Plenary Lectures

Abstract
Dynamic or time-variant uncertain parameters, such as wind excitations on bridges or road excitations on vehicles, exist widely in practical engineering. Traditionally, the stochastic process is adopted to quantify such dynamic uncertainties. However, due to experimental conditions or cost restriction in many practical circumstances, especially in the design stage of products or structures, it is often difficult or even impossible to obtain sufficient experimental samples to construct a credible stochastic process model. Committed to providing a mathematical model for dynamic uncertainty quantification under inadequate sample information, the authors proposed the “interval process model.” As a beneficial supplement for the stochastic process, the interval process employs an interval variable rather than the precise probability distribution to describe the uncertainty of a time-variant parameter at an arbitrary time point, effectively reducing the dependency on large-scale samples. The auto/cross-covariance and auto/cross-correlation coefficient functions are defined to characterize the temporal correlation. Based on the characteristics of the correlation coefficient function, the stationary interval process and its ergodicity can be identified. The definitions of limit and continuity in mathematics are given, based on which the concepts of differential and integral of the interval process are derived. The interval K-L expansion for efficient representation of the interval process is proposed, which significantly facilitates the simulation and subsequent structural dynamic analysis with interval processes. By combining the interval process with mechanical vibration theory, a kind of non-probabilistic analysis method is further proposed to deal with the crucial random vibration problems, i.e., the interval vibration analysis method, which provides the upper and lower response bounds of vibration systems. Furthermore, the interval process model is extended to spatial uncertainty quantification, yielding the interval field model and also the interval finite element method for structural spatial uncertainty analysis.

Abstract
Topology optimization provides a systematic and design-driven framework for material distribution in structures exhibiting nonlinear responses such as large deformation, plasticity, and instability. This plenary lecture presents recent advances in topology optimization for nonlinear structural problems, with particular emphasis on sensitivity analysis. Consistent sensitivity formulations for nonlinear systems are discussed, addressing challenges arising from path dependency and strong nonconvexity, and establishing a rigorous basis for nonlinear design. Building on this foundation, topology optimization methods for elastoplastic materials and/or damage models are introduced, together with their extension to multi-material systems. In particular, a class of approaches that interpolate distinct nonlinear material models is presented, enabling the systematic design of structures with heterogeneous and nonlinear constitutive behavior. Recent developments beyond this scope are also highlighted, including the design of two-scale phononic metamaterials and a multi-material optimization framework based on quantum annealing. These approaches, formulated within linear material settings, provide complementary perspectives on exploring complex design spaces. In this context, manufacturing—particularly additive manufacturing—is viewed as an enabling technology that follows from, rather than drives, the design process, providing practical means to realize the optimized structures.

Abstract
Due to the nature of aerospace systems, which must operate safely in extreme environments, design optimization techniques in aerospace engineering have played a crucial role as a core technology utilizing mathematical modeling and computational analysis to maximize the performance, safety, and economic efficiency of aircraft and spacecraft etc.
The characteristics of aerospace engineering and the resulting design optimization are as follows. First, the fields of aerodynamics, structure, control, and propulsion in aerospace engineering utilize Newton’s law of acceleration and differential equations to formulate complex physical phenomena mathematically, deriving optimal solutions within strict constraints such as stability, environmental conditions, and material limitations. Accordingly, the computational models used in aerospace engineering applications require the solution of nonlinear partial differential equations in three-dimensional domains, which could also be time-dependent. As a representative example, optimal design based on high-precision flow and structural analysis is carried out by utilizing high-accuracy computational analysis such as Computational Fluid Dynamics (CFD) and Finite Element Method (FEM). Second, the various fields of aerospace engineering do not exist independently but influence one another. Modifying the wing shape to improve aerodynamic performance can increase weight, which requires larger engines and consumes more fuel. Therefore, Multidisciplinary Optimization (MDO) is performed from a holistic system perspective to ensure that the optimization of one field does not negatively impact others. MDO is an engineering discipline that utilizes optimization techniques to simultaneously solve design problems spanning multiple fields. Third, due to the nature of the industry where a single failure can lead to fatal accidents, it demands a high level of reliability and safety that requires rigorous certification. Consequently, design is conducted based on data accumulated over a long period, and the process of verifying design suitability using data obtained from ground and flight tests is essential. Third, due to the nature of the industry where a single failure can lead to fatal accidents, it demands a high level of reliability and safety that requires rigorous certification. Consequently, design is conducted based on data accumulated over a long period, and the process of verifying design suitability using data obtained from ground and flight tests is essential. As such, in aerospace engineering, experimental data serves as the link that transforms theoretical possibilities into practical reliability. However, testing requires significant time and cost. Verified high-precision physical simulations can reduce the cost of testing required to acquire data. Nevertheless, running high-precision physical simulations thousands of times during an optimization loop is still impose constraints in terms of time and computational cost. To address this issue, engineers create surrogate models (or response surfaces).
Meanwhile, advancements in aerospace engineering and mobility have given rise to a new concept called Advanced Mobility, which is a new type of system encompassing Electric Vehicles (EVs), Autonomous Vehicles (AVs), and Urban Air Mobility (UAM). Meanwhile, advancements in aerospace engineering and mobility have given rise to a new concept called Advanced Mobility, which is a new type of system encompassing Electric Vehicles (EVs), Autonomous Vehicles (AVs), and Urban Air Mobility (UAM). For example, UAM aircraft typically have the following technological characteristics: First, UAM aircraft can take off and land vertically, enabling operations in urban areas or confined spaces. This involves using various forms of aircraft such as Vectored Thrust, Lift Cruise, and Wingless Multirotor. Second, UAM aircraft use environmentally friendly propulsion systems such as Electric or Hybrid Electric Propulsion. Third, UAM aircraft will have a pilot on board for initial operation, but in the future, autonomous flight technology will be used to set flight paths and reach destinations safely. Fourth, UAM aircraft must satisfy strict environmental noise standards to operate at low altitudes within urban areas. Unlike existing systems, this new concept of advanced mobility lacks accumulated experience data; therefore, advanced design optimization techniques—such as AI-based generative design, digital twin and simulation-based optimization, and data-driven and machine learning optimization—are essential to maximize performance and ensure safety.
This presentation intends to share speaker’s researches on aerospace and advanced mobility to indirectly discuss perspectives on design optimization in “Recent Applications to Advanced Mobility Development.“