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Summary A multi‐scale model is often constructed using different finite elements and consists of a global scale model for the structural system and a few local scale models for critical structural components so that the multi‐scale simulation can concurrently exhibit both global performance and local behavior of the structure. To ensure the multi‐scale model can best represent the real structure, multi‐scale model updating technique shall be developed accordingly. This paper thus presents a multi‐scale model updating method for a transmission tower structure using the Kriging meta‐model that actually is a surrogate for the multi‐scale model. Firstly, the multi‐scale model of a transmission tower is established by using beam elements to simulate global structure and solid elements to simulate local joints with bolt connections. Secondly, the multi‐objective optimization problem that involves multiple objective functions is established to update key parameters of the multi‐scale model so that the errors between the measured and predicted structural dynamic characteristics and multi‐scale responses can be minimized. To improve the computational efficiency and accuracy of optimization, the Kriging meta‐method is used to find the updated key parameters of the tower after a comparison with other meta‐methods is made. Finally, the proposed method is applied to a physical transmission tower model, which has been tested in a laboratory, to demonstrate the feasibility and accuracy of the proposed model‐updating method. The updated results show that the proposed updating method can improve the accuracy of the multi‐scale model of the tower in both global and local structural responses.

Many species distribution models (SDMs) are built with precise but geographically restricted presence–absence data sets (e.g., a country) where only a subset of the environmental conditions experienced by a species across its range is considered (i.e., spatial niche truncation). This type of truncation is worrisome because it can lead to incorrect predictions e.g., when projecting to future climatic conditions belonging to the species niche but unavailable in the calibration area. Data from citizen-science programs, species range maps or atlases covering the full species range can be used to capture those parts of the species’ niche that are missing regionally. However, these data usually are too coarse or too biased to support regional management. Here, we aim to (1) demonstrate how varying degrees of spatial niche truncation affect SDMs projections when calibrated with climatically truncated regional data sets and (2) test the performance of different methods to harness information from larger-scale data sets presenting different spatial resolutions to solve the spatial niche truncation problem. We used simulations to compare the performance of the different methods, and applied them to a real data set to predict the future distribution of a plant species (Potentilla aurea) in Switzerland. SDMs calibrated with geographically restricted data sets expectedly provided biased predictions when projected outside the calibration area or time period. Approaches integrating information from larger-scale data sets using hierarchical data integration methods usually reduced this bias. However, their performance varied depending on the level of spatial niche truncation and how data were combined. Interestingly, while some methods (e.g., data pooling, downscaling) performed well on both simulated and real data, others (e.g., those based on a Poisson point process) performed better on real data, indicating a dependency of model performance on the simulation process (e.g., shape of simulated response curves). Based on our results, we recommend to use different data integration methods and, whenever possible, to make a choice depending on model performance. In any case, an ensemble modeling approach can be used to account for uncertainty in how niche truncation is accounted for and identify areas where similarities/dissimilarities exist across methods.

Aim Bats are important components of mammalian biodiversity and strong bioindicators, but their fine‐scale distributions often remain less known than other taxa (e.g., plants, birds). Yet as highly mobile species with multiple needs in the landscape, bats impose serious modelling challenges, such as advanced use of neighbourhood analyses. The aims of this study were to test the use of a designed sampling of bats for biodiversity and conservation assessments, and to find appropriate modelling solutions for providing nature practitioners with reliable potential bat distribution maps in a mountain area of high conservation interest. Location The western Swiss Alps of Vaud. Methods We conducted a one‐year field survey combining passive acoustic recordings supplemented by mist net catching to collect data on bats. These data were then used to create univariate models with focal land use/cover variables using different focal window sizes to detect the optimal species‐specific scale of influence for each variable. The large number of selected variables was then used to create ensembles of small models at a 100 m × 100 m resolution, and the resulting habitat suitability maps were transformed into species distribution maps for practitioners. Results We were able to collect data to model 14 different bat species representing 66% of the Swiss bat diversity, including four red list species. In general, the most important variables were Euclidean distance to road or water, temperature and slope, but there was large variation among species both for the variable importance and for the optimal focal window size. Main conclusion Our study greatly increased the knowledge of bats in this region and showed that many of the red list species are nowadays disappearing from the intensively used lowland plains and restricted to the remaining forests along the slopes. Additionally, we highlighted the importance of selecting the variable scale on a species‐specific basis accounting for their mobility and range sizes.

The Jiaodong Peninsula in China is rich in metal deposits, but its geological setting is very complex. To ensure the stability of metal mining-induced excavations of the study area, it is necessary to understand the development of regional structures and the distribution of stress fields. Considering the multi-scale characteristics of geological objects, we conducted multi-scale 3D geological modeling and in situ stress inversion from regional large-scale (100km), regional medium-scale (10km), and engineering scale (km) to obtain the in situ stress distribution of several mine areas (Xincheng, Tengjia, and Hongbu mining areas) at the Xincheng Gold Mine, in the Jiaodong Peninsula region and guide engineering practice. The Hermite Radial Basis Function (HRBF) is adopted to obtain multi-scale geological models including small faults, surrounding rocks, and ore bodies by using regional field survey data, exploration profiles, and boreholes. Then, through several groups of measured in situ stress data, multi-scale in situ stress field inversion is carried out by adopting the multiple linear regression method. Then, the distribution of the in situ stress field is analyzed. In this paper, each smaller-scale 3D modeling and in situ stress inversion is refined and corrected based on the larger-scale modeling and inversion. The results show that the calculated in situ stress of multi-scale inversions is more accurate, which verifies the practicability and effectiveness of the multi-scale modeling and in situ stress inversion. Therefore, compared with the single-scale geological model and inversion, the multi-scale model and inversion can predict the in situ stress distribution of rock engineering more accurately.

Across a large mountain area of the western Swiss Alps, we used occurrence data (presence‐only points) of bird species to find suitable modelling solutions and build reliable distribution maps to deal with biodiversity and conservation necessities of bird species at finer scales. We have performed a multi‐scale method of modelling, which uses distance, climatic, and focal variables at different scales (neighboring window sizes), to estimate the efficient scale of each environmental predictor and enhance our knowledge on how birds interact with their complex environment. To identify the best radius for each focal variable and the most efficient impact scale of each predictor, we have fitted univariate models per species. In the last step, the final set of variables were subsequently employed to build ensemble of small models (ESMs) at a fine spatial resolution of 100 m and generate species distribution maps as tools of conservation. We could build useful habitat suitability models for the three groups of species in the national red list. Our results indicate that, in general, the most important variables were in the group of bioclimatic variables including “Bio11” (Mean Temperature of Coldest Quarter), and “Bio 4” (Temperature Seasonality), then in the focal variables including “Forest”, “Orchard”, and “Agriculture area” as potential foraging, feeding and nesting sites. Our distribution maps are useful for identifying the most threatened species and their habitat and also for improving conservation effort to locate bird hotspots. It is a powerful strategy to improve the ecological understanding of the distribution of bird species in a dynamic heterogeneous environment. To know better how bird species and their complex environment interact, we have performed a multi‐scale modelling method using focal variables in different scales to evaluate the efficient scale of each environmental predictor where they are influential.

During a full cardiac cycle, the left atrium successively behaves as a reservoir, a conduit and a pump. This complex behavior makes it unrealistic to apply the time-varying elastance theory to characterize the left atrium, first, because this theory has known limitations, and second, because it is still uncertain whether the load independence hypothesis holds. In this study, we aim to bypass this uncertainty by relying on another kind of mathematical model of the cardiac chambers. In the present work, we describe both the left atrium and the left ventricle with a multi-scale model. The multi-scale property of this model comes from the fact that pressure inside a cardiac chamber is derived from a model of the sarcomere behavior. Macroscopic model parameters are identified from reference dog hemodynamic data. The multi-scale model of the cardiovascular system including the left atrium is then simulated to show that the physiological roles of the left atrium are correctly reproduced. This include a biphasic pressure wave and an eight-shaped pressure-volume loop. We also test the validity of our model in non basal conditions by reproducing a preload reduction experiment by inferior vena cava occlusion with the model. We compute the variation of eight indices before and after this experiment and obtain the same variation as experimentally observed for seven out of the eight indices. In summary, the multi-scale mathematical model presented in this work is able to correctly account for the three roles of the left atrium and also exhibits a realistic left atrial pressure-volume loop. Furthermore, the model has been previously presented and validated for the left ventricle. This makes it a proper alternative to the time-varying elastance theory if the focus is set on precisely representing the left atrial and left ventricular behaviors.

Fractional calculus-based differential equations were found by previous studies to be promising tools in simulating local-scale anomalous diffusion for pollutants transport in natural geological media (geomedia), but efficient models are still needed for simulating anomalous transport over a broad spectrum of scales. This study proposed a hierarchical framework of fractional advection-dispersion equations (FADEs) for modeling pollutants moving in the river corridor at a full spectrum of scales. Applications showed that the fixed-index FADE could model bed sediment and manganese transport in streams at the geomorphologic unit scale, whereas the variable-index FADE well fitted bedload snapshots at the reach scale with spatially varying indices. Further analyses revealed that the selection of the FADEs depended on the scale, type of the geomedium (i.e., riverbed, aquifer, or soil), and the type of available observation dataset (i.e., the tracer snapshot or breakthrough curve (BTC)). When the pollutant BTC was used, a single-index FADE with scale-dependent parameters could fit the data by upscaling anomalous transport without mapping the sub-grid, intermediate multi-index anomalous diffusion. Pollutant transport in geomedia, therefore, may exhibit complex anomalous scaling in space (and/or time), and the identification of the FADE’s index for the reach-scale anomalous transport, which links the geomorphologic unit and watershed scales, is the core for reliable applications of fractional calculus in hydrology.

We survey, in a partial way, multi-scale approaches for the modelling of rubber-like and soft tissues and compare them with classical macroscopic phenomenological models. Our aim is to show how it is possible to obtain practical mathematical models for the mechanical behaviour of these materials incorporating mesoscopic (network scale) information. Multi-scale approaches are crucial for the theoretical comprehension and prediction of the complex mechanical response of these materials. Moreover, such models are fundamental in the perspective of the design, through manipulation at the micro- and nano-scales, of new polymeric and bioinspired materials with exceptional macroscopic properties.

Multi-scale simulations, combining muscle and joint contact force (JCF) from musculoskeletal simulations with adaptive mechanobiological finite element analysis, allow to estimate musculoskeletal loading and predict femoral growth in children. Generic linearly scaled musculoskeletal models are commonly used. This approach, however, neglects subject- and age-specific musculoskeletal geometry, e.g. femoral neck-shaft angle (NSA) and anteversion angle (AVA). This study aimed to evaluate the impact of proximal femoral geometry, i.e. altered NSA and AVA, on hip JCF and femoral growth simulations. Musculoskeletal models with NSA ranging from 120° to 150° and AVA ranging from 20° to 50° were created and used to calculate muscle and hip JCF based on the gait analysis data of a typically developing child. A finite element model of a paediatric femur was created from magnetic resonance images. The finite element model was morphed to the geometries of the different musculoskeletal models and used for mechanobiological finite element analysis to predict femoral growth trends. Our findings showed that hip JCF increase with increasing NSA and AVA. Furthermore, the orientation of the hip JCF followed the orientation of the femoral neck axis. Consequently, the osteogenic index, which is a function of cartilage stresses and defines the growth rate, barely changed with altered NSA and AVA. Nevertheless, growth predictions were sensitive to the femoral geometry due to changes in the predicted growth directions. Altered NSA had a bigger impact on the growth results than altered AVA. Growth simulations based on mechanobiological principles were in agreement with reported changes in paediatric populations.

In this work, three-dimensional thermal simulations of single 18650 lithium-ion battery cell and 75 V lithium-ion battery pack composed of 21 18650 battery cells are performed based on a multi-scale multi-domain (MSMD) battery modeling approach. Different cooling approaches’ effects on 18650 lithium-ion battery and battery pack thermal management under fast discharging and external shorting conditions are investigated and compared. It is found that for the natural convection, forced air cooling, and/or mini-channel liquid cooling approaches, the temperature of battery cell easily exceeds 40 °C under 3C rate discharging condition. While under external shorting condition, the temperature of cell rises sharply and reaches the 80 °C in a short period of time, which can trigger thermal runaway and may even lead to catastrophic battery fire. On the other hand, when the cooling method is single-phase direct cooling with FC-72 as coolant or two-phase immersed cooling by HFE-7000, the cell temperature is effectively limited to a tolerable level under both high C rate discharging and external shorting conditions. In addition, two-phase immersed cooling scheme is found to lead to better temperature uniformity according to the 75 V battery pack simulations.