Accuracy tests for various sensitivity analysis methods with respect to shape variables in planar cantilever beams

Sensitivity information is required in the optimal design process. In structural optimization, sensitivity calculation is a bottleneck due to its complexities. Various schemes have been proposed for the calculation. Analytic and finite difference methods are the most popular at the present time; however, they have their advantages and disadvantages. The semi-analytic method has been suggested to overcome these difficulties. In spite of its excellence, the semi-analytic method has been found to possess numerical errors with respect to shape variables. In this research, the errors from each method are evaluated and compared using a shape variable. A planar beam is selected as an example since it has a mathematical solution. An efficient method is suggested for the structural optimization which utilizes the finite element method.     

Forecasting time series using principal component analysis with respect to instrumental variables

Two new forecasting methods of time series are introduced. They are both based on a factorial analysis method called spline principal component analysis with respect to instrumental variables (spline PCAIV). The first method is a straightforward application of spline PCAIV while the second one is an adaptation of spline PCAIV. In the modified version, the used criteria according to the unknown value that need to be predicted are differentiated. Those two forecasting methods are shown to be well adapted to time series.     

Stabilizing helicopter motion with respect to all variables

We solve the equilibrium stabilization problem for equations that describe the motion of a helicopter. We use transformations to a normal form, partial linearization with feedback, and the method of virtual outputs that let us stabilize the system with respect to all variables.     

Stability robustness of networked control systems with respect to packet loss

This paper is concerned with stability analysis of discrete-time networked control systems over a communication channel subject to packet loss whose behavior is modeled by an i.i.d Bernoulli process with a packet dropping probability bounded by a constant. A necessary and sufficient condition for stability is obtained. A packet dropping margin is introduced as a measure of stability robustness of a system against packet dropping, and a formula for it is derived. A design method is proposed for achieving a large margin subject to a constraint that the system has a set of prescribed nominal closed-loop poles.     

Atomic functions of three variables invariant with respect to a rotation group

Atomic functions of three variables, i.e., infinitely differentiable compactly supported solutions of functional differential equations of special type are considered. The existence theorem, conclusion about additivity of the function inside the carrier, the probability sense, and the algorithm of calculation of the moments of compactly supported functions are presented.Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 118–130, November–December 2004.This revised version was published online in April 2005 with a corrected cover date.     

Accuracy test of sensitivity analysis in the semi-analytic method with respect to configuration variables

Configuration optimization is a structural optimization method where the geometrical shape of the structures can be changed during the optimization process. Sensitivity informations are required in the general optimization and quite costly. Especially, they are extemely expensive in the structural optimization where the finite element analysis is utilized. Since the nodal coordinates are regarded as design variables in the configuration optimization, the sensitivities according to the nodal coordinates must be calculated. The characteristics of the configuration optimization is that the transformation matrix in the finite element analysis is a function of design variables. Thus the sensitivity calculation in the configuration optimization is even more complicated. For the efficient sensitivity calculations, various methods have been proposed. They are the analytic method (AM), overall finite difference method (OFD), and semi-analytic method (SM). The semi-analytic method consists of the forward and central difference approximation. This study has been conducted to choose an appropriate method by comparison based on the mathematical and numerical aspects. Some standard structural problems are selected for the evaluations.     

Adjoint RANS with filtered shape derivatives for hydrodynamic optimisation

The adjoint RANS method has been implemented in the framework of an unstructured general-purpose finite volume code following the derive-then-discretise strategy (continuous adjoint approach). An explicit filtering technique is applied to the shape derivatives in order to extract noise from the mesh-based representation of high-resolution. In a CAD-free optimisation strategy the method is applied to a semi-circular profile in incompressible, external flow. It was observed that the filtering is particularly relevant at high Reynolds-numbers. In the complex scenario of ship hull design, the filtered shape derivative can directly be applied to the base-line configuration in order to support both manual and automatic shape optimisation.     

EM-GPA: Generalized Procrustes analysis with hidden variables for 3D shape modeling

Aligning shapes is essential in many computer vision problems and generalized Procrustes analysis (GPA) is one of the most popular algorithms to align shapes. However, if some of the shape data are missing, GPA cannot be applied. In this paper, we propose EM-GPA, which extends GPA to handle shapes with hidden (missing) variables by using the expectation-maximization (EM) algorithm. For example, 2D shapes can be considered as 3D shapes with missing depth information due to the projection of 3D shapes into the image plane. For a set of 2D shapes, EM-GPA finds scales, rotations and 3D shapes along with their mean and covariance matrix for 3D shape modeling. A distinctive characteristic of EM-GPA is that it does not enforce any rank constraint often appeared in other work and instead uses GPA constraints to resolve the ambiguity in finding scales, rotations, and 3D shapes. The experimental results show that EM-GPA can recover depth information accurately even when the noise level is high and there are a large number of missing variables. By using the images from the FRGC database, we show that EM-GPA can successfully align 2D shapes by taking the missing information into consideration. We also demonstrate that the 3D mean shape and its covariance matrix are accurately estimated. As an application of EM-GPA, we construct a 2D + 3D AAM (active appearance model) using the 3D shapes obtained by EM-GPA, and it gives a similar success rate in model fitting compared to the method using real 3D shapes. EM-GPA is not limited to the case of missing depth information, but it can be easily extended to more general cases.     

A novel self-adaptive hybrid multi-objective meta-heuristic for reliability design of trusses with simultaneous topology,shape and sizing optimisation design variables

Structural and Multidisciplinary Optimization - Performing the design of a truss including topological, shape and sizing (TSS) variables simultaneously is a challenging but important task for a...     

Maximisation of the crushing performance of a tubular device by shape optimisation

A tapered tubular steel component to be used as an energy-absorbing device has been optimised by taking into account two design variables describing the tapering geometry. The minimisation of a load uniformity parameter evaluated as the ratio between the maximum and the average crushing loads has been considered as objective function.The optimisation process has been carried out by using a multi-point approximation scheme based on the response surface methodology. The optimisation process led to the identification of two promising geometrical configurations characterised by a quite low value of the load uniformity parameter. The two solutions have been analysed with respect to their sensitivity towards two model parameters, the sheet thickness and the Young modulus of the material.     

Exact analytical solutions for frequency sensitivity of flat plates with respect to boundary shape change

Exact analytical solutions for the natural frequency sensitivity of flat plates subjected to prescribed shape design changes are obtained. The results are based on the domain mapping idea and are restricted to certain simple changes in domain geometry. Since the approach is exact and analytical it may be used as a reference for a simple yet precise accuracy assessment of more sophisticated and general numerical calculations of boundary shape eigen value sensitivity.     

Analytical derivatives of structural matrices for an eight node isoparametric membrane element with respect to a set of design variables

Analytical derivatives of finite element matrices with respect to a set of design variables are derived. The design variables are—cross-section area (rods), thickness (membranes), angles of anisotropy (membranes, solids), and node point coordinates (all types). The derivations are done in detail for an eight node isoparametric membrane element and more briefly for other membranes, rods and solids.     

Feasibility analysis for robustness quantification by symbolic model checking

We propose and investigate a robustness evaluation procedure for sequential circuits subject to particle strikes inducing bit-flips in memory elements. We define a general fault model, a parametric reparation model and quantitative measures reflecting the robustness capability of the circuit with respect to these fault and reparation models. We provide algorithms to compute these metrics and show how they can be interpreted in order to better understand the robustness capability of several circuits (a simple circuit coming from the VIS distribution, circuits from the itc-99 benchmarks and a CAN-Bus interface).     

节流管孔流动参数与雷诺数关系的数值研究

对初始静止状态的流体,在其压力差为阶跃变化的情况下,通过节流孔的流动过程进行了数值解析计算。特别注目于再附着点距离zats、流量系数cd、惯性长,以及时间常数τq、τz与雷诺数Re的关系。做出了流动参数与雷诺数Re的关系图,并给出了用雷诺数计算时间常数的计算式。数值计算结果说明了对应于流量变化的时间常数τq随着Re数的增加而减少,而对应于流场变化的时间常数τz几乎为一定值。     

Topological sensitivity derivative with respect to area,shape and orientation of an elliptic hole in a plate

The topological sensitivity derivative of a functional expressed in terms of displacement, strain or stress fields and boundary tractions is derived for the case of an elliptical hole introduced in the plate. The derivative is specified with respect to the hole area, the length of ellipse axes and their orientation in terms of primary and adjoint state fields. The shape sensitivity derivative for a finite hole can be applied and the topological derivative with respect to the hole area is obtained in the limiting case. The transition to a plane crack occurs for vanishing length of minor axis and the topological derivative with respect to crack length is then derived from the general formulae. The results can be useful in optimal design procedures by selecting positions, shape and orientation of elliptical cutouts.     

Evaluating shape correspondence for statistical shape analysis: a benchmark study

This paper introduces a new benchmark study to evaluate the performance of landmark-based shape correspondence used for statistical shape analysis. Different from previous shape-correspondence evaluation methods, the proposed benchmark first generates a large set of synthetic shape instances by randomly sampling a given statistical shape model that defines a ground-truth shape space. We then run a test shape-correspondence algorithm on these synthetic shape instances to identify a set of corresponded landmarks. According to the identified corresponded landmarks, we construct a new statistical shape model, which defines a new shape space. We finally compare this new shape space against the ground-truth shape space to determine the performance of the test shape-correspondence algorithm. In this paper, we introduce three new performance measures that are landmark independent to quantify the difference between the ground-truth and the newly derived shape spaces. By introducing a ground-truth shape space that is defined by a statistical shape model and three new landmark-independent performance measures, we believe the proposed benchmark allows for a more objective evaluation of shape correspondence than previous methods. In this paper, we focus on developing the proposed benchmark for $2$D shape correspondence. However it can be easily extended to $3$D cases.     

New approach to time-domain analysis for stability robustness of dynamic systems

This paper presents a new approach to the analysis of the stability robustness of dynamic systems in state-space models. By continuously perturbing the state matrix, instead of solving the Lyapunov equation, an elegant stability robustness fundamental is derived. Subsequently, the allowable norm bound of the error matrix can be obtained under weakly structured perturbations, and the magnitude bound on individual elements of the error matrix can be obtained under highly structured perturbations. The merits of the theorems and corollary developed are demonstrated by two examples where the results achieved are much better than those already published in the literature. The concept that the perturbed state matrix would depend on the operating frequencies is also introduced.     

The gradient with respect to a symmetric matrix

The well-known formulas for gradient matrices can be applied only when the elements of the matrix are independent [1],[2]. In this note, the author derives gradient formulas for two important types of element dependency: symmetry and skew symmetry. Application is made to the sensitivity analysis of optimal estimation systems.