Towards a population-informed approach to the definition of data-driven models for structural dynamics

TL;DR

The paper tackles data scarcity and transferability in structural dynamics by proposing population-informed data-driven models trained on a population of similar structures. It develops two meta-learning frameworks, MAML and CNP, to extract and exploit population knowledge without requiring explicit physics priors. On simulated lumped-mass FRF data with temperature-driven stiffness variations, both methods outperform Gaussian-process baselines and show improved robustness as the population size grows. The work highlights the potential for more trustworthy, transferable, and explainable data-driven models in structural dynamics and outlines paths toward physics-informed extensions and experimental validation.

Abstract

Machine learning has affected the way in which many phenomena for various domains are modelled, one of these domains being that of structural dynamics. However, because machine-learning algorithms are problem-specific, they often fail to perform efficiently in cases of data scarcity. To deal with such issues, combination of physics-based approaches and machine learning algorithms have been developed. Although such methods are effective, they also require the analyser's understanding of the underlying physics of the problem. The current work is aimed at motivating the use of models which learn such relationships from a population of phenomena, whose underlying physics are similar. The development of such models is motivated by the way that physics-based models, and more specifically finite element models, work. Such models are considered transferrable, explainable and trustworthy, attributes which are not trivially imposed or achieved for machine-learning models. For this reason, machine-learning approaches are less trusted by industry and often considered more difficult to form validated models. To achieve such data-driven models, a population-based scheme is followed here and two different machine-learning algorithms from the meta-learning domain are used. The two algorithms are the model-agnostic meta-learning (MAML) algorithm and the conditional neural processes (CNP) model. The algorithms seem to perform as intended and outperform a traditional machine-learning algorithm at approximating the quantities of interest. Moreover, they exhibit behaviour similar to traditional machine learning algorithms (e.g. neural networks or Gaussian processes), concerning their performance as a function of the available structures in the training population.

Figures (21)

• Figure 1: Example of a mass-spring system, with masses $m$, damping coefficients $c$ and spring stiffness $k$, which is a function of the environmental conditions $\bm{e}$.
• Figure 2: Schematic representation of an objective function $\pazocal{L}$ as a function of the trainable parameter $\theta$ and two local minima shown in orange and green.
• Figure 3: Objective function $\pazocal{L}$ for two tasks (magenta and blue lines) as a function of the trainable parameter $\Theta$ and three local minima shown in orange, green and light green.
• Figure 4: Schematic of a fibre bundle of the loss functions of a data-driven model across a population of tasks. The base manifold $\pazocal{T}$ is formed by points representing the tasks $\tau_{i}$ of the population. To every task $\tau_{i}$, a fibre $\pazocal{L}_{i}$ corresponds, which represents the values of the loss function $\pazocal_{L}$ for different values of the trainable parameters of the data-driven model. The orange and green points represent parts of the fibre bundle where local or global minima are observed regarding the loss function. The fibres intercepting an orange area have a local or global minimum at the intersection point between the fibre and the orange area. The same applies for the green area. However, the green area is a continuous cross section along the whole bundle.
• Figure 5: Neural network modelling the population with inputs regarding the external variables $\bm{x}^{e}$ and the structure $\bm{x}^{\tau}$.