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We consider a line-search method for continuous optimization under a stochastic setting where the function values and gradients are available only through inexact probabilistic zeroth and first-order oracles. These oracles capture multiple stan- dard settings including expected loss minimization and zeroth-order optimization. Moreover, our framework is very general and allows the function and gradient estimates to be biased. The proposed algorithm is simple to describe, easy to im- plement, and uses these oracles in a similar way as the standard deterministic line search uses exact function and gradient values. Under fairly general conditions on the oracles, we derive a high probability tail bound on the iteration complexity of the algorithm when applied to non-convex smooth functions. These results are stronger than those for other existing stochastic line search methods and apply in more general settings. 

Previous studies have shown how discontinuous resin formats can increase the robustness of Vacuum Bag Only (VBO) prepregs. Current formats of this discontinuous resin format, dubbed USCPreg, all rely on a discontinuous film being applied on a fiber bed using only pressure. However, efforts are currently being undertaken to apply the discontinuous resin to the fiber bed directly, without a separate filming step. These methods should allow broader and more diverse characteristics of the prepreg, and allow a reduction in bulk factor, customization of the resin distribution, and potentially enable the production of prepreg “on demand.” To understand how applying discontinuous resin to a dry fiber bed at temperatures suitable for resin deposition may affect the final distribution, small-scale experiments were conducted. A fluid with controlled viscosity, matching the viscosity of epoxy resin during hotmelt processing, was used to minimize variability. The experiments consisted of a sessile droplet of facsimile fluid being deposited on the surface of a single ply of reinforcement. The spread of the fluid was then recorded, using a goniometer as well as a standard camera. Post-processing of these recordings was performed to obtain the spreading of the fluid in three directions: in the plane directions and the out-of-plane direction. The fluid was constant, a 30Pa.s rheological standard, but the reinforcement was varied to determine how the fluid interacted with different reinforcements. Macro-scale changes, such as fabric weave and fabric areal weight, and micro-scale parameters, such as tow width and fiber size, were varied to observe their effects on fluid distribution. The experiments yielded maximum in-plane spread distance, time for the resin to fully impregnate into the fibers, and aspect ratio of spreading, particularly for non-symmetric weaves. The results can be used to guide how the resin is deposited on different reinforcements, in order to achieve a resin distribution that will consistently yield high-quality parts. In addition, it is possible these observations can be applied to resin flow in standard continuous film prepreg, such as predicting the final degree of impregnation. 

Previous studies have shown how discontinuous resin formats can increase the robustness of Vacuum Bag Only (VBO) prepregs. Current formats of this discontinuous resin format, dubbed USCPreg, all rely on a discontinuous film being applied on a fiber bed using only pressure. However, efforts are currently being undertaken to apply the discontinuous resin to the fiber bed directly, without a separate filming step. These methods should allow broader and more diverse characteristics of the prepreg, and allow a reduction in bulk factor, customization of the resin distribution, and potentially enable the production of prepreg “on demand.” To understand how applying discontinuous resin to a dry fiber bed at temperatures suitable for resin deposition may affect the final distribution, small-scale experiments were conducted. A fluid with controlled viscosity, matching the viscosity of epoxy resin during hotmelt processing, was used to minimize variability. The experiments consisted of a sessile droplet of facsimile fluid being deposited on the surface of a single ply of reinforcement. The spread of the fluid was then recorded, using a goniometer as well as a standard camera. Post-processing of these recordings was performed to obtain the spreading of the fluid in three directions: in the plane directions and the out-of-plane direction. The fluid was constant, a 30Pa.s rheological standard, but the reinforcement was varied to determine how the fluid interacted with different reinforcements. Macro-scale changes, such as fabric weave and fabric areal weight, and micro-scale parameters, such as tow width and fiber size, were varied to observe their effects on fluid distribution. The experiments yielded maximum in-plane spread distance, time for the resin to fully impregnate into the fibers, and aspect ratio of spreading, particularly for non-symmetric weaves. The results can be used to guide how the resin is deposited on different reinforcements, in order to achieve a resin distribution that will consistently yield high-quality parts. In addition, it is possible these observations can be applied to resin flow in standard continuous film prepreg, such as predicting the final degree of impregnation.