An improved adaptive sampling scheme for the construction of explicit boundaries

Basudhar, Anirban; Missoum, Samy

doi:10.1007/s00158-010-0511-0

Cited by 98 publications

(90 citation statements)

References 18 publications

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“…We employ a POD-DEIM-Galerkin reduced system to speed up the computation. Reduced systems have been extensively studied for computing failure rates and rare event probabilities [6,5,30,13]; however, we consider here POD-DEIM-Galerkin reduced systems based on online adaptive DEIM interpolants that are adapted while they are evaluated by the Monte Carlo method during the online phase. Online adaptivity is well-suited for computing failure rates because it adapts the reduced system to the failure boundaries where a high accuracy is required.…”

Section: Expected Failure Ratementioning

confidence: 99%

Online Adaptive Model Reduction for Nonlinear Systems via Low-Rank Updates

Peherstorfer¹,

Willcox²

2015

SIAM J. Sci. Comput.

185

117

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Abstract. This work presents a nonlinear model reduction approach for systems of equations stemming from the discretization of partial differential equations with nonlinear terms. Our approach constructs a reduced system with proper orthogonal decomposition and the discrete empirical interpolation method (DEIM); however, whereas classical DEIM derives a linear approximation of the nonlinear terms in a static DEIM space generated in an offline phase, our method adapts the DEIM space as the online calculation proceeds and thus provides a nonlinear approximation. The online adaptation uses new data to produce a reduced system that accurately approximates behavior not anticipated in the offline phase. These online data are obtained by querying the full-order system during the online phase, but only at a few selected components to guarantee a computationally efficient adaptation. Compared to the classical static approach, our online adaptive and nonlinear model reduction approach achieves accuracy improvements of up to three orders of magnitude in our numerical experiments with time-dependent and steady-state nonlinear problems. The examples also demonstrate that through adaptivity, our reduced systems provide valid approximations of the full-order systems outside of the parameter domains for which they were initially built in the offline phase.Key words. adaptive model reduction, nonlinear systems, empirical interpolation, proper orthogonal decomposition AMS subject classifications. 65M22, 65N22 DOI. 10.1137/1409891691. Introduction. Model reduction derives reduced systems of large-scale systems of equations, typically using an offline phase in which the reduced system is constructed from solutions of the full-order system, and an online phase in which the reduced system is executed repeatedly to generate solutions for the task at hand. In many situations, the reduced systems yield accurate approximations of the fullorder solutions but with orders of magnitude reduction in computational complexity. Model reduction exploits that often the solutions are not scattered all over the highdimensional solution space, but instead they form a low-dimensional manifold that can be approximated by a low-dimensional (linear) reduced space. In some cases, however, the manifold exhibits a complex and nonlinear structure that can only be approximated well by the linear reduced space if its dimension is chosen sufficiently high. Thus, solving the reduced system can become computationally expensive. We therefore propose a nonlinear approximation of the manifold. The nonlinear approximation is based on adapting the reduced system while the computation proceeds in the online phase, using newly generated data through limited queries to the full-order system at a few selected components. Our online adaptation leads to a reduced system that can more efficiently capture nonlinear structure in the manifold, it ensures computational efficiency by performing low-rank updates, and through the use of new

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Section: Expected Failure Ratementioning

confidence: 99%

Online Adaptive Model Reduction for Nonlinear Systems via Low-Rank Updates

Peherstorfer¹,

Willcox²

2015

SIAM J. Sci. Comput.

185

117

View full text Add to dashboard Cite

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“…Run high-fidelity physics-based models at points that adequately sample the boundary between infeasible regions and feasible regions in the combined vehicle state-control space X × U for a particular damage state d. An adaptive sampling algorithm can be used to pick points intelligently. 25 For each feasible maneuver point [x, u], assign the value +1 and for each infeasible maneuver point, assign the value −1. In addition, for the measurement quantities of interest, record their values for each maneuver point [x, u].…”

Section: Iif Damage Library Construction and Surrogate Modelingmentioning

confidence: 99%

Methodology for Path Planning with Dynamic Data-Driven Flight Capability Estimation

Singh

Willcox

2016

17th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

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This paper presents methodology to enable path planning for an unmanned aerial vehicle that uses dynamic data-driven flight capability estimation. The main contribution of the work is a general mathematical approach that leverages offline vehicle analysis and design data together with onboard sensor measurements to achieve dynamic path planning. The mathematical framework, expressed as a Constrained Partially Observable Markov Decision Process, accounts for vehicle capability constraints and is robust to modeling error and disturbances in both the vehicle process and measurement models. Vehicle capability constraints are incorporated using Probabilistic Support Vector Machine surrogates of highfidelity physics-based models that adequately capture the richness of the vehicle dynamics. Sensor measurements are treated in a general manner and can include combinations of multiple modalities such as GPS/IMU data as well as structural strain data of the airframe. Results are presented for a simulated 3-D environment and point-mass airplane model. The vehicle can dynamically adjust its trajectory according to the observations it receives about its current state of health, thereby retaining a high probability of survival and mission success.

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“…4) Generate a second sample nearby the SVM boundary to prevent SVM locking (see [31] for further explanation).…”

Section: B Adaptive State-space Sampling Techniquementioning

confidence: 99%

Methodology for Dynamic Data-Driven Online Flight Capability Estimation

2015

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This paper presents a data-driven approach for the online updating of the flight envelope of an unmanned aerial vehicle subjected to structural degradation. The main contribution of the work is a general methodology that leverages both physics-based modeling and data to decompose tasks into two phases: expensive offline simulations to build an efficient characterization of the problem and rapid data-driven classification to support online decision making. In the approach, physics-based models at the wing and vehicle level run offline to generate libraries of information covering a range of damage scenarios. These libraries are queried online to estimate vehicle capability states. The state estimation and associated quantification of uncertainty are achieved by Bayesian classification using sensed strain data. The methodology is demonstrated on a conceptual unmanned aerial vehicle executing a pullup maneuver, in which the vehicle flight envelope is updated dynamically with onboard sensor information. During vehicle operation, the maximum maneuvering load factor is estimated using structural strain sensor measurements combined with physics-based information from precomputed damage scenarios that consider structural weakness. Compared to a baseline case that uses a static as-designed flight envelope, the self-aware vehicle achieves both an increase in probability of executing a successful maneuver and an increase in overall usage of the vehicle capability. = number of observable vector data samples N s = number of sensors n = load factor n max = maximum load factor before failure n truth max = truth reference maximum load factor n op = operational load factor decided upon using dynamic capability estimate n static op = operational load factor decided upon using static capability estimate from design n util = average utilization of maximum vehicle capability p· = probability p op = threshold probability for decisions using dynamic capability estimate R = number of damage library records S = support vector machine discriminant function ("score") S = observable vector space s = observable vector s = observable vector measurement V = airspeed w c = chordwise extent of damage on wing w s = spanwise extent of damage on wing X = vehicle state space x = vehicle state α j = support vector machine weight for jth training sample β 1 , β 2 = probabilistic support vector machine regression model parameters ϵ k = kth strain gage rosette output ε k = plane strain at location of kth strain gage rosette

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An improved adaptive sampling scheme for the construction of explicit boundaries

Cited by 98 publications

References 18 publications

Online Adaptive Model Reduction for Nonlinear Systems via Low-Rank Updates

Online Adaptive Model Reduction for Nonlinear Systems via Low-Rank Updates

Methodology for Path Planning with Dynamic Data-Driven Flight Capability Estimation

Methodology for Dynamic Data-Driven Online Flight Capability Estimation

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