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1 – 10 of over 14000Hui Lü, Kun Yang, Wen-bin Shangguan, Hui Yin and DJ Yu
The purpose of this paper is to propose a unified optimization design method and apply it to handle the brake squeal instability involving various uncertainties in a unified…
Abstract
Purpose
The purpose of this paper is to propose a unified optimization design method and apply it to handle the brake squeal instability involving various uncertainties in a unified framework.
Design/methodology/approach
Fuzzy random variables are taken as equivalent variables of conventional uncertain variables, and a unified response analysis method is first derived based on level-cut technique, Taylor expansion and central difference scheme. Next, a unified reliability analysis method is developed by integrating the unified response analysis and fuzzy possibility theory. Finally, based on the unified reliability analysis method, a unified reliability-based optimization model is established, which is capable of optimizing uncertain responses in a unified way for different uncertainty cases.
Findings
The proposed method is extended to perform squeal instability analysis and optimization involving various uncertainties. Numerical examples under eight uncertainty cases are provided and the results demonstrate the effectiveness of the proposed method.
Originality/value
Most of the existing methods of uncertainty analysis and optimization are merely effective in tackling one uncertainty case. The proposed method is able to handle the uncertain problems involving various types of uncertainties in a unified way.
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Lei Wang, Xiaojun Wang and Xiao Li
– The purpose of this paper is to focus on the influences of the uncertain dynamic responses on the reconstruction of loads.
Abstract
Purpose
The purpose of this paper is to focus on the influences of the uncertain dynamic responses on the reconstruction of loads.
Design/methodology/approach
Based on the assumption of unknown-but-bounded (UBB) noise, a time-domain approach to estimate the uncertain time-dependent external loads is presented by combining the inverse system method in modern control theory and interval analysis in interval mathematics. Inspired by the concept of set membership identification in control theory, an interval analysis model of external loads time history, which is indeed a region or feasible set containing all possible loads being consistent with the bounded structural acceleration responses is established and further solved by two interval algorithms.
Findings
Unlike traditional loads identification methods which only give a point estimation, an interval estimation of external loads time history, which is a region containing all the possible loads being consistent with the uncertain structural responses, is determined. The correlation characteristics among the responses of acceleration, velocity, and displacement are also discussed in consideration of the UBB uncertainty.
Originality/value
For one hand, the solution of the inverse problem in original system is transformed to the solution of the direct problem in inverse system; for another, the authors deal with the uncertainty by use of interval analysis method, and the identified interval process, which contains any possible external loads time history being consistent with the bounded structural responses can be approximately obtained.
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İsmail Özcan and Sırma Zeynep Alparslan Gök
This paper deals with cooperative games whose characteristic functions are fuzzy intervals, i.e. the worth of a coalition is not a real number but a fuzzy interval. This means…
Abstract
Purpose
This paper deals with cooperative games whose characteristic functions are fuzzy intervals, i.e. the worth of a coalition is not a real number but a fuzzy interval. This means that one observes a lower and an upper bound of the considered coalitions. This is very important, for example, from a computational and algorithmic viewpoint. The authors notice that the approach is general, since the characteristic function fuzzy interval values may result from solving general optimization problems.
Design/methodology/approach
This paper deals with cooperative games whose characteristic functions are fuzzy intervals, i.e. the worth of a coalition is not a real number but a fuzzy interval. A situation in which a finite set of players can obtain certain fuzzy payoffs by cooperation can be described by a cooperative fuzzy interval game.
Findings
In this paper, the authors extend a class of solutions for cooperative games that all have some egalitarian flavour in the sense that they assign to every player some initial payoff and distribute the remainder of the worth v(N) of the grand coalition N equally among all players under fuzzy uncertainty.
Originality/value
In this paper, the authors extend a class of solutions for cooperative games that all have some egalitarian flavour in the sense that they assign to every player some initial payoff and distribute the remainder of the worth v(N) of the grand coalition N equally among all players under fuzzy uncertainty. Examples of such solutions are the centre-of-gravity of the imputation-set value, shortly denoted by CIS value, egalitarian non-separable contribution value, shortly denoted by ENSC value and the equal division solution. Further, the authors discuss a class of equal surplus sharing solutions consisting of all convex combinations of the CIS value, the ENSC value and the equal division solution. The authors provide several characterizations of this class of solutions on variable and fixed player set. Specifications of several properties characterize specific solutions in this class.
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Lei Wang, Haijun Xia, Yaowen Yang, Yiru Cai and Zhiping Qiu
The purpose of this paper is to propose a novel non-probabilistic reliability-based topology optimization (NRBTO) method for continuum structural design under interval…
Abstract
Purpose
The purpose of this paper is to propose a novel non-probabilistic reliability-based topology optimization (NRBTO) method for continuum structural design under interval uncertainties of load and material parameters based on the technology of 3D printing or additive manufacturing.
Design/methodology/approach
First, the uncertainty quantification analysis is accomplished by interval Taylor extension to determine boundary rules of concerned displacement responses. Based on the interval interference theory, a novel reliability index, named as the optimization feature distance, is then introduced to construct non-probabilistic reliability constraints. To circumvent convergence difficulties in solving large-scale variable optimization problems, the gradient-based method of moving asymptotes is also used, in which the sensitivity expressions of the present reliability measurements with respect to design variables are deduced by combination of the adjoint vector scheme and interval mathematics.
Findings
The main findings of this paper should lie in that new non-probabilistic reliability index, i.e. the optimization feature distance which is defined and further incorporated in continuum topology optimization issues. Besides, a novel concurrent design strategy under consideration of macro-micro integration is presented by using the developed RBTO methodology.
Originality/value
Uncertainty propagation analysis based on the interval Taylor extension method is conducted. Novel reliability index of the optimization feature distance is defined. Expressions of the adjoint vectors between interval bounds of displacement responses and the relative density are deduced. New NRBTO method subjected to continuum structures is developed and further solved by MMA algorithms.
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Perumandla Karunakar and Snehashish Chakraverty
This paper aims to present solutions of uncertain linear and non-linear shallow water wave equations. The uncertainty has been taken as interval and one-dimensional interval…
Abstract
Purpose
This paper aims to present solutions of uncertain linear and non-linear shallow water wave equations. The uncertainty has been taken as interval and one-dimensional interval shallow water wave equations have been solved by homotopy perturbation method (HPM). In this study, basin depth and initial conditions have been taken as interval and the single parametric concept has been used to handle the interval uncertainty.
Design/methodology/approach
HPM has been used to solve interval shallow water wave equation with the help of single parametric concept.
Findings
Previously, few authors found solution of shallow water wave equations with crisp basin depth and initial conditions. But, in actual sense, the basin depth, as well as initial conditions, may not be found in crisp form. As such, here these are considered as uncertain in term of intervals. Hence, interval linear and non-linear shallow water wave equations are solved in this study using single parametric concept-based HPM.
Originality/value
As mentioned above, uncertainty is must in the above-titled problems due to the various parametrics involved in the governing differential equations. These uncertain parametric values may be considered as interval. To the best of the authors’ knowledge, no work has been reported on the solution of uncertain shallow water wave equations. But when the interval uncertainty is involved in the above differential equation, then direct methods are not available. Accordingly, single parametric concept-based HPM has been applied in this study to handle the said problems.
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Xueguang Yu, Xintian Liu, Xu Wang and Xiaolan Wang
This study aims to propose an improved affine interval truncation algorithm to restrain interval extension for interval function.
Abstract
Purpose
This study aims to propose an improved affine interval truncation algorithm to restrain interval extension for interval function.
Design/methodology/approach
To reduce the occurrence times of related variables in interval function, the processing method of interval operation sequence is proposed.
Findings
The interval variable is evenly divided into several subintervals based on correlation analysis of interval variables. The interval function value is modified by the interval truncation method to restrain larger estimation of interval operation results.
Originality/value
Through several uncertain displacement response engineering examples, the effectiveness and applicability of the proposed algorithm are verified by comparing with interval method and optimization algorithm.
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Ömer Utku Kahraman and Erdal Aydemir
The purpose of this paper is to manage the demand uncertainty considered as lower and upper levels for a medium-scale industrial distribution planning problem in a biobjective…
Abstract
Purpose
The purpose of this paper is to manage the demand uncertainty considered as lower and upper levels for a medium-scale industrial distribution planning problem in a biobjective inventory routing problem (IRP). In order to achieve this, the grey system theory is applied since no statistical distribution from the past data and incomplete information.
Design/methodology/approach
This study is investigated with optimizing the distribution plan, which involves 30 customers of 12 periods in a manufacturing company under demand uncertainty that is considered as lower and upper levels for a biobjective IRP with using grey demand parameters as a grey integer programming model. In the data set, there are also some missing demand values for the customers. So, the seven different grey models are developed to eliminat the effects on demand uncertainties in computational analysis using a piece of developed software considering the logistical performance indicators such as total deliveries, total cost, the total number of tours, distribution capacity, average remaining capacity and solution time.
Findings
Results show that comparing the grey models, the cost per unit and the maximum number of vehicle parameters are also calculated as the new key performance indicator, and then results were ranked and evaluated in detail. Another important finding is the demand uncertainties can be managed with a new approach via logistics performance indicators using alternative solutions.
Practical implications
The results enable logistics managers to understand the importance of demand uncertainties if more reliable decisions are wanted to make with obtaining a proper distribution plan for effective use of their expectations about the success factors in logistics management.
Originality/value
The study is the first in terms of the application of grey models in a biobjective IRP with using interval grey demand data. Successful implementation of the grey approaches allows obtaining a more reliable distribution plan. In addition, this paper also offers a new key performance indicator for the final decision.
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Qi Zhou, Xinyu Shao, Ping Jiang, Tingli Xie, Jiexiang Hu, Leshi Shu, Longchao Cao and Zhongmei Gao
Engineering system design and optimization problems are usually multi-objective and constrained and have uncertainties in the inputs. These uncertainties might significantly…
Abstract
Purpose
Engineering system design and optimization problems are usually multi-objective and constrained and have uncertainties in the inputs. These uncertainties might significantly degrade the overall performance of engineering systems and change the feasibility of the obtained solutions. This paper aims to propose a multi-objective robust optimization approach based on Kriging metamodel (K-MORO) to obtain the robust Pareto set under the interval uncertainty.
Design/methodology/approach
In K-MORO, the nested optimization structure is reduced into a single loop optimization structure to ease the computational burden. Considering the interpolation uncertainty from the Kriging metamodel may affect the robustness of the Pareto optima, an objective switching and sequential updating strategy is introduced in K-MORO to determine (1) whether the robust analysis or the Kriging metamodel should be used to evaluate the robustness of design alternatives, and (2) which design alternatives are selected to improve the prediction accuracy of the Kriging metamodel during the robust optimization process.
Findings
Five numerical and engineering cases are used to demonstrate the applicability of the proposed approach. The results illustrate that K-MORO is able to obtain robust Pareto frontier, while significantly reducing computational cost.
Practical implications
The proposed approach exhibits great capability for practical engineering design optimization problems that are multi-objective and constrained and have uncertainties.
Originality/value
A K-MORO approach is proposed, which can obtain the robust Pareto set under the interval uncertainty and ease the computational burden of the robust optimization process.
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When the probability of each model is known, a natural idea is to select the most probable model. However, in many practical situations, the exact values of these probabilities…
Abstract
Purpose
When the probability of each model is known, a natural idea is to select the most probable model. However, in many practical situations, the exact values of these probabilities are not known; only the intervals that contain these values are known. In such situations, a natural idea is to select some probabilities from these intervals and to select a model with the largest selected probabilities. The purpose of this study is to decide how to most adequately select these probabilities.
Design/methodology/approach
It is desirable to have a probability-selection method that preserves independence. If, according to the probability intervals, the two events were independent, then the selection of probabilities within the intervals should preserve this independence.
Findings
The paper describes all techniques for decision making under interval uncertainty about probabilities that are consistent with independence. It is proved that these techniques form a 1-parametric family, a family that has already been successfully used in such decision problems.
Originality/value
This study provides a theoretical explanation of an empirically successful technique for decision-making under interval uncertainty about probabilities. This explanation is based on the natural idea that the method for selecting probabilities from the corresponding intervals should preserve independence.
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Zhongge Guo, Yuhui Wang, Jiale He and Dong Pang
This paper aims to present a novel dynamic reliability model that considers the interval mixed uncertainty for the air-breathing hypersonic flight vehicle (AHFV) to guarantee…
Abstract
Purpose
This paper aims to present a novel dynamic reliability model that considers the interval mixed uncertainty for the air-breathing hypersonic flight vehicle (AHFV) to guarantee flight safety and structural reliability.
Design/methodology/approach
Initially, the force condition of the fuselage is analyzed based on the longitudinal elastic model of an AHFV. Subsequently, a new high-efficiency dynamic reliability model is presented to describe the failure probability evolution of the fuselage structure. For the random uncertainty problem with interval distribution parameters, the interval PHI2 method of time-dependent reliability is used to obtain the time-dependent reliability interval of the AHFV. Finally, the key variables that affect the failure probability accumulation are determined, which provide an important reference for ensuring structural reliability and improving the life span of AHFVs.
Findings
It is demonstrated that the proposed reliability model can obtain more accurate dynamic reliability results for the fuselage, and it is confirmed the key variables that affect the failure probability accumulation. The results also provide an important reference for the reliability analysis of hypersonic vehicles.
Originality/value
The novelty of this work comes from the first application of the PHI2 method (considering the interval mixed uncertainty) in the AHFV and the development of a new reliability model for the entire body of AHFVs. The proposed analysis scheme is implemented on the dynamic model of the AHFV, which provides a more accurate reference for improving the structural reliability and life span of AHFVs.
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