Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Form-Finding and Physical Property Predictions of Tensegrity Structures Using Deep Neural Networks

Muhao Chen, Jing Qin

TL;DR

The paper addresses the challenge of predicting tensegrity form-finding and physical properties under real-world imperfections by proposing a data-driven deep neural network that maps cable rest-length changes to equilibrium geometry and dynamic properties. Employing a sequential feedforward DNN in Keras, it predicts free-nodal coordinates, member tensions, and natural frequencies without solving nonlinear equilibrium repeatedly. Validation on three structures (D-Bar, prism, and lander) shows low output errors that improve with more training data, with frequency predictions often dominating the error budget but remaining at high accuracy for larger datasets. The method offers a practical, scalable tool for real-world tensegrity design and can be extended to other areas of structural physics requiring information identification from geometric changes.

Abstract

In the design of tensegrity structures, traditional form-finding methods utilize kinematic and static approaches to identify geometric configurations that achieve equilibrium. However, these methods often fall short when applied to actual physical models due to imperfections in the manufacturing of structural elements, assembly errors, and material non-linearities. In this work, we develop a deep neural network (DNN) approach to predict the geometric configurations and physical properties-such as nodal coordinates, member forces, and natural frequencies-of any tensegrity structures in equilibrium states. First, we outline the analytical governing equations for tensegrity structures, covering statics involving nodal coordinates and member forces, as well as modal information. Next, we propose a data-driven framework for training an appropriate DNN model capable of simultaneously predicting tensegrity forms and physical properties, thereby circumventing the need to solve equilibrium equations. For validation, we analyze three tensegrity structures, including a tensegrity D-bar, prism, and lander, demonstrating that our approach can identify approximation systems with relatively very small output errors. This technique is applicable to a wide range of tensegrity structures, particularly in real-world construction, and can be extended to address additional challenges in identifying structural physics information.

Form-Finding and Physical Property Predictions of Tensegrity Structures Using Deep Neural Networks

TL;DR

The paper addresses the challenge of predicting tensegrity form-finding and physical properties under real-world imperfections by proposing a data-driven deep neural network that maps cable rest-length changes to equilibrium geometry and dynamic properties. Employing a sequential feedforward DNN in Keras, it predicts free-nodal coordinates, member tensions, and natural frequencies without solving nonlinear equilibrium repeatedly. Validation on three structures (D-Bar, prism, and lander) shows low output errors that improve with more training data, with frequency predictions often dominating the error budget but remaining at high accuracy for larger datasets. The method offers a practical, scalable tool for real-world tensegrity design and can be extended to other areas of structural physics requiring information identification from geometric changes.

Abstract

In the design of tensegrity structures, traditional form-finding methods utilize kinematic and static approaches to identify geometric configurations that achieve equilibrium. However, these methods often fall short when applied to actual physical models due to imperfections in the manufacturing of structural elements, assembly errors, and material non-linearities. In this work, we develop a deep neural network (DNN) approach to predict the geometric configurations and physical properties-such as nodal coordinates, member forces, and natural frequencies-of any tensegrity structures in equilibrium states. First, we outline the analytical governing equations for tensegrity structures, covering statics involving nodal coordinates and member forces, as well as modal information. Next, we propose a data-driven framework for training an appropriate DNN model capable of simultaneously predicting tensegrity forms and physical properties, thereby circumventing the need to solve equilibrium equations. For validation, we analyze three tensegrity structures, including a tensegrity D-bar, prism, and lander, demonstrating that our approach can identify approximation systems with relatively very small output errors. This technique is applicable to a wide range of tensegrity structures, particularly in real-world construction, and can be extended to address additional challenges in identifying structural physics information.
Paper Structure (10 sections, 2 theorems, 4 equations, 6 figures, 3 tables, 1 algorithm)

This paper contains 10 sections, 2 theorems, 4 equations, 6 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Governing Equations of Tensegrity Structures
  3. Tensegrity Structure Notations
  4. Tensegrity Governing Equations
  5. Data-Based Modeling by Deep Neural Networks
  6. Numerical Experiments
  7. Tensegrity D-Bar Unit
  8. Tensegrity Prism
  9. Tensegrity Lander
  10. Conclusion

Key Result

Theorem 2.1

The static equilibrium equations for a tensegrity structure, expressed in terms of the nodal vector $\bm{n}$ and the member force vector $\bm{t}$, are given by: where $\bm{K} =(\bm{C}^T\hat{\bm{x}}\bm{C})\otimes\bm{{ I}}_3$ and $\bm{A}_{t}=(\bm{C}^{T} \otimes \bm{I}_{3}) \bm{b.d.}(\bm{NC^T})\hat{\bm{l}}^{-1}$ represent the stiffness matrix and equilibrium matrix. Here, $\otimes$ denotes the Krone

Figures (6)

  • Figure 1: Geometric configuration of D-Bar Unit. The blue and red lines are bars and strings, respectively. There are four bars and two strings in this unit. The bar length is $l= \sqrt{2}$ m.
  • Figure 2: Prediction errors for the D-bar dataset.
  • Figure 3: Prism geometric configuration: (a) oblique view and (b) top view. The radius and height are $r=0.25$ m and $h=0.5$ m.
  • Figure 4: Prediction errors for the prism dataset.
  • Figure 5: Six-bar tensegrity lander geometric configuration: (a) front view, (b) side view, (c) top view, and (d) oblique view. The bar length is 1 m.
  • ...and 1 more figures

Theorems & Definitions (4)

  • Definition 2.1: Nodal Coordinates
  • Definition 2.2: Connectivity Matrices
  • Theorem 2.1: Tensegrity Statics
  • Theorem 2.2: Tensegrity Modal Information