Optimization problem with normally distributed uncertain parameters

AIChE Journal ◽  
2013 ◽  
Vol 59 (7) ◽  
pp. 2471-2484 ◽  
Author(s):  
Gennady M. Ostrovsky ◽  
Nadir N. Ziyatdinov ◽  
Tatiana V. Lapteva
Keyword(s):  
Optimization Problem ◽  
Uncertain Parameters ◽  
Normally Distributed

scholarly journals STEADY-STATE MODELLING OF PEM FUEL CELLS USING GRADIENT-BASED OPTIMIZER

10.6036/10099 ◽  
2021 ◽  
Vol DYNA-ACELERADO (0) ◽  
pp. [ 8 pp.]-[ 8 pp.]
Author(s):  
SALAH KAMAL ◽  
ATTIA EL-FERGANY ◽  
EHAB EHAB ELSAYED ELATTAR ◽  
AHMED AGWA
Keyword(s):  
Fuel Cells ◽  
Steady State ◽  
Fuel Cell ◽  
Optimization Problem ◽  
Pem Fuel Cells ◽  
Test Cases ◽  
Uncertain Parameters ◽  
Gradient Based ◽  
High Degree ◽  
Exchange Membrane

The accuracy of fuel cell (FC) models is important for the further numerical simulations and analysis at several conditions. The electrical (I-V) characteristic of the polymer exchange membrane fuel cells (PEMFCs) has high degree of nonlinearity comprising uncertain seven parameters as they aren’t given in fabricator's datasheets. These seven parameters need to be obtained to have the PEMFC model in order. This research addresses an up-to-date application of the gradient-based optimizer (GBO) to generate the best estimated values of such uncertain parameters. The estimation of these uncertain parameters is adapted as optimization problem having a cost function (CF) subjects to set of self-constrained limits. Three test cases of widely used PEMFCs units; namely, SR-12, 250-W module and NedStack PS6 to appraise the performance of the GBO are demonstrated and analyzed. The best values of the CF are 0.000142, 0.33598, and 2.10025 V2 for SR-12, 250-W module and NedStack PS6; respectively. Furthermore, the assessment of the GBO-based model is made by comparing its obtained results with the experiential results of these typical PEMFCs plus comparisons to other methods. At a due stage, many scenarios as a result of operating variations in regard to inlet regulation pressures and unit temperatures are performed. The copped reported results of the studied scenarios indicate the effectiveness of the GBO in establishing an accurate PEMFC model.

scholarly journals On the Optimality of Affine Policies for Budgeted Uncertainty Sets

2021 ◽  
Author(s):  
Omar El Housni ◽  
Vineet Goyal
Keyword(s):  
Robust Optimization ◽  
Structural Properties ◽  
Optimization Problem ◽  
Hardness Of Approximation ◽  
Uncertain Parameters ◽  
Two Stage ◽  
Uncertainty Sets ◽  
Adjustable Robust Optimization ◽  
Robust Optimization Problem ◽  
Budgeted Uncertainty

In this paper, we study the performance of affine policies for a two-stage, adjustable, robust optimization problem with a fixed recourse and an uncertain right-hand side belonging to a budgeted uncertainty set. This is an important class of uncertainty sets, widely used in practice, in which we can specify a budget on the adversarial deviations of the uncertain parameters from the nominal values to adjust the level of conservatism. The two-stage adjustable robust optimization problem is hard to approximate within a factor better than [Formula: see text] even for budget of uncertainty sets in which [Formula: see text] is the number of decision variables. Affine policies, in which the second-stage decisions are constrained to be an affine function of the uncertain parameters provide a tractable approximation for the problem and have been observed to exhibit good empirical performance. We show that affine policies give an [Formula: see text]-approximation for the two-stage, adjustable, robust problem with fixed nonnegative recourse for budgeted uncertainty sets. This matches the hardness of approximation, and therefore, surprisingly, affine policies provide an optimal approximation for the problem (up to a constant factor). We also show strong theoretical performance bounds for affine policy for a significantly more general class of intersection of budgeted sets, including disjoint constrained budgeted sets, permutation invariant sets, and general intersection of budgeted sets. Our analysis relies on showing the existence of a near-optimal, feasible affine policy that satisfies certain nice structural properties. Based on these structural properties, we also present an alternate algorithm to compute a near-optimal affine solution that is significantly faster than computing the optimal affine policy by solving a large linear program.

scholarly journals Extending the Scope of Robust Quadratic Optimization

2021 ◽  
Author(s):  
Ahmadreza Marandi ◽  
Aharon Ben-Tal ◽  
Dick den Hertog ◽  
Bertrand Melenberg
Keyword(s):  
Optimization Problem ◽  
Quadratic Optimization ◽  
Uncertain Parameters ◽  
Quadratic Constraints ◽  
Sample Mean ◽  
Quadratic Optimization Problem ◽  
Statistical Confidence ◽  
Robust Counterpart ◽  
Uncertainty Set ◽  
Portfolio Optimization Problem

We derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We do this for a broad range of uncertainty sets. Our results provide extensions to known results from the literature. We also consider hard quadratic constraints: those that are convex in uncertain matrix-valued parameters. For the robust counterpart of such constraints, we derive inner and outer tractable approximations. As an application, we show how to construct a natural uncertainty set based on a statistical confidence set around a sample mean vector and covariance matrix and use this to provide a tractable reformulation of the robust counterpart of an uncertain portfolio optimization problem. We also apply the results of this paper to norm approximation problems. Summary of Contribution: This paper develops new theoretical results and algorithms that extend the scope of a robust quadratic optimization problem. More specifically, we derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We also consider hard quadratic constraints: those that are convex in uncertain matrix-valued parameters. For the robust counterpart of such constraints, we derive inner and outer tractable approximations.

Structural Non-Probabilistic Reliability Analysis Based on SAPSO-DE Hybrid Algorithm

2014 ◽  
Vol 551 ◽  
pp. 679-685
Author(s):  
Chan Hyok Jong ◽  
Guang Wei Meng ◽  
Feng Li ◽  
Yan Hao ◽  
Kwan Gil Kim
Keyword(s):  
Reliability Analysis ◽  
Hybrid Algorithm ◽  
Optimization Problem ◽  
Particle Swarm Optimization Algorithm ◽  
Limit State ◽  
State Function ◽  
Uncertain Parameters ◽  
Convex Model ◽  
Swarm Optimization ◽  
De Algorithm

This paper presents a structural non-probabilistic reliability analysis approach based on a hybrid algorithm of the simulated annealing-particle swarm optimization algorithm and the differential evolution (SAPSO-DE) algorithm. In the structural non-probabilistic reliability analysis, the problem with uncertain parameters can be formulated as an optimization problem using convex model. However, the limit state function is usually implicit for the uncertain parameters. By employing the SAPSO-DE hybrid algorithm based on the evolution of the cognitive and social experiences, the problem of the structural non-probabilistic reliability analysis is solved. A numerical example is given to illustrate the high precision and good feasibility of the present method. The results shows that this proposed approach is effective, and has the predominant capability of global optimization and convergence precision.

scholarly journals Robust Design of a Smart Structure under Manufacturing Uncertainty via Nonsmooth PDE-Constrained Optimization

2018 ◽  
Vol 885 ◽  
pp. 131-144
Author(s):  
Philip Kolvenbach ◽  
Stefan Ulbrich ◽  
Martin Krech ◽  
Peter Groche
Keyword(s):  
Robust Optimization ◽  
Optimization Problem ◽  
Optimization Method ◽  
Smart Structure ◽  
Uncertain Parameters ◽  
Sensing Element ◽  
Sensor Element ◽  
Worst Case ◽  
Sqp Method ◽  
Nonsmooth Problems

We consider the problem of finding the optimal shape of a force-sensing element which is integrated into a tubular structure. The goal is to make the sensor element sensitive to specific forces and insensitive to other forces. The problem is stated as a PDE-constrained minimization program with both nonconvex objective and nonconvex constraints. The optimization problem depends on uncertain parameters, because the manufacturing process of the structures underlies uncertainty, which causes unwanted deviations in the sensory properties. In order to maintain the desired properties of the sensor element even in the presence of uncertainty, we apply a robust optimization method to solve the uncertain program.The objective and constraint functions are continuous but not differentiable with respect to the uncertain parameters, so that existing methods for robust optimization cannot be applied. Therefore, we consider the nonsmooth robust counterpart formulated in terms of the worst-case functions, and show that subgradients can be computed efficiently. We solve the problem with a BFGS--SQP method for nonsmooth problems recently proposed by Curtis, Mitchell and Overton.

scholarly journals Fuzzy Robust Design of Dynamic Vibration Absorbers

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
A. D. G. Silva ◽  
A. A. Cavalini Jr ◽  
V. Steffen Jr
Keyword(s):  
Fuzzy Logic ◽  
Optimization Problem ◽  
Numerical Study ◽  
Uncertain Parameters ◽  
Vibration Absorbers ◽  
Fuzzy Variables ◽  
Dynamic Vibration ◽  
Logic Optimization ◽  
Fuzzy Function ◽  
Dynamic Vibration Absorbers

This paper is dedicated to the development of robust optimization and decision making techniques taking into account the uncertain parameters of linear and nonlinear dynamic vibration absorbers. In this case, novel approaches are proposed regarding different fuzzy logic optimization strategies. The uncertain parameters of the considered mechanical systems are treated as fuzzy variables. Consequently, the associated optimization problem is described as a fuzzy function that maps the fuzzy inputs. The proposed techniques are applied to the design of dynamic vibration absorbers. This numerical study illustrates the versatility and convenience of the proposed fuzzy logic optimization strategies.

Non-Probabilistic Reliability Optimization of Linear Structural System Based on Interval Model

2014 ◽  
Vol 638-640 ◽  
pp. 168-171
Author(s):  
Min Rong Wang ◽  
Zhi Jun Zhou
Keyword(s):  
Linear Function ◽  
Reliability Index ◽  
Maximum Degree ◽  
Optimization Problem ◽  
Uncertain Parameters ◽  
Reliability Optimization ◽  
Geometric Meaning ◽  
Structural System ◽  
Interval Model ◽  
Fluctuation Range

In this paper, the non-probabilistic reliability optimization problem of linear structural system with uncertain parameters described by interval models is proposed. The degree of the uncertainty is described by the size of the hypercube, and the maximum degree of variability the structure allows is measured by the non-probabilistic reliability index. The relation between the target of non-probabilistic reliability index and the fluctuation range of uncertain parameters is described by the geometric meaning of the reliability index. For the linear function, the uncertain parameters are expressed as the expression of the target value of non-probabilistic reliability index. Numerical example shows the validity and efficiency of the proposed method.

Intuitive inference about normally distributed populations.

1968 ◽  
Vol 78 (2, Pt.1) ◽  
pp. 269-275 ◽  
Author(s):  
Wesley M. DuCharme ◽  
Cameron R. Peterson
Keyword(s):  
Normally Distributed

The Estimation of Blood Platelet Survival

1972 ◽  
Vol 28 (03) ◽  
pp. 447-456 ◽  
Author(s):  
E. A Murphy ◽  
M. E Francis ◽  
J. F Mustard
Keyword(s):  
Standard Deviation ◽  
Least Squares ◽  
Experimental Error ◽  
Blood Platelet ◽  
Least Squares Estimation ◽  
Systematic Relationship ◽  
Platelet Survival ◽  
The Mean ◽  
Normally Distributed

SummaryThe characteristics of experimental error in measurement of platelet radioactivity have been explored by blind replicate determinations on specimens taken on several days on each of three Walker hounds.Analysis suggests that it is not unreasonable to suppose that error for each sample is normally distributed ; and while there is evidence that the variance is heterogeneous, no systematic relationship has been discovered between the mean and the standard deviation of the determinations on individual samples. Thus, since it would be impracticable for investigators to do replicate determinations as a routine, no improvement over simple unweighted least squares estimation on untransformed data suggests itself.

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