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 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.     

Time‐Series Models for Nonlinear Systems

Discrete time‐series models can be used for the dynamic response prediction of linear structures. When structural nonlinearities are present, it may be possible to modify the form of the discrete time‐series model to account for the nonlinearities. One approach is to allow the model parameters to become functions of state. This paper explores some possible forms of the parameter functions for various nonlinear structures. Numerical case studies using both a Duffing oscillator and a combined viscous and coulomb damped oscillator are presented. Also, experimental data from a highly nonlinear aircraft landing gear strut are used to evaluate different model forms. The results from these studies show the potential for future applications of nonlinear time‐series models.     

Prediction of Extreme Response Statistics of Narrow-Band Random Vibrations

The paper focuses on the development of a general method for extreme response estimation of dynamical systems subjected to random excitations. One of the most important elements in structural safety is an assessment of the exceedance or failure probability. The frequently used Poisson assumption tends to overestimate the exceedance level if the response spectrum has narrow-banded features since the so-called clustering effects occur. The latter inaccuracy may be corrected by using an alternative approach studied in this paper, which enables accurate prediction of extremes irrespective of clustering effects.     

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.     

Peak Response of a Nonlinear Beam

A model for estimating the peak dynamic response distribution of a nonlinear beam, based on a special class of non-Gaussian stochastic processes, is proposed in this paper. It is shown that the stochastic response of a cantilever beam with geometrically nonlinear behavior can be accurately calibrated with translation processes. Different models to describe the significant bimodal features in the marginal probability density functions of the response time histories are proposed. Finally, two of these models are used to estimate the response peak value distributions and the results are compared. This comparison demonstrates the effects of inaccurate models for the parent response processes on the peaks estimation.     

Upper-Bound Solutions for Rigid-Plastic Beams and Plates of Large Deflections by Variation Principles

This paper demonstrates deriving upper-bound solutions of geometrically nonlinear problems for beams and plates from rigid perfectly plastic material by the principles of virtual work in general form and stationary of total energy. Presented noncomplicated examples justify that the first is more appropriate when a kinematically admissible displacement field is defined by several generalized displacements. The second can serve as effective means for comparison in accuracy solutions corresponding to different displacement fields playing the same role as the upper-bound theorem in the limit analysis. Procedures of the latter for obtaining upper-bound solutions mainly remain valid. Solutions for a beam and rectangular plate subjected to uniformly distributed load illustrate importance of taking into account transformation forms of displacements in loading process.     

Contemporaneous Time Series and Forecasting Methodologies for Predicting Short-Term Productivity

Productivity has a profound impact on projects that depend on time and cost of construction operations. In addition, time and cost estimates are derived from productivity. Thus, accurate prediction of productivity is essential to effectively plan and control construction operations. Predicting productivity of ongoing operations, however, is challenging. Due to dynamic and stochastic changes in productivity over time during construction, frequent and regular forecasting of short-term productivity is critical in managing ongoing operations. The present research investigated the characteristics of series of periodic productivity that should be taken into consideration to effectively predict short-term productivity continually and proactively. Given the identified characteristics, this study reviewed a few potential statistical methodologies that can make full use of contemporaneous time series data related to production for the purpose of predicting short-term productivity by using trend analysis. The methodologies were demonstrated in this paper using an example case, through which data processing and modeling procedure for modeling contemporaneous series data were explained.     

Joint First-Passage Probability and Reliability of Systems under Stochastic Excitation

The first-passage probability, describing the probability that a scalar process exceeds a prescribed threshold during an interval of time, is of great engineering interest. This probability is essential for estimating the reliability of a structural component whose response is a stochastic process. When considering the reliability of an engineering system composed of several interdependent components, the probability that two or more response processes exceed their respective safe thresholds during the operation time of the system is an equally essential quantity. This paper proposes simple and accurate formulas for approximating this joint first-passage probability of a vector process. The nth order joint first-passage probability is obtained from a recursive formula involving lower order joint first-passage probabilities and the out-crossing probability of the vector process over a safe domain. Interdependence between the crossings is approximately accounted for by considering the clumping of these events. The accuracy of the proposed formulas is examined by comparing analytical estimates with those obtained from Monte Carlo simulations for stationary Gaussian processes. As an example application, the reliability of a system of interconnected equipment items subjected to a stochastic earthquake excitation is estimated by linear programming bounds employing marginal and joint component fragilities obtained by the proposed formulas.     

Spectral Analysis and Parametric Study of Stochastic Pavement Loads

This paper investigates the effects of vehicle parameters, speed, and surface roughness on the power spectral density (PSD) of stochastic pavement loads. Pavement surface roughness is modeled as a zero-mean stationary random field. A quarter-vehicle model is established to simulate the vibrations of heavy and passenger vehicles with typical parameters. Tire damping is also included in the consideration of stochastic pavement loads; this was assumed to be zero in many previous investigations. The PSD roughness proposed by the ISO is adopted in the simulation of the loads. An important indicator of the stochastic loads, the so-called energy cumulative distribution function, is introduced to describe the frequency distribution of load energy. The results show that passenger vehicles produce more high-frequency loads than heavy vehicles, while more of the loads generated by heavy vehicle are primarily distributed in the low-frequency region. It is also found that the effect of tire damping on stochastic pavement loads is not negligible especially if the loads of interest are concentrated in the high-frequency region. The results of the study may be useful in optimum design of vehicle suspensions and prediction of dynamic pavement response.     

Dynamic and Seismic Analysis of Foundations based on Free Field B-Spline Characteristic Response Histories

A direct time domain formulation for the analysis of unbounded media and foundations is developed that treats dynamic excitations and ground motion in a uniform manner. The method uses the boundary element method with higher order B-Spline fundamental solutions to compute the characteristic responses of the surface of the elastodynamic domain. Subsequently, time histories of the system response to general excitations are computed by a mere superposition scheme that accommodates in a uniform manner arbitrary time histories of external loads and/or ground motion. The characteristic responses are computed in the form of time dependent flexibility matrices of the medium that are sparse due to the finite duration of the B-Spline excitation signal and the characteristics of the wave propagation. The duration of the B-Spline impulse response is limited to only a few time steps. Consequently, significant savings in computing time and storage requirements are achieved. Furthermore, the characteristic responses do not depend on the type or wave form of the actual external excitations and the presence of rigid foundations. This is a significant advantage when the response of a system to excitations of long duration is to be computed. In addition, the proposed approach significantly reduces the size of the problems under consideration and yet fully considers the effects of the free field. The significance of nonrelaxed boundary conditions and correct representation of the free field is established. The method is demonstrated and validated through applications pertaining to the analysis of foundations and inclusions subjected to transient loads and seismic excitations.     

Performance of Active and Passive Methods for Measuring Low-Frequency Surface Wave Dispersion Curves

This paper examines the consistency between surface wave dispersion curves measured at wavelengths of up to 600 m using active and passive methods at sites in the Mississippi Embayment. Large-diameter (200 m) circular receiver arrays were deployed at five deep soil sites located in Tennessee, Arkansas, and Missouri to record ambient ground vibrations at low frequencies. Measurements were performed at the same locations using linear receiver arrays and actively generated low-frequency energy using the recently developed Network for Earthquake Engineering Simulation (NEES) field vibrator (termed Liquidator). Characteristics of the ambient wavefield measured at the five sites in the Mississippi Embayment are presented along with comparisons between the surface wave dispersion curves obtained from the active and passive measurements at each site. The ambient wavefield measurements exhibited peak levels in the frequency range of 1–5 Hz. Surface wave dispersion curves developed from frequency-wavenumber (f-k) processing of the active and passive methods were in good agreement at four of the sites, with phase velocities from the passive measurements within 5–10 % of the active-source measurements out to wavelengths of about 550 m. Improved comparisons were obtained at the fifth site by applying high-resolution f-k processing.     

Dimensional Analysis of Rigid-Plastic and Elastoplastic Structures under Pulse-Type Excitations

In this paper, the inelastic response of rigid-plastic and elastic-plastic systems subjected to pulse-type excitations is revisited with dimensional analysis. Starting from Newmark’s result on the maximum displacement of a sliding mass resting on a base that is subjected to a rectangular acceleration pulse, the paper introduces an energetic length scale of the excitation and the relevant dimensionless Π-products that govern the response of yielding structures. The introduction of Buckingham’s Π-theorem reduces the number of variables that govern the response of the elastic-plastic system from five (5) to three (3). The proposed dimensionless Π-products are liberated from the associated elastic system response and are consistent with the incremental evolution from the rigid-plastic to the elastic-plastic system. When the response is presented in terms of the dimensionless Π-terms remarkable order emerges. It is shown that for a given value of dimensionless yield displacement the response curves (maximum relative dimensionless displacements) become self-similar and follow a single master curve. The self-similar solutions show clearly how the inelastic response amplifies as the normalized yield displacement increases and that an increase in strength may lead to an increase in inelastic displacements. The main advantage of the analysis presented in this paper is that it brings forward the concept of self-similarity—an invariance with respect to changes in scale or size—which is a decisive symmetry that shapes nonlinear behavior.     

Validity of SDOF Models for Analyzing Two-Way Reinforced Concrete Panels under Blast Loading

The combined manual TM 5-1300/NAVFAC P-397/AFR 88-22, Structures to Resist the Effects of Accidental Explosions, published by the joint departments of the Army, the Navy, and the Air Force, has been used in all NATO countries for the past 50 years for protective design applications. The manual was recently reformatted to meet the Department of Defense Unified Facility Criteria (UFC). As a first step, the current production of the new document, UFC 3-340-02, focused on making the original TM 5-1300 available in a more functional format so that future technical updates can be facilitated. In this study, a single-degree-of-freedom (SDOF) model, based on the guidelines of the UFC 3-340-02, was used to formulate a FORTRAN code to predict the response of SDOF systems under blast. The code was used to generate pressure-impulse (P-I) diagrams for a series of two-way reinforced concrete (RC) panels with different dimensions, aspect and reinforcement ratios, and support conditions. The P-I diagram predictions were compared to the results of experimentally validated nonlinear explicit finite-element (FE) analyses and significant differences in deflection and shear predictions were observed. The general trend of results and the major characteristics of the P-I diagrams were discussed in terms of the discrepancies between the SDOF and the FE predictions. The work presented in this paper is expected to contribute to improving the modeling provisions of the two-way RC panels in the future edition of the UFC 3-340-02 by understanding the limitations of SDOF models using advanced FE analysis techniques.     

Vulnerability Screening and Capacity Assessment of Reinforced Concrete Columns Subjected to Blast

In this study, a nonlinear model is developed to study the response of blast-loaded reinforced concrete (RC) columns. The strain rate dependency and the axial load and P?Δ effects on the flexural rigidity variation along the column heights were implemented in the model. Strain rate and axial load effects on a typical RC column cross section were investigated by developing strain-rate-dependent moment-curvature relationships and force-moment interaction diagrams. Analysis results showed that the column cross section strength and deformation capacity are highly dependent on the level of strain rates. Pressure-impulse diagrams were developed for two different column heights with two different end connection details (ductile and nonductile) and the effects of the axial load on the column midheight deflection and end rotation at failure were evaluated for both connection types. Based on the results of this study, a pressure-impulse band (PIB) technique is proposed. The PIB technique presents a useful tool that covers practical uncertainties associated with RC column reinforcement details as well as possible increase of column axial loads resulting from different blast-induced progressive collapse scenarios. Finally, the uses of the PIB technique for vulnerability screening of critical infrastructure or postblast capacity assessment of RC columns of target structures are presented.     

Model for Predicting Financial Performance of Development and Construction Corporations

Performance forecasting is central to aligning an organization’s operations with its strategic direction. Despite the panoply of approaches to performance predictions, relatively few published studies address model development of financial performance predictions for the construction industry. By analyzing the preceding relationship between financial and economic variables and financial performance, this paper proposes an innovative approach to predicting firm financial performance. First, hypothesis tests using data for 42 development and construction corporations listed in the construction sector of the Taiwan Stock Exchange between 1997 Q1 and 2006 Q4 uncover useful relationships between financial performance and financial and economic variables. Second, based on these relationships, a three-stage mathematical modeling procedure is used for cross-sectional model estimation, which is subsequently refined to create firm-specific financial performance-forecasting models for four sample firms. The out-of-sample forecasting accuracy is evaluated using mean absolute percentage error (MAPE). The results show that the cross-sectional model explains 78.9% of the variation in the cross-sectional performance data, and the MAPE values in the forecasting models range from 9.54 to 19.69%.     

Real-Time Detection of Sanitary Sewer Overflows Using Neural Networks and Time Series Analysis

Sanitary sewer overflows (SSOs) are becoming of increasing concern as a health risk. Utilities and regulators have taken preventive measures but many overflows still occur and are not identifiable, especially in access-challenged locations. Several mathematical approaches are presented for detecting if a disruption in the system is impending or occurring based on measurements at one or more locations in the system. Time series analysis and neural networks are used as prediction tools for expected depths and flows for single measurement locations and a neural network is developed for a multiple monitor system. Control limit theory is applied in all cases for identifying significant deviations of measured values from the expected values that suggest a SSO is occurring. Data from Pima County Wastewater Management’s monitoring system are used in two case studies.     

Analytical Model for Geometric and Material Nonlinear Analysis of Externally Prestressed Beams

The analysis of beams prestressed by external slipping tendons involves various difficulties related to the coupling between the local strain of the tendons and the global deformation of the beam. The structural behavior of the beam–tendon system at collapse is ruled both by the nonlinearity of materials and by geometric nonlinear effects. Recent scientific papers have shown the relevance of the geometric effects in evaluating the failure load of externally prestressed beams by considering the tendon eccentricity variation. The change of eccentricity is however only one of the geometric nonlinear effects. In this work the writers present a complete geometric and mechanical nonlinear analytical model based on the theory of small strains and moderate rotations deduced from the finite deformation theory.     

Reliability Analysis of Laterally Loaded Piles Involving Nonlinear Soil and Pile Behavior

An alternative approach of analyzing laterally loaded piles in the ubiquitous spreadsheet platform is presented. The numerical procedure couples nonlinear pile flexural rigidity (EpIp) with nonlinear p-y analysis. The deterministic study is then extended to carry out reliability analysis, which reflects the uncertainties and correlation structure of the underlying parameters. The reliability index is evaluated based on the alternative intuitive perspective of an expanding equivalent ellipsoid in the original space of the random variables. This paper investigates two modes of failure: deflection and bending moment, and considers non-normal random variables. Spatial variability of the soil medium is accounted for by incorporating an autocorrelation model. The spreadsheet-based reliability approach can also be coupled with stand-alone programs via the response surface method. The probabilities of failure inferred from reliability indices agree well with Monte Carlo simulations. Simple reliability-based design is demonstrated, in which the appropriate pile section or length that satisfies target reliability in one or more limit states is sought.