63,172 research outputs found
Fourier neural operator for learning solutions to macroscopic traffic flow models: Application to the forward and inverse problems
Deep learning methods are emerging as popular computational tools for solving
forward and inverse problems in traffic flow. In this paper, we study a neural
operator framework for learning solutions to nonlinear hyperbolic partial
differential equations with applications in macroscopic traffic flow models. In
this framework, an operator is trained to map heterogeneous and sparse traffic
input data to the complete macroscopic traffic state in a supervised learning
setting. We chose a physics-informed Fourier neural operator (-FNO) as the
operator, where an additional physics loss based on a discrete conservation law
regularizes the problem during training to improve the shock predictions. We
also propose to use training data generated from random piecewise constant
input data to systematically capture the shock and rarefied solutions. From
experiments using the LWR traffic flow model, we found superior accuracy in
predicting the density dynamics of a ring-road network and urban signalized
road. We also found that the operator can be trained using simple traffic
density dynamics, e.g., consisting of vehicle queues and traffic
signal cycles, and it can predict density dynamics for heterogeneous vehicle
queue distributions and multiple traffic signal cycles with an
acceptable error. The extrapolation error grew sub-linearly with input
complexity for a proper choice of the model architecture and training data.
Adding a physics regularizer aided in learning long-term traffic density
dynamics, especially for problems with periodic boundary data
Applications of inverse simulation to a nonlinear model of an underwater vehicle
Inverse simulation provides an important alternative
to conventional simulation and to more formal
mathematical techniques of model inversion. The
application of inverse simulation methods to a nonlinear
dynamic model of an unmanned underwater vehicle with
actuator limits is found to give rise to a number of
challenging problems. It is shown that this particular
problem requires, in common with other applications that
include hard nonlinearities in the model or discontinuities
in the required trajectory, can best be approached using a
search-based optimization algorithm for inverse
simulation in place of the more conventional Newton-
Raphson approach. Results show that meaningful inverse
simulation results can be obtained but that multi-solution
responses exist. Although the inverse solutions are not
unique they are shown to generate the required
trajectories when tested using conventional forward
simulation methods
Feedback methods for inverse simulation of dynamic models for engineering systems applications
Inverse simulation is a form of inverse modelling in which computer simulation methods are used to find the time histories of input variables that, for a given model, match a set of required output responses. Conventional inverse simulation methods for dynamic models are computationally intensive and can present difficulties for high-speed
applications. This paper includes a review of established methods of inverse simulation,giving some emphasis to iterative techniques that were first developed for aeronautical applications. It goes on to discuss the application of a different approach which is based on feedback principles. This feedback method is suitable for a wide range of linear and nonlinear dynamic models and involves two distinct stages. The first stage involves
design of a feedback loop around the given simulation model and, in the second stage, that closed-loop system is used for inversion of the model. Issues of robustness within
closed-loop systems used in inverse simulation are not significant as there are no plant uncertainties or external disturbances. Thus the process is simpler than that required for the development of a control system of equivalent complexity. Engineering applications
of this feedback approach to inverse simulation are described through case studies that put particular emphasis on nonlinear and multi-input multi-output models
Motion Planning of Uncertain Ordinary Differential Equation Systems
This work presents a novel motion planning framework, rooted in nonlinear programming theory, that treats uncertain fully and under-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it, and poor robustness and suboptimal performance result if itâs not accounted for in a given design. In this work uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, the proposed framework allows the user to pose, and answer, new design questions related to uncertain dynamical systems.
Specifically, the new framework is explained in the context of forward, inverse, and hybrid dynamics formulations. The forward dynamics formulation, applicable to both fully and under-actuated systems, prescribes deterministic actuator inputs which yield uncertain state trajectories. The inverse dynamics formulation is the dual to the forward dynamic, and is only applicable to fully-actuated systems; deterministic state trajectories are prescribed and yield uncertain actuator inputs. The inverse dynamics formulation is more computationally efficient as it requires only algebraic evaluations and completely avoids numerical integration. Finally, the hybrid dynamics formulation is applicable to under-actuated systems where it leverages the benefits of inverse dynamics for actuated joints and forward dynamics for unactuated joints; it prescribes actuated state and unactuated input trajectories which yield uncertain unactuated states and actuated inputs.
The benefits of the ability to quantify uncertainty when planning the motion of multibody dynamic systems are illustrated through several case-studies. The resulting designs determine optimal motion plansâsubject to deterministic and statistical constraintsâfor all possible systems within the probability space
Model predictive control architecture for rotorcraft inverse simulation
A novel inverse simulation scheme is proposed for applications to rotorcraft dynamic models. The algorithm adopts an architecture that closely resembles that of a model predictive control scheme, where the controlled plant is represented by a high-order helicopter model. A fast solution of the inverse simulation step is obtained on the basis of a lower-order, simplified model. The resulting control action is then propagated forward in time using the more complex one. The algorithm compensates for discrepancies between the models by updating initial conditions for the inverse simulation step and introducing a simple guidance scheme in the definition of the tracked output variables. The proposed approach allows for the assessment of handling quality potential on the basis of the most sophisticated model, while keeping model complexity to a minimum for the computationally more demanding inverse simulation algorithm. The reported results, for an articulated blade, single main rotor helicopter model, demonstrate the validity of the approach
Manoeuvrability assessment of a hybrid compound helicopter configuration
The compound helicopter design could potentially satisfy the new emerging requirements placed
on the next generation of rotorcraft. The main benefit of the compound helicopter is its ability to
reach speeds that significantly surpass the conventional helicopter. However, it is possible that the
compound helicopter design can provide additional benefits in terms of manoeuvrability. The paper
features a conventional helicopter and a hybrid compound helicopter. The conventional helicopter
features a standard helicopter design with a main rotor providing the propulsive and lifting forces,
whereas a tail rotor, mounted at the rear of the aircraft provides the yaw control. The compound
helicopter configuration, known as the hybrid compound helicopter, features both wing and thrust
compounding. The wing offloads the main rotor at high speeds whereas two propellers provide additional
axial thrust as well as yaw control. This study investigates the manoeuvrability of these
two helicopter configurations using inverse simulation. The results predict that a hybrid compound helicopter configuration is capable of attaining greater load factors than its conventional counterpart,
when flying a Pullup-Pushover manoeuvre. In terms of the Accel-Decel man oeuvre, the two helicopter
configurations are capable of completing the manoeuvre in comparable time-scales. However,
the addition of thrust compounding to the compound helicopter design reduces the pitch attitude
required throughout the acceleration stage of the manoeuvre
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