As an emerging technology in the era of Industry 4.0, digital twin is gaining unprecedented attention because of its promise to further optimize process design, quality control, health monitoring, decision and policy making, and more, by comprehensively modeling the physical world as a group of interconnected digital models. In a two-part series of papers, we examine the fundamental role of different modeling techniques, twinning enabling technologies, and uncertainty quantification and optimization methods commonly used in digital twins. This first paper presents a thorough literature review of digital twin trends across many disciplines currently pursuing this area of research. Then, digital twin modeling and twinning enabling technologies are further analyzed by classifying them into two main categories: physical-to-virtual, and virtual-to-physical, based on the direction in which data flows. Finally, this paper provides perspectives on the trajectory of digital twin technology over the next decade, and introduces a few emerging areas of research which will likely be of great use in future digital twin research. In part two of this review, the role of uncertainty quantification and optimization are discussed, a battery digital twin is demonstrated, and more perspectives on the future of digital twin are shared. Code and preprocessed data for generating all the results and figures presented in the battery digital twin case study in part 2 of this review are available on Github . 

A comprehensive review of digital twin — part 1: modeling and twinning enabling technologies

As an emerging technology in the era of Industry 4.0, digital twin is gaining unprecedented attention because of its promise to further optimize process design, quality control, health monitoring, decision- and policy-making, and more, by comprehensively modeling the physical world as a group of interconnected digital models. In a two-part series of papers, we examine the fundamental role of different modeling techniques, twinning enabling technologies, and uncertainty quantification and optimization methods commonly used in digital twins. This second paper presents a literature review of key enabling technologies of digital twins, with an emphasis on uncertainty quantification, optimization methods, open-source datasets and tools, major findings, challenges, and future directions. Discussions focus on current methods of uncertainty quantification and optimization and how they are applied in different dimensions of a digital twin. Additionally, this paper presents a case study where a battery digital twin is constructed and tested to illustrate some of the modeling and twinning methods reviewed in this two-part review. Code and preprocessed data for generating all the results and figures presented in the case study are available on Github . 

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A comprehensive review of digital twin—part 2: roles of uncertainty quantification and optimization, a battery digital twin, and perspectives

Uncertainty is prevalent in engineering design, statistical learning, and decision making broadly. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative optimization models expressed using measure of risk and related concepts. We survey the rapid development of risk measures over the last quarter century. From its beginning in financial engineering, we recount their spread to nearly all areas of engineering and applied mathematics. Solidly rooted in convex analysis, risk measures furnish a general framework for handling uncertainty with significant computational and theoretical advantages. We describe the key facts, list several concrete algorithms, and provide an extensive list of references for further reading. The survey recalls connections with utility theory and distributionally robust optimization, points to emerging applications areas such as fair machine learning, and defines measures of reliability.

Risk-Adaptive Approaches to Learning and Decision Making: A Survey

Conventional frequentist learning is known to yield poorly calibrated models that fail to reliably quantify the uncertainty of their decisions. Bayesian learning can improve calibration, but formal guarantees apply only under restrictive assumptions about correct model speciﬁcation. Conformal prediction (CP) offers a general framework for the design of set predictors with calibration guarantees that hold regardless of the underlying data generation mechanism. However, when training data are limited, CP tends to produce large, and hence uninformative, predicted sets. This paper introduces a novel meta-learning solution that aims at reducing the set prediction size. Unlike prior work, the proposed meta-learning scheme, referred to as meta-XB, (i) builds on cross-validation-based CP, rather than the less efﬁcient validation-based CP; and (ii) preserves formal per-task calibration guarantees, rather than less stringent task-marginal guarantees.

Few-Shot Calibration of Set Predictors via Meta-Learned Cross-Validation-Based Conformal Prediction

The design and operation of systems are conventionally viewed as a sequential decision-making process that is informed by data from physical experiments and simulations. However, the integration of these high-dimensional and heterogeneous data sources requires the consideration of the impact of a decision on a system’s remaining life cycle. Consequently, this introduces a degree of complexity that in most cases can only be solved through a simplified decision-making approach. In this perspective paper, we use the digital twin concept to formulate an integrated perspective for the design of systems. Specifically, we show how the digital twin concept enables the integration of system design decisions and operational decisions during each stage of a system’s life cycle. This perspective has two advantages: (i) improved system performance as more effective decisions can be made, and (ii) improved data efficiency as it provides a framework to utilize data from multiple sources and design instances. The novelty in the presented perspective is that it necessitates an approach that enables fleet-level (i.e., decisions that influence a plurality of systems) and system-level decisions. From a formal definition, we identify a set of eight capabilities that are vital constructs to bring about the potential, as defined in this paper, that the digital twin concept holds for the design of systems. Subsequently, by comparing these capabilities with the available literature on digital twins, we identify research questions and forecast their broader impact. By conceptualizing the potential that the digital twin concept holds for the design of systems, we hope to contribute to the convergence of definitions, problem formulations, research gaps, and value propositions in this burgeoning field. Addressing the research questions, associated with the digital twin-inspired formulation for the design of systems, will bring about more advanced systems that can meet some of the societies’ grand challenges. 

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Digital twins for the designs of systems: a perspective

Automated operational modal analysis using variational Gaussian mixture model

This paper proposes a seismic resilience grading method for 110Kv and above high-voltage substations, and establishes a quantitative index for evaluating the substation seismic resilience --- seismic resilience index, presents a calculation formula for substation seismic resilience index which takes the respective weight coefficients and seismic damage indexes of buildings and high-voltage electrical equipment as the parameters, determines the relationship between the resilience index and the resilience grade, and establishes the substation resilience matrix through making statistics of actual seismic damage and recovered samples of the substations. The results show that with the decrease of resilience index, the resilience of substation becomes worse and worse. When the resilience index is lower than 0.45, the substation reaches the threshold of extremely difficult to recover. The higher the seismic intensity is, the lower the resilience is, and the longer the recovery time is. In 9 degree seismic intensity region, the substation resilience index begins to decrease rapidly, most substations are recoverable and difficult to recover, and the substations in 10 degrees and above seismic intensity region are extremely difficult to recover.

Zhenxiu Hu

Papers

A comprehensive review of digital twin — part 1: modeling and twinning enabling technologies

A comprehensive review of digital twin—part 2: roles of uncertainty quantification and optimization, a battery digital twin, and perspectives

Automated operational modal analysis using variational Gaussian mixture model

Study on Substation Seismic Resilience Evaluation Index and Resilience Matrix