Multi-objective Optimization of Tree Trunk Axes in Glulam Beam Design Considering Fuzzy Probability Based Random Fields

2021 ◽  
Author(s):  
F. Niklas Schietzold ◽  
Wolfgang Graf ◽  
Michael Kaliske
Keyword(s):  
Random Fields ◽  
A Priori ◽  
Random Variables ◽  
Distribution Functions ◽  
Design Parameters ◽  
Tree Trunk ◽  
Fuzzy Probability ◽  
Glulam Beam ◽  
Fuzzy Variables ◽  
Beam Design

Abstract Deterministic design and a priori parameters are used in traditional optimization approaches. The material characteristics of solid wood are not deterministic in reality. Hence, realistic optimization and simulation methods need to take the uncertainties of parameters into account. The uncertainty characteristics of wood are mainly originated in natural variation. In addition to this, incertitudes from lack of knowledge are inherent. Accordingly, the aleatoric approach of randomness can be expanded to a polymorphic uncertainty model. Fuzzy probability based randomness is used in this work. Therefore, the epistemic approach of fuzziness is taken into account. The distribution functions of random variables are parametrized by fuzzy variables. So coupling of both, aleatoric and epistemic uncertainties, is involved.Interactions of fuzzy variables and crosscorrelations of random variables are considered among and within the parameters. Crosscorrelated random fields are used to represent spatial variation of material parameters. The autocovariance structures are modeled structurally dependent on the tree trunk axes. FEM results are applied as basic solutions of a loaded timber structure. A local orthotropic material formulation with respect to specifically located tree trunk axes is used. The optimal positions of the tree trunk axes for each wooden log are examined as design parameters. Polymorphic uncertainty is used to describe a priori parameters. The developed methods for uncertainty analysis are embedded in an automated and parallelized optimization processing. An analysis of a two-tier glulam beam, according to a purlin of a timber roof construction, is shown as numerical example for the optimization framework.

An Inverse Analysis Method for Design Optimization With Both Statistical and Fuzzy Uncertainties

2006 ◽  
Author(s):  
Liu Du ◽  
Kyung K. Choi
Keyword(s):  
Design Optimization ◽  
Inverse Analysis ◽  
Random Variables ◽  
Mean Value ◽  
Performance Measure ◽  
Distribution Functions ◽  
Analysis Method ◽  
Fuzzy Variables ◽  
Analysis And Design ◽  
Inverse Analysis Method

Structural analysis and design optimization have recently been extended to consider various uncertainties. If the statistical data for the uncertainties are sufficient to construct the input distribution function, the uncertainties can be treated as random variables and RBDO is used; otherwise, the uncertainties can be treated as fuzzy variables and PBDO is used. However, many structural design problems include both uncertainties with sufficient data and uncertainties with insufficient data. For these problems, RBDO will yield an unreliable design since the distribution functions of uncertainties are not believable. On the other hand, treating the random variables as fuzzy variables and invoking PBDO may yield too conservative design with a higher optimum cost. This paper proposes a new design formulation using the performance measure approach (PMA). For the inverse analysis, this paper proposes a new most probable/possible point (MPPP) search method called maximal failure search (MFS), which is an integration of the enhanced hybrid mean value method (HMV+) and maximal possibility search (MPS) method. Some mathematical and physical examples are used to demonstrate the proposed inverse analysis method and design formulation.

scholarly journals Ensuring functional stability of the information system with limited initial information about determining random values

2020 ◽  
Vol 69 (4) ◽  
Author(s):  
Yu. V. Berezovska ◽  
Keyword(s):  
Information System ◽  
Information Systems ◽  
A Priori ◽  
Random Variables ◽  
Distribution Functions ◽  
Functional Stability ◽  
A Priori Information ◽  
Experimental Development ◽  
Reliability Indicators ◽  
Priori Information

Ensuring functional stability, reliability and effective management in information systems is a complex and complex scientific task. At the stage of design and construction of information systems, reliability indicators are interpreted as characteristics of the created probabilistic mathematical models of objects, and at the stage of experimental development, testing and operation, the role of reliability indicators is performed by statistical assessments of the corresponding probabilistic characteristics. When assessing the reliability indicators of information systems, the necessary initial data for a priori probabilistic calculations are often lacking, and the statistical assessment is hampered by a small volume of tests, according to which it is possible to determine only the estimates of the moments of determining random variables of the process of functioning of information systems or its components (mathematical expectations and variances of mean time between failures, recovery time, standby time, etc.). However, in such a situation, it is necessary to substantiate some characteristics of the information system, for example, a reserve of time, guaranteed exact boundaries of the probability of system uptime and the availability factor. When obtaining specific estimates, the minimum a priori information is used, which corresponds to a large number of real situations when assessing the reliability of information systems with time redundancy in the process of design, testing and operation. This article highlights various types of functionals that characterize the efficiency of an information system, under conditions of incomplete a priori information about the distribution function of determining random variables, through which the main indicators of the reliability of information systems are expressed, an analytical method is proposed and substantiated for finding distribution functions that deliver the greatest or least linear value. or linear fractional functionals under moment constraints on variable distribution functions. The method is based on identifying the limiting distribution functions, constructing the corresponding limiting polynomials, and solving special inequalities.

scholarly journals Stochastic Comparisons of Some Distances between Random Variables

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 981
Author(s):  
Patricia Ortega-Jiménez ◽  
Miguel A. Sordo ◽  
Alfonso Suárez-Llorens
Keyword(s):  
Financial Risk ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Stochastic Ordering ◽  
Random Variable ◽  
Distribution Functions ◽  
Stochastic Comparisons ◽  
Stochastic Orderings ◽  
Absolute Value ◽  
The Difference

The aim of this paper is twofold. First, we show that the expectation of the absolute value of the difference between two copies, not necessarily independent, of a random variable is a measure of its variability in the sense of Bickel and Lehmann (1979). Moreover, if the two copies are negatively dependent through stochastic ordering, this measure is subadditive. The second purpose of this paper is to provide sufficient conditions for comparing several distances between pairs of random variables (with possibly different distribution functions) in terms of various stochastic orderings. Applications in actuarial and financial risk management are given.

scholarly journals Finding Maximum Clique in Stochastic Graphs Using Distributed Learning Automata

2015 ◽  
Vol 23 (01) ◽  
pp. 1-31 ◽  
Author(s):  
Alireza Rezvanian ◽  
Mohammad Reza Meybodi
Keyword(s):  
Community Structure ◽  
Dominating Set ◽  
Learning Automata ◽  
Random Variables ◽  
Graph Model ◽  
Maximum Clique ◽  
Distribution Functions ◽  
Maximum Clique Problem ◽  
Stochastic Graphs ◽  
Stochastic Graph

Because of unpredictable, uncertain and time-varying nature of real networks it seems that stochastic graphs, in which weights associated to the edges are random variables, may be a better candidate as a graph model for real world networks. Once the graph model is chosen to be a stochastic graph, every feature of the graph such as path, clique, spanning tree and dominating set, to mention a few, should be treated as a stochastic feature. For example, choosing stochastic graph as the graph model of an online social network and defining community structure in terms of clique, and the associations among the individuals within the community as random variables, the concept of stochastic clique may be used to study community structure properties. In this paper maximum clique in stochastic graph is first defined and then several learning automata-based algorithms are proposed for solving maximum clique problem in stochastic graph where the probability distribution functions of the weights associated with the edges of the graph are unknown. It is shown that by a proper choice of the parameters of the proposed algorithms, one can make the probability of finding maximum clique in stochastic graph as close to unity as possible. Experimental results show that the proposed algorithms significantly reduce the number of samples needed to be taken from the edges of the stochastic graph as compared to the number of samples needed by standard sampling method at a given confidence level.

Adaptive Geometry Representation of Turbine Vane Frames for Use in Optimization

2021 ◽  
Author(s):  
Sebastian F. Riebl ◽  
Christian Wakelam ◽  
Reinhard Niehuis
Keyword(s):  
Design Space ◽  
Cfd Simulation ◽  
A Priori ◽  
Three Dimensional ◽  
Optimization Method ◽  
Three Dimensions ◽  
Design Parameters ◽  
Adjustment Process ◽  
Turbine Vane ◽  
Integrated Concept

Abstract Turbine Vane Frames (TVF) are a way to realize more compact jet engine designs. Located between the high pressure turbine (HPT) and the low pressure turbine (LPT), they fulfill structural and aerodynamic tasks. When used as an integrated concept with splitters located between the structural load-bearing vanes, the TVF configuration contains more than one type of airfoil with sometimes pronouncedly different properties. This system of multidisciplinary demands and mixed blading poses an interesting opportunity for optimization. Within the scope of the present work, a full geometric parameterization of a TVF with splitters is presented. The parameterization is chosen as to minimize the number of parameters required to automatically and flexibly represent all blade types involved in a TVF row in all three dimensions. Typical blade design parameters are linked to the fourth order Bézier-curve controlled camber line-thickness parameterization. Based on conventional design rules, a procedure is presented, which sets the parameters within their permissible ranges according to the imposed constraints, using a proprietary developed code. The presented workflow relies on subsequent three dimensional geometry generation by transfer of the proposed parameter set to a commercially available CAD package. The interdependencies of parameters are discussed and their respective significance for the adjustment process is detailed. Furthermore, the capability of the chosen parameterization and adjustment process to rebuild an exemplary reference TVF geometry is demonstrated. The results are verified by comparing not only geometrical profile data, but also validated CFD simulation results between the rebuilt and original geometries. Measures taken to ensure the robustness of the method are highlighted and evaluated by exploring extremes in the permissible design space. Finally, the embedding of the proposed method within the framework of an automated, gradient free numerical optimization is discussed. Herein, implications of the proposed method on response surface modeling in combination with the optimization method are highlighted. The method promises to be an option for improvement of optimization efficiency in gradient free optimization of interdependent blade geometries, by a-priori excluding unsuitable blade combinations, yet keeping restrictions to the design space as limited as possible.

Enabling Decision-Based Design Using Solution Trajectory Correction and Backtracking Rules

2012 ◽  
Author(s):  
Vijitashwa Pandey ◽  
Zissimos P. Mourelatos ◽  
Monica Majcher
Keyword(s):  
Optimal Design ◽  
Utility Function ◽  
Design Space ◽  
A Priori ◽  
Preference Order ◽  
Beam Design ◽  
Effective Decision ◽  
Suboptimal Design ◽  
Trajectory Correction ◽  
Decision Based Design

Optimization is needed for effective decision based design (DBD). However, a utility function assessed a priori in DBD does not usually capture the preferences of the decision maker over the entire design space. As a result, when the optimizer searches for the optimal design, it traverses (or ends up) in regions where the preference order among different solutions is different from the actual order. For a highly non-convex design space, this can lead to convergence to a grossly suboptimal design depending on the initial design. In this article, we propose two approaches to alleviate this issue. First, we map the trajectory of the solution as generated by the optimizer and generate ranking questions that are presented to the designer to verify the correctness of the utility function. We then propose backtracking rules if a local utility function is very different from the initially assessed function. We demonstrate our methodology using a mathematical example and a welded beam design problem.

scholarly journals Analytic slowing-down distributions as modified by turbulent transport

2018 ◽  
Vol 84 (6) ◽  
Author(s):  
G. J. Wilkie
Keyword(s):  
Particle Density ◽  
Plasma Heating ◽  
Turbulent Transport ◽  
A Priori ◽  
High Energy ◽  
Relative Strength ◽  
Distribution Functions ◽  
Toroidal Plasmas ◽  
Model Distribution ◽  
Phase Space Transport

The effect of electrostatic microturbulence on fast particles rapidly decreases at high energy, but can be significant at moderate energy. Previous studies found that, in addition to changes in the energetic particle density, this results in non-trivial changes to the equilibrium velocity distribution. These effects have implications for plasma heating and the stability of Alfvén eigenmodes, but make multiscale simulations much more difficult without further approximations. Here, several related analytic model distribution functions are derived from first principles. A single dimensionless parameter characterizes the relative strength of turbulence relative to collisions, and this parameter appears as an exponent in the model distribution functions. Even the most simple of these models reproduces key features of the numerical phase-space transport solution and provides a useful a priori heuristic for determining how strong the effect of turbulence is on the redistribution of energetic particles in toroidal plasmas.

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