Industrial Applications of Intelligent Adaptive Sampling Methods for Multi-Objective Optimization

Multi-objective optimization is an essential component of nearly all engineering design. However, for industrial applications, the design process typically demands running expensive computer code and/or real-world experiments putting the design process at risk of finding suboptimal solutions and/or not meeting budget constraints. As a first step toward a remedy, meta-models are built to mimic the response surface at a much lower query cost. We cover a time-tested technology specifically tailored to limited-data scenarios called Bayesian hybrid modeling (GEBHM) developed and maintained at General Electric (GE) research. GEBHM offers Bayesian mean and principled uncertainty predictions allowing a second technology called intelligent design and analysis of experiments (GE-IDACE/IDACE) to perform the optimization task using an adaptive sampling strategy. This chapter first covers the theoretical framework of both GEBHM and GE-IDACE. Then, the impact of GEBHM/GE-IDACE is demonstrated on multiple real-world engineering applications including additive manufacturing, combustion testing, and computational fluid dynamic design modeling. GEBHM and GE-IDACE are used daily and extensively within GE with huge impact in the form of 30–90% cost reduction and superior engineering designs of competitive products

Gene Expression Patterns in Bone Following Mechanical Loading

The advent of high-throughput measurements of gene expression and bioinformatics analysis methods offers new ways to study gene expression patterns. The primary goal of this study was to determine the time sequence for gene expression in a bone subjected to mechanical loading during key periods of the bone-formation process, including expression of matrix-related genes, the appearance of active osteoblasts, and bone desensitization. A standard model for bone loading was employed in which the right forelimb was loaded axially for 3 minutes per day, whereas the left forearm served as a nonloaded contralateral control. We evaluated loading-induced gene expression over a time course of 4 hours to 32 days after the first loading session. Six distinct time-dependent patterns of gene expression were identified over the time course and were categorized into three primary clusters: genes upregulated early in the time course, genes upregulated during matrix formation, and genes downregulated during matrix formation. Genes then were grouped based on function and/or signaling pathways. Many gene groups known to be important in loading-induced bone formation were identified within the clusters, including AP-1-related genes in the early-response cluster, matrix-related genes in the upregulated gene clusters, and Wnt/β-catenin signaling pathway inhibitors in the downregulated gene clusters. Several novel gene groups were identified as well, including chemokine-related genes, which were upregulated early but downregulated later in the time course; solute carrier genes, which were both upregulated and downregulated; and muscle-related genes, which were primarily downregulated. © 2011 American Society for Bone and Mineral Research

Numerical modeling of cortical bone adaptation due to mechanical loading using the finite element method

It is well known that bone tissue adapts its shape and structure according to its mechanical environment. Bone adaptation occurs on the dense cortical bone and porous trabecular bone. The process of bone adaptation is shown to be dependent on a number of mechanical loading parameters such as magnitude, frequency, number of bouts etc. of applied loading through experimental studies. We propose to develop a numerical framework, which can simulate and predict cortical bone adaptation due to diff erent parameters of loading. In pursuit of the development of the framework, we develop a method to generate fi nite element (FE) models of actual rat ulna from micro computed tomography (micro-CT) images. The external adaptation process is implemented in the model by moving the surface nodes of the FE mesh along the normal direction based on an evolution law characterized by two parameters: one that captures the rate of the adaptation process (referred to as gain); and the other characterizing the threshold value of the mechanical stimulus required for adaptation (referred to as threshold-sensitivity). Cortical bone is firstly modeled as an elastic material. Loading from experiments of Robling et al is applied on the FE model and the elastic boundary value problem is solved. Based on the results of the FE solution, the surface nodes are displaced according to the local strain energy density as the growth stimulus. Using this stimulus, we show that the model can simulate the e ffect of the magnitude of applied loading on the growth response. We calibrate the growth law parameters by comparing the results from our model to the experimental results. A parametric study is carried out to evaluate the e ffect of these two parameters on the adaptation response. We show, following comparison of results from the simulations to the experimental observations, that splitting the loading cycles into di fferent number of bouts a ffects the threshold-sensitivity but not the rate of adaptation. We also show that the threshold-sensitivity parameter can quantify the mechanosensitivity of the osteocytes. The use of strain energy density stimulus and elastic material model cannot simulate the e ect of frequency of applied loading on the cortical bone adaptation response. We model cortical bone as a poroelastic material to account for the interstitial fluid flow. We aim to develop a growth stimulus similar to strain energy density for the poroelastic material model. In order to achieve this goal, we develop the FE model of a rectangular beam subjected to pure bending. This geometric model is chosen for simplicity, as an idealized representation of cortical bone. We then propose the use of the dissipation energy of the poroelastic ow as a mechanical stimulus for bone adaptation, and show that it can predict the eff ect of frequency of the applied load. Surface adaptation in the model depends on the weighted average of the mechanical stimulus in a "zone of influence" near each surface point, in order to incorporate the non-locality in the mechanotransduction of osteocytes present in the lacunae. We show that the dissipation energy stimulus and the resulting increase in second moment of inertia of the cross section increase linearly with frequency in the low frequency range (less than 10 Hz) and saturate at the higher frequency range (greater than 10 Hz). Similar non-linear adaptation frequency response also has been observed in numerous experiments. We extend the poroelastic material model, dissipation energy stimulus, and the zone of infuence to the actual rat ulna FE model. We implement orthotropic permeability on the rat ulna model in order to be anatomically consistent. We calibrate the growth law parameters (gain and threshold-sensitivity) using experimental results. We analyze the growth response of cortical bone for a range of frequencies (from 2 Hz to 25 Hz) and show that the adaptation response is non-linear with respect to the frequency of loading