Benjamin Hartmann

Multi-site damage localization in anisotropic plate-like structures using an active guided wave structural health monitoring system

A new approach for structural health monitoring using guided waves in plate-like structures has been developed. In contrast to previous approaches, which mainly focused on isotropic or quasi-isotropic plates, the proposed algorithm does not assume any simplifications regarding anisotropic wave propagation. Thus, it can be used to improve the probability of detection. In this paper the mathematical background for damage localization in anisotropic plates will be introduced. This is an extension of the widely known ellipse method. The formalism is based on a distributed sensor network, where each piezoelectric sensor acts in turn as an actuator. The automatic extraction of the onset time of the first waveform in the differential signal in combination with a statistical post-processing via a two-dimensional probability density function and the application of the expectation-maximization algorithm allows a completely automatic localization procedure. Thus, multiple damages can be identified at the same time. The present study uses ultrasonic signals provided by the spectral element method. This simulation approach shows good agreement with experimental measurements. A local linear neural network is used to model the nonlinear dispersion curves. The benefit of using a neural network approach is to increase the angular resolution that results from the sparse sensor network. Furthermore, it can be used to shorten the computational time for the damage localization procedure.

Supervised Hierarchical Clustering in Fuzzy Model Identification

This paper presents a new, supervised, hierarchical clustering algorithm (SUHICLUST) for fuzzy model identification. The presented algorithm solves the problem of global model accuracy, together with the interpretability of local models as valid linearizations of the modeled nonlinear system. The algorithm combines the advantages of supervised, hierarchical algorithms, which are based on heuristic tree-construction algorithms, together with the advantages of fuzzy product space clustering. The high flexibility of the validity functions that is obtained by fuzzy clustering combined with supervised learning results in an efficient partitioning algorithm, which is independent of initialization and results in a parsimonious fuzzy model. Furthermore, the usability of SUHICLUST is very undemanding, because it delivers, in contrast with many other methods, reproducible results. In order to get reasonable results, the user only has to set either a threshold for the maximum number of local models or a value for the maximum allowed global model error as a termination criterion. For fine-tuning, the interpolation smoothness controls the degree of regularization. The performance is illustrated on both analytical examples and benchmark problems from the literature.

Nonlinear System Identification by Gustafson–Kessel Fuzzy Clustering and Supervised Local Model Network Learning for the Drug Absorption Spectra Process

This paper deals with the problem of fuzzy nonlinear model identification in the framework of a local model network (LMN). A new iterative identification approach is proposed, where supervised and unsupervised learning are combined to optimize the structure of the LMN. For the purpose of fitting the cluster-centers to the process nonlinearity, the Gustafsson-Kessel (GK) fuzzy clustering, i.e., unsupervised learning, is applied. In combination with the LMN learning procedure, a new incremental method to define the number and the initial locations of the cluster centers for the GK clustering algorithm is proposed. Each data cluster corresponds to a local region of the process and is modeled with a local linear model. Since the validity functions are calculated from the fuzzy covariance matrices of the clusters, they are highly adaptable and thus the process can be described with a very sparse amount of local models, i.e., with a parsimonious LMN model. The proposed method for constructing the LMN is finally tested on a drug absorption spectral process and compared to two other methods, namely, Lolimot and Hilomot. The comparison between the experimental results when using each method shows the usefulness of the proposed identification algorithm.

On the smoothness in local model networks

This paper compares flat and hierarchical model structures in local model networks and discusses the side effects of normalization. A new algorithm for automatic transition adjustment between local models avoids undesirable effects that occur with the hierarchical approach and leads to a suitable model structure with better interpretability of local models. Demonstration examples illustrate the advantages over the existing approaches.

Hierarchical local model trees for design of experiments in the framework of ultrasonic structural health monitoring

In this paper, we propose an effective and time-saving algorithm for model-based design of experiments in the framework of a structural health monitoring system. The goal is to identify and locate structural defects in plate-like geometries. The new idea combines a pseudo-random Monte-Carlo sampling with a local model network. The global distribution of data points is based on the input space partitioning which can be seen as a mapping of the non-linearities of the underlying process. This results in an active learning strategy that incorporates the process behavior into the experimental design strategy. The application of the proposed algorithm for ultrasonic imaging in an isotropic non-convex structure shows great potential. It is shown that in contrast to a grid-based approach the spatial discretization can be optimized with high accuracy and adaptivity.

SUpervised HIerarchical CLUSTering (SUHICLUST) for nonlinear system identification

In this paper the new algorithm SUHICLUST (SUpervised HIerarchical CLUSTering) is presented. It unifies the strengths of the supervised, incremental construction scheme LOLIMOT with the advantages of product space clustering. The result of this fusion is a powerful structure identification algorithm that enables approximation of processes with axes-oblique partitioning, high flexible validity functions and local polynomial models. The theoretical comparison with LOLIMOT and product space clustering and a demonstration example underline the usefulness of SUHICLUST.

Structure trade-off strategy for local model networks

For tree-based partitioning algorithms that lead to Takagi-Sugeno fuzzy models the optimization of the consequents part goes hand in hand with the optimization of the premises part. The prediction performance can significantly be improved with the application of subset selection methods for the local polynomial models. Traditionally, the subset selection methods are applied after the model structure is already optimized. The main idea and new contribution of this work is the implementation of a so called structure trade-off procedure which allows to automatically find a good compromise between the number of local models and the flexibility of the local polynomial rule consequents. The main innovation of this approach is that the structure optimization and variable selection can be performed at the same time.

POLYMOT versus HILOMOT - A Comparison of Two Different Training Algorithms for Local Model Networks

Abstract A comparison of the POLYnomial MOdel Tree (POLYMOT) and the HIerarchical LOcal MOdel Tree (HILOMOT) algorithm for the construction of local model networks is presented in this paper. A comprehensive benchmark study with different 2-dimensional test functions as well as four popular measured datasets demonstrates the robustness against noise and overfitting of both algorithms. The major number of axes-oblique local linear models by using HILOMOT is often compensated by a smaller number of more complex axes-orthogonal local polynomial models by using POLYMOT, so that both methods generate the same model quality. However, for high-dimensional input spaces HILOMOT demonstrates its advantage of axis-oblique partitioning.

Modeling of nonlinear wave velocity characteristics in a structural health monitoring system

In the framework of structural health monitoring the research proposed in this paper focuses on a new methodology to model the nonlinear group velocity characteristics of guided waves in plate-like composite materials based on a experimental dataset. The detection and localization of damages in these composite materials is demanding due to the anisotropic wave propagation. Therefore, a well generalizing and smooth nonlinear model for the group velocities is an important part in the damage localization system. The underlying work analyzes and compares different model structures. The incorporation of physical knowledge about the process into the modeling process turns out to be of fundamental importance. Furthermore, this paper points out which nonlinear optimization approach should be applied to deliver reproducible and robust solutions.

Comparison of different subset selection algorithms for learning local model networks with higher degree polynomials

A comparison of three different subset selection methods in combination with a new learning algorithm for nonlinear system identification with local models of higher polynomial degree is presented in this paper. Usually the local models are linearly parameterized and those parameters are typically estimated by some least squares approach. For the utilization of higher degree polynomials this procedure is no longer feasible since the amount of parameters grows rapidly with the number of physical inputs and the polynomial degree. Thus a new learning strategy with the aid of subset selection methods is developed to estimate only the most significant parameters. A forward selection method with orthogonal least squares, a stepwise regression and a least angle regression method are used for training different neural networks. A comparison of the trained networks shows the benefits of each subset selection method.