Dynamic Problem Research Articles

Toward mechanistic models “augmented” by machine learning. Example of a drying simulation data set exploited by a Physics Informed Neural Network

Mechanistic modeling of drying is well-established since several decades. Based on fundamental balance equations and driven by relevant material parameters, it can predict the entire process, including configurations that were not observed before. Besides, thanks to their ability to tackle non-linear and dynamics problems, approaches based on Machine Learning (ML) based are capable of coping with complex situations even better than mechanistic modeling. The main drawback of mechanistic models is their complexity as operational tools, namely in providing the whole set of product characteristics, while the main drawback of ML tools is its restriction to the domain paved by the data set. This paper summarizes the physics of the mechanistic formulation and then presents the different possibilities of coupling the mechanistic and ML approaches to obtain an “augmented” mechanistic model. The idea is to merge the advantages of both worlds. Different strategies can be imagined: A full coupled method (hybrid model) A fully decoupled method A cascade coupling The second part of the paper gives examples of a fully decoupled approach the mechanistic model is used to populate a data set, which is further exploited by a neural network. The originality of the work is to compare a classical neural network with a Physics Informed Neural Network.

Uncertainty quantification analysis of bifurcations of the Allen–Cahn equation with random coefficients

In this work we consider the Allen–Cahn equation, a prototypical model problem in nonlinear dynamics that exhibits bifurcations corresponding to variations of a deterministic bifurcation parameter. Going beyond the state-of-the-art, we introduce a random coefficient in the linear reaction part of the equation, thereby accounting for random, spatially-heterogeneous effects. Importantly, we assume a spatially constant, deterministic mean value of the random coefficient. We show that this mean value is in fact a bifurcation parameter in the Allen–Cahn equation with random coefficients. Moreover, we show that the bifurcation points and bifurcation curves become random objects. We consider two distinct modeling situations: (i) for a spatially-homogeneous coefficient we derive analytical expressions for the distribution of the bifurcation points and show that the bifurcation curves are random shifts of a fixed reference curve; (ii) for a spatially-heterogeneous coefficient we employ a generalized polynomial chaos expansion to approximate the statistical properties of the random bifurcation points and bifurcation curves. We present numerical examples in 1D physical space, where we combine the popular software package Continuation Core and Toolboxes (COCO) for numerical continuation and the Sparse Grids Matlab Kit for the polynomial chaos expansion. Our exposition addresses both dynamical systems and uncertainty quantification, highlighting how analytical and numerical tools from both areas can be combined efficiently for the challenging uncertainty quantification analysis of bifurcations in random differential equations.

Nonlinear Dynamics Research of Ground Undulatory Fin Robot with Flexible Deformation and Frictional Contact.

The unique rigid-flex connection between the fin-rays and fin-surface in a bionic undulatory fin robot endows the fin-surface with both active flexibility and load-bearing capacity, enabling this robot to perform amphibious motions in underwater, terrestrial, and even marshy environments. However, investigations into dynamic modeling problems for the undulatory fin robot, considering the impact of nonlinear deformation and frictional contact on ground locomotion performance, are scarce. Given this, based on the absolute nodal coordinate formulation (ANCF), this paper presents an efficient and accurate nonlinear dynamic model for this robot to elucidate the fin's flexible deformation and motion law. This model considers material, geometric, and boundary nonlinearities, utilizing ANCF thin plate elements and reference nodes to individually describe the fin-surface and fin-rays of the undulatory fin. Then, by using the master-slave technique, a frictional contact formulation for the fin and the ground is proposed. Furthermore, we conduct in-depth research and analysis on the formation and undulatory motion of the undulatory fin, encompassing its static deformation, static contact deformation, and frictional contact motion, and successfully obtain its responses under various conditions. Research indicates that during fin-surface motion, longitudinal sliding or a tendency for sliding at the contact points results in the undulatory fin moving in a crawling gait. The proposed theoretical model correctly captures the fin's complex nonlinear deformations and frictional characteristics and reveals its ground locomotion mechanism, whose effectiveness and superiority are validated through numerical examples and experiments.

Optimizing a Dynamic Vehicle Routing Problem with Deep Reinforcement Learning: Analyzing State-Space Components

Background: The dynamic vehicle routing problem (DVRP) is a complex optimization problem that is crucial for applications such as last-mile delivery. Our goal is to develop an application that can make real-time decisions to maximize total performance while adapting to the dynamic nature of incoming orders. We formulate the DVRP as a vehicle routing problem where new customer requests arrive dynamically, requiring immediate acceptance or rejection decisions. Methods: This study leverages reinforcement learning (RL), a machine learning paradigm that operates via feedback-driven decisions, to tackle the DVRP. We present a detailed RL formulation and systematically investigate the impacts of various state-space components on algorithm performance. Our approach involves incrementally modifying the state space, including analyzing the impacts of individual components, applying data transformation methods, and incorporating derived features. Results: Our findings demonstrate that a carefully designed state space in the formulation of the DVRP significantly improves RL performance. Notably, incorporating derived features and selectively applying feature transformation enhanced the model’s decision-making capabilities. The combination of all enhancements led to a statistically significant improvement in the results compared with the basic state formulation. Conclusions: This research provides insights into RL modeling for DVRPs, highlighting the importance of state-space design. The proposed approach offers a flexible framework that is applicable to various variants of the DVRP, with potential for validation using real-world data.

Heat transfer analysis of Walter’s-B flow over a vertical plate by using fractional operator

The present study deals with the unsteady Walter’s-B fluid with hybrid fractional derivative namely constant proportional Caputo type with singular kernel. In this paper, we find new analytical solutions of a well-known problem of the fluid dynamics known as Stokes’ first problem. Using dimensional variables governing equations convert into dimensionless form. To solve the model analytically, one uses the Laplace transform approach. Analytical and numerical evaluations of the inverse Laplace transform have been conducted. The influence of several embedded flow properties, including the magnetic parameter, Grashof number, dimensionless time, Prandtl number, Schmidt number, and fractional parameter is analyzed graphically. More specifically, compared to the classical model, the fractional model provides a wider range of integral curves and better represents the flow behavior. The temperature and velocity of the fluid decrease with increasing fractional parameters during short intervals of time, but exhibit the reverse pattern over longer durations. Skin friction, the Sherwood number, and the Nusselt number are numerical quantities linked to engineering that are statistically computed and provided in tabular form.

Design and Simulation Analysis of Bridge Anti-collision Structure based on Nonlinear Numerical Simulation

In order to solve the dynamic nonlinear problem of bridge loads and responses during ship collisions, a design method for bridge anti-collision structures based on nonlinear numerical simulation was proposed. The author describes in detail the entire process of collision force evolution, energy conversion, and plastic deformation of the anti-collision energy dissipator, and conducts a comprehensive simulation of it. The experimental results show that when a ship with a mass of 1000 tons collides forward at speeds of 1, 3, and 5 meters per second, the collision depth is 0.23, 1.46, and 3.95 meters, respectively, less than the maximum allowable collision depth of 4.3 meters, and the collision energy dissipator is still in the protective working state for the bridge pier. When a ship with a mass of 3000 tons collides with the collision avoidance energy dissipator at a speed of 3 or 5 meters per second, the collision depth exceeds the maximum allowable collision depth, and the collision avoidance energy dissipator fails, the ship will directly collide with the wharf. The plastic deformation of the anti-collision energy dissipator provided has important reference value for design.

Unsteady Loads of a Scaled Rotor on and Near the Landing Deck of the NATO Generic Destroyer with Concurrent Stereo PIV and Surface Pressure Measurements

Rotorcraft shipboard operations are risky and demand high piloting skills. To gain further understanding and familiarize pilots with these complicated scenarios, various methods of computational simulations have been used in the past decades. Yet, some simulation methods may not capture a realistic response of the rotorcraft due to simplified modeling of the interactional aerodynamics in order to achieve real-time capability for pilot training. Thus, improvements to these simulations are required, and experimental data that unveil the interactional aerodynamics and dynamics between the rotor and ship are needed for computational validation efforts. In this study, an extensive experimental investigation of the ship???rotor dynamic interface problem was conducted to gain a general understanding of the interactional aerodynamics between a 1:100 wind-tunnel-scale NATO Generic Destroyer and a representative single main rotor, operating both stationary and dynamically moving in space in the vicinity of the landing deck. Data obtained through simultaneous measurements of rotor hub loads, ship deck surface pressures, and stereoscopic particle image velocimetry flow fields gave valuable insight into the highly coupled aerodynamic phenomena. Results showed that the rotor hub loads exhibited a high dependency on both the wind direction and also the position of the rotor relative to the landing deck. A bifurcation in the regions of high unsteady thrust was observed under certain wind conditions due to the ship airwake, impacting different portions of the rotor disk. The inflow angles across the rotor disk were estimated and assessed through flow field measurement, revealing how the ship airwake altered the rotor inflow and wake structure that contributed to the unique change in rotor loads under various hovering conditions.

Deep reinforcement learning based proactive dynamic obstacle avoidance for safe human-robot collaboration

Ensuring the health and safety of human operators is paramount in manufacturing, particularly in human-robot collaborative environments. In this paper, we present a deep reinforcement learning-based trajectory planning method for a robotic manipulator designed to avoid collisions with human body parts in real-time while achieving its goal. We modelled the human arm as a freely moving cylinder in 3D space and formulated the dynamic obstacle avoidance problem as a Markov decision process. The algorithm was tested in a simulated environment that closely mimics our laboratory environment, with the goal of training a deep reinforcement learning model for autonomous task completion. A composite reward function was developed to balance the effects of different environmental variables, and the soft-actor critic algorithm was employed. The trained model demonstrated a 93% success rate in avoiding dynamic obstacles while achieving its goals when tested on a generated data set.

Decomposition-Based Multiobjective Evolutionary Optimization With Tabu Search for Dynamic Pickup and Delivery Problems

Decomposition-Based Multiobjective Evolutionary Optimization With Tabu Search for Dynamic Pickup and Delivery Problems

Exploring swirling flow dynamics: Unsupervised machine learning in Maxwell hybrid nanofluid convection over an exponentially stretching cylinder with non-linear radiation effects

This article analyses the flow of Maxwell hybrid nanofluid induced by an exponentially stretching and rotating cylinder. The presence of non-linear convection, non-linear radiation, and magnetic field is also assumed. The factors covered in the study has a wide spectrum of application in various disciplines, and therefore we analyse the influence of different flow parameters after numerically solving the set of modelled differential equations. A data-free physics-informed neural network using a wavelet activation function is used to approximate the numerical solution. The reliability of the used methodology is validated by comparing the results of the limiting case with the available results. The paper demonstrates the effectiveness of using PINN in an unsupervised fashion to tackle fluid flow problems, showcasing their ability to provide reliable and accurate solutions without the need for extensive datasets. This approach highlights the potential of PINN to address complex fluid dynamics problems by utilizing physical laws within the neural network framework. From the numerical study, it is observed that hybrid nanofluid has a better rate of heat transfer compared to the nanofluid. Furthermore, radiation parameter and maxwell flow parameter is seen to exhibit significant impact of the flow profiles.

A comprehensive review of advances in physics-informed neural networks and their applications in complex fluid dynamics

Physics-informed neural networks (PINNs) represent an emerging computational paradigm that incorporates observed data patterns and the fundamental physical laws of a given problem domain. This approach provides significant advantages in addressing diverse difficulties in the field of complex fluid dynamics. We thoroughly investigated the design of the model architecture, the optimization of the convergence rate, and the development of computational modules for PINNs. However, efficiently and accurately utilizing PINNs to resolve complex fluid dynamics problems remain an enormous barrier. For instance, rapidly deriving surrogate models for turbulence from known data and accurately characterizing flow details in multiphase flow fields present substantial difficulties. Additionally, the prediction of parameters in multi-physics coupled models, achieving balance across all scales in multiscale modeling, and developing standardized test sets encompassing complex fluid dynamic problems are urgent technical breakthroughs needed. This paper discusses the latest advancements in PINNs and their potential applications in complex fluid dynamics, including turbulence, multiphase flows, multi-field coupled flows, and multiscale flows. Furthermore, we analyze the challenges that PINNs face in addressing these fluid dynamics problems and outline future trends in their growth. Our objective is to enhance the integration of deep learning and complex fluid dynamics, facilitating the resolution of more realistic and complex flow problems.

Two Numerical Approaches for Solving Fractional Model of Chemical Kinetics Problem via Chebyshev Polynomials

Two Numerical Approaches for Solving Fractional Model of Chemical Kinetics Problem via Chebyshev Polynomials

PERTURBED MOTIONS OF A NEARLY DYNAMICALLY SPHERICAL RIGID BODY WITH A MOVABLE MASS SUBJECT TO CONSTANT BODY-FIXED TORQUE

The problem of motion of a rigid body about a fixed point is one of the classical problems of mechanics. The interest to the problems of the rigid body dynamics has increased in the second half of the XX century in connection with the development of rocket and space technologies. A spacecraft or satellite, while orbiting about its center of mass, experiences torques from forces of diverse physical nature. This includes torques generated by the motion of internal masses, which can arise from factors such as presence of rotating components (like rotors or gyroscopes), and the activities of crew members aboard the crew vehicle. The dynamics of rigid body incorporated moving masses is a significant focal point in classical mechanics. Extensive research is dedicated to investigating the rotation of a rigid body featuring motion of internal masses. It is assumed that the body contains a viscoelastic element that is modeled by a moving mass connected to the body by a strong damper. The moving mass model loosely attached elements in a space vehicles, which can significantly affect the vehicle’s motion about its center of mass during a long period of time. Some cases are considered of the motion of a rigid body containing internal masses connected to the body by means of elastic and dissipative elements. A number of works are devoted to the analysis of various problems of the dynamics of space vehicles containing internal movable masses. The paper develops an approximate solution by means of averaging method to the system of Euler’s equation terms for a nearly dynamically spherical rigid body containing a viscoelastic element under the action of constant body-fixed torque. We obtained the system of motion equations in the standard form which refined in square-approximation by small parameter. Asymptotic approach permits to obtain some qualitative results and to describe evolution of angular motion using simplified averaged equations and numerical solution. The main objective of this paper is to extend the previous results for the problem of motion about a center of mass of a rigid body under the influence of small internal torque (cavity filled with a fluid of high viscosity) or external torque (resistive medium). The importance of the results is in progress of moving mass control motion of spinning projectiles.

Струйный эффект при возникновении присоединенной каверны от системы импульсивных давлений

We consider the plane problem of the emergence of an attached cavity caused by the sudden action of impulsive pressures at some initial time. It is assumed that these pressures are distributed on the upper part of the boundary of a stationary circular cylinder immersed in liquid. A problem with unilateral constraints is formulated, on the basis of which the flow of liquid at the initial moment of time and the initial zone of separation of liquid particles are determined. At the next moments of time, an attached cavity is formed, the shape of which is determined based on the solution of the dynamic initial-boundary value problem of the theory of potential flows of an ideal incompressible fluid with free boundaries. The main unknowns in it are the velocity potential, the shape of the cavity, the dynamics of the separation points, and the perturbation of the external free boundary of the liquid. It is required to study the posed problem at short times, focusing on the behavior of the internal free boundary of the liquid near the separation points. When studying this problem, pressure in the cavern, which is created artificially, plays an important role. At low pressures, the internal free boundary of the liquid near the separation point is located on opposite sides of this point. In this case, the end part of the cavity resembles a stream of gas directed along the boundary of the cylinder towards the liquid.

Integrating machine learning with dynamic multi-objective optimization for real-time decision-making

Real-time decision-making in dynamic multi-objective optimization problems (DMOPs) is challenging due to constantly changing objectives and constraints. This paper integrates machine learning with Non-dominated Sorting Genetic Algorithm II (NSGA-II) to solve DMOPs and make real-time decisions. Learning-based methods have gained popularity for predicting solutions in new environments and capturing changing patterns in optimal solutions. However, existing approaches often struggle with training difficulty and reduced prediction accuracy due to irrelevant or redundant variables. Therefore, we introduce a new interdependent prediction (IDP) technique to identify correlations between variables and prediction targets and select significant variables for a predictive model. In this way, a better initial population is predicted. The IDP strategy is integrated within the dynamic NSGA-II, introducing a new algorithm called IDP-DNSGA-II. This integration facilitates rapid convergence, finding optimal or near-optimal solutions. The proposed method is evaluated against standard benchmarks, demonstrating superior performance in convergence speed and solution diversity with the changes in the problem environment. The IDP-DNSGA-II is validated through real-world optimization challenges in sustainable automobile production distribution in order-to-delivery systems to enhance environmental sustainability and operational efficiency. This study identifies the minimum frequency of change required in real-world problems to adequately track the optimal decision in real-time.

Nonlinear wave model of towed system and numerical method for its calculation

Towed systems have found wide practical applications. Notable underwater systems for the long-distance extraction of minerals (concretions) from the ocean floor extend over 5-10 km. The existing mathematical models for solving dynamic problems of such systems in various environments are not entirely accurate regarding the diversity of wave processes. This necessitates the development of refined wave models. This article presents a new quasi-linear mathematical model describing the nonlinear four-mode dynamics of a towed system in a spatially inhomogeneous field of mass and surface forces. It is described by a nonlinear system of twelve first-order partial differential equations. The principles of boundedness and hyperbolicity are satisfied. The validation of the two-mode reduction of the model is based on the numerical solution of the problem of the propagation of two waves: longitudinal and configurational. Using a numerical algorithm and a program based on the finite difference method, a comparison of two difference schemes – Crank-Nicolson and Euler – was conducted. The main limitations for applying the finite difference method used for numerical modeling of wave propagation and reflection in a towed system are the peculiarities of the defining quasi-linear equations, which are related to the necessity of simultaneous computation of variables responsible for fast and slow processes. For such systems of equations, the term "singularly perturbed system of equations" is used. These perturbations result from the significant differences in the propagation speeds of longitudinal and configurational waves at the physical level. Consequently, it is necessary to employ special time-stepping regularization and filtering methods for numerical results. This imposes certain restrictions on the ability to model real processes and on the accuracy of the obtained results, necessitating the use of implicit difference schemes and high-frequency filtering.

Drive force allocation control based on pump displacement optimization for hydraulic hybrid motor-assisted system

To achieve rational coordination of the front and rear axle torque of commercial vehicles equipped with hydraulic hybrid motor-assisted systems (HHMAS), and further enhance the vehicle’s fuel efficiency and traction capability. A hydraulic pump displacement control strategy based on energy-efficiency-orientation (EEO) is proposed for driving force distribution. Firstly, the efficiency is analyzed from the perspective of system energy flow. Then, considering the time-varying efficiency characteristics of the hydraulic variable pump and hydraulic motor, the stochastic dynamic optimization problem is modeled as a markov decision process, and a value function estimation method is introduced to approximate the optimal energy efficiency of the entire HHMAS. Finally, the results indicate that the EEO strategy can enhance the fuel economy of vehicles, with a fuel-saving rate of 6.3% compared to the wheel-speed-following-control (WSFC) strategy. In addition, the proposed strategy exhibits superior traction capacity and climbing ability compared to the traditional WSFC strategy.

Adaptive formation control for obstacle avoidance of USVs with asymmetric input saturation

Due to the complex maritime navigation environment, Unmanned Surface Vessels (USVs) are influenced by unknown nonlinear dynamics arising from external disturbances and internal uncertainties. Achieving effective formation control while maintaining obstacle avoidance performance presents significant challenges. This article proposes a Neural Networks (NNs) adaptive formation Artificial Potential Field (APF) obstacle avoidance control method for multiple USVs. By employing online updates of Radial Basis Function (RBF) NNs technology, the unknown nonlinear dynamics are approximated, thus addressing complex nonlinear dynamics problems. In scenarios involving multiple USVs navigating under high wind and wave conditions, collisions with obstacles frequently occur. To tackle this issue, a leader-follower control strategy is designed that effectively addresses risk assessment and obstacle avoidance under such challenging conditions. Additionally, to account for saturation constraints or potential faults in the controller inputs commonly encountered in engineering applications, it implements an asymmetric auxiliary control system. Furthermore, the Lyapunov stability theorem is utilized to ensure the stability of both the formation control and obstacle avoidance algorithms for multiple USVs. Finally, the effectiveness of the proposed algorithm is validated through simulations.

Improvements of the dynamics code TMSR3D for molten salt reactor leveraging triangular prism nodal method

Dynamic simulation with coupled model of neutronics/thermal-hydraulics (TH) is one of the crucial aspects in safety analysis for molten salt reactor (MSR), which requires a deeper insight into the interactions among hydrodynamics, heat transfer and neutron kinetics because of its special characteristics induced by fuel drift, in comparison to the traditional reactors using solid fuels. To improve the geometric adaptability and calculation precision of the MSR specific dynamics code TMSR3D based on quadrilateral nodal method and TH module including the multi-channel flow and single-channel heat transfer models, the analytic basis function expansion nodal (ABFEN) method using triangular prism nodes is implemented to solve the static neutron diffusion equations, an implicit backward difference method along with exponential transformation is adopted to deal with the neutron kinetics problems, and the concentration equations of delayed neutron precursors (DNP) considering fuel flow are solved by the method of characteristics. The VVER-440 transient benchmark is first selected to validate capacity of the updated code for simulating core with hexagonal assemblies. Subsequently, the Molten Salt Reactor Experiment (MSRE) is simulated for further validation, in which the steady-state characteristics including delayed neutron loss induced by circulating fuel, profiles of reactor temperature and DNP, impact of fuel residence time in external loop on the effective yields of delayed neutrons, two fuel pump driven transients, and the natural convection are analyzed and discussed in detail. The results agree well with that from similar codes and the experimental values, which indicate that the improvements conducted for TMSR3D are effective and correct.

A new contact force model for revolute joints considering elastic layer characteristics effects

The contact forces generated during the motion of revolute joints with clearances significantly impact the dynamic performance of mechanisms, making it essential to develop an accurate contact force model. Traditional contact models often neglect the influence of elastic layers or assume that the bushing thickness is equal to its radius, which limits their applicability. To address the dynamic contact problem in revolute joints with small clearances, this study employs an improved Winkler elastic foundation model and introduces an elastic layer correction coefficient to refine the static contact model. The model's validity is verified using the finite element method. Building on this, a new contact force model is proposed, incorporating the optimal damping term from multiple continuous contact models. Finally, experimental validation is conducted using the crank-slider mechanism and typical applications in the Variable Stator Vane (VSV) mechanism. The results demonstrate that the proposed contact force model effectively predicts the dynamic characteristics of mechanisms with clearances.