Extreme Value Laws for Superstatistics

Dynamic Threshold Cable-Stayed Bridge Health Monitoring System Based on Temperature Effect Correction

The early health warning of a cable-stayed bridge is of great significance for discovering the abnormal condition of the structure, eliminating the risk factors, and ensuring the normal operation of the bridge in order to set a reasonable safety monitoring threshold to ensure the safety warning and condition assessment of the bridge structure. A method of dynamic early warning by considering the temperature effect is adopted in this paper on the basis of the benchmark threshold. Based on the long-term deflection monitoring data of a bridge in Wuhan, the generalized Pareto distribution (GPD) extreme value analysis theory is used to set the benchmark threshold. Then, by constructing the seasonal autoregressive integrated moving average (SARIMA) long-span bridge temperature effect prediction model, the reference threshold is dynamically adjusted. Finally, it is compared with the traditional fixed threshold monitoring system. The results show that the dynamic threshold has stronger adaptability to the monitoring of cable-stayed bridges and can also achieve effective monitoring of local mutations in other periods. Dynamic threshold early warning can reduce the shortcomings of traditional early warning methods such as underreporting and misreporting. At the same time, the GPD extreme value analysis theory overcomes the disadvantage that the extreme value information is not fully utilized. It has an important application value for bridge health monitoring.

Log-Normal Superstatistics for Brownian Particles in a Heterogeneous Environment

Superstatistical approaches have played a crucial role in the investigations of mixtures of Gaussian processes. Such approaches look to describe non-Gaussian diffusion emergence in single-particle tracking experiments realized in soft and biological matter. Currently, relevant progress in superstatistics of Gaussian diffusion processes has been investigated by applying χ2-gamma and χ2-gamma inverse superstatistics to systems of particles in a heterogeneous environment whose diffusivities are randomly distributed; such situations imply Brownian yet non-Gaussian diffusion. In this paper, we present how the log-normal superstatistics of diffusivities modify the density distribution function for two types of mixture of Brownian processes. Firstly, we investigate the time evolution of the ensemble of Brownian particles with random diffusivity through the analytical and simulated points of view. Furthermore, we analyzed approximations of the overall probability distribution for log-normal superstatistics of Brownian motion. Secondly, we propose two models for a mixture of scaled Brownian motion and to analyze the log-normal superstatistics associated with them, which admits an anomalous diffusion process. The results found in this work contribute to advances of non-Gaussian diffusion processes and superstatistical theory.

Wind Power Persistence Characterized by Superstatistics

Mitigating climate change demands a transition towards renewable electricity generation, with wind power being a particularly promising technology. Long periods either of high or of low wind therefore essentially define the necessary amount of storage to balance the power system. While the general statistics of wind velocities have been studied extensively, persistence (waiting) time statistics of wind is far from well understood. Here, we investigate the statistics of both high- and low-wind persistence. We find heavy tails and explain them as a superposition of different wind conditions, requiring q-exponential distributions instead of exponential distributions. Persistent wind conditions are not necessarily caused by stationary atmospheric circulation patterns nor by recurring individual weather types but may emerge as a combination of multiple weather types and circulation patterns. This also leads to Fréchet instead of Gumbel extreme value statistics. Understanding wind persistence statistically and synoptically may help to ensure a reliable and economically feasible future energy system, which uses a high share of wind generation.

Superstatistical Energy Distributions of an Ion in an Ultracold Buffer Gas

An ion in a radio frequency ion trap interacting with a buffer gas of ultracold neutral atoms is a driven dynamical system which has been found to develop a nonthermal energy distribution with a power law tail. The exact analytical form of this distribution is unknown, but has often been represented empirically by q-exponential (Tsallis) functions. Based on the concepts of superstatistics, we introduce a framework for the statistical mechanics of an ion trapped in an rf field subject to collisions with a buffer gas. We derive analytic ion secular energy distributions from first principles both neglecting and including the effects of the thermal energy of the buffer gas. For a buffer gas with a finite temperature, we prove that Tsallis statistics emerges from the combination of a constant heating term and multiplicative energy fluctuations. We show that the resulting distributions essentially depend on experimentally controllable parameters paving the way for an accurate control of the statistical properties of ion-atom hybrid systems.