Sensor Network and Data Quality Assurance for Digital Twins of Cities

This chapter briefly discusses the design of sensor networks to dynamically deploy and discharge sensors according to needs and model instructions to observe system dynamics over time and space. To make simulations and predictions via digital twins reliable, besides having a model which correctly captures the underlying dynamics of the physical system, accuracy of data which are used to learn the dynamics, especially chaotic dynamics, by the digital twins is pivotal to their trustworthiness. Since data, particularly sensor data, are often noisy or embedded with measurement errors, how to handle noisy data and how to propagate errors in data processing and machine learning constitute a crucial issue in building digital twins of cities. Based on the law of error propagation briefly stated in this chapter, rigorous statistical bounds and level of confidence for the end results of certain data operations can be established by the errors propagated from the inputs to the outputs via a transformation function. In the context of uncovering nonlinear dynamics, the transformation functions can be any of the learning algorithms from which we can derive system-theoretic/process error bounds and error estimates for the reduced-order models in the time or frequency domains.