Sampling-Based Reliability Analysis Using Deep Feedforward Neural Network (DFNN)

Reliability analysis that evaluates a probabilistic constraint is an important part of reliability-based design optimization (RBDO). Inverse reliability analysis evaluates the percentile value of the performance function that satisfies the reliability. To compute the percentile value, analytical methods, surrogate model based methods, and sampling-based methods are commonly used. In case the dimension or nonlinearity of the performance function is high, sampling-based methods such as Monte Carlo simulation, Latin hypercube sampling, and importance sampling can be directly used for reliability analysis since no analytical formulation or surrogate model is required in these methods. The sampling-based methods have high accuracy but require a large number of samples, which can be very time-consuming. Therefore, this paper proposes methods that can improve the accuracy of reliability analysis when the number of samples is not enough and the sampling-based methods are considered to be better candidates. This study starts with the idea of training the relationship between the realization of the performance function at a small sample size and the corresponding true percentile value of the performance function. Deep feedforward neural network (DFNN), which is one of the promising artificial neural network models that approximates high dimensional models using deep layered structures, is trained using the realization of various performance functions at a small sample size and the corresponding true percentile values as input and target training data, respectively. In this study, various polynomial functions and random variables are used to create training data sets consisting of various realizations and corresponding true percentile values. A method that approximates the realization of the performance function through kernel density estimation and trains the DFNN with the discrete points representing the shape of the kernel distribution to reduce the dimension of the training input data is also presented. Along with the proposed reliability analysis methods, a strategy that reuses samples of the previous design point to enhance the efficiency of the percentile value estimation is explained. The results show that the reliability analysis using the DFNN is more accurate than the method using only samples. In addition, compared to the method that trains the DFNN using the realization of the performance function, the method that trains the DFNN with the discrete points representing the shape of the kernel distribution improves the accuracy of reliability analysis and reduces the training time. The proposed sample reuse strategy is verified that the burden of function evaluation at the new design point can be reduced by reusing the samples of the previous design point when the design point changes while performing RBDO.

Development of a Modal Selection Method for Full Strain Field Estimation

Full field response of a structure is critical for evaluating the performance of large slender structures. Since only several discrete measurements can be acquired during operation, the data expansion method is important for the estimation of the full field responses of the large complex structure. In previous studies, modal transformation methods were mainly applied in model reduction/expansion and global shape sensing. Compared to other expansion methods, the modal method is straightforward to implement and computational efficient, which makes it the most suitable approach for real-time expansion. However, only the first several modes were included in the modal transformation method in previous studies. Since the errors due to truncated mode components can occur under high frequency band excitations, it is necessary to include all of the modes that contribute significantly to the responses of the structure. Therefore, in this study, a modal selection method based on operational modal analysis (OMA) is proposed for selecting proper modes. The modal characteristics of the system were derived with the strain data at several discrete locations. The contribution of each mode was quantified. By sorting the modes based on their contribution, the most significant modes can be used in the expansion process. Two operational modal analysis methods, stochastic system identification (SSI) and frequency domain decomposition (FDD), were considered and compared. The proposed approach was implemented with a computational model. Considerable improvement has been observed when high bandwidth excitations were added. The proposed modal selection method can successfully rank the participated modes. It can improve the accuracy of the modal transformation approach as shown in the impact loading case. It can be used for data expansion even when high frequency band is excited. Finally, we believe the novel methods presented in this study could be used in the development of more reliable health monitoring systems for turbomachinery.

Excimer Laser Treatment of Steel Fibers for Improved Adhesion to Silicone Rubber

Former investigators observed characteristic laser-induced structure on synthetic fibers and steel cord surfaces after irradiation, which is considered by us as an advantageous factor in developing bonding strength of fiber-elastomer composites. We applied various UV laser treatments on the surfaces of steel fiber in order to obtain similar topographic features. Surface modification was observed under scanning electron microscope (SEM). In consideration as factors in bonding strength, mechanical properties of the matrix elastomer (silicon rubber) had been tested in addition to its thermal properties by differential scanning calorimetry (DSC) and Carbon Black (CB) filler dispersion properties by atomic force microscopy (AFM). As the main test for adhesion strength, we performed a fiber pull-out test method developed by our research group for bonding strength of cord fibers to silicon rubber in both neat and CB filled forms for comparison purposes. Our experiment results revealed better adhesion strength when using silicone rubber matrix reinforced with CB.

3D-Printed Polymeric Metamaterial Recovery Behavior After Large Deformation

Human-made lattice mechanical metamaterials have recently been shown to exhibit better stiffness or tunable properties than natural materials. We demonstrated that body-centered-cubic (BCC) metamaterials made by 3D-printer stereolithography (SLA) display good recovery properties after undergoing cyclic large compressive deformation. Our experimental results reveal that the strut thickness of BCC metamaterials affect the recovery and mechanical behaviors during compression.

Non-Linear Finite Element Analysis of an Open Spline Connection

Splines are geared mechanical connections widely used for torque transmission. The analysis of splined connections follows straightforward techniques that take into account the stresses developed at the gear root and flanks. Special difficulties arise when the spline connection needs to eliminate backlash and the part’s geometry is not symmetrical. Misalignment, combined loads and differences in stiffness are responsible for causing a non even contact profile between teeth along the spline circumference. These conditions lead to dissimilar stress profiles and some teeth end up being subject to significantly higher stresses. This work analyses the stress profile of a peculiar spline component used in flight control actuation systems of EMBRAER aircraft, tailored to eliminate backlash due to the need of accurate positioning feedback. Normally, for this kind of application, the external spline has an open geometry and the backlash is avoided by means of a bolt used to tighten both sides of the open spline. There are no known analytic solutions that consider the bolt tightening effect and the contact stress distribution appearing on the gear teeth which depends on the spline geometry and local stiffness of the parts being joined. To approximate the spline local stress distributions, a non-linear finite element model was developed and the resulting stresses were compared to those from methodologies available in the literature. Finally the finite element model results were used to successfully approximate the fatigue life and damage tolerance cycles of a spline connection that broke during certification tests of the flap mechanism of an EMBRAER aircraft.

Uncertainty Quantification With Maximum Entropy Method for Fatigue Life Estimation

Use of high-fidelity fatigue models that incorporate not only material uncertainty but also part variability and operational uncertainties can improve the accuracy of predictive maintenance and thus decrease operational cost. However, due to the large number of computationally expensive cost function evaluations necessary, little work has been done to explore this field. In this research, the expected life probability distributions with low computational cost is estimated through a general statistical framework that applies Maximum Entropy Method (MEM), fractional statistical moments and Multiplicative Dimensional Reduction (M-DRM). The framework is tested on advanced models of a 6204 SKF ball bearing. The influence of critical part tolerances and load conditions on fatigue life with a probability density function with only 80 function evaluations is quantified in both a finite element analysis and a non-linear analytical model. The number of function evaluations is one order of magnitude lower than necessary for a comparable accuracy achieved by Monte Carlo simulation.

Excimer Laser Treatment of Nylon Fibers for Improved Adhesion to Vulcanized Natural Rubber

Cords made of steel, nylon or polyester are important reinforcement components used in tire industry. The bond strength between the cords and the rubber matrix is closely related to the surface properties of the cord fibers. Previous research revealed Ultraviolet (UV) laser-induced characteristic topography on synthetic fibers after irradiation, which is considered by us as an advantageous factor in developing bonding strength between fiber-rubber composites. We applied various UV laser treatments on the surfaces of nylon fibers in order to obtain similar topographic features. Adhesion is affected by the valleys and peaks that form on the surface of the fibers by laser radiation. In this study, nylon cords were irradiated with different number of UV pulses using an excimer laser to understand the effect of the laser beam on nylon fiber-rubber adhesion. A fiber pull-out test method developed by our research group for bonding strength of nylon cord fibers to carbon black filled and vulcanized natural rubber was utilized in pull-out configuration. The results showed that the maximum pull-out load was reached at 300 laser pulses and then decreased.

A Computational Framework Enabling Comparative Analysis of Progressive Damage Models for Composite Materials

The present work is motivated by the need for an efficient and quantifiable assessment of how various strain- or stress-based composite materials failure criteria and damage evolution models that capture the load-induced material degradation, along with their intrinsic parameters, can affect our understanding of material behavior and facilitate suitability decisions of such criteria. The difficulty of performing comparative analysis among many of these criteria and models has been a significant impediment to the composite materials design and material certification communities. In response to these needs, the present work describes the development, verification and validation of such a general computational framework. This framework enables not only increasing the user’s understanding of the effect of parameters associated with models under consideration on the model predicted results but also allowing the user to address more advanced problems such as material design, optimization and potentially certification. The framework implemented into “COMSOL Multiphysics” utilizes symbolic algebra to automatically generate the required expressions to be used in the respective computational modules. Two strain-based models for two distinct specimen geometries are used to show the framework capabilities: one model is described by three damage modes and a second one is given by four damage modes. The first geometry is that of a unnotched coupon whereas the second is that of an open hole specimen in tension. The theoretical predictions are compared with the experimental ones in terms of load-strain responses. The results indicate that by proper selection of specific input parameters, these models can accurately predict the structural response of composite laminate structural systems up to failure.