Three‐dimensional simulation of nonwoven fabrics using a greedy approximation of the distribution of fiber directions

An elementary algorithm is used to simulate the industrial production of a fiber of a 3‐dimensional nonwoven fabric. The algorithm simulates the fiber as a polyline where the direction of each segment is stochastically drawn based on a given probability density function (PDF) on the unit sphere. This PDF is obtained from data of directions of fiber fragments which originate from computer tomography scans of a real nonwoven fabric. However, the simulation algorithm requires numerous evaluations of the PDF. Since the established technique of a kernel density estimator leads to very high computational costs, a novel greedy algorithm for estimating a sparse representation of the PDF is introduced. Numerical tests for a synthetic and a real example are presented. In a realistic scenario, the introduced sparsity ansatz leads to a reduction of the computation time for 100 fibers from around 80 days to 2.5 hours. An elementary algorithm is used to simulate the industrial production of a fiber of a 3‐dimensional nonwoven fabric. The algorithm simulates the fiber as a polyline where the direction of each segment is stochastically drawn based on a given probability density function (PDF) on the unit sphere. This PDF is obtained from data of directions of fiber fragments which originate from computer tomography scans of a real nonwoven fabric. However, the simulation algorithm requires numerous evaluations of the PDF. Since the established technique of a kernel density estimator leads to very high computational costs, a novel greedy algorithm for estimating a sparse representation of the PDF is introduced. Numerical tests for a synthetic and a real example are presented. In a realistic scenario, the introduced sparsity ansatz leads to a reduction of the computation time for 100 fibers from around 80 days to 2.5 hours.