This paper presents a review of the state of the art for digital twins in the application domain of engineering dynamics. The focus on applications in dynamics is because: (i) they offer some of the most challenging aspects of creating an effective digital twin, and (ii) they are relevant to important industrial applications such as energy generation and transport systems. The history of the digital twin is discussed first, along with a review of the associated literature; the process of synthesizing a digital twin is then considered, including definition of the aims and objectives of the digital twin. An example of the asset management phase for a wind turbine is included in order to demonstrate how the synthesis process might be applied in practice. In order to illustrate modeling issues arising in the construction of a digital twin, a detailed case study is presented, based on a physical twin, which is a small-scale three-story structure. This case study shows the progression toward a digital twin highlighting key processes including system identification, data-augmented modeling, and verification and validation. Finally, a discussion of some open research problems and technological challenges is given, including workflow, joints, uncertainty management, and the quantification of trust. In a companion paper, as part of this special issue, a mathematical framework for digital twin applications is developed, and together the authors believe this represents a firm framework for developing digital twin applications in the area of engineering dynamics.

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A primary motivation for the development and implementation of structural health monitoring systems, is the prospect of gaining the ability to make informed decisions regarding the operation and maintenance of structures and infrastructure. Unfortunately, descriptive labels for measured data corresponding to health-state information for the structure of interest are seldom available prior to the implementation of a monitoring system. This issue limits the applicability of the traditional supervised and unsupervised approaches to machine learning in the development of statistical classifiers for decision-supporting SHM systems.The current paper presents a risk-based formulation of active learning, in which the querying of class-label information is guided by the expected value of said information for each incipient data point. When applied to structural health monitoring, the querying of class labels can be mapped onto the inspection of a structure of interest in order to determine its health state. In the current paper, the risk-based active learning process is explained and visualised via a representative numerical example and subsequently applied to the Z24 Bridge benchmark. The results of the case studies indicate that a decision-maker's performance can be improved via the risk-based active learning of a statistical classifier, such that the decision process itself is taken into account.

This paper presents a review of advances in the field of Sensor Placement Optimisation (SPO) strategies for Structural Health Monitoring (SHM). This task has received a great deal of attention in the research literature, from initial foundations in the control engineering literature to adoption in a modal or system identification context in the structural dynamics community. Recent years have seen an increasing focus on methods that are specific to damage identification, with the maximisation of correct classification outcomes being prioritised. The objectives of this article are to present the SPO for SHM problem, to provide an overview of the current state of the art in this area, and to identify promising emergent trends within the literature. The key conclusions drawn are that there remains a great deal of scope for research in a number of key areas, including the development of methods that promote robustness to modelling uncertainty, benign effects within measured data, and failures within the sensor network. There also remains a paucity of studies that demonstrate practical, experimental evaluation of developed SHM system designs. Finally, it is argued that the pursuit of novel or highly efficient optimisation methods may be considered to be of secondary importance in an SPO context, given that the optimisation effort is expended at the design stage.

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