphere. If two bounding spheres of two multi‐sphere particles are overlapped, the contacts occurring between the element spheres in the target multi‐sphere particle and in the candidate multi‐sphere particle are checked. Theoretical analysis and numerical tests on the memory requirement and contact detection time of this algorithm have been performed to verify the efficiency of this algorithm. The results showed that this algorithm can effectively deal with the contact problem for multi‐sphere particles. Copyright © 2015 John Wiley & Sons, Ltd.     

A New Approach for Road‐Vehicle Vibration Simulation

A new approach for road‐vehicle vibration simulation is proposed and demonstrated feasible by testing with three express‐road vehicle‐vibration records, that is, record A, two‐wheel electric bicycle, 80% loaded, traveling on urban road; record B, median van, 50% loaded, traveling on urban road; and record C, minivan, 80% loaded, traveling on urban road too. This method decomposes the original signal into a series of approximate Gaussian‐vibration segments and a shock segment with high kurtosis by moving crest factor and one‐tenth peak‐value method. Simulate Gaussian‐distribution vibration one by one from the power spectral density (PSD) of each decomposed segments. The overall signal is simulated by concatenating of each decomposed Gaussian segment. The simulated signal has not only the same overall root‐mean‐square (RMS), duration as the original signal, but also has a similar PSD to the original signal, without incurring excessive acceleration levels. This allows an improved and more representative simulated input signal to be generated that can be use in the current generation of vibration table.     

Non‐linear random response of laminated composite shallow shells using finite element modal method

This paper investigates the large‐amplitude multi‐mode random response of thin shallow shells with rectangular planform at elevated temperatures using a finite element non‐linear modal formulation. A thin laminated composite shallow shell element and the system equations of motion are developed. The system equations in structural node degrees‐of‐freedom (DOF) are transformed into modal co‐ordinates, and the non‐linear stiffness matrices are transformed into non‐linear modal stiffness matrices. The number of modal equations is much smaller than the number of equations in structural node DOF. A numerical integration is employed to determine the random response. Thermal buckling deflections are obtained to explain the intermittent snap‐through phenomenon. The natural frequencies of the infinitesimal vibration about the thermally buckled equilibrium positions (BEPs) are studied, and it is found that there is great difference between the frequencies about the primary (positive) and the secondary (negative) BEPs. All three types of motion: (i) linear random vibration about the primary BEP, (ii) intermittent snap‐through between the two BEPs, and (iii) non‐linear large‐amplitude random vibration over the two BEPs, can be predicted. Copyright © 2006 John Wiley & Sons, Ltd.     

An approach to multi‐start clustering for global optimization with non‐linear constraints

This paper describes a multi‐start with clustering strategy for use on constrained optimization problems. It is based on the characteristics of non‐linear constrained global optimization problems and extends a strategy previously tested on unconstrained problems. Earlier studies of multi‐start with clustering found in the literature have focused on unconstrained problems with little attention to non‐linear constrained problems. In this study, variations of multi‐start with clustering are considered including a simulated annealing or random search procedure for sampling the design domain and a quadratic programming (QP) sub‐problem used in cluster formation. The strategies are evaluated by solving 18 non‐linear mathematical problems and six engineering design problems. Numerical results show that the solution of a one‐step QP sub‐problem helps predict possible regions of attraction of local minima and can enhance robustness and effectiveness in identifying local minima without sacrificing efficiency. In comparison to other multi‐start techniques found in the literature, the strategies of this study can be attractive in terms of the number of local searches performed, the number of minima found, whether the global minimum is located, and the number of the function evaluations required. Copyright © 2002 John Wiley & Sons, Ltd.     

Quantifying the Non‐stationarity of Vehicle Vibrations with the Run Test

This paper investigates the applicability of the run test as a tool to quantify the statistical non‐stationarity of road vehicle vibrations. The run test was applied to the moving root‐mean‐square (RMS) time history of a number of vibration records measured from a variety of vehicle types, routes and vehicle speeds. The paper discusses the limitations associated with calculating the moving RMS of random signals especially with respect to the window width. When applied to the set of vibration records (with segments of inactivity removed), the run test indicates that every record is non‐stationary. A run ratio parameter was introduced to quantify the level of non‐stationarity, which shows that the result is sometimes dependent on the RMS window width. Further analysis correlating the run test results with the statistical distribution or the RMS indicates that the run ratio parameter has some merit in quantifying the level of non‐stationarity in road vehicle vibrations. Copyright © 2013 John Wiley & Sons, Ltd.     

多输入多输出混合振动试验中正弦与随机信号分离方法

研究了多输入多输出正弦加随机混合振动试验的控制方法,指出混合信号中正弦信号和随机信号的精确分离是提高控制精度的关键因素。提出了具有滤波特性的不相关积分法在时域中识别正弦信号,避免了频域识别的泄露误差问题,详细地推导了将给定频率的正弦信号从混合信号中分离出来的公式;数值计算显示该方法的识别精度达到0.44%。以一悬臂梁作为研究对象建立两输入两输出振动试验系统模型,使用比例均方根控制算法和正弦幅值修正法分别对随机振动和正弦振动进行修正,将随机信号控制在参考谱的±3dB以内,将正弦信号的幅值控制在参考值的±10%以内,满足振动试验要求。     

Damping characteristics of magneto‐rheological fluid absorber based on closed‐loop proportion integration differentiation control

Aiming at investigating the working of magneto‐rheological fluid absorber, a test system used for detecting the damping characteristics of the magneto‐rheological fluid absorber was designed. The test system included sensors, data acquisition card, and so on. The vibration signals were detected by the sensors, put into LabVIEW data acquisition system, and then collected through the processing of closed‐loop Proportion Integration Differentiation control algorithm. Considering that the feedback current could be output to the magneto‐rheological fluid absorber by the data acquisition card, thus the damping force could be changed. The test results showed that the amplitude of the structure vibration response was obviously reduced through the closed‐loop Proportion Integration Differentiation control algorithm, and the control damping characteristics of the magneto‐rheological fluid absorber was improved.     

MIMO线性系统输入输出信号统计特征的双谱评定方法

基于高阶统计量具备处理随机信号的特性,提出了一种利用三阶谱(双谱)评定MIMO线性系统时域输入输出信号统计特征的新方法。通过建立线性系统双谱数学模型,根据系统响应、所测得的频响函数以及离散信号的双谱数值估计算法,经逆运算获得系统的双谱驱动信号,随后利用高阶谱对高斯随机信号的盲性判定其输入信号的高斯性。将上述方法与采用传统相位随机化法(对功率谱添加随机相位)所获得的驱动信号分别应用于一悬臂梁模拟控制系统中,通过对输入信号的分析及控制结果的比较,发现基于双谱所生成的时域随机驱动信号呈现出较强的非高斯性且收敛速度更快。对于输出信号统计特征的评定,提出从输入信号与系统频带接近的程度入手,再次利用高阶统计量对高斯随机信号的盲性进行定性判定,对于无法判别满足何种非高斯统计分布特征的,不管是对于输入信号还是输出信号,一律采用绘制信号的概率分布特征曲线进行定量评定。     

A Study of Nonlinear Effects in a Cushion‐Product System on its Vibration Transmissibility Estimates with the Reverse Multiple Input–Single Output Technique

The Reverse Multiple Input–Single Output (R‐MISO) identification technique was implemented to determine vibration transmissibility frequency response functions (FRFs) of a cushion‐product system that accounts for nonlinearities known to exist in such systems. The signed quadratic x|x| nonlinear term was used. The results were compared with the classical linear approximation FRFs calculated with the single input–single output identification method. Comparisons were made for five types of expanded polystyrene (EPS) cushions with varying density and two levels of band‐limited random excitation. It was shown that vibration transmissibility FRFs obtained with the R‐MISO method and with the inclusion of a signed quadratic x|x| nonlinear term significantly (up to ~70%) improved the total coherence of the nonlinear vibration transmissibility FRFs for the EPS cushions subjected to the static load selected to coincide with the optimum of their respective cushion curves. The R‐MISO technique was successful in accounting for some of the nonlinearities in the EPS cushion‐product system. However, its ability to deal with nonlinearities is not specific to the EPS but rather common to cushion‐product systems subjected to vertical vibrations. Copyright © 2012 John Wiley & Sons, Ltd.     

Application of a Multi‐Camera Stereo DIC Set‐up to Assess Strain Fields in an Erichsen Test: Methodology and Validation

Abstract: A multi‐camera stereo digital image correlation (MC‐DIC) set‐up is presented to obtain full displacement and strain fields of a sheet‐metal specimen subjected to an Erichsen test. The set‐up is composed of several conventional stereo DIC systems (two camera set‐up), each of which tracks the deformation of an aspect of the specimen. The individual measurements, including the geometries and the displacements, are then converted to the same reference frame to integrate into a global view. Afterwards, the strain is calculated based on the composed displacement field. It is found that the geometry and the displacement fields of the bulged specimen are ideally stitched, and smooth strain fields are obtained. The influences of the reference frame transformation and the stitching procedure on the MC‐DIC measurement are investigated. A rigid motion test is performed to validate the displacement measurement. It is discussed that the global field is more reliable than the individual measurements for this test set‐up.     

An Efficient Reliability Evaluation Approach for Networks with Simultaneous Multiple‐Node‐Pair Flow Requirements

This paper proposes an efficient approach for reliability evaluation of multiple‐sources and multiple‐destinations flow networks. The proposed approach evaluates multiple node pair capacity related reliability. The proposed approach is a three‐step approach; in the first step, it enumerates network minimal cut sets. These network minimal cut sets are then used to enumerate subset cuts in the second step. Third step involves the evaluation of multiple node pair capacity related reliability from the enumerated subset cuts using a multi‐variable inversion sum‐of‐disjoint set approach. The proposed approach can be used for optimal network design as it combines multiple performance requirements, that is, flow requirements between multiple node pairs and network reliability, in a single criterion. Copyright © 2016 John Wiley & Sons, Ltd.     

Multi‐contrast MR image denoising for parallel imaging using multilayer perceptron

For clinical diagnosis in MRI, multiple examinations are commonly performed to acquire various contrast images. This article presents a learning‐based denoising method for parallel imaging to enhance the quality of multi‐contrast images so that the imaging time can be accelerated highly. Multi‐contrast images share structural information and coil geometry. The proposed method adopts the multilayer perceptron (MLP) model to save the sharable and redundant information among the multi‐contrast images. The images are divided into patches, which are used as the input and output of MLP. A geometry factor map is additionally used to provide noise amplification information of the accelerated MR images. Computer simulation demonstrates that the use of multi‐contrast images and geometry factor contributes to the quality of the reconstructed images. The proposed method reconstructs high‐quality images without impairing details from the subsampled intermediate images, and it shows better results than previous denoising methods.     

Dynamic Characteristic Analysis of Refrigerator‐Truck Transport System by Using Inverse Substructure Method

This paper is a continuation of the previous research. The refrigerator‐truck system is treated as a two‐substructure multi‐coordinate coupled system, which is composed of a refrigerator substructure and a truck substructure coupled by numerous packaging units. Applying the two‐substructure multi‐coordinate coupled inverse substructure method to a product‐transport system, the paper makes an analysis of the dynamic characteristics for the refrigerator‐truck system. In order to validate the method in the refrigerator‐truck system, the measured system‐level frequency response functions (FRFs) were used to predict the substructure‐level FRFs that were compared with those directly measured and found to be in agreement in trend. To evaluate the vibration transmissibility of packaging units, the concepts of the vibration contribution, vibration contribution ratio, overall vibration contribution and overall vibration contribution ratio to product response through each packaging unit are introduced. The vibration contributions to the refrigerator through four coupling points almost coincide with each other in the whole frequency domain. However, the vibration contribution ratios are different at each frequency. The overall vibration contributions to the refrigerator through the frequency domain 10 to 50 Hz through four coupling points are respectively 9.4, 7.5, 9.8 and 11.2 mm/N, and the overall vibration contribution ratios are respectively 0.25, 0.20, 0.26 and 0.29. The vibration transmissibilities of four coupling points are similar. Copyright © 2014 John Wiley & Sons, Ltd.     

The weak substitution method – an application of the mortar method for patch coupling in NURBS‐based isogeometric analysis

In this contribution, a mortar‐type method for the coupling of non‐conforming NURBS (Non‐Uniform Rational B‐spline) surface patches is proposed. The connection of non‐conforming patches with shared degrees of freedom requires mutual refinement, which propagates throughout the whole patch due to the tensor‐product structure of NURBS surfaces. Thus, methods to handle non‐conforming meshes are essential in NURBS‐based isogeometric analysis. The main objective of this work is to provide a simple and efficient way to couple the individual patches of complex geometrical models without altering the variational formulation. The deformations of the interface control points of adjacent patches are interrelated with a master‐slave relation. This relation is established numerically using the weak form of the equality of mutual deformations along the interface. With the help of this relation, the interface degrees of freedom of the slave patch can be condensated out of the system. A natural connection of the patches is attained without additional terms in the weak form. The proposed method is also applicable for nonlinear computations without further measures. Linear and geometrical nonlinear examples show the high accuracy and robustness of the new method. A comparison to reference results and to computations with the Lagrange multiplier method is given. Copyright © 2015 John Wiley & Sons, Ltd.     

Interface Jacobian‐based Co‐Simulation

Co‐simulation is a prominent method to solve multi‐physics problems. Multi‐physics simulations using a co‐simulation approach have an intrinsic advantage. They allow well‐established and specialized simulation tools for different fields and signals to be combined and reused with minor adaptations in contrast to the monolithic approach. However, the partitioned treatment of the coupled system poses the drawback of stability and accuracy challenges. If several different subsystems are used to form the co‐simulation scenario, these issues are especially important. In this work, we propose a new co‐simulation algorithm based on interface Jacobians. It allows for the stable and accurate solution of complex co‐simulation scenarios involving several different subsystems. Furthermore, the Interface Jacobian‐based Co‐Simulation Algorithm is formulated such that it enables parallel execution of the participating subsystems. This results in a high‐efficient procedure. Furthermore, the Interface Jacobian‐based Co‐Simulation Algorithm handles algebraic loops as the co‐simulation scenario is defined in residual form. Copyright © 2014 John Wiley & Sons, Ltd.