A statistical design approach for gigabit-rate fiber-optictransmission systems

A statistical design approach is proposed for the design of fiber-optic transmission systems (FOTSs). It yields increased regenerator spacings up to about 50% over those provided by the traditional worst-case design. The method involves assuming most of the system parameters to be random variables with known probability distributions. The probability distribution of the regenerator spacing is then numerically found by a Monte Carlo simulation from which the regenerator spacing with a given success probability can be determined. A thorough statistical treatment of attenuation, dispersion, and chirp limits is presented, and the effects of varying the probability density functions of underlying optical system parameters are examined. The numerical results shown demonstrate the repeatability of the proposed statistical design approach     

Modal Identification Study of Vincent Thomas Bridge Using Simulated Wind-Induced Ambient Vibration Data

Abstract:   In this article, wind-induced vibration response of Vincent Thomas Bridge, a suspension bridge located in San Pedro near Los Angeles, California, is simulated using a detailed three-dimensional finite element model of the bridge and a state-of-the-art stochastic wind excitation model. Based on the simulated wind-induced vibration data, the modal parameters (natural frequencies, damping ratios, and mode shapes) of the bridge are identified using the data-driven stochastic subspace identification method. The identified modal parameters are verified by the computed eigenproperties of the bridge model. Finally, effects of measurement noise on the system identification results are studied by adding zero-mean Gaussian white noise processes to the simulated response data. Statistical properties of the identified modal parameters are investigated under an increasing level of measurement noise. The framework presented in this article will allow us to investigate the effects of various realistic damage scenarios in long-span cable-supported (suspension and cable-stayed) bridges on changes in modal identification results. Such studies are required to develop robust and reliable vibration-based structural health monitoring methods for this type of bridge, which is a long-term research objective of the authors.     

Reconstruction of the area-moment-of-inertia of a beam using a shifting load and the end-slope data

In recent years, much concern has been reported about the condition of US infrastructure, particularly the bridges. These concerns have brought attention to the area of structural health monitoring and its significance in averting tragedies. The main focus of this study was to develop a mathematical model that could be used to determine the changes in the structural characteristics such as cross-sectional area-moment-of-inertia from the knowledge of a shifting load and the end-slope data. In this investigation, the cross-sectional area-moment-of-inertias of a scaled model of simply supported steel bridge are reconstructed using a shifting load scheme and the corresponding end-slope data. The end-slope data used in this inverse problem were numerically generated using the finite element method. The end-slope data and the loading were then used in the inverse problem to reconstruct the cross-sectional area-moment-of-inertias for the model. To solve the inverse problem, the solution domain was discretized into finite number of elements and nodes. A shifting uniformly distributed load was applied to each element, and the beam equation was integrated to create a set of linear equations in terms of loading and end-slope differences that could be solved simultaneously to recover the area-moment-of-inertia for each element. Comparison of the inverse solutions with the direct solutions confirms that the variations in the area-moment-of-inertia for a bridge cross section can be reconstructed, with a good accuracy, from the knowledge of the shifting load and end-point slopes.     

General Realization Algorithm for Modal Identification of Linear Dynamic Systems

The general realization algorithm (GRA) is developed to identify modal parameters of linear multi-degree-of-freedom dynamic systems subjected to measured (known) arbitrary dynamic loading from known initial conditions. The GRA extends the well known eigensystem realization algorithm (ERA) based on Hankel matrix decomposition by allowing an arbitrary input signal in the realization algorithm. This generalization is obtained by performing a weighted Hankel matrix decomposition, where the weighting is determined by the loading. The state-space matrices are identified in a two-step procedure that includes a state reconstruction followed by a least-squares optimization to get the minimum prediction error for the response. The statistical properties (i.e., bias, variance, and robustness to added output noise introduced to model measurement noise and modeling errors) of the modal parameter estimators provided by the GRA are investigated through numerical simulation based on a benchmark problem with nonclassical damping.     

Uncertainty and Sensitivity Analysis of Damage Identification Results Obtained Using Finite Element Model Updating

Abstract: A full‐scale seven‐story reinforced concrete shear wall building structure was tested on the UCSD‐NEES shake table in the period October 2005–January 2006. The shake table tests were designed so as to damage the building progressively through several historical seismic motions reproduced on the shake table. A sensitivity‐based finite element (FE) model updating method was used to identify damage in the building. The estimation uncertainty in the damage identification results was observed to be significant, which motivated the authors to perform, through numerical simulation, an uncertainty analysis on a set of damage identification results. This study investigates systematically the performance of FE model updating for damage identification. The damaged structure is simulated numerically through a change in stiffness in selected regions of a FE model of the shear wall test structure. The uncertainty of the identified damage (location and extent) due to variability of five input factors is quantified through analysis‐of‐variance (ANOVA) and meta‐modeling. These five input factors are: (1–3) level of uncertainty in the (identified) modal parameters of each of the first three longitudinal modes, (4) spatial density of measurements (number of sensors), and (5) mesh size in the FE model used in the FE model updating procedure (a type of modeling error). A full factorial design of experiments is considered for these five input factors. In addition to ANOVA and meta‐modeling, this study investigates the one‐at‐a‐time sensitivity analysis of the identified damage to the level of uncertainty in the identified modal parameters of the first three longitudinal modes. The results of this investigation demonstrate that the level of confidence in the damage identification results obtained through FE model updating, is a function of not only the level of uncertainty in the identified modal parameters, but also choices made in the design of experiments (e.g., spatial density of measurements) and modeling errors (e.g., mesh size). Therefore, the experiments can be designed so that the more influential input factors (to the total uncertainty/variability of the damage identification results) are set at optimum levels so as to yield more accurate damage identification results.     

Environmental effects on the identified natural frequencies of the Dowling Hall Footbridge

Continuous monitoring of structural vibrations is becoming increasingly common as sensors and data acquisition systems become more affordable, and as system and damage identification methods develop. In vibration-based structural health monitoring, the dynamic modal parameters of a structure are usually used as damage-sensitive features. The modal parameters are often sensitive to changing environmental conditions such as temperature, humidity, or excitation amplitude. Environmental conditions can have as large an effect on the modal parameters as significant structural damage, so these effects should be accounted for before applying damage identification methods. This paper presents results from a continuous monitoring system installed on the Dowling Hall Footbridge on the campus of Tufts University. Significant variability in the identified natural frequencies is observed; these changes in natural frequency are strongly correlated with temperature. Several nonlinear models are proposed to represent the relationship between the identified natural frequencies and measured temperatures. The final model is then validated using independent sets of measured data. Finally, confidence intervals are estimated for the identified natural frequencies as a function of temperature. The ratio of observed outliers to the expected rate of outliers based on the confidence level can be used as a damage detection index.     

An inverse solution for reconstruction of the heat transfer coefficient from the knowledge of two temperature values in a solid substrate

Reconstruction of the heat transfer coefficient from the knowledge of temperature distribution is an inverse problem. The main focus of this study was to develop an inverse model that could be used to determine the heat transfer coefficient associated with a fluid in contact with a solid surface from the knowledge of two measured temperature values (T₁ and T_M) in the solid substrate. The temperature distribution for the inverse problem was numerically generated, for a situation with a known heat transfer coefficient, using an implicit finite-differencing scheme. The solution domain was first discretized in to finite number of small regions and nodes. Conservation of energy was then applied to each of the control volume about the nodal regions. This approach resulted in a set of linear equations that was solved simultaneously. Two nodal temperatures in the substrate, from the direct solution, were then used in the inverse problem to reconstruct the heat transfer coefficient. To solve the inverse problem, the solution domain was divided into two distinct regions (Region I and Region II). Region I contained the solution domain between the two known temperatures (T₁ and T_M), and Region II included the region between T_M and the surface with the convective boundary condition. Again, a finite-differencing scheme was employed to generate a set of linear equations in each region. First, the set of linear equations in Region I was solved simultaneously and the results were then used to reconstruct the nodal temperatures in Region II. The convective surface temperature was then utilized to determine the heat transfer coefficient. A series of numerical experiments were conducted to test the validity of the inverse model. Comparison of the inverse solutions with the direct solutions confirms that the heat transfer coefficient can be reconstructed, with good accuracy, from the knowledge of two temperature points in the solid substrate.     

Reconstruction of the area-moment-of-inertia of a rotor blade using a shifting point-load and the end-slope

The main focus of this study was to develop an inverse model that could be used to determine the changes in sectional area-moment-of-inertia of a helicopter rotor blade from the knowledge of a shifting point-load and the end-slope data. In this investigation, the cross-sectional area-moment-of-inertias of a rotor blade model with n segments are reconstructed using a shifting point-load and the corresponding end-slope data. The end-slope data used in this inverse problem were numerically generated using the finite element method. The end-slope data and the loading were then used in the inverse problem to reconstruct the cross-sectional area-moment-of-inertias for the model. To solve the inverse problem, the solution domain was discretized into finite number of segments, and a shifting point-load was applied to the mid-point of each segment. The beam equation was then integrated to create a set of linear equations in terms of loading and end-slopes. Next, the resulting set of equations was solved simultaneously to recover the area-moment-of-inertia for each segment. A series of numerical experiments were performed to check the validity and sensitivity of the inverse model. Comparison of the inverse solutions with the direct solutions confirms that the variations in the area-moment-of-inertia for a helicopter rotor blade can be reconstructed with good accuracy from the knowledge of the shifting point-load and end-slopes.