Sequential Importance Sampling Algorithm in Damage Detection of a Cable Stayed Bridge

Publication in the conference proceedings of EUSIPCO, Toulouse, France, 2002

Chapter 17 - Particle Filtering

Increasingly, for many application areas, it is becoming important to include elements of nonlinearity and non-Gaussianity in order to model accurately the underlying dynamics of a physical system. Moreover, it is typically crucial to process data on-line as it arrives, both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics. In this paper, we review both optimal and suboptimal Bayesian algorithms for nonlinear/non-Gaussian tracking problems, with a focus on particle filters. Particle filters are sequential Monte Carlo methods based on point mass (or particle) representations of probability densities, which can be applied to any state-space model and which generalize the traditional Kalman filtering methods. Several variants of the particle filter such as SIR, ASIR, and RPF are introduced within a generic framework of the sequential importance sampling (SIS) algorithm. These are discussed and compared with the standard EKF through an illustrative example.

This paper addresses the problem of estimating range-varying parameters of the height-dependent index of refraction over the sea surface in order to predict ducted microwave propagation loss. Refractivity estimation is performed using a Markov model for microwave radar clutter returns from the sea surface. Specifically, the parabolic approximation for numerical solution of the wave equation is used to formulate the problem within a nonlinear recursive Bayesian state estimation framework. Solution for the conditional expectation of range-varying refractivity, given log-amplitude clutter versus range data, is achieved using a sequential importance sampling technique. Simulation results are presented which demonstrate the ability of this approach to synoptically estimate range-varying refractivity parameters by "through-the-sensor" remote sensing.

Random graphs with given degrees are a natural next step in complexity beyond the Erdős–Renyi model, yet the degree constraint greatly complicates simulation and estimation. We use an extension of a combinatorial characterization due to Erdős and Gallai to develop a sequential algorithm for generating a random labeled graph with a given degree sequence. The algorithm is easy to implement and allows for surprisingly efficient sequential importance sampling. The resulting probabilities are easily computed on the fly, allowing the user to reweight estimators appropriately, in contrast to some ad hoc approaches that generate graphs with the desired degrees but with completely unknown probabilities. Applications are given, including simulating an ecological network and estimating the number of graphs with a given degree sequence.

Sequential importance sampling for structural reliability analysis

Assimilating real-time sensor data into large-scale spatial-temporal simulations, such as simulations of wildfires, is a promising technique for improving simulation results. This asks for advanced data assimilation methods that can work with the complex structures and nonlinear behaviors associated with the simulation models. This article presents a data assimilation framework using Sequential Monte Carlo (SMC) methods for wildfire spread simulations. The models and algorithms of the framework are described, and experimental results are provided. This work demonstrates the feasibility of applying SMC methods to data assimilation of wildfire spread simulations. The developed framework can potentially be generalized to other application areas where sophisticated simulation models are used.

Based on the concept of sequential importance sampling (SIS) and the use of Bayesian theory, particle filter is particularly useful in dealing with nonlinear and non-Gaussian problems. In this paper, a new particle filter is proposed that uses a divided difference filter to generate the importance proposal distribution is proposed. The proposal distribution integrates the latest measurements into system state transition density so it can match the posterior density well. The simulation results show that the new particle filter performs superior to the generic particle filter and other particle filters such as the extended Kalman particle filter and the unscented particle filter.

An efficient method for constructing multiple candidate finite element (FE) models which are consistent with the measured dynamic properties of a civil structure is presented. A parameterised sensitivity-based FE model updating method was developed to permit a feasible FE model set for the target structure to be produced. In this method, an aggregated multi-objective function, which is defined by the weighted sum of the error functions, is parameterised by its relative weighting factors. By introducing multiple parameter sets for the weighting factors, a number of optimal updated FE models are produced that permit both the natural frequency errors and mode shape errors to be simultaneously minimised. The effectiveness of the proposed method is illustrated by an example using an existing cable-stayed bridge. The findings show that error-minimised, well-distributed FE models can be obtained in terms of modal frequency errors and mode shape errors. The high quality of the candidate model sets is also verified by observations showing that the distributions of the structural parameters are consistent through each updated FE models, and the characteristic features of the target structure such as non-symmetric mode shapes are relatively well captured.

Recently simulation model becomes an essential tool for analysis and design of a system but it is often expensive and time consuming as it becomes complicate to achieve reliable results. Therefore, high-fidelity simulation model needs to be replaced by an approximate model, the so-called metamodel. Metamodeling techniques include 3 components of sampling, metamodel and validation. Cross-validation approach has been proposed to provide sequnatially new sample point based on cross-validation error but it is very expensive because cross-validation must be evaluated at each stage. To enhance the cross-validation of metamodel, sequential sampling method using candidate points and representative cross-validation is proposed in this paper. The candidate and representative cross-validation approach of sequential sampling is illustrated for two-dimensional domain. To verify the performance of the suggested sampling technique, we compare the accuracy of the metamodels for various mathematical functions with that obtained by conventional sequential sampling strategies such as maximin distance, mean squared error, and maximum entropy sequential samplings. Through this research we learn that the proposed approach is computationally inexpensive and provides good prediction performance.

The nested case-control design is a relatively new type of observational study whereby a case-control approach is employed within an established cohort. In this design, we observe cases and controls longitudinally by sampling all cases whenever they occur but controls at certain time points. Controls can be obtained at time points randomly scheduled or prefixed for operational convenience. This design with longitudinal observations is efficient in terms of cost and duration, especially when the disease is rare and the assessment of exposure levels is difficult. In our design, we propose sequential sampling methods and study both (group) sequential testing and estimation methods so that the study can be stopped as soon as the stopping rule is satisfied. To make such a longitudinal sampling more efficient in terms of both numbers of subjects and replications, we propose applying sequential sampling methods to subjects and replications, simultaneously, until the information criterion is fulfilled. This simultaneous sequential sampling on subjects and replicates is more flexible for practitioners designing their sampling schemes, and is different from the classical approaches used in longitudinal studies. We newly define the σ-field to accommodate our proposed sampling scheme, which contains mixtures of independent and correlated observations, and prove the asymptotic optimality of sequential estimation based on the martingale theories. We also prove that the independent increment structure is retained so that the group sequential method is applicable. Finally, we present results by employing sequential estimation and group sequential testing on both simulated data and real data on children's diarrhea.

The reliability polynomial of a graph gives the probability that a graph is connected as a function of the probability that each edge is connected. The coefficients of the reliability polynomial count the number of connected subgraphs of various sizes. Algorithms based on sequential importance sampling (SIS) have been proposed to estimate a graph's reliability polynomial. We develop a new bottom-up SIS algorithm for estimating the reliability polynomial by choosing a spanning tree and adding edges. This algorithm improves on existing bottom-up algorithms in that it has lower complexity ≈ O(E2) as opposed to O(EV3), and it uses importance sampling to reduce variance.

Model updating-based dynamic collapse analysis of a RC cable-stayed bridge under earthquakes

A binomial sequential sampling procedure based on the presence of five or more Thrips tabaci per onion was as precise as Iwao’s sequential sampling method that requires counting all thrips present. Acceptance boundaries were calculated for economic thresholds of 0.9 and 2.2 thrips per leaf and the plans were validated in fields containing 0.01 to 32.33 thrips per leaf. For both procedures the correct decision was reached >83% of the time by sampling 12 to 14 onions. Error rates were <4%, which is below the theoretical error levels of 10% used for the Iwao procedure and 5% for the binomial procedure. In the remaining situations no decision could be reached because thrips densities were near the economic threshold. Binomial sampling was more time efficient than Iwao’s sampling method, reducing up to 88% of the counting time in no-decision situations. Thrips in onion fields exhibited a contagious distribution.

For the simple bridge structure, the finite element model established by drawing and elastic mechanics method is accurate. However, when faced with large and complex long-span bridge structures, there are inevitable differences between the finite element model and the physical model, where the model has to be updated. It is problematic that the updating structural matrix cannot be fed back into the existing general finite element calculation software in the traditional structural matrix updating method. In this paper, a parameter-type updating method based on the “Kriging model + swarm intelligence” optimization is proposed. The Kriging model, based on Genetic Algorithm (GA), Bird Mating Optimizer (BMO), and Particle Swarm Optimization algorithm (PSO), is introduced into the finite element model, updating this to correct the design parameters of the finite element model. Firstly, a truss structure was used to verify the effectiveness of the proposed optimization method, and then a cable-stayed bridge was taken as an example. Three methods were used to update the finite element model of the bridge, and the results of the three optimization algorithms were compared and analyzed. The results show that, compared with the other two methods, the GA-based model updating method has the least time due to the small computation. The results of the BMO-based model were time consuming compared to the other two algorithms, and the parameter identification results were better than the GA algorithm. The PSO algorithm-based model updating method to solve the finite element model was repeated, which required a large amount of computation and was more time consuming; however, it had the highest parameter correction accuracy.