Accurate Nonlinear Model Research Articles

Bayesian inference of initial conditions from non-linear cosmic structures using field-level emulators

ABSTRACT Analysing next-generation cosmological data requires balancing accurate modelling of non-linear gravitational structure formation and computational demands. We propose a solution by introducing a machine learning-based field-level emulator, within the Hamiltonian Monte Carlo-based Bayesian Origin Reconstruction from Galaxies (BORG) inference algorithm. Built on a V-net neural network architecture, the emulator enhances the predictions by first-order Lagrangian perturbation theory to be accurately aligned with full N-body simulations while significantly reducing evaluation time. We test its incorporation in BORG for sampling cosmic initial conditions using mock data based on non-linear large-scale structures from N-body simulations and Gaussian noise. The method efficiently and accurately explores the high-dimensional parameter space of initial conditions, fully extracting the cross-correlation information of the data field binned at a resolution of $1.95\,h^{-1}$ Mpc. Percent-level agreement with the ground truth in the power spectrum and bispectrum is achieved up to the Nyquist frequency $k_\mathrm{N} \approx 2.79h \,\, \mathrm{Mpc}^{-1}$. Posterior resimulations – using the inferred initial conditions for N-body simulations – show that the recovery of information in the initial conditions is sufficient to accurately reproduce halo properties. In particular, we show highly accurate $M_{200\mathrm{c}}$ halo mass function and stacked density profiles of haloes in different mass bins $[0.853,16]\times 10^{14}\,{\rm M}_{\odot }\,h^{-1}$. As all available cross-correlation information is extracted, we acknowledge that limitations in recovering the initial conditions stem from the noise level and data grid resolution. This is promising as it underscores the significance of accurate non-linear modelling, indicating the potential for extracting additional information at smaller scales.

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.

Pole placement tuning of proportional integral derivative feedback controller for knee extension model

Functional electrical stimulation (FES) has shown potential in rehabilitative exercises for patients recovering from spinal cord injuries. In recent developments, conventional open-loop FES control techniques have evolved into closed-loop systems that employ feedback controllers for automation. However, closed-loop FES systems often face challenges due to muscle non-linear effects, such as fatigue, time delays, stiffness, and spasticity. Therefore, an accurate non-linear knee model is required during the design stage, and precise tuning of the feedback controller parameters is vital. A proportional– integral–derivative (PID) controller is commonly used as a feedback controller due to its simplicity and ease of implementation. However, most PID tuning methods are complex and time consuming. This paper investigates the viability of employing the pole placement technique for tuning a PID controller that regulates the non-linear knee extension model. The pole placement method aims to improve the control and adaptability of the PID controller in closed-loop FES systems, specifically by facilitating knee extension exercises. MATLAB Simulink was used to assess the effectiveness of this tuning approach. Results showed that the PID controller performed satisfactorily without non-linearities, but performance varied with the inclusion of specific non-linearities. The pole placement tuning method facilitated preliminary assessments of PID controller performance, preceding highly advanced optimization.

Graph-enhanced deep material network: multiscale materials modeling with microstructural informatics

AbstractThis study addresses the fundamental challenge of extending the deep material network (DMN) to accommodate multiple microstructures. DMN has gained significant attention due to its ability to be used for fast and accurate nonlinear multiscale modeling while being only trained on linear elastic data. Due to its limitation to a single microstructure, various works sought to generalize it based on the macroscopic description of microstructures. In this work, we utilize a mechanistic machine learning approach grounded instead in microstructural informatics, which can potentially be used for any family of microstructures. This is achieved by learning from the graph representation of microstructures through graph neural networks. Such an approach is a first in works related to DMN. We propose a mixed graph neural network (GNN)-DMN model that can single-handedly treat multiple microstructures and derive their DMN representations. Two examples are designed to demonstrate the validity and reliability of the approach, even when it comes to the prediction of nonlinear responses for microstructures unseen during training. Furthermore, the model trained on microstructures with complex topology accurately makes inferences on microstructures created under different and simpler assumptions. Our work opens the door for the possibility of unifying the multiscale modeling of many families of microstructures under a single model, as well as new possibilities in material design.

Passivity-Based Control with Disturbance Observer of Electromagnetic Formation Flight Spacecraft in the Port-Hamiltonian Framework

Satellite formation flying technology currently represents a focal point in space mission research. Traditional spacecraft payload performance and lifespan are often constrained by propellant limitations. Electromagnetic Formation Flying (EMFF), a propellant-free formation flying technique, has garnered widespread attention. Its inherent strong nonlinearity and coupling present challenges for high-precision control within EMFF. This paper presents the relative motion dynamics of a two-satellite EMFF in the port-Hamiltonian framework and constructs an accurate nonlinear model of the dynamics. Utilizing the concept of Interconnection and Damping Assignment and nonlinear disturbance observer, a composite disturbance-rejection passivity-based controller is designed, offering a method for controlling the magnetic dipole strength of formation satellites. Finally, numerical simulations are conducted to demonstrate the viability of the proposed dynamics model and control strategy.

Fatigue characteristics of deep excavation-disturbed Jinping marble

Deep rocks encountered in underground engineering are frequently in complex in situ environments and experience both excavation disturbance during construction and cyclic loading throughout the long-term operation. Understanding the fatigue behavior of excavation-disturbed rocks in complex stress environments is critical for assessing the long-term stability of deep rock structures. Hence, an experimental method has been developed to capture the fatigue damage process of rocks while considering the in situ environment and excavation disturbance. Using this method, a series of triaxial fatigue damage experiments were conducted on Jinping deep marble samples from various in situ environments of 100 m, 1000 m, 1800 m, and 2400 m to better understand the variation in fatigue characteristics at different depths. With increasing depth, the samples experienced more cycles and greater fatigue deformation before failure. Further insights were gained into the fatigue damage behavior in terms of stiffness degradation, energy dissipation and irreversible strain accumulation. A decrease in the elastic modulus and an increase in the dissipated energy and irreversible strain exhibit an evolution pattern of initial→stabilization→acceleration, reflecting the nonlinear fatigue process that occurs inside marble. With increasing depth, marble samples have longer fatigue lives but exhibit more significant stiffness loss, energy dissipation and irrecoverable deformation accumulation; thus, evaluating the instability of deep rock structures solely using fatigue life alone is inadequate. Moreover, the previously reported inverted S-shaped evolution of fatigue damage was observed, and it was found that an increase in depth leads to an earlier onset of the accelerated fatigue damage stage with greater dominance of fatigue failure. Based on the nonlinear strain, loading cycle variable and fatigue life, a highly accurate nonlinear fatigue model was developed to describe the complete inverted S-shaped evolution pattern of fatigue damage, which demonstrated excellent practical implications for the theoretical characterization of anisotropic fatigue damage in disturbed Jinping marble.

On the Efficient and Accurate Non-linear Computational Modeling of Multilayered Bending Plates. State of the Art and a Novel Proposal: The 2D+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2\ ext {D}+$$\\end{document} Multiscale Approach

After conducting a comprehensive historical review of presently established methods for computational modeling of multilayered bending plates, the present work introduces a novel 2D multiscale strategy, termed the 2D+ approach. The proposed approach is based on the computational homogenization formalism and is envisaged to serve as an appealing alternative to current methodologies for modeling multilayered plates in bending-dominated situations. Such structural elements involve modern and relevant materials, such as laminated composites characterized by the heterogeneous distribution of low-aspect-ratio layers showing substantial non-linear mechanical behavior across their thickness.Within this proposed approach, the 2D plate mid-plane constitutes the macroscopic scale, while a 1D filament-like Representative Volume Element (RVE), orthogonal to the plate mid-plane and spanning the plate thickness, represents the mesoscopic scale. Such RVE, in turn, is capturing the non-linear mechanical behavior throughout the plate thickness at each integration point of the 2D plate-midplane finite element mesh. The chosen kinematics and discretization at the considered scales are particularly selected to (1) effectively capture relevant aspects of non-linear mechanical behavior in multilayered plates under bending-dominated scenarios, (2) achieve affordable computational times (computational efficiency), and (3) provide accurate stress distributions compared to the corresponding high-fidelity 3D simulations (computational accuracy).The proposed strategy aligns with the standard, first-order, hierarchical multiscale setting, involving the linearization of the macro-scale displacement field along the thickness. It employs an additional fluctuating displacement field in the RVE to capture higher-order behavior, which is computed through a local 1D finite element solution of a Boundary Value Problem (BVP) at the RVE. A notable feature of the presented 2D+ approach is the application of the Hill–Mandel principle, grounded in the well-established physical assumption imposing mechanical energy equivalence in the macro and meso scales. This links the 2D macroscopic plate and the set of 1D mesoscopic filaments, in a weakly-coupled manner, and yields remarkable computational savings in comparison with standard 3D modeling. Additionally, solving the resulting RVE problem in terms of the fluctuating displacement field allows the enforcement of an additional condition: fulfillment of linear momentum balance (equilibrium equations). This results in a physically meaningful 2D-like computational setting, in the considered structural object (multilayered plates in bending-dominated situations), which provides accurate stress distributions, typical of full 3D models, at the computational cost of 2D models.

Generalized predictive control application scheme for nonlinear hydro-turbine regulation system: Based on a precise novel control structure

Generalized predictive control (GPC), which has excellent control performance and robustness, is only applicable to the control object that can be expressed in the transfer function and is difficult to be directly applied to the hydraulic turbine regulation system (HTRS) that contain extremely complex nonlinearity. Therefore, considering the practical application of GPC in a hydropower station containing the Francis turbine, the double models, real-time feedback linearization module, and a nonlinear characteristic compensator are designed, and a generalized predictive control strategy combining these modules (GPC-DM-RFLM-NCC) is proposed. Firstly, the salp swarm algorithm (SSA) is improved based on the chaotic mapping and Levy flight, an accurate nonlinear hydraulic turbine model is constructed based on the backpropagation neural network (BPNN) and improved SSA (ISSA), and an HTRS simulation platform with nonlinear characteristics is built by combining modules such as water diversion system, servo system, and generator. Then, the irrationality of the commonly used linear hydraulic turbine models in HTRS dynamic process simulation is verified through quantitative calculation. Furthermore, by combining the real-time feedback linearization method and ISSA-based nonlinear characteristic compensator, the GPC-DM-RFLM-NCC is proposed. Finally, the HTRS simulation platform, which consists of GPC, double models, real-time feedback linearization module, and nonlinear characteristic compensator, is built, and the applicability, reliability, and excellent robustness of the proposed GPC-DM-RFLM-NCC are verified by the real data of a hydropower station.

Global Modeling of Heat-Integrated Distillation Column Based on Limited Local Measurements

The heat-integrated distillation column (HIDiC) has more energy-saving potential than conventional distillation columns. However, its nonlinearity and coupling effects pose significant challenges for the online operation of the HIDiC. To overcome these challenges, it becomes necessary to utilize accurate nonlinear models for design optimization or control schemes. Traditional modeling methods require extensive tray information, implying the impractical use of numerous sensors in real-world applications. This paper proposes a modeling approach for the HIDiC based on a limited number of measurements. It only requires the measurement of a finite amount of tray information to construct a global model of the HIDiC. This method serves as an online observer, providing real-time information about the entire column, and also enables the prediction of tray concentration changes. The proposed model forms the basis for developing model-based online monitoring and control schemes. Experimental simulation results demonstrate that the proposed method achieves high accuracy in global observation and prediction for the HIDiC.

Nonlinear modeling and parameter optimization of the pilot stage applied to the deflector-jet servovalve

Due to its good anti-pollution performance and high reliability, the deflector-jet servovalve is widely used in aerospace engineering. However, because the jet effects such as boundary expansion and adsorption are neglected, the model of the pilot stage applied to the deflector-jet servovalve is inaccurate, making it difficult to simulate the performance and optimize the parameters of the deflector-jet servovalve based on the model. Based on the structure of the jet flow field and the hydraulic resistance network bridge, an accurate nonlinear mathematical model of the pilot stage applied to the deflector-jet servovalve was developed, which considers the influence of the jet effect. Based on the new mathematical model, the structural parameters of the pilot stage were optimized with the maximum pressure, maximum flow, and maximum transmission power as the optimization objectives, respectively. Then the design criteria of the structural parameters were given based on the parameter optimization. Finally, the accuracy of the model was verified by three experiments. The comparison between experiments and this new model showed the maximum relative error of the flow between the model and experiment to be about 8.09%, which is more accurate than the traditional models.

Fast and Accurate Non-linear Model for Synchronous Machines Including Core Losses

Fast and Accurate Non-linear Model for Synchronous Machines Including Core Losses

Neural network-based finite-time command-filtered adaptive backstepping control of electro-hydraulic servo system with a three-stage valve

This paper aims to improve the tracking control performance of the three-stage valve (TSV) controlled electro-hydraulic servo system (EHSS) with parameter uncertainties and other lumped unknown nonlinearities, including unknown dynamics and disturbances. A more accurate nonlinear model of the TSV-controlled EHSS is established and a neural network-based finite-time command-filtered adaptive backstepping control (NNFCABC) method is proposed for the EHSS. Adaptive control is used to deal with the system parameter uncertainties, and the radial basis function neural network (RBFNN) algorithm is introduced to approximate the lumped unknown nonlinearities. The prediction errors of serial-parallel estimation models (SPEMs) and the tracking errors are utilized together to design adaptive laws to estimate the system parameters and the weights of the RBFNNs. The entire control framework utilizes command-filtered control and backstepping techniques. By applying Levant differentiators as command filters and introducing fractional power terms into the virtual control laws and the SPEMs, the proposed NNFCABC theoretically guarantees the tracking performance of the closed-loop control system with finite-time convergence. Comparative simulations and experiments verify the feasibility and superiority of the proposed control scheme.

Efficient and accurate nonlinear model reduction via first-order empirical interpolation

We present a model reduction approach that extends the original empirical interpolation method to enable accurate and efficient reduced basis approximation of parametrized nonlinear partial differential equations (PDEs). In the presence of nonlinearity, the Galerkin reduced basis approximation remains computationally expensive due to the high complexity of evaluating the nonlinear terms, which depends on the dimension of the truth approximation. The empirical interpolation method (EIM) was proposed as a nonlinear model reduction technique to render the complexity of evaluating the nonlinear terms independent of the dimension of the truth approximation. We introduce a first-order empirical interpolation method (FOEIM) that makes use of the partial derivative information to construct an inexpensive and stable interpolation of the nonlinear terms. We propose two different FOEIM algorithms to generate interpolation points and basis functions. We apply the FOEIM to nonlinear elliptic PDEs and compare it to the Galerkin reduced basis approximation and the EIM. Numerical results are presented to demonstrate the performance of the three reduced basis approaches.

Data‐driven state observation for nonlinear systems based on online learning

AbstractFor controlling nonlinear processes represented by state‐space models, a state observer is needed to estimate the states from the trajectories of measured variables. While model‐based observer synthesis is traditionally challenging due to the difficulty of solving pertinent partial differential equations, this article proposes an efficient model‐free, data‐driven approach for state observation, which is suitable for data‐driven nonlinear control without accurate nonlinear models. Specifically, by using a Chen–Fliess series representation of the observer dynamics, state observation is endowed with an online least squares regression formulation that can be solved by gradient flow with performance guarantees. When the target state trajectories for regression are unavailable, by exploiting the Kazantzis–Kravaris/Luenberger observer structure, state observation is reduced to a dimensionality reduction problem amenable to an online implementation of kernel principal component analysis. The proposed approach is demonstrated by a limit cycle dynamics and a chaotic system.

Fuzzy Adaptive Asymptotic Control for a Class of Large-Scale High-Order Unknown Nonlinear Systems

This paper studies the asymptotic control problem of a class of large-scale high-order nonlinear systems (LSHONSs), and an asymptotic fuzzy adaptive dynamic surface controller is developed. Unknown nonlinear terms are learned online by fuzzy logic systems (FLSs) such that the accurate nonlinear model is released in the controller design procedure, where the parameters of FLSs are updated by developing adaptive laws. To compensate for the “boundary error” caused by the dynamic surface control method where a linear filter is added in the backstepping procedure to handle the “explosion of complexity” problem, a nonlinear filter is proposed to eliminate the boundary layer error. Some simulations are given to demonstrate the effectiveness of the proposed algorithm.

Dynamic characteristics of PX single loop gear train considering weak nonlinear factors of intertooth system

Due to the non-linear factors of the single loop gear system and the inter-tooth system, is sometimes difficult to establish an accurate nonlinear dynamic model, which leads to the large deviation between the dynamic characteristics and the actual situation. According to the structural characteristics and dynamic mechanism of nonlinear factors, the bond graph power junction with switching characteristics is adopted. This method is used to establish the model of the single loop gear system and the inter-tooth system respectively. On this basis, the amplitude-phase-frequency characteristics of PX single loop gear systems are obtained by numerical simulation analysis. Eventually, the dynamic stability of single loop gear system is judged based on this characteristic index. The study shows that the dynamic stability of PX type single loop gear system is unsteady in the nonlinear state. In addition, it is concluded that when the whole single loop gear system is unstable, its system module also has the same unstability.

Consensus-Based Distributed Cooperative Perception for Connected and Automated Vehicles

Cooperative perception techniques incorporating Vehicle-to-Everything (V2X) information offer new possibilities for enhancing the perception capability of automated vehicles (AVs), but also present a new challenge of how to maximize the benefits of connected information with limited communication burden. In this context, this paper proposes a novel cooperative perception solution based on consensus theory to improve the accuracy and consistency for the detection and tracking of non-connected targets by combining V2X information. Given the common multi-sensor configurations of AVs, we design a consensus-based distributed cooperative perception (DCP) algorithm in the framework of multi-layer information fusion for local sensors and connected nodes, and give a nonlinear form based on cubature rules to include more accurate nonlinear system models and nonlinear sensors. Considering the high maneuverability of vehicle targets, we then extend the DCP algorithm to a multi-model form (DMMCP) to improve the model uncertainty of maneuvering targets via combining the prior knowledge of multiple models, which also gives a calculation method for model probability and its average consensus in the context of multiple local sensors. Besides, a new consensus information weight strategy and the properties from different consensus information weights are discussed. The simulation results demonstrate the superiority of both our algorithms over the traditional algorithms in accuracy and consistency, moreover, the DMMCP algorithm, which takes into account model uncertainty, shows better performance than DCP in complex conditions.

Multi-source motion constrained model predictive control for tractor-trailer trucks with coupled dynamics

This paper proposes a constrained model predictive control (MPC) for tractor-trailer trucks with the complicated physical characteristics, where motion constraints can be considered to govern the vehicle maneuver. Firstly, a targeted theoretical derivation method is developed to establish a more accurate nonlinear model for articulated vehicles, with expressly considering the articulation coupling effects. As an essential basis, the kinematic coupling behavior is further investigated. Secondly, multi-source motion constraints are introduced in particular with the analysis of nonholonomic constraints on the underactuated trailer: (i) keeping trucks traveling in the feasible domain away from collision; (ii) maintaining the vehicle states in a stable field through the steady-state response and side-slip thresholds. Thirdly, a constrained MPC controller is constructed for the automatic tracking operation, wherein vehicle demands of position security and yaw stability will be taken into reasonable consideration. For this purpose, vehicle states information can be fully utilized in a parallel approach to optimize quadratic programming (QP) in MPC: model prediction and updated constraints. In the end, the contrasted-simulation analysis is carried out to verify the accuracy of derived model and effectiveness of the designed controller, along with the feasibility of the additive multi-source constraints.

Towards inclusive underground public transportation: Gender differences on thermal comfort

As urbanization and societal needs grow, the demand for inclusive, efficient, and sustainable underground public transportation has increased, necessitating a greater focus on enhancing passengers' thermal comfort. However, limited research has addressed the subway station environment, and restricted datasets are challenging to build an accurate nonlinear model. Therefore, this study proposes a thermal comfort data generation algorithm based on 5161 measured data via the Variational Autoencoder (VAE) framework to break data collection constraints and increase thermal comfort model accuracy. By employing a gradient boosting algorithm on the extensively generated dataset, this study investigated factors influencing thermal comfort in subway stations, emphasizing individual gender differences and dynamic environmental variables. The VAE model enhanced the thermal comfort dataset, resulting in a 29% and 35% increase in male and female test set accuracy, respectively. The study suggests that males with a BMI over 27 were more sensitive to temperature. As for the gender-friendly environmental features, people feel most comfortable at temperatures between 24 and 29 °C and relative humidity levels between 20% and 70%. Additionally, the study reveals that a stable environment promotes enhanced thermal comfort for passengers. These insights contribute to developing sustainable, equitable, and user-friendly underground public transportation systems.

400 Gbit/s 4 mode transmission for IM/DD OAM mode division multiplexing optical fiber communication with a few-shot learning-based AffinityNet nonlinear equalizer.

Nonlinear impairment in a high-speed orbital angular momentum (OAM) mode-division multiplexing (MDM) optical fiber communication system presents high complexity and strong stochasticity due to the massive optoelectronic devices. In this paper, we propose an Affinity Network (AffinityNet) nonlinear equalizer for an OAM-MDM intensity-modulation direct-detection (IM/DD) transmission with four OAM modes. The labeled training and testing signals from the OAM-MDM system can be regarded as "small sample" and "large target", respectively. AffinityNet can be used to build an accurate nonlinear model using "small sample" based on few-shot learning and can predict the stochastic characteristic nonlinearity of OAM-MDM with a high level of generalization. As a result, the AffinityNet nonlinear equalizer can effectively compensate the stochastic nonlinearity in the OAM-MDM system, despite the large difference between the training and testing signals due to the stochastic nonlinear impairment. An experiment was conducted on a 400 Gbit/s transmission with four OAM modes using a pulse amplitude modulation-8 (PAM-8) signal over a 2 km ring-core fiber (RCF). Our experimental results show that the proposed nonlinear equalizer outperformed the conventional Volterra equalizer with improvements in receiver sensitivity of 1.7, 1.8, 3, and 3.3 dB for the four OAM modes at the 15% forward error correction (FEC) threshold, respectively. In addition, the proposed equalizer outperformed a convolutional neural network (CNN) equalizer with improvements in receiver sensitivity of 0.8, 0.5, 0.9, and 1.4 dB for the four OAM modes at the 15% FEC threshold. In the experiment, a complexity reduction of 37% and 83% of the AffinityNet equalizer is taken compared to the conventional Volterra equalizer and CNN equalizer, respectively. The proposed equalizer is a promising candidate for a high-speed OAM-MDM optical fiber communication system.