Development of Structural Uncertainty Models

Campbell, Mark; Crawley, Edward F.

doi:10.2514/2.4133

Cited by 11 publications

(2 citation statements)

References 5 publications

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“…For the case of state-space systems driven by white noise, the output steady-state covariance matrix is known to be the solution of a Lyapunov equation [45]. [143] and the work by Campbell and Crawley [14]. An approximate method for predicting worst-case performance RMS values due to parametric uncertainties is that used by Bryson and Mills [12].…”

Section: Literature Reviewmentioning

confidence: 99%

Multivariable Isoperformance Methodology for Precision Opto-Mechanical Systems

Weck

Ladislas

2002

43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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Precision opto-mechanical systems, such as space telescopes, combine structures, optics and controls in order to meet stringent pointing and phasing requirements. In this context a novel approach to the design of complex, multi-disciplinary systems is presented in the form of a multivariable isoperformance methodology. The isoperformance approach first finds a point design within a given topology, which meets the performance requirements with sufficient margins. The performance outputs are then treated as equality constraints and the nonuniqueness of the design space is exploited by trading key disturbance, plant, optics and controls parameters with respect to each other.Three algorithms (branch-and-bound, tangential front following and vector spline approximation) are developed for the bivariate and multivariable problem. The challenges of large order models are addressed by presenting a fast diagonal Lyapunov solver, apriori error bounds for model reduction as well as a governing sensitivity equation for similarity transformed state space realizations. Specific applications developed with this technique are error budgeting and multiobjective design optimization. The goal of the multiobjective design optimization is to achieve a design which is pareto optimal, such that multiple competing objectives can be satisfied within the performance invariant set. Thus, situations are avoided where very costly and hard-to-meet requirements are levied onto one subsystem, while other subsystems hold substantial margins.An experimental validation is carried out on the DOLCE laboratory testbed. The testbed allows verification of the predictive capability of the isoperformance technique on models of increasing fidelity. A comparison with experimental results, trading excitation amplitude and payload mass, is demonstrated. The predicted performance contours match the experimental data very well at low excitation levels, typical of the disturbance environment on precision opto-mechanical systems. The relevance of isoperformance to space systems engineering is demonstrated with a comprehensive NEXUS spacecraft dynamics and controls analysis. It is suggested that isoperformance is a useful concept in other fields of engineering science such as crack growth calculations in structures. The isoperformance approach enhances the understanding of complex opto-mechanical systems beyond the local neighborhood of a particular point design. Sharon-Leah Brown provided encouragement and professional financial management.

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Section: Literature Reviewmentioning

confidence: 99%

Multivariable Isoperformance Methodology for Precision Opto-Mechanical Systems

Weck

Ladislas

2002

43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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“…Therefore certain structural parameters are not known exactly and those uncertainties can be modelled using random variables [1][2][3]. Often, dealing with those systems with uncertain random parameters, one has to solve non-linear problems, which can be achieved using iterative numerical procedure, based on the wellknown successive approximation method.…”

Section: Introductionmentioning

confidence: 99%

Convergence of the fixed point theorem with random parameters

Poirion

2003

Numerical Meth Engineering

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SUMMARYSolving stochastic non-linear dynamical problems represents a formidable task which, in many cases, can be achieved solely through numerical simulation techniques. This is true for high dimensional as well as low dimensional problems. One method to deal with the non-linearity is to use the ÿxed point theorem which gives the convergence conditions of the iterative scheme towards the equilibrium point of the equation. In this paper we look at the particular case where the equilibrium equation depends on a random variable. This case arises for instance in the study of coupled non-linear dynamical systems when structural uncertainties are introduced in the dynamical systems. We give almost sure and L p convergence conditions for the simulation iterative scheme.

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