Linda Mthembu

Sampling Techniques in Bayesian Finite Element Model Updating

Recent papers in the field of Finite Element Model (FEM) updating have highlighted the benefits of Bayesian techniques. The Bayesian approaches are designed to deal with the uncertainties associated with complex systems, which is the main problem in the development and updating of FEMs. This paper highlights the complexities and challenges of implementing any Bayesian method when the analysis involves a complicated structural dynamic model. In such systems an analytical Bayesian formulation might not be available in an analytic form; therefore this leads to the use of numerical methods, i.e. sampling methods. The main challenge then is to determine an efficient sampling of the model parameter space. In this paper, three sampling techniques, the Metropolis-Hastings (MH) algorithm, Slice Sampling and the Hybrid Monte Carlo (HMC) technique, are tested by updating a structural beam model. The efficiency and limitations of each technique is investigated when the FEM updating problem is implemented using the Bayesian Approach. Both MH and HMC techniques are found to perform better than the Slice sampling when Young’s modulus is chosen as the updating parameter. The HMC method gives better results than MH and Slice sampling techniques, when the area moment of inertias and section areas are updated.

Finite element model selection using Particle Swarm Optimization

This paper proposes the application of particle swarm optimization (PSO) to the problem of finite element model (FEM) selection. This problem arises when a choice of the best model for a system has to be made from set of competing models, each developed a priori from engineering judgment. PSO is a population-based stochastic search algorithm inspired by the behaviour of biological entities in nature when they are foraging for resources. Each potentially correct model is represented as a particle that exhibits both individualistic and group behaviour. Each particle moves within the model search space looking for the best solution by updating the parameters values that define it. The most important step in the particle swarm algorithm is the method of representing models which should take into account the number, location and variables of parameters to be updated. One example structural system is used to show the applicability of PSO in finding an optimal FEM. An optimal model is defined as the model that has the least number of updated parameters and has the smallest parameter variable variation from the mean material properties. Two different objective functions are used to compare performance of the PSO algorithm.

Finite element model updating using Hamiltonian Monte Carlo techniques

Abstract Bayesian techniques have been widely used in finite element model (FEM) updating. The attraction of these techniques is their ability to quantify and characterize the uncertainties associated with dynamic systems. In order to update an FEM, the Bayesian formulation requires the evaluation of the posterior distribution function. For large systems, this function is difficult to solve analytically. In such cases, the use of sampling techniques often provides a good approximation of this posterior distribution function. The hybrid Monte Carlo (HMC) method is a classic sampling method used to approximate high-dimensional complex problems. However, the acceptance rate of HMC is sensitive to the system size, as well as to the time step used to evaluate the molecular dynamics trajectory. The shadow HMC technique (SHMC), which is a modified version of the HMC method, was developed to improve sampling for large system sizes by drawing from a modified shadow Hamiltonian function. However, the SHMC algorithm performance is limited by the use of a non-separable modified Hamiltonian function. Moreover, two additional parameters are required for the sampling procedure, which could be computationally expensive. To overcome these weaknesses, the separable shadow HMC (S2HMC) method has been introduced. This method uses a transformation to a different parameter space to generate samples. In this paper, we analyse the application and performance of these algorithms, including the parameters used in each algorithm, their limitations and the effects on model updating. The accuracy and the efficiency of the algorithms are demonstrated by updating the finite element models of two real mechanical structures. It is observed that the S2HMC algorithm has a number of advantages over the other algorithms; for example, the S2HMC algorithm is able to efficiently sample at larger time steps while using fewer parameters than the other algorithms.

Finite Element Model Updating Using the Separable Shadow Hybrid Monte Carlo Technique

The use of Bayesian techniques in Finite Element Model (FEM) updating has recently increased. These techniques have the ability to quantify and characterize the uncertainties of dynamic structures. In order to update a FEM, the Bayesian formulation requires the evaluation of the posterior distribution function. For large systems, this functions is either difficult (or not available) to solve in an analytical way. In such cases using sampling techniques can provide good approximations of the Bayesian posterior distribution function. The Hybrid Monte Carlo (HMC) method is a powerful sampling method for solving higher-dimensional complex problems. The HMC uses the molecular dynamics (MD) as a global Monte Carlo (MC) move to reach areas of high probability. However, the acceptance rate of HMC is sensitive to the system size as well as the time step used to evaluate MD trajectory. To overcome this, we propose the use of the Separable Shadow Hybrid Monte Carlo (S2HMC) method. This method generates samples from a separable shadow Hamiltonian. The accuracy and the efficiency of this sampling method is tested on the updating of a GARTEUR SM-AG19 structure.

Finite Element Model Updating Using Fish School Search Optimization Method

A recent nature inspired optimization algorithm, Fish School Search (FSS) is applied to the finite element model (FEM) updating problem. This method is tested on a GARTEUR SM-AG19 aeroplane structure. The results of this algorithm are compared with two other metaheuristic algorithms, Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). It is observed that on average, the FSS and PSO algorithms give more accurate results than the GA. A minor modification to the FSS is proposed. This modification improves the performance of FSS on the FEM updating problem which has a constrained search space.

An integrated approach to fingerprint indexing using spectral clustering based on minutiae points

Fingerprint indexing is an efficient approach that improves matching performance significantly in Automated Fingerprint Recognition Systems (AFRSs). Fingerprints are currently the most highly reliable and widely biometrics trait for identification and 1-1 matching. Hence, it would be very desirable to optimize them for identification and 1-1 matching applications. This work proposes an indexing approach based on minutiae points to reduce database search space. This is motivated by the fact that predefined classes (Left Loop, Right Loop, Whorl, Tented Arch, Plain Arch) are not always equally distributed in the search space i.e. some classes are more dominant than others. In such cases, a matching module can take hours to find an exact match. We solve this problem by constructing a rotational, scale and translation (RST) invariant fingerprint descriptor based on minutiae points. The proposed RST invariant descriptor dimensions are then reduced and passed to a spectral clustering algorithm which automatically creates 50 classes. Each of these 50 classes are then represented with a B+-Tree data structure for fast indexing. The keys used in each cluster are distances of feature vectors from the center of the cluster where they belong. Instead of searching a query to only a predicted cluster we also proposed to search for it in other clusters by employing triangle inequality rule. The system proposed is 81.4443% accurate on the NIST 4 special database. The results we got are promising because NIST 4 special database contains a lot of partial fingerprint.

Finite Element Model Updating Using an Evolutionary Markov Chain Monte Carlo Algorithm

One challenge in the finite element model (FEM) updating of a physical system is to estimate the values of the uncertain model variables. For large systems with multiple parameters this requires simultaneous and efficient sampling from multiple a prior unknown distributions. A further complication is that the sampling method is constrained to search within physically realistic parameter bounds. To this end, Markov Chain Monte Carlo (MCMC) techniques are popular methods for sampling from such complex distributions. MCMC family algorithms have previously been proposed for FEM updating. Another approach to FEM updating is to generate multiple random models of a system and let these models evolve over time. Using concepts from evolution theory this evolution process can be designed to converge to a globally optimal model for the system at hand. A number of evolution-based methods for FEM updating have previously been proposed. In this paper, an Evolutionary based Markov chain Monte Carlo (EMCMC) algorithm is proposed to update finite element models. This algorithm combines the ideas of Genetic Algorithms, Simulated Annealing, and Markov Chain Monte Carlo techniques. The EMCMC is global optimisation algorithm where genetic operators such as mutation and crossover are used to design the Markov chain to obtain samples. In this paper, the feasibility, efficiency and accuracy of the EMCMC method is tested on the updating of a real structure.

A Fingerprint Indexing Approach Using Multiple Similarity Measures and Spectral Clustering

Fingerprint identification is still an open problem. Many proposed solutions relies on experts predefined classes. Recent studies and experiments have shown that predefined classes are not suitable for large databases. The main challenge is the distribution of predefined experts classes. Most fingerprints are loops; this means an identification system designed based on this classical approach slows down a matching process due to many 1-1 comparisons that need to be done to find an exact match. Beside this, some fingerprints sometimes lose their core points. In such case, it becomes very difficult to find the right class. To solve this problem, minutiae points positions (x,y) and orientations (θ) are proposed in this paper. Minutiae points are extracted and passed to a feature dimensions reduction algorithm composed of locality sensitive hashing (LSH) and histograms. The algorithm proposed creates 260 fixed length feature vectors for each fingerprint. Feature vectors are then passed to a spectral clustering which automatically creates 25 classes. Classes are then indexed through three similarity measures, namely, Euclidean, Cosine and Minkowski distance. The performance of the proposed approach is compared with two fingerprint identification systems which are based on Minutiae Cylinder-Code (MCC) and Minutiae Quadruplets (MQ). The proposed approach is 89.6% accurate while MCC and MQ approaches gets 89.4% and 79.56%, respectively, on a NIST 4 special database.