A polynomial chaos meta‐model for non‐linear stochastic magnet variations

2013 ◽  
Vol 32 (4) ◽  
pp. 1211-1218 ◽  
Author(s):  
Peter Offermann ◽  
Kay Hameyer
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Flux Density ◽  
Polynomial Chaos ◽  
Epistemic Uncertainty ◽  
Limit State ◽  
Element Model ◽  
State Function ◽  
Content Type ◽  
Meta Model

PurposeDue to the production process, arc segment magnets with radial magnetization for surface‐mounted permanent‐magnet synchronous machines (PMSM) can exhibit a deviation from the intended ideal, radial directed magnetization. In such cases, the resulting air gap field may show spatial variations in angle and absolute value of the flux‐density. For this purpose, this paper aims to create and evaluate a stochastic magnet model.Design/methodology/approachIn this paper, a polynomial chaos meta‐model approach, extracted from a finite element model, is compared to a direct sampling approach. Both approaches are evaluated using Monte‐Carlo simulation for the calculation of the flux‐density above one sole magnet surface.FindingsThe used approach allows representing the flux‐density's variations in terms of the magnet's stochastic input variations, which is not possible with pure Monte‐Carlo simulation. Furthermore, the resulting polynomial‐chaos meta‐model can be used to accelerate the calculation of error probabilities for a given limit state function by a factor of ten.Research limitations/implicationsDue to epistemic uncertainty magnet variations are assumed to be purely Gaussian distributed.Originality/valueThe comparison of both approaches verifies the assumption that the polynomial chaos meta‐model of the magnets will be applicable for a complete machine simulation.

Comparison of Monte Carlo Simulation and Response Surface Method by Using ANSYS PDS

2014 ◽  
Vol 578-579 ◽  
pp. 1449-1453
Author(s):  
Chun Xue Song ◽  
Yi Zhang ◽  
Ying Yi Cao
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Probabilistic Analysis ◽  
Limit State ◽  
Design System ◽  
State Function ◽  
Surface Method

Monte Carlo Simulation and Response Surface Method are two very powerful reliability analysis methods. Normally, in the reliability analysis of complex structures, the limit state function often can not be expressed in a closed-form. Usually, the codes for probabilistic analysis need to be combined with finite element models. ANSYS Probabilistic Design System (PDS) has provided a package to conduct probabilistic analysis automatically. This paper is going to compare the performance of these methods through an easy engineering problem in ANSYS. The results are going to be derived to show the feature of applying the corresponding reliability methods.

Local Monte Carlo Simulation for the Reliability Sensitivity Analysis

2011 ◽  
Vol 291-294 ◽  
pp. 2183-2188 ◽  
Author(s):  
Da Wei Li ◽  
Zhen Zhou Lu ◽  
Zhang Chun Tang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Numerical Technique ◽  
Limit State ◽  
Computational Cost ◽  
Simulation Method ◽  
State Function ◽  
Local Domain ◽  
Monte Carlo Simulation Method ◽  
Reliability Sensitivity

An efficient numerical technique, namely the Local Monte Carlo Simulation method, is presented to assess the reliability sensitivity in this paper. Firstly some samples are obtained by the random sampling, then the local domain with a constant probability content corresponding to each sample point can be defined, finally the conditional reliability and reliability sensitivity corresponding to every local region can be calculated by using linear approximation of the limit state function. The reliability and reliability sensitivity can be estimated by the expectation of all the conditional reliability and reliability sensitivity. Three examples testify the applicability, validity and accuracy of the proposed method. The results computed by the Local Monte Carlo Simulation method and the Monte Carlo method are compared, which demonstrates that, without losing precision, the computational cost by the former method is much less than the later.

Reliability Analysis With Monte Carlo Simulation and Dependent Kriging Predictions

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
Zhifu Zhu ◽  
Xiaoping Du
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Reliability Analysis ◽  
Surrogate Model ◽  
Limit State ◽  
Convergence Criterion ◽  
State Function ◽  
Kriging Method ◽  
Learning Function ◽  
Highly Nonlinear

Reliability analysis is time consuming, and high efficiency could be maintained through the integration of the Kriging method and Monte Carlo simulation (MCS). This Kriging-based MCS reduces the computational cost by building a surrogate model to replace the original limit-state function through MCS. The objective of this research is to further improve the efficiency of reliability analysis with a new strategy for building the surrogate model. The major approach used in this research is to refine (update) the surrogate model by accounting for the full information available from the Kriging method. The existing Kriging-based MCS uses only partial information. Higher efficiency is achieved by the following strategies: (1) a new formulation defined by the expectation of the probability of failure at all the MCS sample points, (2) the use of a new learning function to choose training points (TPs). The learning function accounts for dependencies between Kriging predictions at all the MCS samples, thereby resulting in more effective TPs, and (3) the employment of a new convergence criterion. The new method is suitable for highly nonlinear limit-state functions for which the traditional first- and second-order reliability methods (FORM and SORM) are not accurate. Its performance is compared with that of existing Kriging-based MCS method through five examples.

scholarly journals A CONDITIONAL STOCHASTIC PROJECTION METHOD APPLIED TO A PARAMETRIC VIBRATIONS PROBLEM

2014 ◽  
Vol 20 (6) ◽  
pp. 810-818 ◽  
Author(s):  
Wlodzimierz Brzakala ◽  
Aneta Herbut
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Polynomial Chaos ◽  
Excitation Frequency ◽  
Finite Sequence ◽  
Excitation Amplitude ◽  
Random Excitation ◽  
Parametric Vibrations ◽  
Representative Points ◽  
Cable Stayed Bridges

Parametric vibrations can be observed in cable-stayed bridges due to periodic excitations caused by a deck or a pylon. The vibrations are described by an ordinary differential equation with periodic coefficients. The paper focuses on random excitations, i.e. on the excitation amplitude and the excitation frequency which are two random variables. The excitation frequency ωL is discretized to a finite sequence of representative points, ωL,i Therefore, the problem is (conditionally) formulated and solved as a one-dimensional polynomial chaos expansion generated by the random excitation amplitude. The presented numerical analysis is focused on a real situation for which the problem of parametric resonance was observed (a cable of the Ben-Ahin bridge). The results obtained by the use of the conditional polynomial chaos approximations are compared with the ones based on the Monte Carlo simulation (truly two-dimensional, not conditional one). The convergence of both methods is discussed. It is found that the conditional polynomial chaos can yield a better convergence then the Monte Carlo simulation, especially if resonant vibrations are probable.

Risk assessment of construction projects using Monte Carlo simulation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Abroon Qazi ◽  
Mecit Can Emre Simsekler
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Risk Attitude ◽  
High Impact ◽  
Risk Exposure ◽  
Risk Matrix ◽  
Content Type ◽  
Simulation Based ◽  
Project Risks ◽  
Low Probability

PurposeThis paper aims to develop a process for prioritizing project risks that integrates the decision-maker's risk attitude, uncertainty about risks both in terms of the associated probability and impact ratings, and correlations across risk assessments.Design/methodology/approachThis paper adopts a Monte Carlo Simulation-based approach to capture the uncertainty associated with project risks. Risks are prioritized based on their relative expected utility values. The proposed process is operationalized through a real application in the construction industry.FindingsThe proposed process helped in identifying low-probability, high-impact risks that were overlooked in the conventional risk matrix-based prioritization scheme. While considering the expected risk exposure of individual risks, none of the risks were located in the high-risk exposure zone; however, the proposed Monte Carlo Simulation-based approach revealed risks with a high probability of occurrence in the high-risk exposure zone. Using the expected utility-based approach alone in prioritizing risks may lead to ignoring few critical risks, which can only be captured through a rigorous simulation-based approach.Originality/valueMonte Carlo Simulation has been used to aggregate the risk matrix-based data and disaggregate and map the resulting risk profiles with underlying distributions. The proposed process supported risk prioritization based on the decision-maker's risk attitude and identified low-probability, high-impact risks and high-probability, high-impact risks.

OCTO SCM: assessment of determinants of seaport logistics for the export supply chain of agricultural products

2021 ◽  
Vol 11 (3) ◽  
pp. 1-18
Author(s):  
Raj V. Amonkar ◽  
Tuhin Sengupta ◽  
Debasis Patnaik
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Supply Chain ◽  
Learning Outcomes ◽  
Agricultural Products ◽  
Supply Chain Design ◽  
Content Type ◽  
Focus Session ◽  
Academic Level ◽  
Design Structure

Learning outcomes The learning outcomes of this paper are as follows: to understand the context of seaport logistics and supply chain design structure, to apply Monte Carlo simulation in the interface of the supply chain and to analyze the Monte Carlo simulation algorithm and statistical techniques for identifying the key seaport logistics factors. Case overview/synopsis It was 9:00 p.m. on November 10, 2020, and Nishadh Amonkar, the CEO of OCTO supply chain management (SCM) was glued to the television watching the final cricket match of the Indian Premier League, 2020. Amonkar’s mobile phone rang and it was a call from Vinod Nair, a member Logistics Panel of Ranji Industries Federation. Nair informed Amonkar that it was related to the rejection of several export consignments of agricultural products from Ranji (in the western part of India). The rejection was due to the deterioration in the quality of the exported agricultural products during transit from Ranji to various locations in Europe. Complexity academic level This course is suitable at the MBA level for the following courses: Operations research (Focus/Session: Applications on Monte Carlo Simulation). SCM (Focus/Session: Global SCM, Logistics Planning, Distribution Network). Logistics management (Focus/Session: Transportation Planning). Business statistics (Focus/Session: Application of Hypothesis Testing). Supplementary materials Teaching Notes are available for educators only. Subject code CSS 9: Operations and logistics.

Testing for bubbles in housing markets: some evidence for Brazil

2018 ◽  
Vol 11 (5) ◽  
pp. 754-770 ◽  
Author(s):  
Cássio da Nóbrega Besarria ◽  
Nelson Leitão Paes ◽  
Marcelo Eduardo Alves Silva
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Housing Prices ◽  
Market Price ◽  
Housing Markets ◽  
Cointegration Analysis ◽  
Small Samples ◽  
Content Type ◽  
Long Run ◽  
Cointegration Tests

Purpose Housing prices in Brazil have displayed an impressive growth in recent years, raising some concerns about the existence of a bubble in housing markets. In this paper, the authors implement an empirical methodology to identify whether or not there is a bubble in housing markets in Brazil. Design/methodology/approach Based on a theoretical model that establish that, in the absence of a bubble, a long-run equilibrium relationship should be observed between the market price of an asset and its dividends. The authors implement two methodologies. First, the authors assess whether there is a cointegration relationship between housing prices and housing rental prices. Second, the authors test whether the price-to-rent ratio is stationary. Findings The authors’ results show that there is evidence of a bubble in housing prices in Brazil. However, given the short span of the data, the authors perform a Monte Carlo simulation and show that the cointegration tests may be biased in small samples. Therefore, the authors should be caution when assessing the results. Research limitations/implications The results obtained from the cointegration analysis can be biased for small samples. Practical implications The information on the excessive increase of the prices of the properties in relation to their fundamental value can help in the decision-making on investment of the economic agents. Social implications These results corroborate the hypothesis that Brazil has an excessive appreciation in housing prices, and, as Silva and Besarria (2018) have suggested, this behavior explains, in part, the fact that the central bank has taken this issue into account when deciding about the stance of monetary policy of Brazil. Originality/value The originality is linked to the use of the Gregory-Hansen method of cointegration in the identification of bubbles and discussion of the limitations of the research through Monte Carlo simulation.

Robustness-based multi-objective optimization for repetitive projects under work continuity uncertainty

2020 ◽  
Vol 27 (10) ◽  
pp. 3095-3113
Author(s):  
Lihui Zhang ◽  
Guyu Dai ◽  
Xin Zou ◽  
Jianxun Qi
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Negative Impact ◽  
Project Performance ◽  
Project Managers ◽  
Multi Objective Optimization ◽  
Negative Effects ◽  
Content Type ◽  
Multi Objective ◽  
New Type

PurposeInterrupting work continuity provides a way to improve some project performance, but unexpected and harmful interruptions may impede the implementation. This paper aims to mitigate the negative impact caused by work continuity uncertainty based on the notion of robustness.Design/methodology/approachThis paper develops a float-based robustness measurement method for the work continuity uncertainty in repetitive projects. A multi-objective optimization model is formulated to generate a schedule that achieves a balance between crew numbers and robustness. This model is solved using two modules: optimization module and decision-making module. The Monte Carlo simulation is designed to validate the effectiveness of the generated schedule.FindingsThe results confirmed that it is necessary to consider the robustness as an essential factor when scheduling a repetitive project with uncertainty. Project managers may develop a schedule that is subject to delays if they only make decisions according to the results of the deadline satisfaction problem. The Monte Carlo simulation validated that an appropriate way to measure robustness is conducive to generating a schedule that can avoid unnecessary delay, compared to the schedule generated by the traditional model.Originality/valueAvailable studies assume that the work continuity is constant, but it cannot always be maintained when affected by uncertainty. This paper regards the work continuity as a new type of uncertainty factor and investigates how to mitigate its negative effects. The proposed float-based robustness measurement can measure the ability of a schedule to absorb unpredictable and harmful interruptions, and the proposed multi-objective scheduling model provides a way to incorporate the uncertainty into a schedule.

Application of life cycle assessment and Monte Carlo simulation for enabling sustainable product design

2014 ◽  
Vol 12 (3) ◽  
pp. 307-315 ◽  
Author(s):  
Sekar Vinodh ◽  
Gopinath Rathod
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Life Cycle Assessment ◽  
Life Cycle ◽  
Product Design ◽  
Sustainable Product Design ◽  
Content Type ◽  
Sustainable Product ◽  
Manufacturing Organization

Purpose – The purpose of this paper is to present an integrated technical and economic model to evaluate the reusability of products or components. Design/methodology/approach – Life cycle assessment (LCA) methodology is applied to obtain the product’s environmental performance. Monte Carlo simulation is utilized for enabling sustainable product design. Findings – The results show that the model is capable of assessing the potential reusability of used products, while the usage of simulation significantly increases the effectiveness of the model in addressing uncertainties. Research limitations/implications – The case study has been conducted in a single manufacturing organization. The implications derived from the study are found to be practical and useful to the organization. Practical implications – The paper reports a case study carried out for an Indian rotary switches manufacturing organization. Hence, the model is practically feasible. Originality/value – The article presents a study that investigates LCA and simulation as enablers of sustainable product design. Hence, the contributions of this article are original and valuable.

An Efficient Reliability Analysis Method for Structures With Epistemic Uncertainty Using Evidence Theory

2014 ◽  
Author(s):  
Zhe Zhang ◽  
Chao Jiang ◽  
G. Gary Wang ◽  
Xu Han
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Epistemic Uncertainty ◽  
Limit State ◽  
Computational Cost ◽  
Evidence Theory ◽  
State Function ◽  
Limited Information ◽  
Design Point ◽  
Engineering Problems

Evidence theory has a strong ability to deal with the epistemic uncertainty, based on which the uncertain parameters existing in many complex engineering problems with limited information can be conveniently treated. However, the heavy computational cost caused by its discrete property severely influences the practicability of evidence theory, which has become a main difficulty in structural reliability analysis using evidence theory. This paper aims to develop an efficient method to evaluate the reliability for structures with evidence variables, and hence improves the applicability of evidence theory for engineering problems. A non-probabilistic reliability index approach is introduced to obtain a design point on the limit-state surface. An assistant area is then constructed through the obtained design point, based on which a small number of focal elements can be picked out for extreme analysis instead of using all the elements. The vertex method is used for extreme analysis to obtain the minimum and maximum values of the limit-state function over a focal element. A reliability interval composed of the belief measure and the plausibility measure is finally obtained for the structure. Two numerical examples are investigated to demonstrate the effectiveness of the proposed method.

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