Hilbert-Huang Transform Analysis of Dynamic and Earthquake Motion Recordings

This study examines the rationale of Hilbert-Huang transform (HHT) for analyzing dynamic and earthquake motion recordings in studies of seismology and engineering. In particular, this paper first provides the fundamentals of the HHT method, which consist of the empirical mode decomposition (EMD) and the Hilbert spectral analysis. It then uses the HHT to analyze recordings of hypothetical and real wave motion, the results of which are compared with the results obtained by the Fourier data processing technique. The analysis of the two recordings indicates that the HHT method is able to extract some motion characteristics useful in studies of seismology and engineering, which might not be exposed effectively and efficiently by Fourier data processing technique. Specifically, the study indicates that the decomposed components in EMD of HHT, namely, the intrinsic mode function (IMF) components, contain observable, physical information inherent to the original data. It also shows that the grouped IMF components, namely, the EMD-based low- and high-frequency components, can faithfully capture low-frequency pulse-like as well as high-frequency wave signals. Finally, the study illustrates that the HHT-based Hilbert spectra are able to reveal the temporal-frequency energy distribution for motion recordings precisely and clearly.     

Performance of Wavelet Transform and Empirical Mode Decomposition in Extracting Signals Embedded in Noise

Time-frequency transformations have gained increasing attention for the characterization of nonstationary signals in a broad spectrum of science and engineering applications. This study evaluates the performance of two popular transformations, the continuous wavelet transform and empirical mode decomposition with Hilbert transform (EMD+HT), in estimating instantaneous frequency (IF) in the presence of noise. The findings demonstrate that under these conditions wavelets seeking harmonic similitude at various scales produce lower variance IF estimates than EMD+HT. The shortcomings of the latter approach are attributed to its empirical, envelope-dependent nature, leading to bases that are themselves derived from noise.     

Nonlinear Identification of Lumped-Mass Buildings Using Empirical Mode Decomposition and Incomplete Measurement

Most structures exhibit some degrees of nonlinearity such as hysteretic behavior especially under damage. It is necessary to develop applicable methods that can be used to characterize these nonlinear behaviors in structures. In this paper, one such method based on the empirical mode decomposition (EMD) technique is proposed for identifying and quantifying nonlinearity in damaged structures using incomplete measurement. The method expresses nonlinear restoring forces in semireduced-order models in which a modal coordinate approach is used for the linear part while a physical coordinate representation is retained for the nonlinear part. The method allows the identification of parameters from nonlinear models through linear least-squares. It has been shown that the intrinsic mode functions (IMFs) obtained from the EMD of a response measured from a nonlinear structure are numerically close to its nonlinear modal responses. Hence, these IMFs can be used as modal coordinates as well as provide estimates for responses at unmeasured locations if the mode shapes of the structure are known. Two procedures are developed for identifying nonlinear damage in the form of nonhysteresis and hysteresis in a structure. A numerical study on a seven-story shear-beam building model with cubic stiffness and hysteretic nonlinearity and an experimental study on a three-story building model with frictional magnetoreological dampers are performed to illustrate the proposed method. Results show that the method can quite accurately identify the presence as well as the severity of different types of nonlinearity in the structure.     

Identification of Natural Frequencies and Dampings of In Situ Tall Buildings Using Ambient Wind Vibration Data

An accurate prediction for the response of tall buildings subject to strong wind gusts or earthquakes requires the information of in situ dynamic properties of the building, including natural frequencies and damping ratios. This paper presents a method of identifying natural frequencies and damping ratios of in situ tall buildings using ambient wind vibration data. Our approach is based on the empirical mode decomposition (EMD) method, the random decrement technique (RDT), and the Hilbert–Huang transform. Our method requires only one acceleration sensor. The noisy measurement of the building acceleration is first processed through the EMD method to determine the response of each mode. Then, RDT is used to obtain the free vibration modal response. Finally, the Hilbert transform is applied to each free vibration modal response to identify natural frequencies and damping ratios of in situ tall buildings. The application of the proposed methodology is demonstrated in detail using simulated response data of a 76-story benchmark building polluted by noise. Both the along-wind and across-wind vibration measurements have been illustrated. Simulation results demonstrate that the accuracy of the proposed method in identifying natural frequencies and damping ratios is remarkable. The methodology proposed herein provides a new and effective tool for the parametric identification of in situ tall buildings.     

Hilbert-Huang Based Approach for Structural Damage Detection

When measured data contain damage events of the structure, it is important to extract the information of damage as much as possible from the data. In this paper, two methods are proposed for such a purpose. The first method, based on the empirical mode decomposition (EMD), is intended to extract damage spikes due to a sudden change of structural stiffness from the measured data thereby detecting the damage time instants and damage locations. The second method, based on EMD and Hilbert transform is capable of (1) detecting the damage time instants, and (2) determining the natural frequencies and damping ratios of the structure before and after damage. The two proposed methods are applied to a benchmark problem established by the ASCE Task Group on Structural Health Monitoring. Simulation results demonstrate that the proposed methods provide new and useful tools for the damage detection and evaluation of structures.     

Efficacy of Hilbert and Wavelet Transforms for Time-Frequency Analysis

Two independently emerging time-frequency transformations in Civil Engineering, namely, the wavelet transform and empirical mode decomposition with Hilbert transform (EMD+HT), are discussed in this study. Their application to a variety of nonstationary and nonlinear signals has achieved mixed results, with some comparative studies casting significant doubt on the wavelet’s suitability for such analyses. Therefore, this study shall revisit a number of applications of EMD+HT in the published literature, offering a different perspective to these commentaries and highlighting situations where the two approaches perform comparably and others where one offers an advantage. As this study demonstrates, much of the differing performance previously observed is attributable to EMD+HT representing nonlinear characteristics solely through the instantaneous frequency, with the wavelet relying on both this measure and the instantaneous bandwidth. Further, the resolutions utilized by the two approaches present a secondary factor influencing performance.     

Proper Orthogonal Decomposition-Based Modeling, Analysis, and Simulation of Dynamic Wind Load Effects on Structures

Multicorrelated stationary random processes/fields can be decomposed into a set of subprocesses by diagonalizing their covariance or cross power spectral density (XPSD) matrices through the eigenvector/modal decomposition. This proper orthogonal decomposition (POD) technique offers physically meaningful insight into the process as each eigenmode may be characterized on the basis of its spatial distribution. It also facilitates characterization and compression of a large number of multicorrelated random processes by ignoring some of the higher eigenmodes associated with smaller eigenvalues. In this paper, the theoretical background of the POD technique based on the decomposition of the covariance and XPSD matrices is presented. A physically meaningful linkage between the wind loads and the attendant background and resonant response of structures in the POD framework is established. This helps in better understanding how structures respond to the spatiotemporally varying dynamic loads. Utilizing the POD-based modal representation, schemes for simulation and state-space modeling of random fields are presented. Finally, the accuracy and effectiveness of the reduced-order modeling in representing local and global wind loads and their effects on a wind-excited building are investigated.     

基于经验模态分解方法的拉曼光谱信号处理研究

经验模态分解(EMD)方法是一个以信号内在物理频率成分为对象的自适应时频分析方法,而常见的非平稳信号分析方法,比如小波分析,它需要选择小波基,不同小波基的分析结果不同;拉曼光谱信号是典型的非线性和非平稳信号,EMD方法充分地保留了信号本身的非线性和非平稳的特征,适应于拉曼光谱信号的分析。实验在自行研制的拉曼光谱测试平台上获得了原始的拉曼光谱信号,并通过经验模态分解将信号分解成不同频率的10个本征模式分量,信号能量集中在750cm^-1和1500cm^-1左右,最后进行了频率成分分析和去噪处理,并和小波分析方法进行了对比,验证了EMD方法的有效性和实用性,该方法在拉曼光谱信号分析中有较好的应用前景。     

基于EMD的复合故障诊断方法

针对转子不平衡故障和滚动轴承微弱损伤性故障的复合故障诊断问题,提出了一种基于经验模式分解的故障诊断方法,进行复合故障的耦合特征分离和轴承损伤性故障信号特征提取研究.该方法首先通过经验模式分解将复合信号分解为若干个本征模函数(intrinsic mode function,IMF);然后通过计算各IMF与原始复合信号的相关系数确定包含故障特征信息的主要成分,除去虚假分量;最后针对主要成分中的低频成分进行频谱分析提出转子故障特征,针对主要成分中的高频成分进行Hilbert包络解调提取调制故障特征,即轴承损伤性故障特征.仿真及实验结果表明该方法的有效性和实用性.     

Using the Long Term Pavement Performance Database in Pavement Design Courses

The Strategic Highway Research Program Long Term Pavement Performance (LTPP) database provides considerable information about a large number of pavement test sections. The information may be easily accessed using DataPave 2.0 software, available free from the Federal Highway Administration. This software provides information on approximately 3,000 sections, with several modules for data analysis and extraction. This paper describes the integration of LTPP DataPave 2.0 software into a pavement design course. The database was used at several points throughout the course, including lessons on traffic characterization, materials, reliability, performance, and design. Twelve Texas pavement case studies were used. Each student was required to complete an individual project requiring the use of the database. Student projects and student evaluations of the use of the DataPave 2.0 software in this course are also discussed. This paper provides sufficient information for interested faculty to implement the use of DataPave 2.0 in their own courses in pavement design and related areas.     

A Study of the Equipment Fault Diagnosing Method Based on EMD and Holo-spectrum

We first introduce the empirical mode decomposition (EMD) and holo-spectrum analysis.Then we decom- pose the vibration signal of the equipment by EMD, re-organize the signal closely associated with the original sig- nal, eliminate the noise signal better, and analyze the holographic re-signal spectrum, which makes the amplitude, frequency and phase combine completely, reflecting the equipment vibration morphology fully.Particularly applying a two-dimensional holo-spectrum can obtain the direction of rotation order harmonic, size, shape, and the relation- ship between order harmonic generation rotor vibrations, and so on.The traditional signal processing methods can not eliminate noise well.We apply this method to the rotor vibration signal of fault diagnosis, eliminate noise and reflect the equipment vibration characteristics well.     

EH4高频大地电磁测深数据的时频分析

介绍了EH4高频大地电磁测深原理,以及希尔伯特-黄变换（HHT）的时频分析原理。应用HHT分析了大地电磁信号的时频分布特征。基于matlab平台,编制了EH4时间序列读取及信号分析程序。结果表明,希尔伯特-黄变换是分析EH4非高斯、非平稳信号的有效方法。     

浅论水泥混凝土道路的施工与养护

结合公司道路情况，简述混凝土道路的施工与养护工作，有效保障混凝土道路的使用寿命。     

Analysis and Implementation of Resilient Modulus Models for Granular Solids

Constitutive equations based upon stress dependent moduli, like K-θ and Uzan-Witczak, are widely used to characterize the resilient response of granular materials for the analysis and design of pavement systems. These constitutive models are motivated by the observation that the granular layers used in pavement structures shake down to (nonlinear) elastic response under construction loads and will, therefore, respond elastically under service loads typically felt by these systems. Due to their simplicity, their great success in organizing the response data from cyclic triaxial tests, and their success relative to competing material models in predicting the behavior observed in the field, these resilient modulus constitutive models have been implemented in many computer programs used by researchers and design engineers. This paper provides an analysis of the nonlinear solution algorithms that have been used in implementing these models in a conventional nonlinear 3D finite-element framework. The analysis shows that these conventional algorithms are destined to fail at higher load levels. The paper offers two competitive methods for global analysis with these models. A comparative study of eight possible implementations of the algorithms described in the paper is made through two simulation examples.     

电工钢张力测量数据分析及闭环控制的建立

运用现代化测量技术，采用数字管理手段，实现了对张力传感器测量信号的实时监测、记录及异常报警信息收集。同时，采用现代信号处理和分析方法，提出EMD（经验模式分解）算法分解张力信号，可以在线实时提取和分析张力传感器故障特征，并进行闭环控制，可用于检测与诊断传感器早期故障，优化张力差控制轧制模型，提高轧制后的电工钢产品质量。     

Seasonal Deterioration of Unsurfaced Roads

Seasonal deformation of unsurfaced roads was observed over several years and was studied using pavement deterioration models and finite-element analysis. The Mathematical Model of Pavement Performance is a model designed for pavement deterioration prediction and was successfully used for seasonal deterioration modeling because of its flexibility in defining the pavement structure, properties, and seasonal impact. However, these types of models are designed for highways and are somewhat limited in soils characterization and manipulation of the forces at the road–tire interface. Therefore, a three-dimensional dynamic finite-element model of a wheel rolling over soil was applied to simulate local vehicle traffic on a secondary unpaved road. These simulations were used to study the effects of vehicle speed, load, suspension system, wheel torque, and wheel slip on rutting and washboard formation. Modeling results are compared to field measurements and observations.     

Information Theory and Neural Networks for Managing Uncertainty in Flood Routing

This paper presents an approach for handling uncertainties arising mainly from ignored or misrepresented processes in physically based models. The approach is based on the application of a parallel artificial neural network (ANN) model that uses state variables, input and output data, and previous model errors at specific time steps to predict the errors of a physically based model. Concepts from information theory are used to discover the relationships between the variables and the model errors, which also serves as a mechanism to detect the predictability of the errors. The resulting information is used to select the best related input data for the error prediction model. The error prediction model is then trained and applied to improve the forecasts made by the physically based model. This approach was applied to a routing model of a 70 km reach of the River Wye, United Kingdom. The results demonstrate that errors from the physically based model show a consistent trend governed by some dynamics of their own, which can be modeled with learning algorithms. Errors were forecasted at different lead times. In all cases the forecasts made by the combined application of both models were more accurate than those made by the physically based model alone. From this it was concluded that, along with proper information analysis techniques, the use of ANN models to predict the forecast errors of physically based models can help to improve significantly the prediction and therefore to reduce the associated uncertainty.     

Nonlinear Signal Analysis: Time-Frequency Perspectives

Recently, there has been growing utilization of time-frequency transformations for the analysis and interpretation of nonlinear and nonstationary signals in a broad spectrum of science and engineering applications. The continuous wavelet transform and empirical mode decomposition in tandem with Hilbert transform have been commonly utilized in such applications, with varying success. This study evaluates the performance of the two approaches in the analysis of a variety of classical nonlinear signals, underscoring a fundamental difference between the two approaches: the instantaneous frequency derived from the Hilbert transform characterizes subcyclic and supercyclic nonlinearities simultaneously, while wavelet-based instantaneous frequency captures supercyclic nonlinearities with a complementary measure of instantaneous bandwidth characterizing subcyclic nonlinearities. This study demonstrates that not only is the spectral content of the wavelet instantaneous bandwidth measure consistent with that of the Hilbert instantaneous frequency, but in the case of the R?ssler system, produces identical oscillatory signature.     

Structural Damage Detection Using Empirical Mode Decomposition: Experimental Investigation

This paper presents an experimental investigation on the applicability of the empirical mode decomposition (EMD) for identifying structural damage caused by a sudden change of structural stiffness. A three-story shear building model was constructed and installed on a shaking table with two springs horizontally connected to the first floor of the building to provide additional structural stiffness. Structural damage was simulated by suddenly releasing two pretensioned springs either simultaneously or successively. Various damage severities were produced using springs of different stiffness. A series of free vibration, random vibration, and earthquake simulation tests were performed on the building with sudden stiffness changes. Dynamic responses including floor accelerations and displacements, column strains, and spring releasing time instants were measured. The EMD was then applied to measured time histories to identify damage time instant and damage location for various test cases. The comparison of identified results with measured ones showed that damage time instants could be accurately detected in terms of damage spikes extracted directly from the measurement data by EMD. The damage location could be determined by the spatial distribution of the spikes along the building. The influence of damage severity, sampling frequency, and measured quantities on the performance of EMD for damage detection was also discussed.