510 Mathematik
Refine
Document Type
- Conference Proceeding (22)
- Article (5)
Institute
- Institut für Strukturmechanik (ISM) (27) (remove)
Keywords
- Computerunterstütztes Verfahren (22)
- Architektur <Informatik> (17)
- Angewandte Informatik (12)
- Angewandte Mathematik (12)
- CAD (10)
- Computer Science Models in Engineering; Multiscale and Multiphysical Models; Scientific Computing (7)
- Building Information Modeling (4)
- Data, information and knowledge modeling in civil engineering; Function theoretic methods and PDE in engineering sciences; Mathematical methods for (robotics and) computer vision; Numerical modeling in engineering; Optimization in engineering applications (3)
- Maschinelles Lernen (3)
- OA-Publikationsfonds2020 (3)
In this paper, we present an open-source code for the first-order and higher-order nonlocal operator method (NOM) including a detailed description of the implementation. The NOM is based on so-called support, dual-support, nonlocal operators, and an operate energy functional ensuring stability. The nonlocal operator is a generalization of the conventional differential operators. Combined with the method of weighed residuals and variational principles, NOM establishes the residual and tangent stiffness matrix of operate energy functional through some simple matrix without the need of shape functions as in other classical computational methods such as FEM. NOM only requires the definition of the energy drastically simplifying its implementation. The implementation in this paper is focused on linear elastic solids for sake of conciseness through the NOM can handle more complex nonlinear problems. The NOM can be very flexible and efficient to solve partial differential equations (PDEs), it’s also quite easy for readers to use the NOM and extend it to solve other complicated physical phenomena described by one or a set of PDEs. Finally, we present some classical benchmark problems including the classical cantilever beam and plate-with-a-hole problem, and we also make an extension of this method to solve complicated problems including phase-field fracture modeling and gradient elasticity material.
This study aims to evaluate a new approach in modeling gully erosion susceptibility (GES) based on a deep learning neural network (DLNN) model and an ensemble particle swarm optimization (PSO) algorithm with DLNN (PSO-DLNN), comparing these approaches with common artificial neural network (ANN) and support vector machine (SVM) models in Shirahan watershed, Iran. For this purpose, 13 independent variables affecting GES in the study area, namely, altitude, slope, aspect, plan curvature, profile curvature, drainage density, distance from a river, land use, soil, lithology, rainfall, stream power index (SPI), and topographic wetness index (TWI), were prepared. A total of 132 gully erosion locations were identified during field visits. To implement the proposed model, the dataset was divided into the two categories of training (70%) and testing (30%). The results indicate that the area under the curve (AUC) value from receiver operating characteristic (ROC) considering the testing datasets of PSO-DLNN is 0.89, which indicates superb accuracy. The rest of the models are associated with optimal accuracy and have similar results to the PSO-DLNN model; the AUC values from ROC of DLNN, SVM, and ANN for the testing datasets are 0.87, 0.85, and 0.84, respectively. The efficiency of the proposed model in terms of prediction of GES was increased. Therefore, it can be concluded that the DLNN model and its ensemble with the PSO algorithm can be used as a novel and practical method to predict gully erosion susceptibility, which can help planners and managers to manage and reduce the risk of this phenomenon.
In this study, a new approach to basis of intelligent systems and machine learning algorithms is introduced for solving singular multi-pantograph differential equations (SMDEs). For the first time, a type-2 fuzzy logic based approach is formulated to find an approximated solution. The rules of the suggested type-2 fuzzy logic system (T2-FLS) are optimized by the square root cubature Kalman filter (SCKF) such that the proposed fineness function to be minimized. Furthermore, the stability and boundedness of the estimation error is proved by novel approach on basis of Lyapunov theorem. The accuracy and robustness of the suggested algorithm is verified by several statistical examinations. It is shown that the suggested method results in an accurate solution with rapid convergence and a lower computational cost.
In this research, an attempt was made to reduce the dimension of wavelet-ANFIS/ANN (artificial neural network/adaptive neuro-fuzzy inference system) models toward reliable forecasts as well as to decrease computational cost. In this regard, the principal component analysis was performed on the input time series decomposed by a discrete wavelet transform to feed the ANN/ANFIS models. The models were applied for dissolved oxygen (DO) forecasting in rivers which is an important variable affecting aquatic life and water quality. The current values of DO, water surface temperature, salinity, and turbidity have been considered as the input variable to forecast DO in a three-time step further. The results of the study revealed that PCA can be employed as a powerful tool for dimension reduction of input variables and also to detect inter-correlation of input variables. Results of the PCA-wavelet-ANN models are compared with those obtained from wavelet-ANN models while the earlier one has the advantage of less computational time than the later models. Dealing with ANFIS models, PCA is more beneficial to avoid wavelet-ANFIS models creating too many rules which deteriorate the efficiency of the ANFIS models. Moreover, manipulating the wavelet-ANFIS models utilizing PCA leads to a significant decreasing in computational time. Finally, it was found that the PCA-wavelet-ANN/ANFIS models can provide reliable forecasts of dissolved oxygen as an important water quality indicator in rivers.
FCS-MBFLEACH: Designing an Energy-Aware Fault Detection System for Mobile Wireless Sensor Networks
(2019)
Wireless sensor networks (WSNs) include large-scale sensor nodes that are densely distributed over a geographical region that is completely randomized for monitoring, identifying, and analyzing physical events. The crucial challenge in wireless sensor networks is the very high dependence of the sensor nodes on limited battery power to exchange information wirelessly as well as the non-rechargeable battery of the wireless sensor nodes, which makes the management and monitoring of these nodes in terms of abnormal changes very difficult. These anomalies appear under faults, including hardware, software, anomalies, and attacks by raiders, all of which affect the comprehensiveness of the data collected by wireless sensor networks. Hence, a crucial contraption should be taken to detect the early faults in the network, despite the limitations of the sensor nodes. Machine learning methods include solutions that can be used to detect the sensor node faults in the network. The purpose of this study is to use several classification methods to compute the fault detection accuracy with different densities under two scenarios in regions of interest such as MB-FLEACH, one-class support vector machine (SVM), fuzzy one-class, or a combination of SVM and FCS-MBFLEACH methods. It should be noted that in the study so far, no super cluster head (SCH) selection has been performed to detect node faults in the network. The simulation outcomes demonstrate that the FCS-MBFLEACH method has the best performance in terms of the accuracy of fault detection, false-positive rate (FPR), average remaining energy, and network lifetime compared to other classification methods.
The extended finite element method (XFEM) offers an elegant tool to model material discontinuities and cracks within a regular mesh, so that the element edges do not necessarily coincide with the discontinuities. This allows the modeling of propagating cracks without the requirement to adapt the mesh incrementally. Using a regular mesh offers the advantage, that simple refinement strategies based on the quadtree data structure can be used to refine the mesh in regions, that require a high mesh density. An additional benefit of the XFEM is, that the transmission of cohesive forces through a crack can be modeled in a straightforward way without introducing additional interface elements. Finally different criteria for the determination of the crack propagation angle are investigated and applied to numerical tests of cracked concrete specimens, which are compared with experimental results.
Major problems of applying selective sensitivity to system identification are requirement of precise knowledge about the system parameters and realization of the required system of forces. This work presents a procedure which is able to deriving selectively sensitive excitation by iterative experiments. The first step is to determine the selectively sensitive displacement and selectively sensitive force patterns. These values are obtained by introducing the prior information of system parameters into an optimization which minimizes the sensitivities of the structure response with respect to the unselected parameters while keeping the sensitivities with respect to the selected parameters as a constant. In a second step the force pattern is used to derive dynamic loads on the tested structure and measurements are carried out. An automatic control ensures the required excitation forces. In a third step, measured outputs are employed to update the prior information. The strategy is to minimize the difference between a predicted displacement response, formulated as function of the unknown parameters and the measured displacements, and the selectively sensitive displacement calculated in the first step. With the updated values of the parameters a re-analysis of selective sensitivity is performed and the experiment is repeated until the displacement response of the model and the actual structure are conformed. As an illustration a simply supported beam made of steel, vibrated by harmonic excitation is investigated, thereby demonstrating that the adaptive excitation can be obtained efficiently.
The Element-free Galerkin Method has become a very popular tool for the simulation of mechanical problems with moving boundaries. The internally applied Moving Least Squares approximation uses in general Gaussian or cubic weighting functions and has compact support. Due to the approximative character of this method the obtained shape functions do not fulfill the interpolation condition, which causes additional numerical effort for the imposition of the essential boundary conditions. The application of a singular weighting function, which leads to singular coefficient matrices at the nodes, can solve this problem, but requires a very careful placement of the integration points. Special procedures for the handling of such singular matrices were proposed in literature, which require additional numerical effort. In this paper a non-singular weighting function is presented, which leads to an exact fulfillment of the interpolation condition. This weighting function leads to regular values of the weights and the coefficient matrices in the whole interpolation domain even at the nodes. Furthermore this function gives much more stable results for varying size of the influence radius and for strongly distorted nodal arrangements than classical weighting function types. Nevertheless, for practical applications the results are similar as these obtained with the regularized weighting type presented by the authors in previous publications. Finally a new concept will be presented, which enables an efficient analysis of systems with strongly varying node density. In this concept the nodal influence domains are adapted depending on the nodal configuration by interpolating the influence radius for each direction from the distances to the natural neighbor nodes. This approach requires a Voronoi diagram of the domain, which is available in this study since Delaunay triangles are used as integration background cells. In the numerical examples it will be shown, that this method leads to a more uniform and reduced number of influencing nodes for systems with varying node density than the classical circular influence domains, which means that the small additional numerical effort for interpolating the influence radius leads to remarkable reduction of the total numerical cost in a linear analysis while obtaining similar results. For nonlinear calculations this advantage would be even more significant.
The modeling of crack propagation in plain and reinforced concrete structures is still a field for many researchers. If a macroscopic description of the cohesive cracking process of concrete is applied, generally the Fictitious Crack Model is utilized, where a force transmission over micro cracks is assumed. In the most applications of this concept the cohesive model represents the relation between the normal crack opening and the normal stress, which is mostly defined as an exponential softening function, independently from the shear stresses in tangential direction. The cohesive forces are then calculated only from the normal stresses. By Carol et al. 1997 an improved model was developed using a coupled relation between the normal and shear damage based on an elasto-plastic constitutive formulation. This model is based on a hyperbolic yield surface depending on the normal and the shear stresses and on the tensile and shear strength. This model also represents the effect of shear traction induced crack opening. Due to the elasto-plastic formulation, where the inelastic crack opening is represented by plastic strains, this model is limited for applications with monotonic loading. In order to enable the application for cases with un- and reloading the existing model is extended in this study using a combined plastic-damage formulation, which enables the modeling of crack opening and crack closure. Furthermore the corresponding algorithmic implementation using a return mapping approach is presented and the model is verified by means of several numerical examples. Finally an investigation concerning the identification of the model parameters by means of neural networks is presented. In this analysis an inverse approximation of the model parameters is performed by using a given set of points of the load displacement curves as input values and the model parameters as output terms. It will be shown, that the elasto-plastic model parameters could be identified well with this approach, but require a huge number of simulations.
In engineering science the modeling and numerical analysis of complex systems and relations plays an important role. In order to realize such an investigation, for example a stochastic analysis, in a reasonable computational time, approximation procedure have been developed. A very famous approach is the response surface method, where the relation between input and output quantities is represented for example by global polynomials or local interpolation schemes as Moving Least Squares (MLS). In recent years artificial neural networks (ANN) have been applied as well for such purposes. Recently an adaptive response surface approach for reliability analyses was proposed, which is very efficient concerning the number of expensive limit state function evaluations. Due to the applied simplex interpolation the procedure is limited to small dimensions. In this paper this approach is extended for larger dimensions using combined ANN and MLS response surfaces for evaluating the adaptation criterion with only one set of joined limit state points. As adaptation criterion a combination by using the maximum difference in the conditional probabilities of failure and the maximum difference in the approximated radii is applied. Compared to response surfaces on directional samples or to plain directional sampling the failure probability can be estimated with a much smaller number of limit state points.