Special issue: scientific machine learning for manufacturing processes and material systems

Computational modeling, simulation, and optimization of manufacturing processes and materials systems have been a persistent endeavor of the engineering research community at large. Significant progress has been achieved in this field due to the exponential increase in computing power, and the incorporation of data-driven modeling methods. Process and systems modeling often involves expensive and time-intensive simulations and experiments. Incorporation of machine-learning (ML) models as efficient surrogate models has been proven to enhance the human understanding of the behavior of the system at hand and reduce the computational optimization cost of the concerned processes and systems. However, there is a rising need to go beyond the conventional data-driven techniques to address challenges, such as presence of noise in data, limited budget, data sparsity, lack of interpretability of ML models, etc. Tackling these issues will enable more comprehensive modeling of manufacturing processes and discovery of novel material systems

Application of probabilistic modeling and automated machine learning framework for high-dimensional stress field

Modern computational methods, involving highly sophisticated mathematical formulations, enable several tasks like modeling complex physical phenomenon, predicting key properties and design optimization. The higher fidelity in these computer models makes it computationally intensive to query them hundreds of times for optimization and one usually relies on a simplified model albeit at the cost of losing predictive accuracy and precision. Towards this, data-driven surrogate modeling methods have shown a lot of promise in emulating the behavior of the expensive computer models. However, a major bottleneck in such methods is the inability to deal with high input dimensionality and the need for relatively large datasets. With such problems, the input and output quantity of interest are tensors of high dimensionality. Commonly used surrogate modeling methods for such problems, suffer from requirements like high number of computational evaluations that precludes one from performing other numerical tasks like uncertainty quantification and statistical analysis. In this work, we propose an end-to-end approach that maps a high-dimensional image like input to an output of high dimensionality or its key statistics. Our approach uses two main framework that perform three steps: a) reduce the input and output from a high-dimensional space to a reduced or low-dimensional space, b) model the input-output relationship in the low-dimensional space, and c) enable the incorporation of domain-specific physical constraints as masks. In order to accomplish the task of reducing input dimensionality we leverage principal component analysis, that is coupled with two surrogate modeling methods namely: a) Bayesian hybrid modeling, and b) DeepHyper's deep neural networks. We demonstrate the applicability of the approach on a problem of a linear elastic stress field data.Comment: 17 pages, 16 figures, IDETC Conference Submissio

Data-Driven Modeling of Multiaxial Fatigue of Structures in Frequency Domain

Multiaxial fatigue failure can be a major concern in the design and evaluation of structures subjected to multiple time-varying loads or excitations. Multiaxial fatigue analysis can be carried out in both time and frequency domains. Time domain analyses are applied to a concerned stress or strain time history which are obtained through expensive numerical simulations or experiments. On the other hand, frequency domain fatigue analyses are applied to the stress or strain spectrum, which are obtained through transfer functions and load spectrums. Compared to frequency domain analyses, time domain analyses are computationally expensive and highly time-consuming. Thus, there has been increased interest in developing robust frequency domain fatigue evaluation. The existing frequency domain methods for multiaxial fatigue analysis capture the underlying mechanism implicitly or through certain postulated effective stress parameters. None of them are based on a consistent cycle counting method which becomes more challenging when non-proportional multiaxial variable amplitude loading conditions are present. Most recent developments in addressing both multiaxial fatigue cycle counting and a consistent fatigue damage parameter definition include the two variations of Path Dependent Maximum Range Cycle Counting (PDMR) namely path length based PDMR (PDMRPL) and moment of load path based PDMR (PDMRMLP). The fundamental aim of this doctoral work is to develop a multiaxial fatigue evaluation methodology in frequency domain that can tackle non-proportionality or capture the underlying fatigue damage mechanisms explicitly based on PDMR methods. This is done through the following three major steps. The first step towards realizing the primary goal is to first affirm the validity and applicability of PDMRPL and PDMRMLP for random multiaxial loadings. The PDMRPL and PDMRMLP methods are extensively studied and analyzed using multiaxial synchronous and asynchronous experimental data across four different materials (aluminum alloy, non-alloy steels and austenite steel). Parametric analysis is carried out to provide key insights into the non-proportionality damage that occur across different amplitude ratios and frequency ratios of loading. As a second step towards achieving the frequency domain formulation, a transfer function based PDMRMLP is developed. The developed approach is studied through multiple numerical test cases conducted on a fillet welded doubling plate component. Previously developed transfer function based PDMRPL is also studied and analyzed to understand its capabilities and limitations. The major finding from the analysis was that for highly non-proportional load paths, transfer function based frequency domain PDMRPL provided un-conservative estimations compared to time domain PDMRPL. Based on the limitations of the transfer function based approaches, a data-driven approach was then adopted to fulfill the primary objectives of this dissertation. A robust methodology is developed for building customized data-driven models. The methodology consists of three stages: exploratory study, data generation, and model development. Essentially, neural network models are built on simulated data in a dimensionally reduced parameter space to model two primary multiaxial fatigue parameters (i.e. damage per cycle and number of PDMR cycles). The developed models are able to tackle non-proportionality explicitly and are independent of bandwidth or origin of the spectrum. Through the case example of a doubling plate structure, the proposed methodology is implemented and studied. Additionally, the developed models are also tested on a rectangular beam structure to articulate their generality. The models are applied for both proportional and non-proportional cases. The performance and capabilities of the models are articulated through the test cases.PHDNaval Architecture & Marine EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/172683/1/sandippk_1.pd

Heterogenous Multi-Source Data Fusion Through Input Mapping and Latent Variable Gaussian Process

Artificial intelligence and machine learning frameworks have served as computationally efficient mapping between inputs and outputs for engineering problems. These mappings have enabled optimization and analysis routines that have warranted superior designs, ingenious material systems and optimized manufacturing processes. A common occurrence in such modeling endeavors is the existence of multiple source of data, each differentiated by fidelity, operating conditions, experimental conditions, and more. Data fusion frameworks have opened the possibility of combining such differentiated sources into single unified models, enabling improved accuracy and knowledge transfer. However, these frameworks encounter limitations when the different sources are heterogeneous in nature, i.e., not sharing the same input parameter space. These heterogeneous input scenarios can occur when the domains differentiated by complexity, scale, and fidelity require different parametrizations. Towards addressing this void, a heterogeneous multi-source data fusion framework is proposed based on input mapping calibration (IMC) and latent variable Gaussian process (LVGP). In the first stage, the IMC algorithm is utilized to transform the heterogeneous input parameter spaces into a unified reference parameter space. In the second stage, a multi-source data fusion model enabled by LVGP is leveraged to build a single source-aware surrogate model on the transformed reference space. The proposed framework is demonstrated and analyzed on three engineering case studies (design of cantilever beam, design of ellipsoidal void and modeling properties of Ti6Al4V alloy). The results indicate that the proposed framework provides improved predictive accuracy over a single source model and transformed but source unaware model.Comment: 20 Pages,9 Figures, Data is available per reques