30,952 research outputs found
Simultaneous Optimal Uncertainty Apportionment and Robust Design Optimization of Systems Governed by Ordinary Differential Equations
The inclusion of uncertainty in design is of paramount practical importance because all real-life systems are affected by it. Designs that ignore uncertainty often lead to poor robustness, suboptimal performance, and higher build costs. Treatment of small geometric uncertainty in the context of manufacturing tolerances is a well studied topic. Traditional sequential design methodologies have recently been replaced by concurrent optimal design methodologies where optimal system parameters are simultaneously determined along with optimally allocated tolerances; this allows to reduce manufacturing costs while increasing performance. However, the state of the art approaches remain limited in that they can only treat geometric related uncertainties restricted to be small in magnitude.
This work proposes a novel framework to perform robust design optimization concurrently with optimal uncertainty apportionment for dynamical systems governed by ordinary differential equations. The proposed framework considerably expands the capabilities of contemporary methods by enabling the treatment of both geometric and non-geometric uncertainties in a unified manner. Additionally, uncertainties are allowed to be large in magnitude and the governing constitutive relations may be highly nonlinear.
In the proposed framework, uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach allows statistical moments of the uncertain system to be explicitly included in the optimization-based design process. The framework formulates design problems as constrained multi-objective optimization problems, thus enabling the characterization of a Pareto optimal trade-off curve that is off-set from the traditional deterministic optimal trade-off curve. The Pareto off-set is shown to be a result of the additional statistical moment information formulated in the objective and constraint relations that account for the system uncertainties. Therefore, the Pareto trade-off curve from the new framework characterizes the entire family of systems within the probability space; consequently, designers are able to produce robust and optimally performing systems at an optimal manufacturing cost.
A kinematic tolerance analysis case-study is presented first to illustrate how the proposed methodology can be applied to treat geometric tolerances. A nonlinear vehicle suspension design problem, subject to parametric uncertainty, illustrates the capability of the new framework to produce an optimal design at an optimal manufacturing cost, accounting for the entire family of systems within the associated probability space. This case-study highlights the general nature of the new framework which is capable of optimally allocating uncertainties of multiple types and with large magnitudes in a single calculation
Optimization Under Uncertainty Using the Generalized Inverse Distribution Function
A framework for robust optimization under uncertainty based on the use of the
generalized inverse distribution function (GIDF), also called quantile
function, is here proposed. Compared to more classical approaches that rely on
the usage of statistical moments as deterministic attributes that define the
objectives of the optimization process, the inverse cumulative distribution
function allows for the use of all the possible information available in the
probabilistic domain. Furthermore, the use of a quantile based approach leads
naturally to a multi-objective methodology which allows an a-posteriori
selection of the candidate design based on risk/opportunity criteria defined by
the designer. Finally, the error on the estimation of the objectives due to the
resolution of the GIDF will be proven to be quantifiableComment: 20 pages, 25 figure
Uncertainty Updating in the Description of Coupled Heat and Moisture Transport in Heterogeneous Materials
To assess the durability of structures, heat and moisture transport need to
be analyzed. To provide a reliable estimation of heat and moisture distribution
in a certain structure, one needs to include all available information about
the loading conditions and material parameters. Moreover, the information
should be accompanied by a corresponding evaluation of its credibility. Here,
the Bayesian inference is applied to combine different sources of information,
so as to provide a more accurate estimation of heat and moisture fields [1].
The procedure is demonstrated on the probabilistic description of heterogeneous
material where the uncertainties consist of a particular value of individual
material characteristic and spatial fluctuations. As for the heat and moisture
transfer, it is modelled in coupled setting [2]
Maxallent: Maximizers of all Entropies and Uncertainty of Uncertainty
The entropy maximum approach (Maxent) was developed as a minimization of the
subjective uncertainty measured by the Boltzmann--Gibbs--Shannon entropy. Many
new entropies have been invented in the second half of the 20th century. Now
there exists a rich choice of entropies for fitting needs. This diversity of
entropies gave rise to a Maxent "anarchism". Maxent approach is now the
conditional maximization of an appropriate entropy for the evaluation of the
probability distribution when our information is partial and incomplete. The
rich choice of non-classical entropies causes a new problem: which entropy is
better for a given class of applications? We understand entropy as a measure of
uncertainty which increases in Markov processes. In this work, we describe the
most general ordering of the distribution space, with respect to which all
continuous-time Markov processes are monotonic (the Markov order). For
inference, this approach results in a set of conditionally "most random"
distributions. Each distribution from this set is a maximizer of its own
entropy. This "uncertainty of uncertainty" is unavoidable in analysis of
non-equilibrium systems. Surprisingly, the constructive description of this set
of maximizers is possible. Two decomposition theorems for Markov processes
provide a tool for this description.Comment: 23 pages, 4 figures, Correction in Conclusion (postprint
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