SPDE-derived random fields in structural optimisation and elastodynamics

Random imperfections are an inherent aspect of engineered systems, originating from various sources such as manufacturing variations, material heterogeneity, and environmental factors. These imperfections inevitably introduce uncertainties in the performance of structures which are rarely independent and tend to exhibit spatial correlations, which can exacerbate performance deviations. This thesis focuses on incorporating random fields to model material variability with applications on structural optimisation and statistical inference. Gaussian random fields on lattice structures are modelled by exploiting the established connection between random fields and stochastic partial differential equations (SPDEs). For a random field with Matérn covariance, the precision matrix (the inverse of the covariance matrix) corresponds to the finite element stiffness matrix of a potentially fractional PDE involving a second-order elliptic operator. By discretising the PDE using finite element methods on the lattice, a random field is generated that inherently considers the geometry and connectivity of the structure. This random field can be interpreted as a physics-informed prior, reflecting the hypothesis that the elliptic PDE captures physical processes like heat and mass diffusion occurring during manufacturing or construction. In order to design a structure that is less sensitive to variations in the random field, we consider robust optimisation, which takes into account the statistical properties of the structural response. We demonstrate the effectiveness of the proposed method through various lattice examples, incorporating isotropic, anisotropic, and non-stationary random fields, and handling up to eighty thousand random and optimisation variables. Following the structural optimisation, we further extend our approach to modelling random fields to structural dynamics. We introduce a probabilistic forward model approach that accounts for the propagation of initial material uncertainties and random forcing. Instead of linearising the system before discretisation, we apply the statistical linearisation first, allowing us to avoid dealing with two time integrations. We employ a probabilistic forward model approach to estimate the system’s physical state and an inverse problem approach to infer parameters. Rather than estimating the material properties individually, we efficiently determine the correlation length of the random process using Bayesian optimisation.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2025

Author dc:creator

• Yuksel, Ahmet Oguzhan

Advisor dc:contributor.advisor

• Cirak, Fehmi

• Bayesian filtering
• Bayesian inference
• Gaussian Processes
• random fields
• Robust optimisation
• Structural dynamics
• topology optimisation

Licence

• https://www.repository.cam.ac.uk/bitstreams/f75cdb31-af03-4fee-8015-20ab8cb02662/download
• http://purl.org/NET/rdflicense/allrightsreserved

Language dc:language

eng

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.120617

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/388134