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The great magnitude differences between the integral tunnel and its structure details make it impossible to numerically model and analyze the global and local seismic behavior of large-scale shield tunnels using a unified spatial scale, even with the help of supercomputers. The paper aims to present a combined equivalent & multi-scale simulation method, by which the tunnel's major mechanical properties under seismic loads can be represented by the equivalent model, and the seismic responses of the interested details can be studied efficiently by the coupled multi-scale model.

The nominal orthotropic material constants of the equivalent tunnel model are inversely determined by fitting the modal characteristics of the equivalent model with the corresponding segmental lining model. The critical sections are selected by comprehensive analyzing of the integral compression/extension and bending loads in the equivalent lining under the seismic shaking and the coupled multi-scale model containing the details of interest is solved by the mixed time explicit integration algorithm.

The combined equivalent & multi-scale simulation method is an effective and efficient way for seismic analyses of large-scale tunnels. The response of each flexible joint is related to its polar location on the lining ring, and the mixed time integration method can speed-up the calculation process for hybrid FE model with great differences in element sizes.

The orthotropic equivalent assumption is, to the best of the authors’ knowledge, for the first time, used in the 3D simulation of the shield tunnel lining, representing the rigidity discrepancies caused by the structural property.

The purpose of this study is to enable performing reliability-based design optimisation (RBDO) for a composite component while accounting for several multi-scale uncertainties using a large representative volume element (LRVE). This is achieved using an efficient finite element analysis (FEA)-based multi-scale reliability framework and sequential optimisation strategy.

An efficient FEA-based multi-scale reliability framework used in this study is extended and combined with a proposed sequential optimisation strategy to produce an efficient, flexible and accurate RBDO framework for fibre-reinforced composite laminate components. The proposed RBDO strategy is demonstrated by finding the optimum design solution for a composite component under the effect of multi-scale uncertainties while meeting a specific stiffness reliability requirement. Performing this using the double-loop approach is computationally expensive because of the number of uncertainties and function evaluations required to assess the reliability. Thus, a sequential optimisation concept is proposed, which starts by finding a deterministic optimum solution, then assesses the reliability and shifts the constraint limit to a safer region. This is repeated until the desired level of reliability is reached. This is followed by a final probabilistic optimisation to reduce the mass further and meet the desired level of stiffness reliability. In addition, the proposed framework uses several surrogate models to replace expensive FE function evaluations during optimisation and reliability analysis. The numerical example is also used to investigate the effect of using different sizes of LRVEs, compared with a single RVE. In future work, other problem-dependent surrogates such as Kriging will be used to allow predicting lower probability of failures with high accuracy.

The integration of the developed multi-scale reliability framework with the sequential RBDO optimisation strategy is proven computationally feasible, and it is shown that the use of LRVEs leads to less conservative designs compared with the use of single RVE, i.e. up to 3.5% weight reduction in the case of the 1 × 1 RVE optimised component. This is because the LRVE provides a representation of the spatial variability of uncertainties in a composite material while capturing a wider range of uncertainties at each iteration.

Fibre-reinforced composite laminate components designed using reliability and optimisation have been investigated before. Still, they have not previously been combined in a comprehensive multi-scale RBDO. Therefore, this study combines the probabilistic framework with an optimisation strategy to perform multi-scale RBDO and demonstrates its feasibility and efficiency for an fibre reinforced polymer component design.

The purpose of this paper is to show how investors can incorporate the multi-scale nature of asset and factor returns into their portfolio decisions and to evaluate the out-of-sample performance of such strategies.

The authors decompose daily return series of common risk factors and of all stocks listed in the Dow Jones Industrial Index (DJI) from 2000 to 2015 into different time scales to separate short-term noise from long-run trends. Then, the authors apply various (multi-scale) factor models to determine variance-covariance matrices which are used for minimum variance portfolio selection. Finally, the portfolios are evaluated by their out-of-sample performance.

The authors find that portfolios which are constructed on variance-covariance matrices stemming from multi-scale factor models outperform portfolio allocations which do not take the multi-scale nature of asset and factor returns into account.

The results of this paper provide evidence that accounting for the multi-scale nature of return distributions in portfolio decisions might be a promising approach from a portfolio performance perspective.

The authors demonstrate how investors can incorporate the multi-scale nature of returns into their portfolio decisions by applying wavelet filter techniques.

To improve the speed and accuracy of turbine blade film cooling design process, the most advanced deep learning models were introduced into this study to investigate the most suitable define for prediction work. This paper aims to create a generative surrogate model that can be applied on multi-objective optimization problems.

The latest backbone in the field of computer vision (Swin-Transformer, 2021) was introduced and improved as the surrogate function for prediction of the multi-physics field distribution (film cooling effectiveness, pressure, density and velocity). The basic samples were generated by Latin hypercube sampling method and the numerical method adopt for the calculation was validated experimentally at first. The training and testing samples were calculated at experimental conditions. At last, the surrogate model predicted results were verified by experiment in a linear cascade.

The results indicated that comparing with the Multi-Scale Pix2Pix Model, the Swin-Transformer U-Net model presented higher accuracy and computing speed on the prediction of contour results. The computation time for each step of the Swin-Transformer U-Net model is one-third of the original model, especially in the case of multi-physics field prediction. The correlation index reached more than 99.2% and the first-order error was lower than 0.3% for multi-physics field. The predictions of the data-driven surrogate model are consistent with the predictions of the computational fluid dynamics results, and both are very close to the experimental results. The application of the Swin-Transformer model on enlarging the different structure samples will reduce the cost of numerical calculations as well as experiments.

The number of U-Net layers and sample scales has a proper relationship according to equation (8). Too many layers of U-Net will lead to unnecessary nonlinear variation, whereas too few layers will lead to insufficient feature extraction. In the case of Swin-Transformer U-Net model, incorrect number of U-Net layer will reduce the prediction accuracy. The multi-scale Pix2Pix model owns higher accuracy in predicting a single physical field, but the calculation speed is too slow. The Swin-Transformer model is fast in prediction and training (nearly three times faster than multi Pix2Pix model), but the predicted contours have more noise. The neural network predicted results and numerical calculations are consistent with the experimental distribution.

This paper creates a generative surrogate model that can be applied on multi-objective optimization problems. The generative adversarial networks using new backbone is chosen to adjust the output from single contour to multi-physics fields, which will generate more results simultaneously than traditional surrogate models and reduce the time-cost. And it is more applicable to multi-objective spatial optimization algorithms. The Swin-Transformer surrogate model is three times faster to computation speed than the Multi Pix2Pix model. In the prediction results of multi-physics fields, the prediction results of the Swin-Transformer model are more accurate.

The multi-scale numerical simulation method, able to represent the complexity of the random structures and capture phase degradation, is an effective way to investigate the long-term behavior of concrete in service and bridges the gap between research on the material and on the structural level. However, the combined chemical-physical deterioration mechanisms of concrete remain a challenging task. The purpose of this paper is to investigate the degradation mechanism of concrete at the waterline in cold regions induced by combined calcium leaching and frost damage.

With the help of the NIST’s three-dimensional (3D) hydration model and the random aggregate model, realistic 3D representative volume elements (RVEs) of concrete at the micro-, the meso-, and the macro-scales can be reconstructed. The boundary problem method is introduced to compute the homogenized mechanical properties for both sound and damaged RVEs. According to the damage characteristics, the staggering method including a random dissolution model and a thermo-mechanical coupling model is developed to simulate the synergy deterioration effects of interacted calcium leaching and frost attacks. The coupled damage procedure for the frost damage process is based on the hydraulic pressure theory and the ice lens growth theory considering the relationship between the frozen temperature and the radius of the capillary pore. Finally, regarding calcium leaching as the leading role in actual engineering, the numerical methodology for combined leaching and frost damage on concrete property is proposed using a successive multi-scale method.

On the basis of available experimental data, this methodology is employed to explore the deterioration process. The results agree with the experimental ones to some extent, chemical leaching leads to the nucleation of some micro-cracks (i.e. damage), and consequently, to the decrease of the frost resistance.

It is demonstrated that the multi-scale numerical methodology can capture potential aging and deterioration evolution processes, and can give an insight into the macroscopic property degradation of concrete under long-term aggressive conditions.

The purpose of this paper is to capture the actual structural behavior of the longest timber footbridge in Spain by means of a multi-scale model updating approach in conjunction with ambient vibration tests.

In a first stage, a numerical pre-test analysis of the full bridge is performed, using standard beam-type finite elements with isotropic material properties. This approach offers a first structural model in which optimal sensor placement (OSP) methodologies are applied to improve the system identification process. In particular, the effective independence (EFI) method is used to determine the optimal locations of a set of sensors. Ambient vibration tests are conducted to determine experimentally the modal characteristics of the structure. The identified modal parameters are compared with those values obtained from this preliminary model. To improve the accuracy of the numerical predictions, the material response is modeled by means of a homogenization-based multi-scale computational approach. In a second stage, the structure is modeled by means of three-dimensional solid elements with the above material definition, capturing realistically the full orthotropic mechanical properties of wood. A genetic algorithm (GA) technique is adopted to calibrate the micromechanical parameters which are either not well-known or susceptible to considerable variations when measured experimentally.

An overall good agreement is found between the results of the updated numerical simulations and the corresponding experimental measurements. The longitudinal and transverse Young's moduli, sliding and rolling shear moduli, density and natural frequencies are computed by the present approach. The obtained results reveal the potential predictive capabilities of the present GA/multi-scale/experimental approach to capture accurately the actual behavior of complex materials and structures.

The uniqueness and importance of this structure leads to an intensive study of its structural behavior. Ambient vibration tests are carried out under environmental excitation. Extraction of modal parameters is obtained from output-only experimental data. The EFI methodology is applied for the OSP on a large-scale structure. Information coming from several length scales, from sub-micrometer dimensions to macroscopic scales, is included in the material definition. The strong differences found between the stiffness along the longitudinal and transverse directions of wood lumbers are incorporated in the structural model. A multi-scale model updating approach is carried out by means of a GA technique to calibrate the micromechanical parameters which are either not well-known or susceptible to considerable variations when measured experimentally.

The paper aims to investigate the possibilities to control friction in lubricated systems by surface patterning, making use of a multi-scale approach. Surface patterns inside the tribological contact zone tend to directly reduce friction, whereas surface patterns located in the close proximity of the contact area can improve the tribological performance by avoiding lubricant starvation and migration. Finally, optimized surface patterns were identified by preliminary laboratory tests and transferred to a journal bearing, thus testing them under more realistic conditions.

Surface patterns on a large scale (depth > 10 µm) were fabricated by micro- and roller-coining, whereas surface patterns on a small scale (depth < 2 µm) were produced by direct laser interference patterning. The combination of both techniques resulted in multi-scale surface patterns. Tribologically beneficial surface patterns (verified in ball-on-disk laboratory tests) were transferred onto a journal bearing’s shaft and tested on a special test-rig. To characterize the lubricant spreading behavior, a new test-rig was designed, which allowed for the study of the lubricant’s motion on patterned surfaces under the influence of a precisely controlled temperature gradient.

All tested patterns accounted for a pronounced friction reduction and/or an increase in oil film lifetime. The results from the preliminary laboratory tests matched well, with results from the journal bearing test-rig, both tests showing a maximum friction reduction by a factor of 3-4. Numerical investigations, as well as experiments, have shown the possibility to actively guide lubricant over patterned surfaces. Smaller periodicities, as well as greater structural depths and widths, led to a more pronounced anisotropic spreading and/or greater spreading velocities. Multi-scale surfaces demonstrated the strongest effects regarding the lubricant’s spreading behavior.

Friction, as well as lubricant migration, can be successfully controlled by using micro-coined, laser-patterned and/or multi-scale surfaces. To the best of the authors’ knowledge, the study demonstrates for the first time the unique possibility to transfer results obtained in laboratory tests to a real machine component.

The purpose of this paper is to investigate the mechanical properties’ behaviors of woven composite cut-out structures with specific parameters. Because of the complexity of micro-scale and meso-scale structure, it is difficult to accurately predict the mechanical material behavior of woven composites. Numerical simulations are increasingly necessary for the design and optimization of test procedures for composite structures made by the woven composite. The results of the proposed method are well satisfied with the results obtained from the experiment and other studies. Moreover, parametric studies on different plates based on the stacking sequences are investigated.

A multi-scale modeling approach is suggested. Back-propagation neural networks (BPNN), radial basis function (RBF) and least square support vector regression are integrated with efficient global optimization (EGO) to reduce the weight of assigned structure. Optimization results are verified by finite element analysis.

Compared with other similar studies, the advantage of the suggested strategy uses homogenized properties behaviors with more complex analysis of woven composite structures. According to investigation results, it can be found that 450/−450 ply-orientation is the best buckling load value for all the cut-out shape requirements. According to the optimal results, the BPNN-EGO is the best candidate for the EGO to optimize the woven composite structures.

A multi-scale approach is used to investigate the mechanical properties of a complex woven composite material architecture. Buckling of different cut-out shapes with the same area is surveyed. According to investigation, 45°/−45° ply-orientation is the best for all cut-out shapes. Different surrogate models are integrated in EGO for optimization. The BPNN surrogate model is the best choice for EGO to optimization difficult problems of woven composite materials.

To provide a computational strategy for highly accurate analyses of non‐linear inelastic behaviour for heterogeneous structures in civil and mechanical engineering applications

Adapts recent developments on mathematical formulations of multi‐scale problems to the recently developed component technology based on C++ generic templates programming.

Provides the understanding how theoretical hypotheses, concerning essentially the multi‐scale interface conditions, affect the computational precision of the strategy.

The present approach allows a very precise modelling of multi‐scale aspects in structural mechanics problems and can play an essential tool in searching for an optimal structural design.

Provides all the ingredients for constructing an efficient multi‐scale computational framework, from the theoretical formulation to the implementation for parallel computing. It is addressed to researchers and engineers analysing composite structures under extreme loading.

The purpose of this paper is to develop an empiricism free, first principle‐based model to simulate fluid flow and heat transfer through porous media.

Conventional approaches to the problem are reviewed. A multi‐scale approach that makes use of the sample simulations at the individual pore levels is employed. The effect of porous structures on the global fluid flow is accounted for via local volume averaged governing equations, while the closure terms are accounted for via averaging flow characteristics around the pores.

The performance of the model has been tested for an isothermal flow case. Good agreement with experimental data were achieved. Both the permeability and Ergun coefficient are shown to be flow properties as opposed to the empirical approach which typically results in constant values of these parameters independent of the flow conditions. Hence, the present multi‐scale approach is more versatile and can account for the possible changes in flow characteristics.

Further validation including non‐isothermal cases is necessary. Current scope of the model is limited to incompressible flows. The methodology can accommodate extension to compressible flows.

This paper proposes a method that eliminates the dependence of the numerical porous media simulations on empirical data. Although the model increases the fidelity of the simulations, it is still computationally affordable due to the use of a multi‐scale methodology.