Ground-penetrating radar time-frequency analysis method based on synchrosqueezing wavelet transformation

Compared with conventional time-frequency analysis method, synchrosqueezing wavelet transformation (SST) exhibits high resolution capability and good application effect. In this study, SST is introduced to ground-penetrating radar (GPR) processing. This method is applied to analyze a continuous electromagnetic signal. SST can obtain a higher resolution and a better processing effect than conventional wavelet transform and short-time Fourier analysis. In the application of GPR forward analysis data, the transform can correctly distinguish different interfaces and objects. Its resolution increases as frequency increases. However, compression wavelet modulus gradually decays as frequency increases. The proposed method is applied to detect tunnel lining under actual conditions and in a strong noise background. Indeed, the method can efficiently identify interfaces and abnormalities

Low strain pile testing based on synchrosqueezing wavelet transformation analysis

Low strain detection, an indirect and nondestructive testing method, is one of the main pile integrity testing methods. We propose low strain testing analysis based on a synchrosqueezing wavelet transformation (SST). Through a typical model pile test, the SST is applied to identify pile bottom signal reflection time and to separate signal from noise. It is also compared with the conventional wavelet de-noising and the empirical mode decomposition (EMD) de-noising method. Results show that the SST technique can be used to identify the reflected signal of the pile bottom, achieve signal and noise separation, and improve signal-to-noise ratio. The method has significant advantage in low strain detection signal processing compared to other methods

Ground-penetrating radar time-frequency analysis method based on synchrosqueezing wavelet transformation

Compared with conventional time-frequency analysis method, synchrosqueezing wavelet transformation (SST) exhibits high resolution capability and good application effect. In this study, SST is introduced to ground-penetrating radar (GPR) processing. This method is applied to analyze a continuous electromagnetic signal. SST can obtain a higher resolution and a better processing effect than conventional wavelet transform and short-time Fourier analysis. In the application of GPR forward analysis data, the transform can correctly distinguish different interfaces and objects. Its resolution increases as frequency increases. However, compression wavelet modulus gradually decays as frequency increases. The proposed method is applied to detect tunnel lining under actual conditions and in a strong noise background. Indeed, the method can efficiently identify interfaces and abnormalities

Ground-penetrating radar time-frequency analysis method based on synchrosqueezing wavelet transformation

Compared with conventional time-frequency analysis method, synchrosqueezing wavelet transformation (SST) exhibits high resolution capability and good application effect. In this study, SST is introduced to ground-penetrating radar (GPR) processing. This method is applied to analyze a continuous electromagnetic signal. SST can obtain a higher resolution and a better processing effect than conventional wavelet transform and short-time Fourier analysis. In the application of GPR forward analysis data, the transform can correctly distinguish different interfaces and objects. Its resolution increases as frequency increases. However, compression wavelet modulus gradually decays as frequency increases. The proposed method is applied to detect tunnel lining under actual conditions and in a strong noise background. Indeed, the method can efficiently identify interfaces and abnormalities

Low strain pile testing based on synchrosqueezing wavelet transformation analysis

Low strain detection, an indirect and nondestructive testing method, is one of the main pile integrity testing methods. We propose low strain testing analysis based on a synchrosqueezing wavelet transformation (SST). Through a typical model pile test, the SST is applied to identify pile bottom signal reflection time and to separate signal from noise. It is also compared with the conventional wavelet de-noising and the empirical mode decomposition (EMD) de-noising method. Results show that the SST technique can be used to identify the reflected signal of the pile bottom, achieve signal and noise separation, and improve signal-to-noise ratio. The method has significant advantage in low strain detection signal processing compared to other methods

Low strain pile testing based on synchrosqueezing wavelet transformation analysis

Low strain detection, an indirect and nondestructive testing method, is one of the main pile integrity testing methods. We propose low strain testing analysis based on a synchrosqueezing wavelet transformation (SST). Through a typical model pile test, the SST is applied to identify pile bottom signal reflection time and to separate signal from noise. It is also compared with the conventional wavelet de-noising and the empirical mode decomposition (EMD) de-noising method. Results show that the SST technique can be used to identify the reflected signal of the pile bottom, achieve signal and noise separation, and improve signal-to-noise ratio. The method has significant advantage in low strain detection signal processing compared to other methods

Data-driven time-frequency analysis of multivariate data

Empirical Mode Decomposition (EMD) is a data-driven method for the decomposition and time-frequency analysis of real world nonstationary signals. Its main advantages over other time-frequency methods are its locality, data-driven nature, multiresolution-based decomposition, higher time-frequency resolution and its ability to capture oscillation of any type (nonharmonic signals). These properties have made EMD a viable tool for real world nonstationary data analysis. Recent advances in sensor and data acquisition technologies have brought to light new classes of signals containing typically several data channels. Currently, such signals are almost invariably processed channel-wise, which is suboptimal. It is, therefore, imperative to design multivariate extensions of the existing nonlinear and nonstationary analysis algorithms as they are expected to give more insight into the dynamics and the interdependence between multiple channels of such signals. To this end, this thesis presents multivariate extensions of the empirical mode de- composition algorithm and illustrates their advantages with regards to multivariate non- stationary data analysis. Some important properties of such extensions are also explored, including their ability to exhibit wavelet-like dyadic filter bank structures for white Gaussian noise (WGN), and their capacity to align similar oscillatory modes from multiple data channels. Owing to the generality of the proposed methods, an improved multi- variate EMD-based algorithm is introduced which solves some inherent problems in the original EMD algorithm. Finally, to demonstrate the potential of the proposed methods, simulations on the fusion of multiple real world signals (wind, images and inertial body motion data) support the analysis

Discerning non-autonomous dynamics

Structure and function go hand in hand. However, while a complex structure can be relatively safely broken down into the minutest parts, and technology is now delving into nanoscales, the function of complex systems requires a completely different approach. Here the complexity clearly arises from nonlinear interactions, which prevents us from obtaining a realistic description of a system by dissecting it into its structural component parts. At best, the result of such investigations does not substantially add to our understanding or at worst it can even be misleading. Not surprisingly, the dynamics of complex systems, facilitated by increasing computational efficiency, is now readily tackled in the case of measured time series. Moreover, time series can now be collected in practically every branch of science and in any structural scale—from protein dynamics in a living cell to data collected in astrophysics or even via social networks. In searching for deterministic patterns in such data we are limited by the fact that no complex system in the real world is autonomous. Hence, as an alternative to the stochastic approach that is predominantly applied to data from inherently non-autonomous complex systems, theory and methods specifically tailored to non-autonomous systems are needed. Indeed, in the last decade we have faced a huge advance in mathematical methods, including the introduction of pullback attractors, as well as time series methods that cope with the most important characteristic of non-autonomous systems—their time-dependent behaviour. Here we review current methods for the analysis of non-autonomous dynamics including those for extracting properties of interactions and the direction of couplings. We illustrate each method by applying it to three sets of systems typical for chaotic, stochastic and non-autonomous behaviour. For the chaotic class we select the Lorenz system, for the stochastic the noiseforced Duffing system and for the non-autonomous the Poincaré oscillator with quasiperiodic forcing. In this way we not only discuss and review each method, but also present properties which help to clearly distinguish the three classes of systems when analysed in an inverse approach—from measured, or numerically generated data. In particular, this review provides a framework to tackle inverse problems in these areas and clearly distinguish non-autonomous dynamics from chaos or stochasticity

Adaptive data analysis for damage detection and system identification in civil infrastructure

Time-varying structural systems are often encountered in civil engineering. As extreme events occur more frequently and severely in recent years, more structures are loaded beyond their elastic conditions and may thus experience damage in the years to come. Even if structures remain elastic, energy dissipation devices installed on structures often reveal hysteretic behaviors under earthquake loads. Therefore, it is imperative to develop and implement novel technologies that enable the identification and damage detection of time-varying systems. In this dissertation, adaptive wavelet transform (AWT) and multiple analytical mode decomposition (M-AMD) are proposed and applied to identify system properties and detect damage in structures. AWT is an optimized time-frequency representation of dynamic responses for the extraction of features. It is defined as an average of overlapped short-time wavelet transforms with time-varying wavelet parameters in order to extract time-dependent frequencies. The effectiveness of AWT is demonstrated by various analytical signals, acoustic emission and impact echo responses. M-AMD is a response decomposition method for the identification of weakly to moderately nonlinear oscillators based on vibration responses. It can be used to accurately separate the low and high frequency components of time-varying stiffness and damping coefficients in dynamic systems. The efficiency and accuracy of the proposed M-AMD are evaluated with three characteristic nonlinear oscillators and a 1/4-scale 3-story building model with frictional damping under seismic excitations. Finally, AWT-based M-AMD is applied to decompose the measured dynamic responses of a 1/20-scale cable-stayed bridge model tested on four shake tables and evaluate the progression of damage under increasing earthquake loads --Abstract, page iii

A Statistical Perspective of the Empirical Mode Decomposition

This research focuses on non-stationary basis decompositions methods in time-frequency analysis. Classical methodologies in this field such as Fourier Analysis and Wavelet Transforms rely on strong assumptions of the underlying moment generating process, which, may not be valid in real data scenarios or modern applications of machine learning. The literature on non-stationary methods is still in its infancy, and the research contained in this thesis aims to address challenges arising in this area. Among several alternatives, this work is based on the method known as the Empirical Mode Decomposition (EMD). The EMD is a non-parametric time-series decomposition technique that produces a set of time-series functions denoted as Intrinsic Mode Functions (IMFs), which carry specific statistical properties. The main focus is providing a general and flexible family of basis extraction methods with minimal requirements compared to those within the Fourier or Wavelet techniques. This is highly important for two main reasons: first, more universal applications can be taken into account; secondly, the EMD has very little a priori knowledge of the process required to apply it, and as such, it can have greater generalisation properties in statistical applications across a wide array of applications and data types. The contributions of this work deal with several aspects of the decomposition. The first set regards the construction of an IMF from several perspectives: (1) achieving a semi-parametric representation of each basis; (2) extracting such semi-parametric functional forms in a computationally efficient and statistically robust framework. The EMD belongs to the class of path-based decompositions and, therefore, they are often not treated as a stochastic representation. (3) A major contribution involves the embedding of the deterministic pathwise decomposition framework into a formal stochastic process setting. One of the assumptions proper of the EMD construction is the requirement for a continuous function to apply the decomposition. In general, this may not be the case within many applications. (4) Various multi-kernel Gaussian Process formulations of the EMD will be proposed through the introduced stochastic embedding. Particularly, two different models will be proposed: one modelling the temporal mode of oscillations of the EMD and the other one capturing instantaneous frequencies location in specific frequency regions or bandwidths. (5) The construction of the second stochastic embedding will be achieved with an optimisation method called the cross-entropy method. Two formulations will be provided and explored in this regard. Application on speech time-series are explored to study such methodological extensions given that they are non-stationary