Acquiring engineering data is frequently expensive, resulting in sparse data that may lead to a lack of knowledge for design and analysis. Thus, it is not always feasible to precisely determine the probability density functions (PDFs) of uncertain model parameters. Under such circumstances that involve simultaneous aleatory and epistemic uncertainties, repeated uncertainty propagation (UP) analysis is generally required. In this paper, a novel approach for hybrid UP is proposed by integrating B-spline chaos and augmented change of probability measure (aCOM) for meeting different goals. The B-spline chaos is adopted to represent the complicated computational model as a function of an arbitrary input random variable, while the aCOM is employed to reconstruct the PDF of the model output when the input PDF is changed due to epistemic uncertainty. In the case of small epistemic uncertainty, hybrid UP can be achieved directly by changing the assigned probabilities of existing sample results. While in the case of large epistemic uncertainty, additional samples from an augmenting PDF are generated. The proposed method is compatible with both cases. The numerical algorithm of the proposed method is presented and illustrated by four benchmark problems. Further, the accuracy and efficiency of the proposed method are substantiated by four numerical examples compared with analytical solutions or Monte Carlo simulations. An attempt to enhance the proposed method with the aid of active subspace methods to handle high-dimensional problems is also discussed in this work. The limitations and potential improvements of the proposed approach are outlined as well.

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Urban areas face a variety of ecological challenges in their development. To improve urban ecology, strategic use of vegetation, particularly trees, is essential. As the amount of land available in cities decreases, the combination of buildings with vertically planted trees has become a popular way to increase urban greenery. However, this presents new challenges, such as the mechanical stability of trees and their sustainable maintenance. To address the challenge of tree mechanics, this research introduces a pioneering natural fixation technique from a structural engineering viewpoint. In this natural fixation, the trees are connected by self-growing connections and form in pairs as the interconnected tree system, or living structures. The fusion of a self-growing connection is based on the adaptive mechanism of trees. In recent years, in the field of architecture and botany, there has been a gradual attention to the implementation of self-growing connections. However, the understanding of the living structures requires cross-disciplinary studies, and to the best of the author's knowledge, there is little directly relevant literature; and most discussions focus on qualitative analysis. Therefore, the focus of this dissertation is on the quantitative examination of the fundamental characteristics and mechanical properties of self-growing connections and interconnected tree systems. To fill this gap, two tree species, Ficus benjamina L. and Tilia cordata Mill., were studied. The self-growing connection fused by Ficus benjamina was characterized both at the macroscopic and microscopic levels. On the macroscopic scale, the self-growing connection was studied from three main aspects, namely the density distribution, geometric variation, and fiber structures. The results showed that the density of the intersected region was higher than that of the stem region in the same cross section within the self-growing connection. In the same cross-sectional view, the measured area of the intersected region was found to be larger than that of the stem region, indicating a greater allocation of material in the intersected region. Regarding fiber structures, the self-growing connection was primarily characterized by three groups of fibers, namely merged fibers, deviated fibers, and normal fibers. The group of merged fiber bundles combined two stems and played an important role in the structural integrity and mechanical strength of a self-growing connection. At the microscopic level, the investigations were performed on the cellular and tissue scales. The results indicated that on the edge of the interconnected region, especially at the small cross angle, the material was primarily composed of bark tissue. Notably, merged fibers were observed in the outer layer of the intersected region. In contrast, the inner section of the intersected region showed a lower concentration of continuous merged fibers. Additionally, within the intersected region, the presence of tension wood with G-layers was identified.  Following that, four-point spatial tensile tests were performed to investigate the tensile properties of self-growing connections. To characterize their fusion condition, two parameters (fusion degree and interface curvature) were proposed. During the tensile tests, it was observed that the connection gradually cracked from approximately 0.8 times its ultimate load. The propagation of cracks was primarily affected by the geometry of the interface and the content of the merged fibers. The failure occurred at the interface when the fusion degree reached around 15%; however, when the fusion degree exceeded this threshold, the failure cracks extended across the stems, forming a ‘Y’ shape. Additionally, statistical analyses of geometric parameters with mechanical properties were performed. Tensile strength exhibited negative correlations with cone ratio and interface curvature, whereas it had positive correlations with average diameter and fusion degree. The interface curvature was found to have a mediate correlation with the tensile strength. In comparison to fusion degree, the interface curvature can better predict the tensile strength of a self-growing connection. After analyses of self-growing connections, this research focused on investigating the biomechanical characteristics of interconnected tree systems fused by Tilia cordata, including cross interconnected trees, parallel interconnected trees, and single standing trees. Investigations were carried out repeatedly before and after a two-year growth period. Experimental pulling tests were conducted under various loading scenarios, classified as in-plane and out-of-plane loading, with respect to the tree connecting plane. The results revealed that the rigidity of all the interconnected systems increased as a result of tree growth. Regarding the cross interconnected tree system, an evident bracing effect was observed in the in-plane loading scenario. Regarding the parallel interconnected trees, they exhibited an increase in basal stiffness compared to single standing trees as a result of the formation of a self-growing connection in the lower region. Finally, the growth of self-growing connections was investigated using the micro-drilling technique. The method was first applied to self-growing connections fused by Ficus benjamina to explain the resistance distribution pattern in facilitation with anatomical characteristics and density changes. Subsequently, the approach was utilized to deduce internal features from self-growing connections fused by Tilia cordata. Regarding self-growing connections fused by Ficus benjamina, in the intersected region, a drop-down effect was identified in the resistance profile. This effect corresponded to the findings of microscopic observations of the location of the included bark. Regarding the self-growing living connection fused by Tilia cordata, the resistance profile can provide information about the location of internal discontinuities (i.e., bark tissues). However, further conclusions require validation through anatomical studies. Self-growing structures have three key benefits over traditional structures: entirely natural, developing geometry and material properties, as well as the potential to be adaptive and self-optimizing. Through quantitative studies, the purpose of this research is to provide insights and knowledge for the structural design of living structures for future cities.@en

The integration of buildings into vegetation has become a necessity in many metropolitan areas of the world today. It expands the potential of vertical and horizontal, exterior and interior, exposed and enclosed spaces in a building that can be used to accommodate plants. Green infrastructures have benefits both on urban and building scales. They can be categorized into green roofs and vertical greenery systems that can be divided further into green façade, green wall, green terraces, elevated forest and vertical forest. There are many design and planting considerations for architects, structural engineers and botanists when using living architectures to mimic natural systems, such as plant characteristics and environmental conditions. Plants used for vertical greenery are more likely to be hardwood species to adjust solar radiation during cooling and heating periods, as well as for aesthetic pleasure. Take Bosco Verticale, which is located in Milan, as an example to look into engineering methods when trees grow on balconies of high-rise buildings. It can be concluded that planting restraint safety systems and regular maintenance are necessary for the tree growth in the sky. However, the change in growing conditions causes various problems such as stability and irregular growth of trees. Instead of using steel cables and cages to prevent trees from falling off in the sky, the concept of self-growing connections is proposed to act as natural bracings and provide the stability for vertical forests. This paper is meant to generate awareness of the possibilities of the vertical integration of trees into buildings, show application considerations, and inspire future developments.

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Living architecture is thriving. The integration of buildings with vegetation has become a necessity in many metropolitan areas of the world today, including Singapore, New York City, Shanghai and Milan, to name a few. It expands the potential of vertical and horizontal, exterior and interior, exposed and enclosed spaces in a building that can be used to accommodate plants. Green infrastructures have benefits both on urban and building scales. They can be categorized into green roofs and vertical greenery systems that can be divided further into green façade, green/living wall, green terraces, elevated forests and vertical forests. There are many design and planting considerations for architects, structural engineers and botanists when using living architectures to mimic natural systems, such as climatic and regional considerations, primary functions and design objectives, structural support systems, maintenance, irrigation and so on. Plants used for vertical greenery are more likely to be hardwood species to adjust solar radiation during cooling and heating periods, and also for aesthetic pleasure. Take Bosco Verticale, which is located in Milan, as an example to look into engineering methods when trees grow on balconies of high rise buildings. It could be concluded that planting restraint safety system and regular maintenance are necessary for trees growing in the sky. But the change of growing conditions causes various problems such as stability and growth of trees. Instead of using steel cages and bracings to prevent falling off of trees in the sky, the concept of self-growing connections is proposed to provide the stability of vertical forests. This paper is meant to generate awareness of the possibilities of the integration of greenery vertically with buildings, show application considerations, and inspire future developments in typologies and integration with forests.@en