Applied Mechanics and Data Analysis (AMDA)

The main research interest is in investigating the behaviour of structures subjected to dynamic loads (such as vibrations, impacts, and fluctuating forces), and uncertainties (e.g. material variation, unknown boundary conditions, not fully known interface conditions, and similar). This area of study is particularly relevant in understanding how vibrations affect the integrity and performance of materials and structures. Of special interest is the phenomenon of stochastic fracture propagation, where dynamic stresses can initiate and accelerate crack growth, leading to potential failure. Research in this domain focuses on stochastic finite element type of modelling and analyzing vibration-induced stress distribution, the interaction of cracks with vibrational modes, and predicting fracture initiation and progression. Next to this, we focus on modelling stochastic non-smooth dynamics appearing in contacts, collisions and friction in imperfect interfaces between components in the system, as well as crash simulation. The developed models are then integrated with experimental data by using data fusion techniques.

The main research interest is to incorporate flexible bodies in a nonlinear stochastic dynamic simulation on a system level. The uncertainties appearing in the system are of various origins such as unknown interface conditions, lack of knowledge on the physics-based models or boundary conditions. New numerical methods are developed that enable more realistic coupled simulation of large system motions and elastic deformations, but also incorporation of material nonlinearity. Reuse of finite ellement models of individual bodies allows for the application of powerful system level and  model order reduction techniques and efficient computations of natural frequences and internal stresses during motion. In this way, realistic and reliable strength, buckling and durability analyses can be performed.

The main aim is to understand and model the behaviour of possibly anisotropic and heterogenous materials/meta-materials spanning multiple scales under quasi-static and dynamic loads as the material experiences during the manufacturing process as well as throughout its life cycle. The focus is on the stochastic/probabilistic modelling of the material behaviour due to the presence of inherent material variations (aleatory uncertainty) the origin of which is for example due to variations in the manufacturing process, or due to lack of expert's knowledge (epistemic uncertainty). Next to this, the focus is on modelling variations in the external loading conditions or boundary conditions on the system or the component level, as well as uncertainty in the knowledge of the physics-based model, the system model itself, or its design variations.  The considered physics can be diverse such as static, quasi-static, dynamics, see Physics-based modelling section. With stochastic formulation of these physics-based modelled problems, along with use of appropriate downscaling and upscaling techniques, complex behaviour of the material due to the interactions between different constituents at various scales are studied. Our attention is focused on the fracture and fatigue type of material behaviour. Typical techniques used to quantify and propagate the uncertainties include spectral methods such as polynomial chaos expansion and advanced Monte-Carlo algorithms; homogenization and stochastic representative volume elements for downscaling and upscaling. Several mechanical characterization techniques are used to characterize the uncertainties such as micro-computational tomography (micro-CT), scanning electron microscopy and various other testing techniques. Furthermore, the properties of a range of materials and metamaterials are driven by their structural descriptors. A key focus lies on identifying the descriptors that dictate the mechanical, thermal, or acoustic properties of such materials. Computational methods of interest here include Langevin and Brownian dynamics, discrete and finite element methods, and graph theory.  The knowledge obtained on the resulting uncertainties in the response variables can then be used to optimize the design, manufacturing process and the mechanical properties of multiscale materials such as composites materials.

The main research interest is active sound and vibration control with the primary objective to control the acoustic field. This comprises development of control algorithms, which can be adaptive, non-adaptive or semi-active, sensors and actuators, and signal processing techniques such as virtual sensors, beamformers, and model reduction methods. A further research interest is active and semi-active metamaterials that are effective in a broad frequency range, as well as passive methods combined with active control methods.

Predictive modelling using data-driven and physics-based machine learning (ML) combines the strengths of statistical learning and domain knowledge on stochastic dynamics and multiscale systems. Our group works on data-driven ML models that leverage small and large datasets to identify complex patterns and relationships in various application domains. To constrain ML models to physics we incorporate fundamental laws of nature into the training of ML architecture. This hybrid approach enhances accuracy, interpretability, and generalization, especially in scenarios with limited or noisy data. By integrating physics-based constraints into data-driven algorithms, such models provide more robust predictions in fields like predicting the dynamics of the systems and predicting performance of materials. Next to this we incorporate probabilistic training into architectures to obtain uncertainty prediction on the obtained Quantity of Interest (QoI).

Incapability to extricate model parameter values or even a data driven or physics-based model form in some cases given experimental/monitoring data, the absence of available data sets at sufficiently large space and/or time scales, and the never-ending issue of model validation are some of the main reasons for uncertainty quantification and data analysis of real-world phenomena. Today it is desired to quantitatively characterize and reduce uncertainties in both computational and real-world applications in either probabilistic or polymorphic forms. The research in the group is based on an interdisciplinary approach combining experiments, mathematical modelling and numerical approaches to the quantification of uncertainty, its prediction and data assimilation. The main goal is to develop efficient and robust learning and uncertainty quantification numerical algorithms of wide range purposes as stated in Physics based modelling section.  The group develops surrogate models based on the polynomial chaos approximation, Gaussian processes, radial basis functions, machine and deep learning and similar surrogate approaches. Next to this we work on the model order reduction for stochastic parametric models, and machine learning driven surrogate models used to predict uncertainty. Similarly, we also develop algorithms for uncertainty quantification in machine/deep learning models.

System identification, data assimilation, and parameter identification are critical techniques for modelingmodelling , control and optimizing stochastic mechanical systems. System identification involves constructing mathematical models from observed data, while data assimilation integrates real-time sensor data with predictive models to improve accuracy.  Our focus is on constructing effective and online algorithms for parameter identification based on the probability theory. We work on the approximate Bayesian methods for state and parameter identification such as generalized and nonlinear Kalman filters. By combining experimental data with physics based and mathematical modelling, these approaches allow calibration of physics-based models and sensors, performing the sensitivity analysis of the system output given input features, predictive modelling of the system, control and online monitoring of processes and systems.

Data-driven control and optimization using reinforcement learning (RL) in mechanical engineering offers innovative solutions for managing complex systems. RL allows mechanical systems to autonomously learn optimal control policies or optimal designs by interacting with their environment and continuously improving performance. By utilizing real-time data and or physics-based models, RL can optimize the behaviour of systems such as 3D printing by collaborative robotics, smart manufacturing, and energy-efficient HVAC systems. This approach eliminates the need for precise system models, making it effective for stochastic dynamic and nonlinear mechanical systems and processes. The group is focusing on the development of combination of RL with data-driven strategies, and physics-based models. Next to this, we strongly focus on the application of RL in the areas as mentioned in Physics-based modelling.