Sensitivity Analysis and Optimization of Design Variables Related to an Algorithm for Loss of Balance Detection

Efficient and reliable sensitivity analyses are critical for topology optimization, especially for multibody dynamics systems, because of the large number of design variables and the complexities and expense in solving the state equations. This research addresses a general and efficient sensitivity analysis method for topology optimization with design objectives associated with time dependent dynamics responses of multibody dynamics systems that include nonlinear geometric effects associated with large translational and rotational motions. An iterative sensitivity analysis relation is proposed, based on typical finite difference methods for the differential algebraic equations (DAEs). These iterative equations can be simplified for specific cases to obtain more efficient sensitivity analysis methods. Since finite difference methods are general and widely used, the iterative sensitivity analysis is also applicable to various numerical solution approaches. The proposed sensitivity analysis method is demonstrated using a truss structure topology optimization problem with consideration of the dynamic response including large translational and rotational motions. The topology optimization problem of the general truss structure is formulated using the SIMP (Simply Isotropic Material with Penalization) assumption for the design variables associated with each truss member. It is shown that the proposed iterative steps sensitivity analysis method is both reliable and efficient.

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Design Sensitivity Analysis of Nonlinear Multidisciplinary Multibody Systems in the MIXEDMODELS Platform

Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C ◽

10.1115/detc2007-35493 ◽

2007 ◽

Author(s):

Shilpa A. Vaze ◽

Prakash Krishnaswami ◽

James DeVault

Keyword(s):

Sensitivity Analysis ◽

Multibody Systems ◽

Design Sensitivity ◽

Differential Algebraic Equations ◽

The State ◽

Design Sensitivity Analysis ◽

Design Parameters ◽

State Variables ◽

Sensitivity Coefficients ◽

Design Variables

Most state-of-the-art multibody systems are multidisciplinary and encompass a wide range of components from various domains such as electrical, mechanical, hydraulic, pneumatic, etc. The design considerations and design parameters of the system can come from any of these domains or from a combination of these domains. In order to perform analytical design sensitivity analysis on a multidisciplinary system (MDS), we first need a uniform modeling approach for this class of systems to obtain a unified mathematical model of the system. Based on this model, we can derive a unified formulation for design sensitivity analysis. In this paper, we present a modeling and design sensitivity formulation for MDS that has been successfully implemented in the MIXEDMODELS (Multidisciplinary Integrated eXtensible Engine for Driving Metamodeling, Optimization and DEsign of Large-scale Systems) platform. MIXEDMODELS is a unified analysis and design tool for MDS that is based on a procedural, symbolic-numeric architecture. This architecture allows any engineer to add components in his/her domain of expertise to the platform in a modular fashion. The symbolic engine in the MIXEDMODELS platform synthesizes the system governing equations as a unified set of non-linear differential-algebraic equations (DAE’s). These equations can then be differentiated with respect to design to obtain an additional set of DAE’s in the sensitivity coefficients of the system state variables with respect to the system’s design variables. This combined set of DAE’s can be solved numerically to obtain the solution for the state variables and state sensitivity coefficients of the system. Finally, knowing the system performance functions, we can calculate the design sensitivity coefficients of these performance functions by using the values of the state variables and state sensitivity coefficients obtained from the DAE’s. In this work we use the direct differentiation approach for sensitivity analysis, as opposed to the adjoint variable approach, for ease in error control and software implementation. The capabilities and performance of the proposed design sensitivity analysis formulation are demonstrated through a numerical example consisting of an AC rectified DC power supply driving a slider crank mechanism. In this case, the performance functions and design variables come from both electrical and mechanical domains. The results obtained were verified by perturbation analysis, and the method was shown to be very accurate and computationally viable.

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Optimal design of a parallel robotic gripper using enhanced multi-objective ant lion optimizer with a sensitivity analysis approach

Assembly Automation ◽

10.1108/aa-08-2019-0145 ◽

2020 ◽

Vol 40 (5) ◽

pp. 703-721

Author(s):

Golak Bihari Mahanta ◽

Deepak BBVL ◽

Bibhuti B. Biswal ◽

Amruta Rout

Keyword(s):

Sensitivity Analysis ◽

Distribution Function ◽

Design Parameters ◽

Objective Functions ◽

Content Type ◽

Multi Objective ◽

The Past ◽

Design Variables ◽

Pick And Place ◽

Ant Lion

Purpose From the past few decades, parallel grippers are used successfully in the automation industries for performing various pick and place jobs due to their simple design, reliable nature and its economic feasibility. So, the purpose of this paperis to design a suitable gripper with appropriate design parameters for better performance in the robotic production systems. Design/methodology/approach In this paper, an enhanced multi-objective ant lion algorithm is introduced to find the optimal geometric and design variables of a parallel gripper. The considered robotic gripper systems are evaluated by considering three objective functions while satisfying eight constraint equations. The beta distribution function is introduced for generating the initial random number at the initialization phase of the proposed algorithm as a replacement of uniform distribution function. A local search algorithm, namely, achievement scalarizing function with multi-criteria decision-making technique and beta distribution are used to enhance the existing optimizer to evaluate the optimal gripper design problem. In this study, the newly proposed enhanced optimizer to obtain the optimum design condition of the design variables is called enhanced multi-objective ant lion optimizer. Findings This study aims to obtain optimal design parameters of the parallel gripper with the help of the developed algorithms. The acquired results are investigated with the past research paper conducted in that field for comparison. It is observed that the suggested method to get the best gripper arrangement and variables of the parallel gripper mechanism outperform its counterparts. The effects of the design variables are needed to be studied for a better design approach concerning the objective functions, which is achieved by sensitivity analysis. Practical implications The developed gripper is feasible to use in the assembly operation, as well as in other pick and place operations in different industries. Originality/value In this study, the problem to find the optimum design parameter (i.e. geometric parameters such as length of the link and parallel gripper joint angles) is addressed as a multi-objective optimization. The obtained results from the execution of the algorithm are evaluated using the performance indicator algorithm and a sensitivity analysis is introduced to validate the effects of the design variables. The obtained optimal parameters are used to develop a gripper prototype, which will be used for the assembly process.

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A Multi-Fidelity Model for Simulations and Sensitivity Analysis of Piezoelectric Inkjet Printheads

Micromachines ◽

10.3390/mi12091038 ◽

2021 ◽

Vol 12 (9) ◽

pp. 1038

Author(s):

Vinh-Tan Nguyen ◽

Jason Yu Chuan Leong ◽

Satoshi Watanabe ◽

Toshimitsu Morooka ◽

Takayuki Shimizu

Keyword(s):

Sensitivity Analysis ◽

Three Dimensional ◽

Element Model ◽

Geometrical Parameters ◽

Generation Process ◽

Mechanical Coupling ◽

Design Variables ◽

Computational Structural Mechanics ◽

Lumped Element Model ◽

Inkjet Printhead

The ink drop generation process in piezoelectric droplet-on-demand devices is a complex multiphysics process. A fully resolved simulation of such a system involves a coupled fluid–structure interaction approach employing both computational fluid dynamics (CFD) and computational structural mechanics (CSM) models; thus, it is computationally expensive for engineering design and analysis. In this work, a simplified lumped element model (LEM) is proposed for the simulation of piezoelectric inkjet printheads using the analogy of equivalent electrical circuits. The model’s parameters are computed from three-dimensional fluid and structural simulations, taking into account the detailed geometrical features of the inkjet printhead. Inherently, this multifidelity LEM approach is much faster in simulations of the whole inkjet printhead, while it ably captures fundamental electro-mechanical coupling effects. The approach is validated with experimental data for an existing commercial inkjet printhead with good agreement in droplet speed prediction and frequency responses. The sensitivity analysis of droplet generation conducted for the variation of ink channel geometrical parameters shows the importance of different design variables on the performance of inkjet printheads. It further illustrates the effectiveness of the proposed approach in practical engineering usage.

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Study on Kinematics Sensitivities of Folder Mechanism with Clearance

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.121-126.4764 ◽

2011 ◽

Vol 121-126 ◽

pp. 4764-4769

Author(s):

Ying Cai Yuan ◽

Yan Li ◽

Yi Ming Wang ◽

Qiang Guo

Keyword(s):

Sensitivity Analysis ◽

High Velocity ◽

High Speed ◽

Development Trend ◽

Matrix Analysis ◽

Analysis Model ◽

Design Variables ◽

The Matrix ◽

The Stability ◽

Definition Of

High velocity and stability are the development trend and inevitable requirement, but the clearance would make the stability of mechanical system deceased, especially in high speed. To the folder mechanism with clearances in high velocity, combined with the definition of sensitivity and the kinematics analysis, the kinematics sensitivity analysis model is derived by the matrix analysis method. Through the sensitivity analysis model, it can be easy to get the relationship of the design variables and the mechanism’s robustness, which provides the base to design the folder mechanism in high velocity.

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Design Sensitivity Analysis for the Meshfree Shell Structure

Volume 2A: 27th Design Automation Conference ◽

10.1115/detc2001/dac-21042 ◽

2001 ◽

Author(s):

Kyung K. Choi ◽

Nam H. Kim ◽

Mark E. Botkin

Keyword(s):

Sensitivity Analysis ◽

Shell Structure ◽

Design Sensitivity ◽

Design Sensitivity Analysis ◽

Analysis Method ◽

Sensitivity Equation ◽

Material Derivative ◽

Design Variables ◽

Sensitivity Analysis Method ◽

Shell Formulation

Abstract A unified design sensitivity analysis method for a meshfree shell structure with respect to sizing, shape, and configuration design variables is presented in this paper. A shear deformable shell formulation is characterized by a CAD connection, thickness degeneration, meshfree discretization, and nodal integration. The design variable is selected from the CAD parameters, and a consistent design velocity field is then computed by perturbing the surface geometric matrix. The material derivative concept is used to obtain a design sensitivity equation in the parametric domain. Numerical examples show the accuracy and efficiency of the proposed design sensitivity analysis method compared to the analytical solution and the finite difference solution.

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Design Sensitivity Analysis and Optimization of Nonlinear Anisotropic Structures

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.261-263.809 ◽

2004 ◽

Vol 261-263 ◽

pp. 809-814

Author(s):

Tae Hee Lee ◽

J.J. Jung

Keyword(s):

Sensitivity Analysis ◽

Nonlinear Analysis ◽

Yield Criterion ◽

Design Sensitivity ◽

Euler Method ◽

Design Sensitivity Analysis ◽

Design Variables ◽

Nonlinear Constitutive Equation ◽

Anisotropic Structures ◽

Hill's Yield Criterion

Nonlinear analysis of anisotropic structures is described by using Hill's yield criterion that anisotropic yield contour is assumed to be retained its shape during the hardening process. Nonlinear constitutive equation of anisotropic material is derived using plastic potential concept. Linear strain hardening model is utilized and forward Euler method is employed as a stress integration method. Newton-Raphson method is implemented for numerical nonlinear analysis. Direct differentiation method differentiating directly the equilibrium equation with respect to design variables is applied to design sensitivity analysis of nonlinear anisotropic plate. The results of design sensitivity analysis are compared with those of finite difference method to verify the accuracy. Optimization is accomplished for a rectangular plate using evaluated sensitivity coefficients.

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Three-dimensional optimum design of the cooling lines of injection moulds based on boundary element design sensitivity analysis

Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture ◽

10.1243/09544050260174265 ◽

2002 ◽

Vol 216 (7) ◽

pp. 1067-1071 ◽

Cited By ~ 4

Author(s):

H Zhou ◽

D Li ◽

S Cui

Keyword(s):

Sensitivity Analysis ◽

Objective Function ◽

Boundary Element ◽

Optimum Design ◽

Three Dimensional ◽

Design Sensitivity ◽

Boundary Integral ◽

Optimization Techniques ◽

Design Sensitivity Analysis ◽

Design Variables

A three-dimensional numerical simulation using the boundary element method is proposed, which can predict the cavity temperature distributions in the cooling stage of injection moulding. Then, choosing the radii and positions of cooling lines as design variables, the boundary integral sensitivity formulations are deduced. For the optimum design of cooling lines, the squared difference between the objective temperature and the temperature of the cavity is taken as the objective function. Based on the optimization techniques with design sensitivity analysis, an iterative algorithm to reach the minimum value of the objective function is introduced, which leads to the optimum design of cooling lines at the same time.

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Reliability-Based Robust Design Optimization of Structures Considering Uncertainty in Design Variables

Mathematical Problems in Engineering ◽

10.1155/2015/280940 ◽

2015 ◽

Vol 2015 ◽

pp. 1-8 ◽

Cited By ~ 2

Author(s):

Shujuan Wang ◽

Qiuyang Li ◽

Gordon J. Savage

Keyword(s):

Sensitivity Analysis ◽

Design Optimization ◽

Robust Design ◽

Structural Reliability ◽

Computational Cost ◽

Optimization Process ◽

Robust Design Optimization ◽

Global Approximation ◽

Design Variables ◽

Uncertainty In Design

This paper investigates the structural design optimization to cover both the reliability and robustness under uncertainty in design variables. The main objective is to improve the efficiency of the optimization process. To address this problem, a hybrid reliability-based robust design optimization (RRDO) method is proposed. Prior to the design optimization, the Sobol sensitivity analysis is used for selecting key design variables and providing response variance as well, resulting in significantly reduced computational complexity. The single-loop algorithm is employed to guarantee the structural reliability, allowing fast optimization process. In the case of robust design, the weighting factor balances the response performance and variance with respect to the uncertainty in design variables. The main contribution of this paper is that the proposed method applies the RRDO strategy with the usage of global approximation and the Sobol sensitivity analysis, leading to the reduced computational cost. A structural example is given to illustrate the performance of the proposed method.

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