Adjoint sensitivity analysis and optimization of hysteretic dynamic systems with nonlinear viscous dampers

In this paper we discuss the adjoint sensitivity analysis and optimization of hysteretic systems equipped with nonlinear viscous dampers and subjected to transient excitation. The viscous dampers are modeled via the Maxwell model, considering at the same time the stiffening and the damping contribution of the dampers. The time-history analysis adopted for the evaluation of the response of the systems relies on the Newmark-β time integration scheme. In particular, the dynamic equilibrium in each time-step is achieved by means of the Newton-Raphson and the Runge-Kutta methods. The sensitivity of the system response is calculated with the adjoint variable method. In particular, the discretize-then-differentiate approach is adopted for calculating consistently the sensitivity of the system. The importance and the generality of the sensitivity analysis discussed herein is demonstrated in two numerical applications: the retrofitting of a structure subject to seismic excitation, and the design of a quarter-car suspension system. The MATLAB code for the sensitivity analysis considered in the first application is provided as “Supplementary Material”.     

Adjoint sensitivity analysis of hybrid multibody dynamical systems

Multibody System Dynamics - Sensitivity analysis computes the derivatives of general cost functions that depend on the system solution with respect to parameters or initial conditions. This work...     

Adjoint parameter sensitivity analysis for the hydrodynamic lattice Boltzmann method with applications to design optimization

We present an adjoint parameter sensitivity analysis formulation and solution strategy for the lattice Boltzmann method (LBM). The focus is on design optimization applications, in particular topology optimization. The lattice Boltzmann method is briefly described with an in-depth discussion of solid boundary conditions. We show that a porosity model is ideally suited for topology optimization purposes and models no-slip boundary conditions with sufficient accuracy when compared to interpolation bounce-back conditions. Augmenting the porous boundary condition with a shaping factor, we define a generalized geometry optimization formulation and derive the corresponding sensitivity analysis for the single relaxation LBM for both topology and shape optimization applications. Using numerical examples, we verify the accuracy of the analytical sensitivity analysis through a comparison with finite differences. In addition, we show that for fluidic topology optimization a scaled volume constraint should be used to obtain the desired “0-1” optimal solutions.     

Singular value decomposition for dynamic system design sensitivity analysis

A computer-based method for automatic generation and efficient numerical solution of mixed differential-algebraic equations for dynamic and design sensitivity analysis of dynamic systems is developed. The equations are written in terms of a maximal set of Cartesian coordinates to facilitate general formulation of kinematic and design constraints and forcing functions. Singular value decomposition of the system Jacobian matrix generates a set of composite generalized coordinates that are best suited to represent the system. The coordinates naturally partition into optimal independent and dependent sets, and integration of only the independent coordinates generates all of the system information. An adjoint variable method is used to compute design sensitivities of dynamic performance measures of the system. A general-purpose computer program incorporating these capabilities has been developed. A numerical example is presented to illustrate accuracy and properties of the method.     

Sensitivity analysis of structural response uncertainty propagation using evidence theory

Sensitivity analysis for the quantified uncertainty in evidence theory is developed. In reliability quantification, classical probabilistic analysis has been a popular approach in many engineering disciplines. However, when we cannot obtain sufficient data to construct probability distributions in a large-complex system, the classical probability methodology may not be appropriate to quantify the uncertainty. Evidence theory, also called Dempster–Shafer Theory, has the potential to quantify aleatory (random) and epistemic (subjective) uncertainties because it can directly handle insufficient data and incomplete knowledge situations. In this paper, interval information is assumed for the best representation of imprecise information, and the sensitivity analysis of plausibility in evidence theory is analytically derived with respect to expert opinions and structural parameters. The results from the sensitivity analysis are expected to be very useful in finding the major contributors for quantified uncertainty and also in redesigning the structural system for risk minimization.     

Pavement crack detection using hessian structure propagation

Pavement images are widely used in transportation agencies to detect cracks accurately so that the best proper plans of maintenance and rehabilitation could be made. Although crack in a pavement image is perceived because the intensity of crack pixels contrasts with that of the pavement background, there are still challenges in distinguishing cracks from complex textures, heavy noise, and interference. Unlike the intensity or the first-order edge feature of crack, this paper proposes the second-order directional derivative to characterize the directional valley-like structure of crack. The multi-scale Hessian structure is first proposed to analytically adapt to the direction and valley of cracking in the Gaussian scale space. The crack structure field is then proposed to mimic the curvilinear propagation of crack in the local area, which is iteratively applied at every point of the crack curve to infer the crack structure at the gaps and intersections. Finally, the most salient centerline of the crack within its curvilinear buffer is exactly located with non-maximum suppression along the perpendicular direction of crack. The experiments on large numbers of images of various crack types and with diverse conditions of noise, illumination and interference demonstrate the proposed method can detect pavement cracks well with an average Precision, Recall and F-measure of 92.4%, 88.4%, and 90.4% respectively. Also, the proposed method achieves the best performance of crack detection on the benchmark datasets among methods that also require no training and publicly offer the detection results for every image.     

基于随机灵敏度分析的化工过程裕量设计

对化工过程进行最优设计时,由于过程中参数的不确定性,需要在既满足过程约束又保证经济效益最优的前提下对设计变量增加裕量。本文考虑过程不确定参数的随机分布,结合灵敏度分析,提出一种基于随机灵敏度的化工过程最优裕量设计方法。首先,取不确定参数的标称值,进行化工过程最优设计,得到最优设计点的标称值;其次,假设过程不确定参数服从正态分布,基于灵敏度分析确定约束变量的均值和方差,在保证低概率违反约束的条件下优化求解设计裕量,定量分析不确定参数对设计变量的影响;最后,通过对串联连续搅拌釜式反应器（Continuous stirred tank reactor,CSTR）系统进行仿真实验,说明该裕量设计方法的具体步骤,并得到合理的设计裕量值,验证所提方法的正确性。     

Second-order shape design sensitivity using P-version finite element analysis

Thep-version finite element analysis (FEA) approach is attractive for design sensitivity analysis (DSA) and optimization due to its high accuracy of analysis results, even with coarse mesh; insensitivity to finite element mesh distortion and aspect ratio; and tolerance for large shape design changes during design iterations. A continuum second-order shape DSA formulation is derived and implemented usingp-version FEA. The second-order shape design sensitivity can be used for reliability based analysis and design optimization by incorporating it with the second-order reliability analysis method (SORM). Both the second-order shape DSA formulations with respect to the single and mixed shape design parameters are derived for elastic solids using the material derivative concept. Both the direct differentiation and hybrid methods are presented in this paper. A shape DSA is implemented by using an establishedp-version FEA code, STRESS CHECK. Two numerical examples, a connecting rod and bracket, are presented to demonstrate the feasibility and accuracy of the proposed seond-order shape DSA approach.     

Improvement of dynamic characteristics for optical pickup actuator using sensitivity analysis

 The disk rotation speed of optical disk drives (ODD) has been increasing rapidly to achieve high data transfer rates. High servo bandwidths for focusing and tracking actuator are required to follow dynamic disturbance by high rotation speed in ODD. However, the servo bandwidth is significantly limited by some vibration modes which are induced by the flexibility of the moving part. In this work, the vibration modes affecting the bandwidth of actuators are shifted to high frequency range and suppressed by modifying the FE model which is used to analyze the motion of the actuator. Some local dimensions of the lens holder, which is included in the moving part, are selected as design variables to increase the stiffness without changing the material properties. Selected modal frequencies of the moving part are raised about 10%, while the performances of actuator such as DC and AC sensitivities are hardly affected by the modification. Received: 8 November 2001/Accepted: 18 March 2002 This work was supported by the Korea Science and Engineering Foundation (KOSEF) through the CISD at Yonsei University under grant No. 2001G0101.     

Interval observer-based fault detectability analysis using mixed set-invariance theory and sensitivity analysis approach

This paper addresses the characterisation of the minimum detectable fault (MDF) by means of residual sensitivity integrated with the set-invariance theory when using an interval observer-based approach as a fault detection (FD) scheme. Uncertainties (disturbances and noise) are considered as of unknown but bounded nature (i.e. in the set-membership framework). A zonotopic-set representation towards reducing set operations to simple matrix calculations is utilised to bound the state/output estimations provided by the interval observer-based approach. In order to show the connection between sensitivity and set-invariance analyses, mathematical expressions of the MDF are derived when considering different types of faults. Finally, a simulation case study based on a quadruple-tank system is employed to both illustrate and discuss the effectiveness of the proposed approach. The interval observer-based FD scheme is used to test the MDF obtained from the integration of both residual sensitivity analysis and set-invariance theory in the considered case study.     

Efficient design sensitivity analysis of incompressible fluids using SPH projection method

Using the direct differentiation method, a design sensitivity analysis method for time-dependent incompressible fluids is developed. The fluid behavior is described as the motion of particles involved by the SPH method. In the SPH projection method, instead of changing the fluid density, incompressibility is enforced by the pressure Poisson equation derived from pressure projection, which enable to use larger time steps. In spite of the additional pressure Poisson equation, the computational cost for the design sensitivity is not expensive since the factorized system matrix of pressure Poisson equation can be utilized. Aforementioned computational efficiency is very beneficial for the design sensitivity computation required for every time step in explicit time integration and updated Lagrangian schemes, for which an update scheme of design velocity field is developed using the velocity sensitivity. Through demonstrative numerical examples, the developed DSA method turns out to be efficient and shows excellent agreement with finite differencing.     

Simulation of three-dimensional fatigue crack propagation using enriched finite elements

A three-dimensional methodology for simulation of fatigue crack propagation is presented. The method is leveraged by the use of enriched crack tip elements to compute the mixed-mode stress intensity factors. The crack growth model used and the crack propagation life calculation are also described. As examples, fatigue crack propagation of a mode-I surface crack and crack advancements of mixed-mode surface cracks are simulated. The predicted results showed excellent agreement with experimental data from the literature. Thus, it is concluded that the crack propagation method developed allows efficient and accurate simulation of three-dimensional fatigue crack propagation problems.     

翼伞系统最优归航轨迹设计的敏感度分析方法

本文对三自由度翼伞系统归航轨迹优化问题进行了研究,采用控制变量参数化与时间尺度变换相结合的优化算法对翼伞系统的最优控制问题进行数值求解.该方法是基于灵敏度分析的优化算法,将控制量以及控制量转换时间转化为一系列参数优化问题同时进行求解.仿真结果表明,相对于基于两端边值优化算法而言,灵敏度分析法只需要正向积分进行求解,因而具有计算简单、耗时短等优点,其控制效果良好,距离偏差和方向偏差均满足实际需求,有效地提高了翼伞系统的着陆精度,验证了该优化算法的可行性.     

X-FEM a good candidate for energy conservation in simulation of brittle dynamic crack propagation

This paper is devoted to the simulation of dynamic brittle crack propagation in an isotropic medium. It focuses on cases where the crack deviates from a straight-line trajectory and goes through stop-and-restart stages. Our argument is that standard methods such as element deletion or remeshing, although easy to use and implement, are not robust tools for this type of simulation essentially because they do not enable one to assess local energy conservation. Standard cohesive zone models behave much better when the crack’s path is known in advance, but are difficult to use when the crack’s path is unknown. The simplest method which consists in placing the cohesive segments along the sides of the finite elements leads to crack trajectories which are mesh-sensitive. The adaptive cohesive element formulation, which adds new cohesive elements when the crack propagates, is shown to have the proper energy conservation properties during remeshing. We show that the X-FEM is a good candidate for the simulation of complex dynamic crack propagation. A two-dimensional version of the proposed X-FEM approach is validated against dynamic experiments on a brittle isotropic plate.