Variance-Reduced Particle Filters for Structural System Identification Problems

A few variance reduction schemes are proposed within the broad framework of a particle filter as applied to the problem of structural system identification. Whereas the first scheme uses a directional descent step, possibly of the Newton or quasi-Newton type, within the prediction stage of the filter, the second relies on replacing the more conventional Monte Carlo simulation involving pseudorandom sequence with one using quasi-random sequences along with a Brownian bridge discretization while representing the process noise terms. As evidenced through the derivations and subsequent numerical work on the identification of a shear frame, the combined effect of the proposed approaches in yielding variance-reduced estimates of the model parameters appears to be quite noticeable. DOI: 10.1061/(ASCE)EM.1943-7889.0000480. (C) 2013 American Society of Civil Engineers.

The FCLT with Dependent Errors: an Helicopter Tour of the Quality of the Approximation

This note investigates the adequacy of the finite-sample approximation provided by the Functional Central Limit Theorem (FCLT) when the errors are allowed to be dependent. We compare the distribution of the scaled partial sums of some data with the distribution of the Wiener process to which it converges. Our setup is purposely very simple in that it considers data generated from an ARMA(1,1) process. Yet, this is sufficient to bring out interesting conclusions about the particular elements which cause the approximations to be inadequate in even quite large sample sizes.

The uniqueness of signature problem in the non-Markov setting

We establish a general framework for a class of multidimensional stochastic processes over [0,1] under which with probability one, the signature (the collection of iterated path integrals in the sense of rough paths) is well-defined and determines the sample paths of the process up to reparametrization. In particular, by using the Malliavin calculus we show that our method applies to a class of Gaussian processes including fractional Brownian motion with Hurst parameter H>1/4, the Ornstein–Uhlenbeck process and the Brownian bridge.

Shifting Processes with Cyclically Exchangeable Increments at Random

International audience

Hilbert Space Valued Signal Plus Noise Models: Analysis of Structural Breaks under High Dimensionality and Temporal Dependence

This thesis is concerned with change point analysis for time series, i.e. with detection of structural breaks in time-ordered, random data. This long-standing research field regained popularity over the last few years and is still undergoing, as statistical analysis in general, a transformation to high-dimensional problems. We focus on the fundamental »change in the mean« problem and provide extensions of the classical non-parametric Darling-Erdős-type cumulative sum (CUSUM) testing and estimation theory within highdimensional Hilbert space settings. In the first part we contribute to (long run) principal component based testing methods for Hilbert space valued time series under a rather broad (abrupt, epidemic, gradual, multiple) change setting and under dependence. For the dependence structure we consider either traditional m-dependence assumptions or more recently developed m-approximability conditions which cover, e.g., MA, AR and ARCH models. We derive Gumbel and Brownian bridge type approximations of the distribution of the test statistic under the null hypothesis of no change and consistency conditions under the alternative. A new formulation of the test statistic using projections on subspaces allows us to simplify the standard proof techniques and to weaken common assumptions on the covariance structure. Furthermore, we propose to adjust the principal components by an implicit estimation of a (possible) change direction. This approach adds flexibility to projection based methods, weakens typical technical conditions and provides better consistency properties under the alternative. In the second part we contribute to estimation methods for common changes in the means of panels of Hilbert space valued time series. We analyze weighted CUSUM estimates within a recently proposed »high-dimensional low sample size (HDLSS)« framework, where the sample size is fixed but the number of panels increases. We derive sharp conditions on »pointwise asymptotic accuracy« or »uniform asymptotic accuracy« of those estimates in terms of the weighting function. Particularly, we prove that a covariance-based correction of Darling-Erdős-type CUSUM estimates is required to guarantee uniform asymptotic accuracy under moderate dependence conditions within panels and that these conditions are fulfilled, e.g., by any MA(1) time series. As a counterexample we show that for AR(1) time series, close to the non-stationary case, the dependence is too strong and uniform asymptotic accuracy cannot be ensured. Finally, we conduct simulations to demonstrate that our results are practically applicable and that our methodological suggestions are advantageous.

Review of vibration-based damage detection and condition assessment of bridge structures using structural health monitoring

As a part of vital infrastructure and transportation networks, bridge structures must function safely at all times. However, due to heavier and faster moving vehicular loads and function adjustment, such as Busway accommodation, many bridges are now operating at an overload beyond their design capacity. Additionally, the huge renovation and replacement costs always make the infrastructure owners difficult to undertake. Structural health monitoring (SHM) is set to assess condition and foresee probable failures of designated bridge(s), so as to monitor the structural health of the bridges. The SHM systems proposed recently are incorporated with Vibration-Based Damage Detection (VBDD) techniques, Statistical Methods and Signal processing techniques and have been regarded as efficient and economical ways to solve the problem. The recent development in damage detection and condition assessment techniques based on VBDD and statistical methods are reviewed. The VBDD methods based on changes in natural frequencies, curvature/strain modes, modal strain energy (MSE) dynamic flexibility, artificial neural networks (ANN) before and after damage and other signal processing methods like Wavelet techniques and empirical mode decomposition (EMD) / Hilbert spectrum methods are discussed here.

Damage assessment in multiple-girder composite bridge using vibration characteristics

This paper uses dynamic computer simulation techniques to apply a procedure using vibration-based methods for damage assessment in multiple-girder composite bridge. In addition to changes in natural frequencies, this multi-criteria procedure incorporates two methods, namely the modal flexibility and the modal strain energy method. Using the numerically simulated modal data obtained through finite element analysis software, algorithms based on modal flexibility and modal strain energy change before and after damage are obtained and used as the indices for the assessment of structural health state. The feasibility and capability of the approach is demonstrated through numerical studies of proposed structure with six damage scenarios. It is concluded that the modal strain energy method is competent for application on multiple-girder composite bridge, as evidenced through the example treated in this paper.

Whole of life cycle cost analysis in bridge rehabilitation

The report presents a methodology for whole of life cycle cost analysis of alternative treatment options for bridge structures, which require rehabilitation. The methodology has been developed after a review of current methods and establishing that a life cycle analysis based on a probabilistic risk approach has many advantages including the essential ability to consider variability of input parameters. The input parameters for the analysis are identified as initial cost, maintenance, monitoring and repair cost, user cost and failure cost. The methodology utilizes the advanced simulation technique of Monte Carlo simulation to combine a number of probability distributions to establish the distribution of whole of life cycle cost. In performing the simulation, the need for a powerful software package, which would work with spreadsheet program, has been identified. After exploring several products on the market, @RISK software has been selected for the simulation. In conclusion, the report presents a typical decision making scenario considering two alternative treatment options.

User friendly guide for rehabilitation or strengthening of bridge structures using fiber reinforced polymer composites

A worldwide interest is being generated in the use of fibre reinforced polymer composites (FRP) in rehabilitation of reinforced concrete structures. As a replacement for the traditional steel plates or external post-tensioning in strengthening applications, various types of FRP plates, with their high strength to weight ratio and good resistance to corrosion, represent a class of ideal material in external retrofitting. Within the last ten years, many design guidelines have been published to provide guidance for the selection, design and installation of FRP systems for external strengthening of concrete structures. Use of these guidelines requires understanding of a number of issues pertaining to different properties and structural failure modes specific to these materials. A research initiative funded by the CRC for Construction Innovation was undertaken (primarily at RMIT) to develop a decision support tool and a user friendly guide for use of fibre reinforced polymer composites in rehabilitation of concrete structures. The user guidelines presented in this report were developed after industry consultation and a comprehensive review of the state of the art technology. The scope of the guide was mainly developed based on outcomes of two workshops with Queensland Department of Main Roads (QDMR). The document covers material properties, recommended construction requirements, design philosophy, flexural, shear and torsional strengthening of beams and strengthening of columns. In developing this document, the guidelines published on FIB Bulletin 14 (2002), Task group 9.3, International Federation of Structural Concrete (FIB) and American Concrete Institute Committee 440 report (2002) were consulted in conjunction with provisions of the Austroads Bridge design code (1992) and Australian Concrete Structures code AS3600 (2002). In conclusion, the user guide presents design examples covering typical strengthening scenarios.

Trip to Sunshine Coast Queensland, September 2004 visit to bridge and foreshore

A trip was undertaken to look at concerns of Public Works and Main Roads Departments of Queensland. David Paterson and Wayne Ganther from CSIRO travelled to the Sunshine Coast with Alan Carse of Queensland Department of Main Roads and Michael Ball of Queensland Department of Public Works. We were also joined for part of the visits by Ed Bowers of QBuild which is a commercial unit of Public Works responsible for maintenance of Public Works. During the trip we visited a bridge on the David Low Way at Sunrise Beach near Noosa. This bridge was in a serve marine environment with high salt content in the concrete and corrosion of the galvanised guardrails and barriers. Also the foreshore at Coolum was visited and the use of stainless steel was examined. This is discussed in this report. Most problems stemmed from incorrect specification due to lack of awareness of the severity of the environment. The companion report Visit to Schools Report 2002-059-B No 7. covers the visit to four schools north of Caloundra.

Effect of height of bridge above water on salt deposition levels

Maintenance of bridge structures is a major issue for the Queensland Department of Main Roads. In the previous phase of this CRC project an initial approach was made towards the development of a program for lifetime prediction of metallic bridge components. This involved the analysis of five representative bridge structures with respect to salt deposition (a major contributor to metallic corrosion) to determine common elements to be used as “cases” - those defined for buildings are not applicable. The five bridges analysed included the Gladstone Port Access Road Overpass, Stewart Road Overpass, South Johnstone River Bridge, Johnson Creek Bridge and the Ward River Bridge.