Contact:

Héctor Flores-Cantú

Mobil: 01 7665 987 835
Phone: +49 (0) 631 31600 - 4255
TU Kaiserslautern. Fraunhofer, ITWM.
Kaiserslautern, Germany.



Interests:

Industrial/Applied Mathematics.
Mathematical Modelling.
Optimization.
Decision Making.
Sensitivity Analysis.
Scientific Visualization.


Actual Project:
PhD student at TU Kaiserslautern and Fraunhofer ITWM . Industrial Mathematics.

The project is related with the simulation and optimization of the deposition of fibers in spunbond nonwoven processes. This is, by the way, a multi-criteria problem. In this kind of problems there are no unique solution, because of the multiple objectives. (You can not improve everything with limited resources). I want to design tools to allow the exploration of the set of efficient solutions for non-linear multicriteria problems, in the Multicriteria argot, this set is called the Pareto Set.

Abstract:
In spundbonding processes the deposition of extruded filaments over a moving belt generates the web for the final fabric. After the web is formed bonding methods are used to increase its strength. Unfortunately, no bonding method will correct a wrong web. This fact indicates that special care should be taken when designing a particular web formation process.

It is known that the visual and mechanical properties of the fabric depends strongly on the web homogeneity, and that, in an ideal web any two pair of spots should "look alike". The inhomogeneity could occur when the filaments are concentrated more/less than the average on a spot, or when to many parallel fibers appear together there. Two kind of defects are reflected here "cloudiness" and "ships".

The production method we are studying uses a rotating system of deflector surfaces to spread the filaments after extruded from the spinneret. The combination of this rotation and the linear movement of the belt generates a particular kind of depositing trajectory for the filaments, cycloids. A matrix of spinnerets, more than a hundred, produce the web. In this process the homogeneity of the web could be related to a particular set of machine parameters. The more important of them being the relative positions of the spinnerets and its fiber deposition profile. The problem belongs to the class of "Uniform Coverage Problems" where a surface needs to be covered uniformly using a material.
For this process a model has been developed and simulations implemented where the user can explore in real time the effects of a particular change in the machine parameters.
If we want to find optimal parameters we need a quantification of the visual homogeneity, but there is no trivial numerical measure for this. At least I can assure you that measuring fluctuations using a P-norm or some sort of entropy is not very useful. Besides, the model generates only approximations of the real process and the uncertainty in the output should be considered and optimized too. Here we are forced to consider a sensitivity analysis for the process.
We are confronted with multiple measures (criteria). In mathematical optimization this is called a "Multi-Criteria Problem". For this problems no optimal solution exists, but a set of optimal solutions. By exploring this set of optimal solutions the expert could choose the one he thinks is the best. We are using as an starting point an evolutionary algorithm to compute this set of solutions and developing software tools to allow their exploration.
The full set of solutions is then approximated by using continuation methods , I am interested in versions of this methods using some sort of derivative free algorithms.


Old projects:


Studies


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