The objective of this research is to identify optimal temperature sensor locations in a laminated die system for the purpose of predicting the temperature distribution throughout the die to control heating and cooling rates. Potential locations (referred to as target nodes) are grouped based on the similarity of their thermal response using both K-means and a proposed temperature ratio clustering method. A sensitivity analysis of the temperature distribution for these groups of target nodes identifies the sensor location for each cluster that exhibits the highest sensitivity to variable inputs. A comparison of sensor locations identified by each clustering method with the sensitivity analysis is presented and is used to evaluate the optimal sensor location in terms of consistency in generating these sensor locations, the degree of sensitivity, the mutual interaction through principal component analysis, limiting the number of sensors, and the accuracy in estimating the temperature distribution.
Issue Section:
Research Papers
Keywords:
laminated die,
clustering,
sensitivity analysis,
optimal sensor location,
die casting,
injection moulding,
estimation of temperature,
cooling,
die casting,
dies (machine tools),
heating,
pattern clustering,
principal component analysis,
sensitivity analysis,
sensor placement,
temperature sensors
References
1.
Demetriou
, M.
, 2005, “Robust Sensor Location Optimization in Distributed Parameter Systems Using Functional Observers
,” Proceedings of 44th IEEE Conference on Decision and Control and European Control Conference
, Seville, Spain, pp. 7187
–7192
.2.
Udwadia
, F.
, 1994, “Methodology for Optimum Sensor Locations for Parameter Identification in Dynamic Systems
,” J. Eng. Mech.
, 120
(2
), pp. 368
–390
.3.
Fadale
, T.
, Nenarokomov
, A.
, and Emery
A.
, 1995, “Two Approaches to Optimal Sensor Locations
,” ASME J. Heat Trans.
, 117
(2
), pp. 373
–379
.4.
Papadimitriou
, C.
, Beck
, J.
, and Au
, S.
, 2000, “Entropy-Based Optimal Sensor Location for Structural Model Updating
,” J. Vib. Control
, 6
(5
), pp. 781
–800
.5.
Papadimitriou
, C.
, 2005, “Pareto Optimal Sensor Locations for Structural Identification
,” Comput. Methods Appl. Mech. Eng.
, 194
, pp. 1655
–1673
.6.
Yao
, L.
, Sethares
, W.
, and Kammer
, D.
, 1993, “Sensor Placement for on Orbit Modal Identification via a Genetic Algorithm
,” AIAA J.
, 31
(10
), pp. 1167
–1169
.7.
Rao
, A.
, and Anandakumar
, G.
, 2007, “Optimal Placement of Sensors for Structural System Identification and Health Monitoring Using a Hybrid Swarm Intelligence Technique
,” Smart Mater. Struct.
, 16
, pp. 2658
–2672
.8.
Dour
, G.
, Dargusch
, M.
, and Davidson
, C.
, 2006, “Recommendations and Guidelines for the Performance of Accurate Heat Transfer Measurements in Rapid Forming Processes
,” Int. J. Heat Mass Trans.
, 49
, pp. 1773
–1789
.9.
Hamasaiid
, A.
, Dour
, G.
, Dargusch
, M.
, Loulou
, T.
, Davidson
, C.
, and Savage
, G.
, 2008, “Heat-Transfer Coefficient and In-Cavity Pressure at the Casting-Die Interface During High-Pressure Die Casting of the Magnesium Alloy AZ91D
,” Phys. Metall. Mater. Sci.
, 39
(4
), pp. 853
–864
.10.
Gibbons
, G.
, Hansell
, R.
, Norwood
, A.
, and Dickens
, P.
, 2003, “Rapid Laminated Die-Cast Tooling
,” Assem. Autom.
, 23
(4
), pp. 372
–381
.11.
Dickens
, P.
, 1995, “Research Developments in Rapid Prototyping
,” Proc. Inst. Mech. Eng., Part B: J. Eng. Manuf.
, 209
, pp. 261
–266
.12.
Xu
, X.
, Sachs
, E.
, and Allen
, S.
, 2001, “The Design of Conformal Cooling Channels in Injection Molding Tooling
,” Polym. Eng. Sci.
, 41
(7
), pp. 1265
–1279
.15.
Hutton
, D.
, 2004, Fundamentals of Finite Element Analysis
, McGraw-Hill
, New York
, 2004, pp. 163
–166
, Chap. 6.16.
Zheng
, C.
, and Bennett
, G.
, 2002, Applied Contaminant Transport Modelling
, Wiley-Interscience
, New York
, pp. 343
–348
, Chap. 12.17.
Choi
, K.
, and Kim
, N.
, 2005, Structural Sensitivity Analysis and Optimization 1: Linear Systems
, Springer-Verlag
, New York
, pp. 3
–34
, Chap. 1.18.
Chen
, B.
, Tai
, P.
, Harrison
, R.
, and Pan
, Y.
, 2005, “Novel Hybrid Hierarchical-K-Means Clustering Method (H-K-Means) for Microarray Analysis
,” Proceedings of 2005 IEEE Computational Systems Bioinformatics Conference
, pp.105
–108
.19.
Jun
, S.
, and Oh
, I.
, 2007, “A Co-Evolutionary K-Means Algorithm
,” Int. J. Soft Comput.
, 2
(5
), pp. 624
–627
.20.
Moore
, C.
, 1992, “Selection of Controlled and Manipulated Variables
,” Practical Distillation Control
, Van Nostrand Reinold
, New York
, pp. 140
–177
.21.
Jolliffe
, I.
, 2002, Principal Component Analysis, Series: Springer Series in Statistics
, Springer
, New York
, pp. 10
–27
, Chap. 2.22.
Zamprogna
, E.
, Barolo
, M.
, and Seborg
, D.
, 2005, “Optimal Selection of Soft Sensor Inputs for Batch Distillation Columns Using Principal Component Analysis
,” J. Process Control
, 15
(1
), pp. 39
–52
.23.
He
, X.
, and Asada
, H.
, 1993, “A New Method for Identifying Orders of Input–Output Models for Nonlinear Dynamic Systems
,” Proceedings of American Control Conference
, San Francisco, CA, pp. 2520
–2523
.24.
Seo
, J.
, Khajepour
, A.
, and Huissoon
, J.
, 2011, “Identification of Die Thermal Dynamics Using Neural Networks
,” ASME J. Dyn. Syst., Meas.
, Control (in press).Copyright © 2012
by American Society of Mechanical Engineers
You do not currently have access to this content.
