Engineering with Computers

Exact boundary conditions (BCs) imposition technique is widely used in physics-informed neural networks (PINNs) for solving boundary value problems (BVPs). In this regard, the selection of trial function satisfying essential BCs becomes hard to determine when complex geometric domain or essential BCs are considered. To address this challenge, an unified physics-informed neural network (UPINN) model is developed, in which the trial function is fully provided by deep neural networks (DNNs). The UPINN is a combination of two phases being implemented sequentially. The first one is to find DNN-based trial functions satisfying essential BCs in homogeneous form using loss function regulating the corresponding BCs. Then, the remaining one is to solve BVPs based on their strong or weak (variational) forms, in which the exact BCs imposition procedure is employed to constrain network outputs using the UPINN trial functions obtained from the first phase. The advantages of the proposed UPINN are demonstrated in terms of prediction accuracy and training cost for several solid mechanics problems with different BCs, even for complicated ones that restrict the regular PINNs significantly.

This study constructs an automatic model for detecting and classifying asphalt pavement crack. Image processing techniques including steerable filters, projective integral of image, and an enhanced method for image thresholding are employed for feature extraction. Different scenarios of feature selection have been attempted to create data sets from digital images. These data sets are then employed to train and verify the performance of machine learning algorithms including the support vector machine (SVM), the artificial neural network (ANN), and the random forest (RF). The feature set that consists of the properties derived from the projective integral and the properties of crack objects can deliver the most desirable outcome. Experimental results supported by the Wilcoxon signed-rank test show that SVM has achieved the highest classification accuracy rate (87.50%), followed by ANN (84.25%), and RF (70%). Accordingly, the proposed automatic approach can be helpful to assist transportation agencies and inspectors in the task of pavement condition assessment.

In this paper the concept for a software environment for developing engineering application systems for multiprocessor hardware (MIMD) is presented. The philosophy employed is to solve the largest problems possible in a reasonable amount of time, rather than solve existing problems faster. In the proposed environment most of the problems concerning parallel computation and handling of large distributed data spaces are hidden from the application program developer, thereby facilitating the development of large-scale software applications. Applications developed under the environment can be executed on a variety of MIMD hardware; it protects the application software from the effects of a rapidly changing MIMD hardware technology.

Our main aim in the current paper is to find a numerical plan for 2D Rayleigh–Stokes model with fractional derivative on irregular domains such as circular, L-shaped and a unit square with a circular and square hole. The employed fractional derivative is the Riemann–Liouville sense. Also, by integrating the equation corresponding to the time variable and then using the Galerkin FEM for the space direction, we obtain a full discrete scheme. The unconditional stability and the convergence estimate of the new scheme have been concluded. Finally, we evaluate results of Galerkin FEM with other numerical methods.

Field measured data reflect real response of soil slopes under rainfall infiltration and can provide representative estimates of in situ soil properties. In this study, an efficient probabilistic back analysis method for characterization of spatial variability of soil properties is used to investigate the effects of field responses with various monitoring schemes on characterization of spatial variability in unsaturated soil slope. A hypothetical heterogeneous slope of spatially varied saturated hydraulic conductivity subjecting to steady-state rainfall infiltration is analyzed as a numerical example. The spatially varied soil saturated hydraulic conductivity is parameterized by the Karhunen–Loève expansion (KLE) with a given covariance. The random variables corresponding to the truncated KLE terms are considered as variables to be estimated with Bayesian inverse method. Synthetic pore water pressure data corrupted with artificial noise are utilized as measurement data. Nine schemes with various locations, spacings and depths of monitoring sections are discussed. The results show that the local variability can be reduced substantially around the monitoring points of pore pressure. The spatial variability can be estimated more accurately with a smaller spacing of measurement points. When measurement points are installed with a spacing of 16.5 m, the posterior average COV of ks field is around 2% and the RMSE of the MAP field is only 5.90 × 10− 7 m/s. For schemes with different depths, the RMSEs of the MAP field does not change much but the posterior uncertainty of the estimated field is reduced with the increase of borehole depth.

To relieve the computational burden and improve the global optimizing ability of Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for real-world expensive problems, an elite-driven surrogate-assisted CMA-ES (ES-CMA-ES) algorithm by the improved Lower Confidence Bound (ILCB) method is proposed in this paper. Firstly, the ILCB method is established by introducing the step size, which captures the trend of exploration and exploitation in CMA-ES, to control the uncertainty term of the ILCB formula adaptively. Next, based on the ILCB method, a novel model management consisting of the efficient pre-screening strategy and the competitive chaotic operator is developed. In each generation of ES-CMA-ES, a large number of candidate points are sampled first, and then a few of them with better ILCB predicted values are screened out by the efficient pre-screening strategy, aiming to enhance the sampling quality and accelerate the optimization convergence. Moreover, the local search is performed on the best-performing screened sample points utilizing the competitive chaotic operator, with the purpose of increasing the diversity of populations in ES-CMA-ES and avoiding being trapped in the local optima. By means of the above procedures of the model management, the elite sample points are finally obtained which will be evaluated by true fitness function in each generation of ES-CMA-ES. To verify the effectiveness of ES-CMA-ES, five known black-box optimization algorithms are employed to make a comparison. Firstly, seven typical numerical examples of 10-dimensional and 20-dimensional benchmark functions are carried out, respectively. Furthermore, a 20-dimensional engineering example of the aerospace variable-stiffness composite shell under combined loadings is studied. Results indicate the outstanding efficiency, global optimizing ability and applicability of the proposed ES-CMA-ES compared to its counterpart algorithms.

In this paper, a new subdomain solution of the boundary element method based on complex variable fundamental solutions for non-homogeneous materials is developed. Being different from the conventional BEM, subdomains in the method presented can be produced by considering not only the properties of materials, but also the geometry and correspondent boundary conditions of the problem. The formulation may be combined with other complex variable fundamental solutions to provide higher accuracy and better efficiency. The coupling formulations are given in matrix form, and the numerical procedure is described. the advantages and high efficiency of the present method are demonstrated by two numerical examples.