We consider the problem of detecting anomalies in the directional distribution of fibre materials observed in 3D images. We divide the image into a set of scanning windows and classify them into two clusters: homogeneous material and anomaly. Based on a sample of estimated local fibre directions, for each scanning window we compute several classification attributes, namely the coordinate wise means of local fibre directions, the entropy of the directional distribution, and a combination of them. We also propose a new spatial modification of the Stochastic Approximation Expectation-Maximization (SAEM) algorithm. Besides the clustering we also consider testing the significance of anomalies. To this end, we apply a change point technique for random fields and derive the exact inequalities for tail probabilities of a test statistics. The proposed methodology is first validated on simulated images. Finally, it is applied to a 3D image of a fibre reinforced polymer.
The paper considers the problem of anomaly detection in 3D images of fibre materials. The spatial Stochastic Expectation Maximisation algorithm and Adaptive Weights Clustering are applied to solve this problem. The initial 3D grey scale image was divided into small cubes subject to clustering. For each cube clustering attributes values were calculated: mean local direction and directional entropy. Clustering is conducted according to the given attributes. The proposed methods are tested on the simulated images and on real fibre materials.
Introduction.Nowadays, there exists a large amount of novel materials with interesting physical properties. For instance, reinforcement of polymers with fibres significantly increases the mechanical properties of the materials. The materials' performance is determined mostly by their composition as well as by allocation and directions of the reinforcing fibres.Due to the production process, an anomaly region may be formed in the material. We define it as an area where the distribution of fibre directions differs from the remaining material. To keep the stated material's properties, it is necessary to identify regions with untypical fibre distribution. For this purpose, high-resolution microcomputer tomography reaching a level of microns [1,2] is used to observe the fibre system in a composite sample, cf. Figure 1 (right).Our main task is then to find the areas with anomalous directional properties of fibres in the 3D image. This is done by means of cluster analysis dividing the whole image volume into two clusters: the smaller "anomaly" region and the bigger "normal" material.
This paper considers a hybrid approach to the identification of dynamical systems based on a self-configuring genetic programming algorithm and a differential evolution method. The value of this approach is in the automatic determination of the order, structure and parameters of differential equation, i.e., a model of a dynamic system. The application of the differential evolution method can significantly increase the accuracy of the resulting model confirmed by the results of the experiments presented in this paper.
The paper considers a reduction of differential equations identification problem to the symbolic regression task. The current approach allows automatic determining the structure of a differential equation via the usage of the self-configuring genetic programming algorithm. The a priori information needed is only the dynamic system initial point and the sample of input and output effects. The stability of the proposed approach to the presence of noise in the sample and the small amount of data is investigated.
Evolutionary approaches are widely applied in solving various types of problems. The paper considers the application of EvolODE and EvolODES approaches to the identification of dynamic systems. EvolODE helps to obtain a model in the form of an ordinary differential equation without restrictions on the type of the equation. EvolODES searches for a model in the form of an ordinary differential equation system. The algorithmic basis of these approaches is a modified genetic programming algorithm for finding the structure of ordinary differential equations and differential evolution to optimize the values of numerical constants used in the equation. Testing for these approaches on problems in the form of ordinary differential equations and their systems was conducted. The influence of noise present in the data and the sample size on the model error was considered for each of the approaches. The symbolic accuracy of the resulting equations was studied. The proposed approaches make it possible to obtain models in symbolic form. They will provide opportunities for further interpretation and application.
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