838 research outputs found
Stochastic Nonlinear Model Predictive Control with Efficient Sample Approximation of Chance Constraints
This paper presents a stochastic model predictive control approach for
nonlinear systems subject to time-invariant probabilistic uncertainties in
model parameters and initial conditions. The stochastic optimal control problem
entails a cost function in terms of expected values and higher moments of the
states, and chance constraints that ensure probabilistic constraint
satisfaction. The generalized polynomial chaos framework is used to propagate
the time-invariant stochastic uncertainties through the nonlinear system
dynamics, and to efficiently sample from the probability densities of the
states to approximate the satisfaction probability of the chance constraints.
To increase computational efficiency by avoiding excessive sampling, a
statistical analysis is proposed to systematically determine a-priori the least
conservative constraint tightening required at a given sample size to guarantee
a desired feasibility probability of the sample-approximated chance constraint
optimization problem. In addition, a method is presented for sample-based
approximation of the analytic gradients of the chance constraints, which
increases the optimization efficiency significantly. The proposed stochastic
nonlinear model predictive control approach is applicable to a broad class of
nonlinear systems with the sufficient condition that each term is analytic with
respect to the states, and separable with respect to the inputs, states and
parameters. The closed-loop performance of the proposed approach is evaluated
using the Williams-Otto reactor with seven states, and ten uncertain parameters
and initial conditions. The results demonstrate the efficiency of the approach
for real-time stochastic model predictive control and its capability to
systematically account for probabilistic uncertainties in contrast to a
nonlinear model predictive control approaches.Comment: Submitted to Journal of Process Contro
Polynomial Chaos reformulation in Nonlinear Stochastic Optimal Control with application on a drivetrain subject to bifurcation phenomena
This paper discusses a method enabling optimal control of nonlinear systems
that are subject to parametric uncertainty. A stochastic optimal tracking
problem is formulated that can be expressed in function of the first two
stochastic moments of the state. The proposed formulation allows to penalize
system performance and system robustness independently. The use of polynomial
chaos expansions is investigated to arrive at a computationally tractable
formulation expressing the stochastic moments in function of the polynomial
expansion coefficients rigorously. It is then demonstrated how the stochastic
optimal control problem can be reformulated as a deterministic optimal control
problem in function of these coefficients. The proposed method is applied to
find a robust control input for the start-up of an eccentrically loaded drive
train that is inherently prone to bifurcation behaviour. A reference trajectory
is chosen to deliberately provoke a bifurcation. The proposed framework is able
to avoid the bifurcation behaviour regardlessly.Comment: 7 pages; 5 figures; ICSTCC 2018, 22nd International Conference on
System Theory, Control and Computing. 10 - 12 October. Sinaia - Romani
Uncertainty quantification of coal seam gas production prediction using Polynomial Chaos
A surrogate model approximates a computationally expensive solver. Polynomial
Chaos is a method to construct surrogate models by summing combinations of
carefully chosen polynomials. The polynomials are chosen to respect the
probability distributions of the uncertain input variables (parameters); this
allows for both uncertainty quantification and global sensitivity analysis.
In this paper we apply these techniques to a commercial solver for the
estimation of peak gas rate and cumulative gas extraction from a coal seam gas
well. The polynomial expansion is shown to honour the underlying geophysics
with low error when compared to a much more complex and computationally slower
commercial solver. We make use of advanced numerical integration techniques to
achieve this accuracy using relatively small amounts of training data
Stochastic collocation on unstructured multivariate meshes
Collocation has become a standard tool for approximation of parameterized
systems in the uncertainty quantification (UQ) community. Techniques for
least-squares regularization, compressive sampling recovery, and interpolatory
reconstruction are becoming standard tools used in a variety of applications.
Selection of a collocation mesh is frequently a challenge, but methods that
construct geometrically "unstructured" collocation meshes have shown great
potential due to attractive theoretical properties and direct, simple
generation and implementation. We investigate properties of these meshes,
presenting stability and accuracy results that can be used as guides for
generating stochastic collocation grids in multiple dimensions.Comment: 29 pages, 6 figure
UQ and AI: data fusion, inverse identification, and multiscale uncertainty propagation in aerospace components
A key requirement for engineering designs is that they offer good performance across a range of uncertain conditions while exhibiting an admissibly low probability of failure. In order to design components that offer good performance across a range of uncertain conditions, it is necessary to take account of the effect of the uncertainties associated with a candidate design. Uncertainty Quantification (UQ) methods are statistical methods that may be used to quantify the effect of the uncertainties inherent in a system on its performance. This thesis expands the envelope of UQ methods for the design of aerospace components, supporting the integration of UQ methods in product development by addressing four industrial challenges.
Firstly, a method for propagating uncertainty through computational models in a hierachy of scales is described that is based on probabilistic equivalence and Non-Intrusive Polynomial Chaos (NIPC). This problem is relevant to the design of aerospace components as the computational models used to evaluate candidate designs are typically multiscale. This method was then extended to develop a formulation for inverse identification, where the probability distributions for the material properties of a coupon are deduced from measurements of its response. We demonstrate how probabilistic equivalence and the Maximum Entropy Principle (MEP) may be used to leverage data from simulations with scarce experimental data- with the intention of making this stage of product design less expensive and time consuming.
The third contribution of this thesis is to develop two novel meta-modelling strategies to promote the wider exploration of the design space during the conceptual design phase. Design Space Exploration (DSE) in this phase is crucial as decisions made at the early, conceptual stages of an aircraft design can restrict the range of alternative designs available at later stages in the design process, despite limited quantitative knowledge of the interaction between requirements being available at this stage. A histogram interpolation algorithm is presented that allows the designer to interactively explore the design space with a model-free formulation, while a meta-model based on Knowledge Based Neural Networks (KBaNNs) is proposed in which the outputs of a high-level, inexpensive computer code are informed by the outputs of a neural network, in this way addressing the criticism of neural networks that they are purely data-driven and operate as black boxes.
The final challenge addressed by this thesis is how to iteratively improve a meta-model by expanding the dataset used to train it. Given the reliance of UQ methods on meta-models this is an important challenge. This thesis proposes an adaptive learning algorithm for Support Vector Machine (SVM) metamodels, which are used to approximate an unknown function. In particular, we apply the adaptive learning algorithm to test cases in reliability analysis.Open Acces
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