Batch Process and Sensitivity Analysis of Collision Detection of Planar Convex Polygons in Motion

2013 ◽  
Vol 13 (4) ◽  
Author(s):  
Cheng-fu Chen
Keyword(s):  
Sensitivity Analysis ◽  
Programming Problem ◽  
Collision Detection ◽  
Parametric Programming ◽  
Batch Process ◽  
Detection Problem ◽  
Convex Polygons ◽  
Parametric Problem ◽  
Decomposition Procedure ◽  
Two Parameters

A new method for formulation, solution, and sensitivity analysis of collision detection of convex objects in motion is presented. The collision detection problem is formulated as a parametric programming problem governed by the changes in the relative translation and relative rotation between the two objects considered. The two parameters together determine all the possible relative configurations between two moving convex objects. Therefore, solving this parametric problem allows for knowing the proximity information for all the possible configurations of the objects. We develop a two-step decomposition procedure to solve this parametric programming problem, and show that the solution is a convex function of the two parameters. This convexity feature enables an archive of the proximity information and sensitivity analysis for the collision detection problem.

MILP Sensitivity Analysis for Short-Term Scheduling of Batch Plants under Uncertainty

2011 ◽  
Vol 181-182 ◽  
pp. 577-582
Author(s):  
Jin Zhu ◽  
Xiu Mei Zhang ◽  
Wei Kang
Keyword(s):  
Sensitivity Analysis ◽  
Branch And Bound ◽  
Parametric Programming ◽  
Uncertain Parameters ◽  
Deterministic Case ◽  
Short Term ◽  
Batch Plants ◽  
Bound Solution ◽  
Solution Methodology

In this paper, An integrated framework is developed to handle uncertainty in short-term scheduling based on the idea of inference-based sensitivity analysis for MILP problems and the utilization of a branch and bound solution methodology. The proposed method leads to the determination of the importance of different parameters and the constraints on the objective function and the generation and evaluation of a set of alternative schedules given the variability of the uncertain parameters. The main advantage of the proposed method is that no substantial complexity is added compared with the solution of the deterministic case because the only additional required information is the dual information at the leaf nodes of the branch-and-bound tree. Two case studies are presented to highlight the information extracted by the proposed approach and the complexity involved compared with parametric programming studies.

ON THE COLLISION DETECTION PROBLEM FOR ROBOT MANIPULATORS

1995 ◽  
Vol 26 (2) ◽  
pp. 189-210 ◽  
Author(s):  
Mark Gill ◽  
Albert Zomaya
Keyword(s):  
Collision Detection ◽  
Robot Manipulators ◽  
Detection Problem

scholarly journals Generalization of parameters in the storage–discharge relation for a low flow based on the hydrological analysis of sensitivity

2015 ◽  
Vol 371 ◽  
pp. 69-73 ◽  
Author(s):  
K. Fujimura ◽  
Y. Iseri ◽  
S. Kanae ◽  
M. Murakami
Keyword(s):  
Climate Change ◽  
Sensitivity Analysis ◽  
Water Resource Management ◽  
Hydrological Model ◽  
Low Flow ◽  
Optimum Parameters ◽  
Proportional Relationship ◽  
Two Parameters ◽  
The Impact ◽  
Different Climates

Abstract. The storage-discharge relations have been widely used for water resource management and have led to reliable estimation of the impact of climate change on water resources. In a previous study, we carried out a sensitivity analysis of the parameters in a discharge-storage relation in the form of a power function and found that the optimum parameters can be characterized by an exponential function (Fujimura et al., 2014). The aim of this study is to extend the previous study to clarify the properties of the parameters in the storage–discharge relations by carrying out a sensitivity analysis of efficiency using a hydrological model. The study basins are four mountainous basins in Japan with different climates and geologies. The results confirm that the two parameters in the storage–discharge relations can be expressed in an inversely proportional relationship. In addition, we can conveniently assume a practical function for the storage–discharge relations where only one parameter is used on the basis of the new relationship between the two parameters.

scholarly journals MULTI-OBJECTIVE PROBABILISTIC FRACTIONAL PROGRAMMING PROBLEM INVOLVING TWO PARAMETERS CAUCHY DISTRIBUTION

2019 ◽  
Vol 24 (3) ◽  
pp. 385-403
Author(s):  
Srikumar Acharya ◽  
Berhanu Belay ◽  
Rajashree Mishra
Keyword(s):  
Mathematical Model ◽  
Mathematical Programming ◽  
Programming Problem ◽  
Fractional Programming ◽  
Cauchy Distribution ◽  
Solution Procedure ◽  
Mathematical Programming Problem ◽  
Multi Objective ◽  
Fractional Programming Problem ◽  
Two Parameters

The paper presents the solution methodology of a multi-objective probabilistic fractional programming problem, where the parameters of the right hand side constraints follow Cauchy distribution. The proposed mathematical model can not be solved directly. The solution procedure is completed in three steps. In first step, multi-objective probabilistic fractional programming problem is converted to deterministic multi-objective fractional mathematical programming problem. In the second step, it is converted to its equivalent multi-objective mathematical programming problem. Finally, ε -constraint method is applied to find the best compromise solution. A numerical example and application are presented to demonstrate the procedure of proposed mathematical model.

CONTINUOUS PATH VERIFICATION IN MULTI-AXIS NC-MACHINING

2005 ◽  
Vol 15 (04) ◽  
pp. 351-377 ◽  
Author(s):  
RON WEIN ◽  
OLEG ILUSHIN ◽  
GERSHON ELBER ◽  
DAN HALPERIN
Keyword(s):  
Collision Detection ◽  
Translational Motion ◽  
Lower Envelope ◽  
Critical Surface ◽  
Efficient Computation ◽  
Detection Problem ◽  
Surface Patches ◽  
Radial Projection ◽  
Tool Axis ◽  
Nc Machine

We introduce a new approach to the problem of collision detection between a rotating milling-cutter of an NC-machine and a model of a solid workpiece, as the rotating cutter continuously moves near the workpiece. Having five degrees of motion freedom, this problem is hard to solve exactly and we approximate the motion of the tool by a sequence of sub-paths of pure translations interleaved with pure rotations. The collision-detection problem along each sub-path is then solved by using radial projection of the obstacles (the workpiece and the static parts of the NC-machine) around the tool axis to obtain a collection of critical surface patches in ℝ3, and by examining planar silhouettes of these surface patches. We thus reduce the problem to successive computations of the lower envelope of a set of planar curves, which we intersect with the profile of the tool. Our reduction is exact, and incurs no loss of accuracy. We have implemented our algorithm in the IRIT environment for solid modeling, using an extension package of the CGAL library for computing envelopes. The algorithm, combined with the proper data structures, solves the collision detection problem in a robust manner, yet it yields efficient computation times as our experiments show. Our approach produces exact results in case of purely translational motion, and provides guaranteed (and good) approximation bounds in case the motion includes rotation.

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