Search Results (5)

Tropical cyclone prediction is often described as chaotic and unpredictable on time scales that cross into stochastic regimes. Predictions are bounded by the depth of understanding and the limitations of the physical dynamics that govern them. Slight changes in global atmospheric and oceanic conditions may significantly alter tropical cyclone genesis regions and intensity. The purpose of this paper is to characterize the predictability of seasonal storm characteristics in the North Atlantic basin by utilizing the Largest Lyapunov Exponent and Takens’ Theorem, which is rarely used in weather or climatological analysis. This is conducted for a post-weather satellite era (1960–2022). Based on the accumulated cyclone energy (ACE) time series in the North Atlantic basin, cyclone activity can be described as predictable at certain timescales. Insight and understanding into this coupled non-linear system through an analysis of time delay, embedded dimension, and Lyapunov exponent-reconstructed phase space have provided critical information for the system’s predictability. Full article

The atmosphere is a complex nonlinear system, with the information of its temperature, water vapor, pressure, and cloud being crucial aspects of remote-sensing data analysis. There exist intricate interactions among these internal components, such as convection, radiation, and humidity exchange. Atmospheric phenomena span multiple spatial and temporal scales, from small-scale thunderstorms to large-scale events like El Niño. The dynamic interactions across different scales, along with external disturbances to the atmospheric system, such as variations in solar radiation and Earth surface conditions, contribute to the chaotic nature of the atmosphere, making long-term predictions challenging. Grasping the intrinsic chaotic dynamics is essential for advancing atmospheric analysis, which holds profound implications for enhancing meteorological forecasts, mitigating disaster risks, and safeguarding ecological systems. To validate the chaotic nature of the atmosphere, this paper reviewed the definitions and main features of chaotic systems, elucidated the method of phase space reconstruction centered on Takens’ theorem, and categorized the qualitative and quantitative methods for determining the chaotic nature of time series data. Among quantitative methods, the Wolf method is used to calculate the Largest Lyapunov Exponents, while the G–P method is used to calculate the correlation dimensions. A new method named Improved Saturated Correlation Dimension method was proposed to address the subjectivity and noise sensitivity inherent in the traditional G–P method. Subsequently, the Largest Lyapunov Exponents and saturated correlation dimensions were utilized to conduct a quantitative analysis of FY-4A and Himawari-8 remote-sensing infrared observation data, and ERA5 reanalysis data. For both short-term remote-sensing data and long-term reanalysis data, the results showed that more than 99.91% of the regional points have corresponding sequences with positive Largest Lyapunov exponents and all the regional points have correlation dimensions that tended to saturate at values greater than 1 with increasing embedding dimensions, thereby proving that the atmospheric system exhibits chaotic properties on both short and long temporal scales, with extreme sensitivity to initial conditions. This conclusion provided a theoretical foundation for the short-term prediction of atmospheric infrared radiation field variables and the detection of weak, time-sensitive signals in complex atmospheric environments. Full article

This study compares three methods for optimizing the hyper-parameters m (embedding dimension) and $\tau$ (time delay) from Taken’s Theorem for time-series forecasting to train a Support Vector Regression system (SVR). Firstly, we use a method which utilizes Mutual Information for optimizing $\tau$ and a technique referred to as “Dimension Congruence” to optimize m. Secondly, we employ a grid search and random search, combined with a cross-validation scheme, to optimize m and $\tau$ hyper-parameters. Lastly, various real-world time series are used to analyze the three proposed strategies. Full article

In order to accurately diagnose the health of high-order statically indeterminate structures, most existing structural health monitoring (SHM) methods require multiple sensors to collect enough information. However, comprehensive data collection from multiple sensors for high degree-of-freedom structures is not typically available in practice. We propose a method that reconciles the two seemingly conflicting difficulties. Takens’ embedding theorem is used to augment the dimensions of data collected from a single sensor. Taking advantage of the success of machine learning in image classification, high-dimensional reconstructed attractors were converted into images and fed into a convolutional neural network (CNN). Attractor classification was performed for 10 damage cases of a 3-story shear frame structure. Numerical results show that the inherently high dimension of the CNN model allows the handling of higher dimensional data. Information on both the level and the location of damage was successfully embedded. The same methodology will allow the extraction of data with unsupervised CNN classification to be consistent with real use cases. Full article

The precision of soft measurement for biochemical oxygen demand (BOD) is always restricted due to various factors in the wastewater treatment plant (WWTP). To solve this problem, a new soft measurement modeling method based on chaos theory is proposed and is applied to BOD measurement in this paper. Phase space reconstruction (PSR) based on Takens embedding theorem is used to extract more information from the limited datasets of the chaotic system. The WWTP is first testified as a chaotic system by the correlation dimension (D), the largest Lyapunov exponents (λ₁), the Kolmogorov entropy (K) of the BOD and other water quality parameters time series. Multivariate chaotic time series modeling method with principal component analysis (PCA) and artificial neural network (ANN) is then adopted to estimate the value of the effluent BOD. Simulation results show that the proposed approach has higher accuracy and better prediction ability than the corresponding modeling approaches not based on chaos theory. Full article