Hilbert Transform applications in signal analysis and non-parametric identification of linear and nonlinear systems

Hilbert Huang Transform faces several challenges in dealing with closely-spaced frequency components, short-time and weak disturbances, and interrelationships between two time-varying modes of nonlinear vibration due to its mixed mode problem associated with empirical mode decomposition (EMD). To address these challenges, analytical mode decomposition (AMD) based on Hilbert Transform is proposed and developed for an adaptive data analysis of both stationary and non-stationary responses. With a suite of predetermined bisecting frequencies, AMD can analytically extract the individual components of a structural response between any two bisecting frequencies and function like an adaptive bandpass filter that can deal with frequency-modulated responses with significant frequency overlapping. It is simple in concept, rigorous in mathematics, and reliable in signal processing. In this dissertation, AMD is studied for various effects of bisecting frequency selection, response sampling rate, and noise. Its robustness, accuracy, efficiency, and adaptability in signal analysis and system identification of structures are compared with other time-frequency analysis techniques such as EMD and wavelet analysis. Numerical examples and experimental validations are extensively conducted for structures under impulsive, harmonic, and earthquake loads, respectively. They consistently demonstrate AMD\u27s superiority to other time-frequency analysis techniques. In addition, to identify time-varying structural properties with a narrow band excitation, a recursive Hilbert Huang Transform method is also developed. Its effectiveness and accuracy are illustrated by both numerical examples and shake table tests of a power station structure --Abstract, page iii

A Wavelet Packet Based Sifting Process and Its Application for Structural Health Monitoring

In this work an innovative wavelet packet based sifting process for signal decomposition has been developed and its application for health monitoring of time-varying structures is presented. With the proposed sifting process, a signal can be decomposed into its mono-frequency components by examining the energy content in the wavelet packet components of a signal, and imposing certain decomposition criteria. The method is illustrated for simulation data of a linear three degree-of-freedom spring-mass-damper system and the results are compared with those obtained using the empirical mode decomposition (EMD) method. Both methods provide good approximations, as compared with the exact solution for modal responses from a conventional modal analysis. Incorporated with the classical Hilbert transform, the proposed sifting process may be effectively used for structural health monitoring by monitoring instantaneous modal parameters of the structure for both, cases of abrupt structural stiffness loss and progressive stiffness degradation. The effectiveness of this method for practical application is evaluated by applying the methodology for experimental data and the results obtained matched with the field observations. The proposed methodology has shown better results in a comparison study which is done to evaluate performance of the proposed approach with other available SHM techniques, namely EMD technique and Continuous Wavelet Transform (CWT) method, for cases characterized by different damage scenarios and noise conditions

A Comparative Analysis of Signal Decomposition Techniques for Structural Health Monitoring on an Experimental Benchmark

Signal Processing is, arguably, the fundamental enabling technology for vibration-based Structural Health Monitoring (SHM), which includes damage detection and more advanced tasks. However, the investigation of real-life vibration measurements is quite compelling. For a better understanding of its dynamic behaviour, a multi-degree-of-freedom system should be efficiently decomposed into its independent components. However, the target structure may be affected by (damage-related or not) nonlinearities, which appear as noise-like distortions in its vibrational response. This response can be nonstationary as well and thus requires a time-frequency analysis. Adaptive mode decomposition methods are the most apt strategy under these circumstances. Here, a shortlist of three well-established algorithms has been selected for an in-depth analysis. These signal decomposition approaches—namely, the Empirical Mode Decomposition (EMD), the Hilbert Vibration Decomposition (HVD), and the Variational Mode Decomposition (VMD)—are deemed to be the most representative ones because of their extensive use and favourable reception from the research community. The main aspects and properties of these data-adaptive methods, as well as their advantages, limitations, and drawbacks, are discussed and compared. Then, the potentialities of the three algorithms are assessed firstly on a numerical case study and then on a well-known experimental benchmark, including nonlinear cases and nonstationary signals

Densely distributed and real-time scour hole monitoring using piezoelectric rod sensors

This study aims to validate a piezoelectric driven-rod scour monitoring system that can sense changes in scour depth along the entire rod at its instrumented location. The proposed sensor is a polymeric slender rod with a thin strip of polyvinylidene fluoride that runs through its midline. Extraction of the fundamental frequency allows the direct calculation of the exposed length (or scour depth) of the slender rod undergoing fluid flow excitation. First, laboratory validation in dry conditions is presented. Second, hydrodynamic testing of the sensor system in a soil-bed flume is discussed. Each rod was installed using a three-dimensional-printed footing designed for ease of installation and stabilization during testing. The sensors were installed in a layout designed to capture symmetric scour conditions around a scaled pier. In order to analyze the system out of steady-state conditions, water velocity was increased in stages during testing to induce different degrees of scour. As ambient water flow excited the portion of the exposed rods, the embedded piezoelectric element outputted a time-varying voltage signal. Different methods were then employed to extract the fundamental frequency of each rod, and the results were compared. Further testing was also performed to characterize the relationship between frequency outputs and flow velocity, which were previously thought to be independent. In general, the proposed driven-rod scour monitoring system successfully captured changing frequencies under varied flow conditions

Friction, Vibration and Dynamic Properties of Transmission System under Wear Progression

This reprint focuses on wear and fatigue analysis, the dynamic properties of coating surfaces in transmission systems, and non-destructive condition monitoring for the health management of transmission systems. Transmission systems play a vital role in various types of industrial structure, including wind turbines, vehicles, mining and material-handling equipment, offshore vessels, and aircrafts. Surface wear is an inevitable phenomenon during the service life of transmission systems (such as on gearboxes, bearings, and shafts), and wear propagation can reduce the durability of the contact coating surface. As a result, the performance of the transmission system can degrade significantly, which can cause sudden shutdown of the whole system and lead to unexpected economic loss and accidents. Therefore, to ensure adequate health management of the transmission system, it is necessary to investigate the friction, vibration, and dynamic properties of its contact coating surface and monitor its operating conditions

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

Instationary modal Analysis for Impulse-type stimulated structures

In order to determine modal parameters, classical experimental modal analysis can be used in engineering application. This method finds a system frequency response function using fast Fourier Transform (FFT). The Fourier Transform is one type of global data analysis method. The frequency resolution is equal to the reciprocal of the total sample time. So applying the FFT is not suitable for any transient signal to reveal local characteristics. However, in modern manufacturing industries, processing forces are rapidly changing. The dynamic behavior may vary rapidly in a short time due to variations in the machining parameters and changes in boundary conditions. These nonlinear and non-stationary dynamic parameters are not constant during machining operations identification using FFT. In this research, an innovative transient signal analysis approach has been developed, which is based on an application of the least squares estimation. The proposed method provides transient information with high resolution and to identify the time-varying modal parameters during machining. Least squares estimation can be augmented with a sliding-window operation (SWLSE) to reveal the actual system dynamic behavior at any moment. The accuracy of this method depends on the window size, the noise ratio and the sampling rate etc. The estimation accuracy of modal parameters is discussed in this work. To examine the efficiency of the SWLSE method experimental tests are performed on a laboratory beam system and the results are compared with the classical experimental modal analysis (CEMA) method. The laboratory beam system is designed and assembled that the stiffness and damping ratio of the structure can be adjusted. Additionally, the proposed method is applied to the identification of the actual modal parameters of machine tools during machining operations. In another application, the proposed method provides also the process varied damping information in a process monitoring

Structural health monitoring and bridge condition assessment

Thesis (Ph.D.) University of Alaska Fairbanks, 2016This research is mainly in the field of structural identification and model calibration, optimal sensor placement, and structural health monitoring application for large-scale structures. The ultimate goal of this study is to identify the structure behavior and evaluate the health condition by using structural health monitoring system. To achieve this goal, this research firstly established two fiber optic structural health monitoring systems for a two-span truss bridge and a five-span steel girder bridge. Secondly, this research examined the empirical mode decomposition (EMD) method’s application by using the portable accelerometer system for a long steel girder bridge, and identified the accelerometer number requirements for comprehensively record bridge modal frequencies and damping. Thirdly, it developed a multi-direction model updating method which can update the bridge model by using static and dynamic measurement. Finally, this research studied the optimal static strain sensor placement and established a new method for model parameter identification and damage detection.Chapter 1: Introduction -- Chapter 2: Structural Health Monitoring of the Klehini River Bridge -- Chapter 3: Ambient Loading and Modal Parameters for the Chulitna River Bridge -- Chapter 4: Multi-direction Bridge Model Updating using Static and Dynamic Measurement -- Chapter 5: Optimal Static Strain Sensor Placement for Bridge Model Parameter Identification by using Numerical Optimization Method -- Chapter 6: Conclusions and Future Work