A boundary determination problem in steady-state heat conduction – a solution and sensitivity analysis

2019 ◽  
Vol 30 (5) ◽  
pp. 2351-2362
Author(s):  
Leszek Hożejowski
Keyword(s):  
Sensitivity Analysis ◽  
Heat Conduction ◽  
Measurement Errors ◽  
Numerical Procedure ◽  
Sensitivity Factor ◽  
Unknown Boundary ◽  
Trefftz Method ◽  
Content Type ◽  
Boundary Points ◽  
Boundary Reconstruction

Purpose The purpose of this paper is to propose a numerical procedure for discrete identification of the missing part of the domain boundary in a heat conduction problem. A new approach to sensitivity analysis is intended to give a better understanding of the influence of measurement error on boundary reconstruction. Design/methodology/approach The solution of Laplace’s equation is obtained using the Trefftz method, and then each of the sought boundary points can be derived numerically from a nonlinear equation. The sensitivity analysis comes down to the analytical evaluation of a sensitivity factor. Findings The proposed method very accurately recovers the unknown boundary, including irregular shapes. Even a very large number of the boundary points can be determined without causing computational problems. The sensitivity factor provides quantitative assessment of the relationship between the temperature measurement errors and boundary identification errors. The numerical examples show that some boundary reconstruction problems are error-sensitive by nature but such problems can be recognized with the use of a sensitive factor. Originality/value The present approach based on the Trefftz method separates, in terms of computation, specification of the coefficients appearing in the Trefftz method and missing coordinates of the sought boundary points. Due to introducing a sensitivity factor, a more profound sensitivity analysis was successfully conducted.

scholarly journals An inverse geometric problem in steady state heat conduction – the solution and stability analysis

2018 ◽  
Vol 240 ◽  
pp. 01013
Author(s):  
Leszek Hożejowski
Keyword(s):  
Measurement Errors ◽  
Numerical Procedure ◽  
Sensitivity Factor ◽  
Unknown Boundary ◽  
Trefftz Method ◽  
Geometric Problem ◽  
Boundary Identification ◽  
Steady State Heat ◽  
The Given ◽  
The Relationship

The paper addresses a numerical method for boundary identification in a problem governed by Laplace’s equation. The proposed numerical procedure for discrete reconstruction of the unknown boundary from the given temperature data is based on the Trefftz method. In contrast to the procedures described in the reference papers, the present approach requires significantly less and easier computation. The paper undertakes analysis of the resistance of the solution to small perturbations of the prescribed temperature condition at the unknown part of the boundary. We define and then estimate a sensitivity factor which allows quantitative assessment of the relationship between temperature measurement errors and boundary identification errors, even if the exact solution is not known. The included numerical examples demonstrate the effectiveness of the proposed method for boundary reconstruction and present the analysis of numerical stability using a sensitivity factor.

BEM Solution With Minimal Energy Technique for the Geometrical Inverse Heat Conduction Problem in a Doubly Connected Domain

2003 ◽  
Vol 125 (1) ◽  
pp. 109-117 ◽  
Author(s):  
Chang-Yong Choi ◽  
Jong Chull Jo
Keyword(s):  
Heat Conduction ◽  
Boundary Element ◽  
Measurement Errors ◽  
Heat Conduction Problem ◽  
Boundary Surface ◽  
Inverse Heat Conduction Problem ◽  
Unknown Boundary ◽  
Inverse Heat Conduction ◽  
Minimal Energy ◽  
Element Analysis

This article addresses the use of boundary element method in conjunction with minimal energy technique for solving a geometrical inverse heat conduction problem. The problem considered in this study is to estimate the unknown inner boundary position in an irregular-shaped hollow body of which the inner boundary surface is subjected to a specified temperature condition. For solving the problem, first boundary element equations are converted into the quadratic programming problem by minimizing the energy functional with a constraint, next a hypothetical inner boundary is defined such that the actual inner boundary is located interior of the hypothetical solution domain, then temperatures at hypothetical inner boundary are determined to meet the constraints of measurement error in inner surface temperatures, and finally boundary element analysis is performed for the position of an unknown boundary. Based on these main solution procedures, an effective detection algorithm is provided. In addition, the solution method is numerically tested to investigate the effects of measurement errors on the accuracy of estimation.

Dynamic supplier selection approach for mining equipment company

2019 ◽  
Vol 14 (1) ◽  
pp. 77-105 ◽  
Author(s):  
Md. Tanweer Ahmad ◽  
Sandeep Mondal
Keyword(s):  
Sensitivity Analysis ◽  
Supplier Selection ◽  
Business Environment ◽  
Spare Parts ◽  
Mixed Integer ◽  
Optimal Order ◽  
Mining Equipment ◽  
Order Allocation ◽  
Managerial Implication ◽  
Content Type

PurposeThis paper aims to address the supplier selection (SS) problem under dynamic business environments to optimize the procurement cost of spare-parts in the context of a mining equipment company (MEC). Practically, involved parameters’ value does not remain constant as planning periods due to fluctuation in the demand and their market dynamics. Therefore, dynamicity in the parameter is considered as an important factor when a company forms a responsive chain through most eligible suppliers with respect to planning periods. This area of study may be considered for their complexities to the approaches toward order-allocations with bi-products of unused and repair spare-parts.Design/methodology/approachAn integrated methodology of analytic hierarchy process (AHP) and mixed-integer non-linear programming (MILP) is implemented in the two stages during each planning periods. In the first stage, AHP is used to obtain the relative weights with respect to each spare-parts of each criterion and based on that, the ranking is evaluated in accordance with case considered. And in the second stage, MILP is formulated to find the allocations of each spare-part with two distinct approaches through Model-1 and Model-2 separately. Moreover, Model-1 and Model-2 are outlined based on the ranking and efficient parameters-value under cost, limited capacities, quality level and delay lead time respectively.FindingsThe ranking and their optimal order-allocation of potential suppliers are obtained during consecutive planning periods for both unused and repair spare-parts. Subsequently, sensitivity analysis is conducted to deduce the key nuggets with the comparison of Model-1 and Model-2 in the changing of capacity, demand and cost per spare-parts. From this analysis, it is found that suppliers who have optimal parameter settings would be better for order-allocations than ranking during the changing planning period.Practical implicationsThis paper points out the situation-specific approach for SS problem for a mining industry which often faces disruptive supplying environments. The managerial implication between ranking and parameters are highlighted through Model-1 and Model-2 by sensitivity analysis.Originality/valueIt provides useful directions for managers who are involved in the procurement of spare-parts in the mining environment. For this, suppliers are selected for order-allocation by using Model-1 and Model-2 in the dynamic business environment. The solvability of the model is presented using LINGO 17. Furthermore, the case company selected in this study can be extended to other sectors.

Optimal design of a parallel robotic gripper using enhanced multi-objective ant lion optimizer with a sensitivity analysis approach

2020 ◽  
Vol 40 (5) ◽  
pp. 703-721
Author(s):  
Golak Bihari Mahanta ◽  
Deepak BBVL ◽  
Bibhuti B. Biswal ◽  
Amruta Rout
Keyword(s):  
Sensitivity Analysis ◽  
Distribution Function ◽  
Design Parameters ◽  
Objective Functions ◽  
Content Type ◽  
Multi Objective ◽  
The Past ◽  
Design Variables ◽  
Pick And Place ◽  
Ant Lion

Purpose From the past few decades, parallel grippers are used successfully in the automation industries for performing various pick and place jobs due to their simple design, reliable nature and its economic feasibility. So, the purpose of this paperis to design a suitable gripper with appropriate design parameters for better performance in the robotic production systems. Design/methodology/approach In this paper, an enhanced multi-objective ant lion algorithm is introduced to find the optimal geometric and design variables of a parallel gripper. The considered robotic gripper systems are evaluated by considering three objective functions while satisfying eight constraint equations. The beta distribution function is introduced for generating the initial random number at the initialization phase of the proposed algorithm as a replacement of uniform distribution function. A local search algorithm, namely, achievement scalarizing function with multi-criteria decision-making technique and beta distribution are used to enhance the existing optimizer to evaluate the optimal gripper design problem. In this study, the newly proposed enhanced optimizer to obtain the optimum design condition of the design variables is called enhanced multi-objective ant lion optimizer. Findings This study aims to obtain optimal design parameters of the parallel gripper with the help of the developed algorithms. The acquired results are investigated with the past research paper conducted in that field for comparison. It is observed that the suggested method to get the best gripper arrangement and variables of the parallel gripper mechanism outperform its counterparts. The effects of the design variables are needed to be studied for a better design approach concerning the objective functions, which is achieved by sensitivity analysis. Practical implications The developed gripper is feasible to use in the assembly operation, as well as in other pick and place operations in different industries. Originality/value In this study, the problem to find the optimum design parameter (i.e. geometric parameters such as length of the link and parallel gripper joint angles) is addressed as a multi-objective optimization. The obtained results from the execution of the algorithm are evaluated using the performance indicator algorithm and a sensitivity analysis is introduced to validate the effects of the design variables. The obtained optimal parameters are used to develop a gripper prototype, which will be used for the assembly process.

Hybrid filters and feedback mechanism for wearable-based human-manipulator interface

2015 ◽  
Vol 42 (5) ◽  
pp. 485-495 ◽  
Author(s):  
Ping Zhang ◽  
Bei Li ◽  
Guanglong Du
Keyword(s):  
Kalman Filter ◽  
Measurement Errors ◽  
Unscented Kalman Filter ◽  
Robot Manipulator ◽  
Experimental Studies ◽  
Feedback Mechanism ◽  
Content Type ◽  
System States ◽  
Noisy Measurements ◽  
Hybrid Filters

Purpose – This paper aims to develop a wearable-based human-manipulator interface which integrates the interval Kalman filter (IKF), unscented Kalman filter (UKF), over damping method (ODM) and adaptive multispace transformation (AMT) to perform immersive human-manipulator interaction by interacting the natural and continuous motion of the human operator’s hand with the robot manipulator. Design/methodology/approach – The interface requires that a wearable watch is tightly worn on the operator’s hand to track the continuous movements of the operator’s hand. Nevertheless, the measurement errors generated by the sensor error and tracking failure signicantly occur several times, which means that the measurement is not determined with sufficient accuracy. Due to this fact, IKF and UKF are used to compensate for the noisy and incomplete measurements, and ODM is established to eliminate the influence of the error signals like data jitter. Furthermore, to be subject to the inherent perceptive limitations of the human operator and the motor, AMT that focuses on a secondary treatment is also introduced. Findings – Experimental studies on the GOOGOL GRB3016 robot show that such a wearable-based interface that incorporates the feedback mechanism and hybrid filters can operate the robot manipulator more flexibly and advantageously even if the operator is nonprofessional; the feedback mechanism introduced here can successfully assist in improving the performance of the interface. Originality/value – The interface uses one wearable watch to simultaneously track the orientation and position of the operator’s hand; it is not only avoids problems of occlusion, identification and limited operating space, but also realizes a kind of two-way human-manipulator interaction, a feedback mechanism can be triggered in the watch to reflect the system states in real time. Furthermore, the interface gets rid of the synchronization question in posture estimation, as hybrid filters work independently to compensate the noisy measurements respectively.

Inverse problem solution for a laser flash studies of a thin layer coatings

2017 ◽  
Vol 27 (3) ◽  
pp. 698-710 ◽  
Author(s):  
Wit Stryczniewicz ◽  
Janusz Zmywaczyk ◽  
Andrzej Jaroslaw Panas
Keyword(s):  
Inverse Problem ◽  
Heat Conduction ◽  
Thin Layer ◽  
Laser Flash ◽  
Problem Solution ◽  
Flake Graphite ◽  
Estimation Technique ◽  
Content Type ◽  
Inverse Problem Solution ◽  
Layer Sample

Purpose The paper aims to discuss the inverse heat conduction methodology in solution of a certain parameter identification problem. The problem itself concerns determination of the thermophysical properties of a thin layer coating by applying the laser flash apparatus. Design/methodology/approach The modelled laser flash diffusivity data from the three-layer sample investigation are used as input for the following parameter estimation procedure. Assuming known middle layer, i.e. substrate properties, the thermal diffusivity (TD) of the side layers’ material is determined. The estimation technique utilises the finite element method for numerical solution of the direct, 2D axisymmetric heat conduction problem. Findings The paper presents methodology developed for a three-layer sample studies and results of the estimation technique testing and evaluation based on simulated data. The multi-parametrical identification procedure results in identification of the out of plane thin layer material diffusivity from the inverse problem solution. Research limitations/implications The presentation itself is limited to numerical simulation data, but it should be underlined that the flake graphite thermophysical parameters have been utilised in numerical tests. Practical implications The developed methodology is planned to be applied in detailed experimental studies of flake graphite. Originality/value In the course of a present study, a methodology of the thin-coating layer TD determination was developed. In spite of the fact that it has been developed for the graphite coating investigation, it was planned to be universal in application to any thin–thick composite structure study.

A Numerical Procedure for Shock Problem Using Artificial Heat Conduction

1966 ◽  
Vol 21 (12) ◽  
pp. 2715-2724 ◽  
Author(s):  
Purushottam Lal Sachdev ◽  
Phoolan Prasad
Keyword(s):  
Heat Conduction ◽  
Numerical Procedure ◽  
Artificial Heat

Exploring incomplete information in maintenance materials inventory optimization

2014 ◽  
Vol 114 (1) ◽  
pp. 144-158 ◽  
Author(s):  
Antti Puurunen ◽  
Jukka Majava ◽  
Pekka Kess
Keyword(s):  
Sensitivity Analysis ◽  
Simulation Model ◽  
Input Data ◽  
Real Life ◽  
Significant Risk ◽  
Service Level ◽  
Content Type ◽  
Imperfect Data ◽  
Inventory Optimization ◽  
Critical Materials

Purpose – Ensuring the sufficient service level is essential for critical materials in industrial maintenance. This study aims to evaluate the use of statistically imperfect data in a stochastic simulation-based inventory optimization where items' failure characteristics are derived from historical consumption data, which represents a real-life situation in the implementation of such an optimization model. Design/methodology/approach – The risks of undesired shortages were evaluated through a service-level sensitivity analysis. The service levels were simulated within the error of margin of the key input variables by using StockOptim optimization software and real data from a Finnish steel mill. A random sample of 100 inventory items was selected. Findings – Service-level sensitivity is item specific, but, for many items, statistical imprecision in the input data causes significant uncertainty in the service level. On the other hand, some items seem to be more resistant to variations in the input data than others. Research limitations/implications – The case approach, with one simulation model, limits the generalization of the results. The possibility that the simulation model is not totally realistic exists, due to the model's normality assumptions. Practical implications – Margin of error in input data estimation causes a significant risk of not achieving the required service level. It is proposed that managers work to improve the preciseness of the data, while the sensitivity analysis against statistical uncertainty, and a correction mechanism if necessary, should be integrated into optimization models. Originality/value – The output limitations in the optimization, i.e. service level, are typically stated precisely, but the capabilities of the input data have not been addressed adequately. This study provides valuable insights into ensuring the availability of critical materials.

Sign in / Sign up

Export Citation Format

Share Document