Bayesian on-line anticipation of critical transitions

The design of reliable indicators to anticipate critical transitions in complex systems is an important task in order to detect imminent regime shifts and to intervene at an early stage to either prevent them or mitigate their consequences. We present a data-driven method based on the estimation of a parameterized nonlinear stochastic differential equation that allows for a robust anticipation of critical transitions even in the presence of strong noise which is a characteristic of many real world systems. Since the parameter estimation is done by a Markov chain Monte Carlo approach, we have access to credibility bands allowing for a better interpretation of the reliability of the results. We also show that the method can yield meaningful results under correlated noise. By introducing a Bayesian linear segment fit it is possible to give an estimate for the time horizon in which the transition will probably occur based on the current state of information. This approach is also able to handle nonlinear time dependencies of the parameter that controls the transition. The method can be used as a tool for on-line analysis to detect changes in the resilience of the system and to provide information on the probability of the occurrence of critical transitions in future. Additionally, it can give valuable information about the possibility of noise induced transitions. The discussed methods are made easily accessible via a flexibly adaptable open source toolkit named 'antiCPy' which is implemented in the programming language Python

Methods and Technologies for Mastering Uncertainty

Uncertainty affects all phases of the product life cycle of technical systems, from design and production to their usage, even beyond the phase boundaries. Its identification, analysis and representation are discussed in the previous chapter. Based on the gained knowledge, our specific approach on mastering uncertainty can be applied. These approaches follow common strategies that are described in the subsequent chapter, but require individual methods and technologies. In this chapter, first legal and technical aspects for mastering uncertainty are discussed. Then, techniques for product design of technical systems under uncertainty are presented. The propagation of uncertainty is analysed for particular examples of process chains. Finally, semi-active and active technical systems and their relation to uncertainty are discussed