Deep Learning based method for the prediction of the buckling resistance of SHS and RHS

Abstract

This paper proposes a data‐driven and deep learning based model for the prediction of the buckling load of square and rectangular hollow sections (SHS and RHS) based on Finite Element Method (FEM) results of the local buckling effects. The data was elaborated during the EU‐funded research project – HOLLOSSTAB (2016‐2019), where a new design method – termed the “Generalized Slenderness‐based Resistance Method” (GSRM) ‐ was developed, aiming to simplify through a unified analytical approach time consuming computational analyses for the prediction of the local resistance of SHS and RHS. This method further generalizes the concepts of established design methods such as the Direct Strength Method. This paper investigates an alternative approach to the development of design rules for this same mechanical problem: the application of deep learning models for the prediction of the buckling load through simple input parameters, such as geometric quantities, material values and applied load to circumvent the application of the analytical formulae. Thereby, a Deep Neural Network (DNN) model is created and calibrated for the prediction of the buckling loads of SHS and RHS based on the training data given by the extensive FEM parametric study. A statistical evaluation in accordance with EN1990 elaborates a partial safety factor for the proposed DNN. The predictions from the DNN are then compared to the numerical results from FEM analyses and to the predictions of the GSRM and EC3. Since the numerical results were originally validated against large scale experimental tests, this newly developed DNN makes use of a very large set of very representative (numerical) tests. A further comparison assesses the computed partial safety factor and the related quantities of interest for the DNN to the respective counterparts of the GSRM method. This work represents one of the first steps for the development of design methods in the field structural design adopting the most recent advances in computer sciences, and future enhancements of the currently developed models are discussed and proposed as a conclusion.

Scientific Machine and Deep Learning Investigations of the Local Buckling Behaviour of Hollow Sections

“…In addition to the standard Euclidean or Squared-error loss function, the L1 or L2 method (i.e. Lasso regression or Ridge regression) for example penalize the loss function for high number of weights to overcome overfitting problems ( [3], [4]). Those parameters in general need to be optimized to deliver suitable and problem oriented network architectures.…”

“…Based on the initial proposal of using deep learning for this task in prior work of the authors, cf. [3] and [4][2], a derived neural network architecture as well as the results of the predicted maximum reached, profile specific peak loads are subsequently presented in Sec. 4 of this paper, underlining the potential of such machine and deep learning driven applications.…”

“…The data basis for the later on described and used deep neural networks (DNN) is provided by advanced finite element GMNIA (geometrically material nonlinear analysis with imperfections) simulations using shell elements (s. Sec. 2.1), an approach that was already tested successfully within [3] and [4]. This so called "design by analysis" approach provides more realistic and accurate solutions (always depending on the level of the modelling effort) compared in general to code specifications of DIN EN 1993-1-5 [5] for the verification of the local buckling phenomena, where the designers is forced to carry out a purely elastic structural analysis and limit the elastic stresses to conservative estimations of ultimate buckling 1.…”

Erklärbare domänenspezifische Künstliche Intelligenz im Massiv‐ und Brückenbau

“…Quelle: [7] AUFSATZ ARTICLE [5], den Stahlbau in [6] sowie für den Massivund Brückenbau in [7] zu finden. [6,9] gezeigt. Für Entwurfsaufgaben, welche über den normativen oder datenbasierten Bereich hinausgehen, können XAI-Methoden neue Lösungen liefern und diese Vorhersagen aus den zugrunde liegenden Entscheidungen begründen.…”

“…Die Entwicklung von Methoden zur Berechnung und Bemessung von bautypischen Elementen wie Balken, Stützen oder Rahmen mit hoher Genauigkeit hat sich über Dekaden gezogen und wird vermutlich nicht durch den Einsatz von KI abgelöst, vielmehr besitzt XAI aber das Potenzial, für komplexe neue Systeme und Materialien einen hohen Grad an Genauigkeit bei den Vorhersagemodellen aufgrund der heute erheblich leichter zu erhebenden Daten zu ermöglichen, wie beispielsweise für geometrisch‐materiell nichtlineares Beulen in [6, 9, 10] gezeigt. Die Anwendung und Einbindung bautechnisch etablierter Konzepte zur Unsicherheitsquantifizierung und Bemessungssystematik auf die KI‐ und XAI‐Modelle ist einfach möglich und wurde ebenfalls in [6, 9] gezeigt. Für Entwurfsaufgaben, welche über den normativen oder datenbasierten Bereich hinausgehen, können XAI‐Methoden neue Lösungen liefern und diese Vorhersagen aus den zugrunde liegenden Entscheidungen begründen.…”