scholarly journals An α-Model Parametrization Algorithm for Optimization with Differential-Algebraic Equations

2022 ◽  
Vol 12 (2) ◽  
pp. 890
Author(s):  
Paweł Dra̧g
Keyword(s):  
Optimization Algorithm ◽  
Numerical Optimization ◽  
Differential Algebraic Equations ◽  
Multiple Shooting ◽  
Small Range ◽  
Algebraic Equations ◽  
New Approach ◽  
Highly Nonlinear ◽  
Special Cases ◽  
Wide Range

An optimization task with nonlinear differential-algebraic equations (DAEs) was approached. In special cases in heat and mass transfer engineering, a classical direct shooting approach cannot provide a solution of the DAE system, even in a relatively small range. Moreover, available computational procedures for numerical optimization, as well as differential- algebraic systems solvers are characterized by their limitations, such as the problem scale, for which the algorithms can work efficiently, and requirements for appropriate initial conditions. Therefore, an αDAE model optimization algorithm based on an α-model parametrization approach was designed and implemented. The main steps of the proposed methodology are: (1) task discretization by a multiple-shooting approach, (2) the design of an α-parametrized system of the differential-algebraic model, and (3) the numerical optimization of the α-parametrized system. The computations can be performed by a chosen iterative optimization algorithm, which can cooperate with an outer numerical procedure for solving DAE systems. The implemented algorithm was applied to solve a counter-flow exchanger design task, which was modeled by the highly nonlinear differential-algebraic equations. Finally, the new approach enabled the numerical simulations for the higher values of parameters denoting the rate of changes in the state variables of the system. The new approach can carry out accurate simulation tests for systems operating in a wide range of configurations and created from new materials.

scholarly journals Assessment of Linearization Approaches for Multibody Dynamics Formulations

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Francisco González ◽  
Pierangelo Masarati ◽  
Javier Cuadrado ◽  
Miguel A. Naya
Keyword(s):  
Mechanical System ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Practical Applications ◽  
Linearization Methods ◽  
Highly Nonlinear ◽  
Wide Range ◽  
The Way

Formulating the dynamics equations of a mechanical system following a multibody dynamics approach often leads to a set of highly nonlinear differential-algebraic equations (DAEs). While this form of the equations of motion is suitable for a wide range of practical applications, in some cases it is necessary to have access to the linearized system dynamics. This is the case when stability and modal analyses are to be carried out; the definition of plant and system models for certain control algorithms and state estimators also requires a linear expression of the dynamics. A number of methods for the linearization of multibody dynamics can be found in the literature. They differ in both the approach that they follow to handle the equations of motion and the way in which they deliver their results, which in turn are determined by the selection of the generalized coordinates used to describe the mechanical system. This selection is closely related to the way in which the kinematic constraints of the system are treated. Three major approaches can be distinguished and used to categorize most of the linearization methods published so far. In this work, we demonstrate the properties of each approach in the linearization of systems in static equilibrium, illustrating them with the study of two representative examples.

Model-Based Design and Optimization of Passive Shoulder Exoskeletons

2021 ◽  
Author(s):  
Ali Nasr ◽  
Spencer Ferguson ◽  
John McPhee
Keyword(s):  
Elevation Angle ◽  
Differential Algebraic Equations ◽  
Joint Torque ◽  
Algebraic Equations ◽  
Joint Torques ◽  
Design And Optimization ◽  
Passive Mechanism ◽  
Wide Range ◽  
Passive Exoskeleton ◽  
Selection Of

Abstract To physically assist workers in reducing musculoskeletal strain or to develop motor skills for patients with neuromuscular disabilities, recent research has focused on Exoskeletons (Exos). Designing active Exos is challenging due to the complex human geometric structure, the human-Exoskeleton wrench interaction, the kinematic constraints, and the selection of power source characteristics. Because of the portable advantages of passive Exos, designing a passive shoulder mechanism has been studied here. The study concentrates on modeling a 3D multibody upper-limb human-Exoskeleton, developing a procedure of analyzing optimal assistive torque profiles, and optimizing the passive mechanism features for desired tasks. The optimization objective is minimizing the human joint torques. For simulating the complex closed-loop multibody dynamics, differential-algebraic equations (DAE)s of motion have been generated and solved. Three different tasks have been considered, which are common in industrial environments: object manipulation, over-head work, and static pointing. The resulting assistive Exoskeleton’s elevation joint torque profile could decrease the specific task’s human shoulder torque. Since the passive mechanism produces a specific torque for a given elevation angle, the Exoskeleton is not versatile or optimal for different dynamic tasks. We concluded that designing a passive Exoskeleton for a wide range of dynamic applications is impossible. We hypothesize that augmenting an actuator to the mechanism can provide the necessary adjustment torque and versatility for multiple tasks.

On the Axial-Flexural-Torsional Coupling of Underwater Slender Cylinders

2012 ◽  
Author(s):  
Waldir T. Pinto ◽  
Carlos A. Levi
Keyword(s):  
Large Strains ◽  
Element Formulation ◽  
Algebraic Equations ◽  
Three Dimensional Model ◽  
Cylindrical Structures ◽  
Highly Nonlinear ◽  
Wide Range ◽  
Torsional Coupling ◽  
Lift Forces ◽  
Drag And Lift

This paper presents a numerical model for the simulation of the axial-flexural-torsional coupling of undewater cylindrical structures. Cylindrical structures are largely utilized in the marine environment in a wide range of applications as in risers, marine cables, flexible pipes, mooring systems and so on. They may exhibit complex axial-flexural-torsional coupling, which makes the structural analysis highly nonlinear. In addition, the fluid-structure interaction may include flow induced vibrations, frequency lock-in and internal flow effects. The proposed three-dimensional model assumes that the structure aspect ratio is very high, its cross section is circular, the cable is elastic and may experience large displacements and large strains, as long as the elastic regime holds. The steady state load on the cylinder consists of the self-weight and buoyancy, drag and lift forces, in addition to a distributed residual twist along the cylinder. The drag and lift forces are evaluated by Morison type formulation. The governing differential equations are derived from first principles, assuming Newtonian mechanics. Then, they are solved numerically by a finite element formulation based on nonlinear space frame elements. The resulting set of algebraic equations is solved by a minimization technique that uses the Newton-Raphson algorithm. Results show the ability of the model to predict the static configuration of equilibrium of the cylinder and to capture the coupling between axial, flexural and torsional responses of the cylinder.

Dynamic Modeling and Simulation of Parallel Mechanisms Using the Virtual Spring Approach

2000 ◽  
Author(s):  
Jiegao Wang ◽  
Clément M. Gosselin ◽  
Li Cheng
Keyword(s):  
Closed Loop ◽  
Differential Algebraic Equations ◽  
Parallel Mechanisms ◽  
Algebraic Equations ◽  
New Approach ◽  
Flexible Links ◽  
Simulation Results ◽  
Loop Constraints ◽  
Virtual Springs ◽  
Good Agreement

Abstract A new approach for the dynamic simulation of parallel mechanisms or mechanical systems is presented in this paper. This approach uses virtual springs and dampers to include the closed-loop constraints thereby avoiding the solution of differential-algebraic equations. Examples illustrating the approach are given and include the four-bar mechanism with both rigid and flexible links as well as the 6-dof Gough-Stewart platform. Simulation results are given for the four-bar linkages and the 6-dof manipulator. The results achieve a good agreement with the results obtained from other conventional approaches.

Comparison of Modeling Techniques for a Landing Gear

2010 ◽  
Author(s):  
Rebecca Margetts ◽  
Roger F. Ngwompo
Keyword(s):  
Block Diagram ◽  
Differential Algebraic Equations ◽  
Landing Gear ◽  
Algebraic Equations ◽  
Bond Graphs ◽  
Aircraft Landing ◽  
Aircraft Landing Gear ◽  
Wide Range ◽  
Modeling Techniques ◽  
Computational Errors

A wide range of modeling techniques is available to the engineer. The objective of this paper is to compare some typical modeling techniques for the simulation of a multi-domain mechatronic system. Usual dynamic modeling methods, such as block diagrams and iconic diagrams, can cause problems for the engineer. Differential algebraic equations (DAEs) and algebraic loops can significantly increase simulation times and cause numeric errors. Bond graphs are less common in industry, and are presented here as a method which allows the engineer to easily identify causal loops and elements in differential causality. These can indicate DAEs in the underlying equations. An aircraft landing gear is given as an example of a multi-domain system, and is modeled as a block diagram, an iconic diagram and as a bond graph. The time to construct the model, time to solve and problems faced by the analyst are presented. Bond graphs offer distinct advantages in terms of the ease of implementing algebraic equations and visibility of causality. The time taken to model a system can be significantly reduced and the results appear free from computational errors. Bond graphs are therefore recommended for this type of multi-domain systems analysis.

scholarly journals The multilevel ant stigmergy algorithm for numerical optimization

2006 ◽  
Vol 19 (2) ◽  
pp. 247-260 ◽  
Author(s):  
Peter Korosec ◽  
Jurij Silc
Keyword(s):  
Differential Evolution ◽  
Optimization Algorithm ◽  
Numerical Optimization ◽  
Optimization Techniques ◽  
Industrial Case Study ◽  
New Approach ◽  
Collective Work ◽  
Better Than

The Multilevel Ant Stigmergy Algorithm (MASA) is a new approach to solving multi-parameter problems based on stigmergy, a type of collective work that can be observed in nature. In this paper we evaluate the performance of MASA regarding its applicability as numerical optimization techniques. The evaluation is performed with several widely used benchmarks functions, as well as on an industrial case study. We also compare the MASA with Differential Evolution, well-known numerical optimization algorithm. The average solution obtained with the MASA was better than a solution recently found using Differential Evolution.

scholarly journals A Generalized State-Space Aeroservoelastic Model Based on Tangential Interpolation

Aerospace ◽  
2019 ◽  
Vol 6 (1) ◽  
pp. 9 ◽  
Author(s):  
David Quero ◽  
Pierre Vuillemin ◽  
Charles Poussot-Vassal
Keyword(s):  
State Space ◽  
Reference Model ◽  
Differential Algebraic Equations ◽  
Summation Method ◽  
Algebraic Equations ◽  
Minimal Order ◽  
New Approach ◽  
Model Based ◽  
Generalized State Space ◽  
Generalized State

In this work, a new approach for the generation of a generalized state-space aeroservoelastic model based on tangential interpolation is presented. The resulting system of differential algebraic equations (DAE) is reduced to a set of ordinary differential equations (ODE) by residualization of the non-proper part of the transfer function matrix. The generalized state-space is of minimal order and allows for the application of the force summation method (FSM) for the aircraft loads recovery. Compared to the classical rational function approximation (RFA) approach, the presented method provides a minimal order realization with exact interpolation of the unsteady aerodynamic forces in tangential directions, avoiding any selection of poles (lag states). The new approach is applied first for the generation of an aerodynamic model for the bidimensional unsteady incompressible flow in the time domain. Next, an application on the generation of an aeroservoelastic model for loads evaluation of the flutter reduced order assessment (FERMAT) model under atmospheric disturbances is done, showing an excellent agreement with the reference model in the frequency domain. The proposed aeroservoelastic model of minimal order is suited for loads analysis and multivariable control design, and an application to a gust loads alleviation (GLA) strategy is shown.

A Computer-Aided Environment for Analysis and Design of Mechanical Systems

1991 ◽  
Author(s):  
Hamid M. Lankarani ◽  
Behnam Bahr ◽  
Saeid Motavalli
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Differential Algebraic Equations ◽  
General Purpose ◽  
Design System ◽  
Integrated Analysis ◽  
Algebraic Equations ◽  
Efficient Design ◽  
Analysis And Design ◽  
Wide Range

Abstract This paper presents the description of an ideal tool for analysis and design of complex multibody mechanical systems. It is in the form of a general-purpose computer program, which can be used for simulation of many different systems. The generality of this computer-integrated environment allows a wide range of applications with significant engineering importance. No matter how complicated the mechanical system under consideration is, a numerical multibody model of the system is constructed. The governing mixed differential/algebraic equations of motion are automatically formulated and numerically generated. State-of-the-art numerical techniques and computational methods are employed and developed which produce in the response of the system at discrete time junctures. Postprocessing of the results in the form of graphical images or real-time animations provides an enormous aid in visualizing motion of the system. The analysis package may be merged with an efficient design optimization algorithm. The developed integrated analysis/design system is a valuable tool for researchers, design engineers, and analysts of mechanical systems. This computer-integrated tool provides an important bridge between the classical decision making process by an engineer and the emerging technology of computers.

scholarly journals Linguistic Weighted Aggregation under Confidence Levels

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Chonghui Zhang ◽  
Weihua Su ◽  
Shouzhen Zeng ◽  
Linyun Zhang
Keyword(s):  
Decision Making ◽  
Multicriteria Decision Making ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
New Approach ◽  
Confidence Levels ◽  
Ordered Weighted Averaging ◽  
Special Cases ◽  
Wide Range ◽  
Information Providers

We develop some new linguistic aggregation operators based on confidence levels. Firstly, we introduce the confidence linguistic weighted averaging (CLWA) operator and the confidence linguistic ordered weighted averaging (CLOWA) operator. These two new linguistic aggregation operators are able to consider the confidence level of the aggregated arguments provided by the information providers. We also study some of their properties. Then, based on the generalized means, we introduce the confidence generalized linguistic ordered weighted averaging (CGLOWA) operator. The main advantage of the CGLOWA operator is that it includes a wide range of special cases such as the CLOWA operator, the confidence linguistic ordered weighted quadratic averaging (CLOWQA) operator, and the confidence linguistic ordered weighted geometric (CLOWG) operator. Finally, we develop an application of the new approach in a multicriteria decision-making under linguistic environment and illustrate it with a numerical example.

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