International Journal of Computational Methods

In engineering practice, the uncertainty and correlation may coexist in the input parameters, as well as in the output responses. To address such cases, several methods are developed for the non-probabilistic uncertainty and correlation propagation analysis in this study. In the proposed methods, the multidimensional parallelepiped model (MPM) is introduced to quantify the uncertainty and correlation of input parameters. In the uncertainty propagation analysis, three methods are presented to calculate the interval bounds of output responses. Among the methods, the Monte Carlo uncertainty analysis method (MCUAM) is firstly presented as a reference method, and then the first-order perturbation method (FOPM) is employed to promote the computational efficiency, and the sub-parallelepiped perturbation method (SPPM) is further developed to handle the correlated parameters with large uncertainty. In the correlation propagation analysis, the Monte Carlo correlation analysis method (MCCAM) is proposed based on the MPM and Monte Carlo simulation, which aims to compute the correlation among different output responses. The uncertainty domains between any two responses can also be constructed by the MCCAM. The effectiveness of the proposed methods on dealing with the uncertainty and correlation propagation problems is demonstrated by three numerical examples.

In this paper, by applying the accelerated technique and relaxation two-sweep strategy to the modulus-based matrix splitting iteration method, we establish the accelerated relaxation two-sweep modulus-based matrix splitting method. The proposed method contains the accelerated modulus-based matrix splitting and the generalized accelerated modulus-based matrix splitting methods presented recently as special cases. Compared with some existing methods, the proposed method can use more information during each iteration, which may lead to higher computational efficiency. We investigate the convergence properties of the new method, and prove that it is convergent under certain assumptions. Also, for the accelerated relaxation two-sweep modulus-based accelerated overrelaxation method, we analyze the convergence regions of the parameters in detail. Numerical examples are offered to show that the proposed method is efficient and performs better than the generalized accelerated modulus-based matrix splitting one in actual implementation.

The segmentation and classification of brain tumor are a attractive regions, which distinguish tumor as well as nontumor cells for identifying a level of tumor. Segmentation and classification from MRI images is a great challenge due to their altering image sizes and vast databases. Various schemes are designed for the segmentation and classification of the brain tumor, but these methods failed to offer better classification accuracy and decision-making. Here, Circle-inspired sine cosine Optimization_conditional random field-recurrent neural network (CISCO-CRF-RNN) and CISCO-Zeiler and Fergus network (CISCO-ZFNet) are introduced for brain tumor segmentation and classification. A pre-processing phase in this research is executed by the median filter to eliminate noises from an image. The segmentation is done by CRF-RNN, which is trained by CISCO. Furthermore, CISCO is newly introduced by incorporation of Circle-Inspired Optimization Algorithm (CIOA) and Sine Cosine Algorithm (SCA). Thereafter, image augmentation is performed utilizing some image augmentation techniques, and thereafter, features namely statistical features, Convolutional Neural Network (CNN) features, haralick features, pyramid histogram of orientation gradients (PHoG), and Local Vector Pattern (LVP) are extracted. Finally, the classification of brain tumor is accomplished utilizing ZFNet, which is tuned using CISCO. In addition, CISCO-CRF-RNN obtained maximal segmentation accuracy of 90.6% whereas CISCO-ZFNet achieved maximum pixel accuracy, negative predictive value (NPV), positive predictive value (PPV), and True positive rate TPR of 92.5%, 89.2%, 90.1% and 93% as well as minimum FNR of 15%.

The inherent sparse structure of impact forces has garnered considerable attention in the field of impact force identification. However, conventional convex sparse regularization methods, including the widely used ${\ell }_1$ regularization, often encounter challenges such as underestimation of impact amplitudes and biased estimations. To address these limitations, we propose a robust nonconvex sparse regularization method for impact force identification. The key advantage of our method is the simultaneous retention of robustness and unbiasedness. The robustness of our method is primarily achieved through an efficient solver developed within the alternating direction method of multipliers (ADMM) framework. By combining convex and nonconvex strategies, the ADMM solver separates the intractable nonconvex problem into more manageable convex sub-problems. Additionally, the ADMM solver incorporates the firm-thresholding operator, which ensures an unbiased amplitude distribution and preserves the impact amplitudes. With a sparse and under-determined sensor configuration, our proposed method enables simultaneous impact localization and time-history reconstruction. We comprehensively demonstrate the algorithmic performance through a series of numerical simulations and laboratory experiments on typical composite structures. The comparative results clearly indicate that our proposed approach achieves significant improvements in identification accuracy compared to classical sparse regularization methods, such as ${\ell }_1$ and ${\ell }_0$ regularization.

In this paper, we present a new splitting nearly-analytic symplectic partitioned Runge–Kutta (SNSPRK) method for the two-dimensional (2D) elastic wave equations. It is an extension to elastic wave equation of our recent work on the locally one-dimensional nearly-analytic symplectic partitioned Runge–Kutta (LOD-NSPRK) method for the 2D acoustic wave equations. The method is based on the spatial differential operator-split technique, in which the resulting spatial discrete matrices are symmetric unlike the conventional nearly-analytic symplectic partitioned Runge–Kutta (NSPRK) method. The stability condition is given, which has more relax restriction for the time step than the NSPRK schemes. To show the performance of the new method, numerical experiments are given. Numerical results illustrate that the SNSPRK method has better long-term calculation capability as time proceeds than the NSPRK method.

Coupled mechanical systems can be complex, especially if there are many systems connected together and nonlinearities are present. Soil-structure interaction refers to the interaction between a structure and the soil or foundation upon which it is built. This interaction is important because it can affect the behavior of the structure, particularly during earthquakes or other dynamic events. For the wind turbine foundation design, the soil should support the weight of a wind turbine and anchor it to the ground. This paper presents a nonlinear material behavior soil coupled to elastic structure in offshore conditions. The goal of this work is to develop a coupled structural finite element procedure using Localized Lagrange Multipliers (LLM) at idealized offshore wind turbines with nonlinear poroelastic model for soil foundation. In this work, an anisotropic sand constitutive model is used to describe the soil foundation behavior. This model is based in a critical state soil mechanics and bounding surface plasticity. Classical elasto-plasticity theory is used to obtain the soil stiffness. The numerical model is validated through a fully coupled model at classical problems results. The mixed formulation $(u,p)$ is used to model the interface frames between the domains. The momentum equilibrium and mass continuity equations are solved by algebraic equation system imposed by Lagrange multipliers methodology. In order to excite the system, aerodynamic forces are imposed in random wind velocity conditions. In another numerical case, the response of coupled system during shaking is simulated by a horizontal input motion at bottom of soil foundation. Some computational aspects are discussed and the numerical model is clarified. The classical Newton Method to solve nonlinear problems is used in a finite element approach. In addition, two foundation models are tested and time dynamic responses are evaluated for a range of physical parameters including the wind nature and soil properties.