Real-Time Structural Deflection Estimation in Hydraulically Actuated Systems Using 3D Flexible Multibody Simulation and DNNs

TL;DR

This work tackles real-time estimation of structural deflection in hydraulically actuated 3D flexible multibody systems by integrating SLIDE-based data acquisition with DNN regression. It presents a physics-informed SLIDE framework that computes an effective SLIDE window $t_d$ without solving full EOMs and trains a neural network to predict deflections from limited sensor inputs, yielding speed-ups of up to $10^{7}$x while maintaining $MAPE$ below $1.5\%$ across various payloads. The approach leverages CMS-based modal reduction, lumped-fluid hydraulics, Exudyn for simulation, and PyTorch with ADAM for training, demonstrating robust single-step and multi-step estimation under diverse operating conditions. The method enables real-time control, robotic manipulation, and structural health monitoring for automated heavy machinery, offering significant computational gains with potential industrial impact, while acknowledging limitations such as neglect of joint friction and contacts that warrant future experimental validation.

Abstract

The precision, stability, and performance of lightweight high-strength steel structures in heavy machinery is affected by their highly nonlinear dynamics. This, in turn, makes control more difficult, simulation more computationally intensive, and achieving real-time autonomy, using standard approaches, impossible. Machine learning through data-driven, physics-informed and physics-inspired networks, however, promises more computationally efficient and accurate solutions to nonlinear dynamic problems. This study proposes a novel framework that has been developed to estimate real-time structural deflection in hydraulically actuated three-dimensional systems. It is based on SLIDE, a machine-learning-based method to estimate dynamic responses of mechanical systems subjected to forced excitations.~Further, an algorithm is introduced for the data acquisition from a hydraulically actuated system using randomized initial configurations and hydraulic pressures.~The new framework was tested on a hydraulically actuated flexible boom with various sensor combinations and lifting various payloads. The neural network was successfully trained in less time using standard parameters from PyTorch, ADAM optimizer, the various sensor inputs, and minimal output data. The SLIDE-trained neural network accelerated deflection estimation solutions by a factor of $10^7$ in reference to flexible multibody simulation batches and provided reasonable accuracy. These results support the studies goal of providing robust, real-time solutions for control, robotic manipulators, structural health monitoring, and automation problems.

Figures (17)

• Figure 1: Proposed method—A general framework of SLIDE-neural network model.
• Figure 2: Flexible system -- A system consisting of two flexible bodies $\text{A}$ and $\text{B}$ connected at the joint $P$, controlled by hydraulic actuation -- The position of the joint is ${\mathbf{r}}_{\mathrm{P}} = \mathbf{q}_{{\mathrm{t}}_{\text{A}}}+{{\mathbf{A}}_{\mathrm{A}}}({\bar{\mathbf{u}}}_{{\mathrm{o}}_{\text{A}}}+ {\bar{\mathbf{c}}}_{{\mathrm{f}}_\text{A}})$, where $\mathbf{q}_{{\mathrm{t}}_{\text{A}}} \in \mathbb{R}^{3 \times 1}$ is the translational coordinates vector, ${\mathbf{A}}_\text{A} = {\mathbf{A}} (\mathbf{\theta}_{\text{A}})$ is the rotation matrix, $\mathbf{\theta}_{\text{A}} \in \mathbb{R}^{n_{\mathrm{r}} \times 1}$ is the rotational parametrization vector, ${\bar{\mathbf{u}}}_{{\mathrm{o}}_{\text{A}}}$ is the local coordinate vector, and ${\bar{\mathbf{c}}}_{{\mathrm{f}}_\text{A}} \in \mathbb{R}^{3 \times 1}$ is the local flexible coordinates vector in body $\text{A}$. Additionally, ${n_{\mathrm{r}}}$ is the rotational DOFs.
• Figure 3: SLIDE data acquisition -- A method for generating data from hydraulically actuated mechanical systems at random initial configurations -- Initial pressures are calculated based on the static equilibrium force for each system configuration. The SLIDE window ${\mathrm{t}}_{\text{d}}$ is also determined during the data acquisition, and the data is arranged accordingly.
• Figure 4: Simulation setup -- A hydraulically actuated flexible boom lifting a payload $m$ -- The flexible boom is attached to rigid pillar at node $b_1$. It is actuated by a hydraulic cylinder, which has been added between the nodes $a_1$ and $b_2$. The known payload $m$ is connected to the flexible boom at node $b_4$, and tip deflection is measured at node $b_3$.
• Figure 5: Workflow for modeling flexible boom in the Exudyn software gerstmayr2023exudyn -- The commercial Abaqus® environment is used to perform FE discretization of the three-dimensional lift boom model. The nodes $b_1, b_2$ and $b_3$ on the flexible boom describe the boundary conditions in the flexible multibody system.