Inertial Model Research Articles

Research on Transfer Alignment Algorithms Based on SE(3) in ECEF Frame

The initial attitude error is challenging to satisfy the requirements of the linear model due to the complex nature of the ocean environment. This presents a challenge in the transfer alignment of the ship. In order to enhance the precision and velocity of ship transfer alignment, as well as to streamline the alignment processes, this paper proposes a transfer alignment methodology based on the Earth-Centered Earth-Fixed (ECEF) frame special Euclidean group (SE(3)) matrix Lie group. After introducing the two navigation states, velocity and attitude, from the ECEF frame into SE(3), the nonlinear inertial navigation system error state model and its corresponding measurement equations are derived based on the mapping relationship between the Lie groups and Lie algebra. The method effectively solves the error problem due to linear approximation in the traditional transfer alignment method, and applies to misalignment angles of arbitrary scale. The simulation results verify the effectiveness and rapidity of the proposed alignment method in the case of arbitrary misalignment angles.

Control Parameters of a Wall Heating and Cooling Module with Heat Pipes—An Experimental Study

Heat pipes filled with a thermodynamic medium are energy-saving and stable heat exchangers that have been used for years in various fields of science and technology, including building heating and cooling installations. This article presents the results of research on the energy efficiency of wall-mounted concrete heating and cooling modules with heat pipes, which can be a structural element of external and internal walls of buildings for various purposes. A series of measurement tests were performed, which allowed the determination of how the thermal power and control parameters of the module (amplification factor and time constants) change under operating conditions. A first- and second-order inertial model was used to describe the control properties of the module. The measurements were performed in heating and cooling mode for three different values of supply water flow, both when increasing the supply temperature and when decreasing it. Based on the results of the measurements, calculations and analysis, it was found that the thermal power and control parameters of the module change significantly; these changes result from both the design features of the module (the type of thermodynamic medium in the heat pipe and the technical aspects of the execution and assembly of the connections between the collector and the heat pipe) and the operating conditions (the value of the direction of temperature change and the flow of the supply water). It was shown that the supply temperature has a much greater impact on the values of the module’s control parameters than the flow rate of the supply water. The tested module is characterized by slow changes in temperature on its surface (high values of time constants). The time of stabilization of the temperature on the module’s surface, after step forcing, is 8–10 h. This can cause greater fluctuations in the indoor air temperature, lower thermal comfort in the room and lower energy efficiency of the process. These issues can be prevented by using complex algorithms for thermal comfort control, which in turn increase the cost of the control system.

An Improved Unscented Kalman Filter Applied to Positioning and Navigation of Autonomous Underwater Vehicles.

To enhance the positioning accuracy of autonomous underwater vehicles (AUVs), a new adaptive filtering algorithm (RHAUKF) is proposed. The most widely used filtering algorithm is the traditional Unscented Kalman Filter or the Adaptive Robust UKF (ARUKF). Excessive noise interference may cause a decrease in filtering accuracy and is highly likely to result in divergence by means of the traditional Unscented Kalman Filter, resulting in an increase in uncertainty factors during submersible mission execution. An estimation model for system noise, the adaptive Unscented Kalman Filter (UKF) algorithm was derived in light of the maximum likelihood criterion and optimized by applying the rolling-horizon estimation method, using the Newton-Raphson algorithm for the maximum likelihood estimation of noise statistics, and it was verified by simulation experiments using the Lie group inertial navigation error model. The results indicate that, compared with the UKF algorithm and the ARUKF, the improved algorithm reduces attitude angle errors by 45%, speed errors by 44%, and three-dimensional position errors by 47%. It can better cope with complex underwater environments, effectively address the problems of low filtering accuracy and even divergence, and improve the stability of submersibles.

КОНВЕРГЕНЦИЯ ГОСУДАРСТВЕННЫХ ПРОГРАММ РАЗВИТИЯ ЛЕСНОГО КОМПЛЕКСА

In the article the questions of improvement of program-targeted planning of development of forest complex of the Russian Federation are discussed on the example of state programs of the Russian Federation «Forestry Development» and «Development of industry and improvement of its competitiveness». The structural elements, indicators and expected results of existing public forest programmes are analysed for their sufficiency and effectiveness in achieving the objectives of strategic forest planning. Selected economic parameters characterizing the interface between government programmes in the area of forestry and forest industry. The paper provides a framework for the inertia and management of forests and presents a formula for the profitability of the harvesting industry through which cause and effect is givenThe link between the current selection by the logger of an inertial forest management model. On the basis of the results of the scientific research carried out, it is proposed to carry out a convergence of State programmes for the development of the forest complex, in terms of forestry and the forest industry, in order to improve the effectiveness of the implementation of the policy-oriented and targeted method of managing the sector.

Single inertial neuron with forced bipolar pulse: chaotic dynamics, circuit implementation, and color image encryption

Abstract The bipolar pulse current can effectively mimic the external time-varying stimulus of neurons, and its effect of neuronal dynamics has rarely been reported. To this end, this paper reports the effects of bipolar pulses on a two-dimensional single inertial neuron model, showcasing the chaotic dynamics of hidden attractors and coexisting symmetric attractors, which is of significant importance for understanding the complex behaviors of neuron dynamics under time-varying external stimuli and its application. Firstly, the mathematical model of the single intertial neuron model with forced bipolar pulse is presented, and then the equilibrium states behaving as unstable saddle point (USP), stable node-focus (SNF), and stable node point (SNP) are analyzed. Additionally, by using multiple dynamical methods including bifurcation plots, basins of attraction, and phase plots, complex dynamics of interesting bifurcation behaviors and coexisting attractors are revealed, which are induced by the forced bipolar pulse current as well as initial values, both. In addition, such effets are well valideted via a simple multiplerless electronic neuron circuit. The implementation circuit of presented model is constructed on the analog level and executed using PSIM circuit platform. The measurement results verified the double-scroll chaotic attractors and the coexisting period/chaos behaviors. Finally, the chaotic sequences of the model are applied to color image encryption for the benefit of requirements on modern security field. The encryption effectiveness is demonstrated through various evaluation indexes, including histogram analysis, information entropy, correlation coefficient, plaintext sensitivity, and resistance to noise attacks.

Emergent behaviors of two thermodynamically consistent inertial spin models

We propose two thermodynamically consistent inertial spin models generalizing the inertial spin model for the ensemble of mechanical particles with spin. For the collective dynamics modeling consistent with an entropy principle, we use two modeling ideas based on Hamiltonian formulation and flocking formalism for the coupling of the inertial spin model and temperatures introduced by Ha and Ruggeri [Arch. Ration. Mech. Anal. 223, 1397 (2017)]. The resulting models admit several constants of motions and are consistent with the entropy principle. We present several sufficient frameworks leading to the asymptotic vanishing of spins and velocity alignment. We also implement several numerical simulations and compare them with analytical results.

РАСЧЕТНО-ЭКСПЕРИМЕНТАЛЬНОЕ ИССЛЕДОВАНИЕ ДИНАМИКИ ОБВОДА ГУСЕНИЧНОГО ДВИЖИТЕЛЯ ТРАНСПОРТНОЙ МАШИНЫ ВЫСОКОЙ ПРОХОДИМОСТИ

The article presents an analysis of the methods for studying the dynamics of the branches of the track bypass, substantiates and proposes a research methodology and a simulation spatial model of the track mover of a cross-country transport vehicle, which differs from the common string inertialess and rod inertial models of the branches of the track mover by the ability to take into account a complex set of kinematic and force factors excited during the movement of the tracked vehicle in steady and transient motion modes. The model is developed in the “Universal Mechanism” software package, combines the main dependencies of the machine’s suspension system operation in various driving conditions and the dependencies of the interaction of the track links with each other, taking into account the radial, longitudinal and torsional rigidities during their interaction. The model allows for further development for the purpose of in-depth study and consideration of various factors acting in the design elements of the track mover, such as the features of the interaction of the support rollers with the links in the support branch of the track, the formation features of the moment of resistance to rotation and the turning moment depending on the type of the turning mechanism — stepped, differential hydrostatic. The efficiency of the model is assessed using the example of studying the phenomenon of “capture” of the track by the drive wheel when running over a typical unevenness of a sinusoidal profile. The substantiation of the technical solution option for the problem is given, installation of a free branch damper, and the results of determining the numerical parameters of its dynamic loading in relation to the object of study, a cross-country tracked transport vehicle. Thus, based on the results of the studies, the features of dynamic processes in the track mover were established, the main patterns of the formation process of transverse oscillations, their dependence on the design parameters of the bypass and various operational factors were revealed.

Inertial mass modeling and compensation for an energy-harvesting vehicle suspension system with limited-DOF parallel mechanisms actuator

An energy-harvesting suspension can improve the energy efficiency of vehicle. By introducing a lower-mobility parallel mechanism as motion transfer in the energy-harvesting suspension, the stiffness of the system is significantly improved. However, the overlage equivalent of inertial mass make the system is difficult to control and imped the development of this kind of suspension. To solve the problem, an equivalent linearization model to calculate the nonlinear inertial mass of low-DOF (Degree Of Freedom) parallel mechanism actuator is studied firstly. Furthermore, a 2-DOF 1/4 suspension system dynamic model that includes inertial mass is proposed to analyze the vehicle acceleration, dynamic tire load, and dynamic stroke. On this basis, the linear-quadratic Gaussian (LQG) controller is adopted to compensate the inertial mass of the suspension to improve the system performance. Results show that the proposed model accurately reflects the characteristics of the suspension inertial mass, the root-mean-square (RMS) value of the vehicle body acceleration and suspension dynamic stroke through compensation controller is reduced by 33.4% and 30.89%, respectively. Moreover, the RMS of the dynamic tire load is reduced by 3.06%, and the system stability is improved significantly.

Temporal Action Localization for Inertial-based Human Activity Recognition

As of today, state-of-the-art activity recognition from wearable sensors relies on algorithms being trained to classify fixed windows of data. In contrast, video-based Human Activity Recognition, known as Temporal Action Localization (TAL), has followed a segment-based prediction approach, localizing activity segments in a timeline of arbitrary length. This paper is the first to systematically demonstrate the applicability of state-of-the-art TAL models for both offline and near-online Human Activity Recognition (HAR) using raw inertial data as well as pre-extracted latent features as input. Offline prediction results show that TAL models are able to outperform popular inertial models on a multitude of HAR benchmark datasets, with improvements reaching as much as 26% in F1-score. We show that by analyzing timelines as a whole, TAL models can produce more coherent segments and achieve higher NULL-class accuracy across all datasets. We demonstrate that TAL is less suited for the immediate classification of small-sized windows of data, yet offers an interesting perspective on inertial-based HAR - alleviating the need for fixed-size windows and enabling algorithms to recognize activities of arbitrary length. With design choices and training concepts yet to be explored, we argue that TAL architectures could be of significant value to the inertial-based HAR community. The code and data download to reproduce experiments is publicly available via github.com/mariusbock/tal_for_har.

A Novel Approach for Kalman Filter Tuning for Direct and Indirect Inertial Navigation System/Global Navigation Satellite System Integration.

This work presents an innovative approach for tuning the Kalman filter in INS/GNSS integration, combining states from the inertial navigation system (INS) and data from the Global Navigation Satellite System (GNSS) to enhance navigation accuracy. The INS uses measurements from accelerometers and gyroscopes, which are subject to uncertainties in scale factor, misalignment, non-orthogonality, and bias, as well as temporal, thermal, and vibration variations. The GNSS receiver faces challenges such as multipath, temporary signal loss, and susceptibility to high-frequency noise. The novel approach for Kalman filter tuning involves previously performing Monte Carlo simulations using ideal data from a predetermined trajectory, applying the inertial sensor error model. For the indirect filter, errors from inertial sensors are used, while, for the direct filter, navigation errors in position, velocity, and attitude are also considered to obtain the process noise covariance matrix Q. This methodology is tested and validated with real data from Castro Leite Consultoria's commercial platforms, PINA-F and PINA-M. The results demonstrate the efficiency and consistency of the estimation technique, highlighting its applicability in real scenarios.

Dynamic modeling of variable speed left ventricular assist devices coupled to the cardiovascular system.

Most of the modeling of the Left Ventricular Assist Devices (LVADs) coupled with the cardiovascular system is based on the assumption of constant rotational speed. Compared with the traditional inertial model, the validated hysteresis model can take into account the unsteady characteristics of LVADs, but it fails to work under the condition of variable speed modulation. This study takes into consideration the impact of speed variations on the unsteady hysteresis effects. The time constant in the hysteresis model is treated as a time-varying parameter, thereby developing a new model applicable to variable speed modulation. Under sinusoidal speed modulation at various phases, a comparative analysis was undertaken among the steady-state model, inertial model, and the new model. Transient Computational Fluid Dynamics (CFD) simulations and existing experimental results are used for validation. The new model provides a more accurate method for the predicting the characteristics of LVAD in the coupled model under varying pump speeds, and exhibits higher linearity in the work done by the left ventricle and the blood pump, and , which is aligning closely with the experimental results. This enhancement renders it applicable for proactive control predictions and passive control validations.

Analysis of Alignment Accuracy due to Velocity/Attitude Error of Master Inertial Navigation System in Velocity/Attitude Matching Transfer Alignment

This paper theoretically analyzes the effect of the velocity and attitude errors of Master Inertial Navigation System(MINS) on the accuracy of Slave Inertial Navigation System(SINS) transfer alignment in velocity and attitude matching, and validates the analysis through simulation. Theoretical analysis involves deriving a new state equation that considers the velocity and attitude errors of MINS from the state equation of the transfer alignment filter, and deriving the state estimation equation of the Kalman filter based on this. The analysis confirms that MINS's velocity and attitude errors induce the same level of velocity and attitude errors in SINS. A reference inertial navigation system model is added to the simulation model, and the transfer alignment accuracy is analyzed by comparing the navigation information of MINS and SINS with the reference inertial navigation system. It is confirmed that the accuracy analysis results through simulation are consistent with the theoretically analyzed results, and through this, the validity of the theoretically analysis in this paper is verified. The research findings indicate that when performing transfer alignment using MINS, which is likely to be operated for prolonged periods in pure inertial navigation mode, the navigation errors of MINS are transferred to SINS. This implies that initial correction navigation is necessary to be considered for SINS

Analytical solution for the skip trajectory of hypersonic vehicles with time-varying aerodynamic coefficients

Abstract An analytical method is proposed for calculating the altitude and flight path angle of hypersonic vehicles’ skip trajectories under the influence of arbitrary time-varying aerodynamic coefficients. First, a longitudinal plane dynamics equation is established based on the inertial Earth model and the specific kinetic energy is introduced as independent variable to simplify the derivation. Subsequently, the solution is obtained through the perturbation method, where the zero-order analytical solution is based on existing literature, and the first-order linear time-varying system is decoupled through matrix linear transformation. Finally, by comparing numerical integration and analytical solutions with constant aerodynamic coefficients, the precision of this method in dealing with time-varying aerodynamic coefficients is verified, demonstrating its advantages over analytical solutions with constant aerodynamic coefficients.

Discrete Laplacian thermostat for flocks and swarms: the fully conserved Inertial Spin Model

Abstract Experiments on bird flocks and midge swarms reveal that these natural systems are well described by an active theory in which conservation laws play a crucial role. By building a symplectic structure that couples the particles’ velocities to the generator of their internal rotations (spin), the Inertial Spin Model (ISM) reinstates a second-order temporal dynamics that captures many phenomenological traits of flocks and swarms. The reversible structure of the ISM predicts that the total spin is a constant of motion, the central conservation law responsible for all the novel dynamical features of the model. However, fluctuations and dissipation introduced in the original model to make it relax, violate the spin conservation law, so that the ISM aligns with the biophysical phenomenology only within finite-size regimes, beyond which the overdamped dynamics characteristic of the Vicsek model takes over. Here, we introduce a novel version of the ISM, in which the irreversible terms needed to relax the dynamics strictly respect the conservation of the spin. We perform a numerical investigation of the fully conservative model, exploring both the fixed-network case, which belongs to the equilibrium class of Model G, and the active case, characterized by self-propulsion of the agents and an out-of-equilibrium reshuffling of the underlying interaction network. Our simulations not only capture the correct spin wave phenomenology of the ordered phase, but they also yield dynamical critical exponents in the near-ordering phase that agree very well with the theoretical predictions.

Evaluating Joint Angle Data for Clinical Assessment Using Multidimensional Inverse Kinematics with Average Segment Morphometry.

Movement analysis is a critical tool in understanding and addressing various disabilities associated with movement deficits. By analyzing movement patterns, healthcare professionals can identify the root causes of these alterations, which is essential for preventing, diagnosing, and rehabilitating a broad spectrum of medical conditions, disabilities, and injuries. With the advent of affordable motion capture technologies, quantitative data on patient movement is more accessible to clinicians, enhancing the quality of care. Nonetheless, it is crucial that these technologies undergo rigorous validation to ensure their accuracy in collecting and monitoring patient movements, particularly for remote healthcare services where direct patient observation is not possible. In this study, motion capture technology was used to track upper extremity movements during a reaching task presented in virtual reality. Kinematic data was then calculated for each participant using a scaled dynamic inertial model. The goal was to evaluate the accuracy of joint angle calculations using inverse kinematics from motion capture relative to the typical movement redundancy. Shoulder, elbow, radioulnar, and wrist joint angles were calculated with models scaled using either direct measurements of each individual's arm segment lengths or those lengths were calculated from individual height using published average proportions. The errors in joint angle trajectories calculated using the two methods of model scaling were compared to the inter-trial variability of those trajectories. The variance of this error was primarily within the normal range of variability between repetitions of the same movements. This suggests that arm joint angles can be inferred with good enough accuracy from motion capture data and individual height to be useful for the clinical assessment of motor deficits.

Inertial spin model of flocking with position-dependent forces.

We propose an extension to the inertial spin model (ISM) of flocking and swarming. The model has been introduced to explain certain dynamic features of swarming (second sound, a lower than expected dynamic critical exponent) while preserving the mechanism for onset of order provided by the Vicsek model. The inertial spin model (ISM) has only been formulated with an imitation ("ferromagnetic") interaction between velocities. Here we show how to add position-dependent forces in the model, which allows to consider effects such as cohesion, excluded volume, confinement, and perturbation with external position-dependent field, and thus study this model without periodic boundary conditions. We study numerically a single particle with an harmonic confining field and compare it to a Brownian harmonic oscillator and to a harmonically confined active Browinian particle, finding qualitatively different behavior in the three cases.

Numerical study of the influence of electron inertial effects and electron dynamics on tearing mode instability

The tearing mode instabilities were numerically studied in two distinct models: the finite electron inertial magnetohydrodynamics (MHD) and the electron MHD (EMHD). The finite electron inertial MHD model employed a modified Hall-MHD model that incorporated the electron inertial effects in the generalized Ohm’s Law. On the other hand, the electron dynamics were described by the EMHD model. It is found that both electron inertial effects and electron dynamics significantly influence the linear and nonlinear growth of tearing mode instabilities, with electron dynamics playing a more dominant role. The dependence of the linear growth rate of tearing modes on the electron inertial length de was investigated. The results show that electron inertial effects enhance the growth rate but resemble the behavior of resistivity η. Whereas, in the EMHD model, electron inertia plays a dominant role in tearing mode instabilities. Additionally, a study on the nonlinear saturation of (2,1) tearing modes was conducted, demonstrating consistency with relevant analytical theories. The study indicates that, in both models, the magnetic island exhibits faster growth and achieves a larger saturated island width as de increases.

How to Choose Suitable Physics‐Based Models Without Tuning and System Identification for Model‐Predictive Control of Open Water Channels?

AbstractModel predictive control (MPC) is used to manage water systems, and its performance depends on the (internal or control‐oriented) model it is based on. Several models for the hydraulics of open water systems are presented in literature and used in applications, but their performance has not yet been investigated systematically, and no guideline exists on which model to select for a certain channel. The aim of this research is to present a guideline for model choice based on the geometry of the channel and the flow conditions. The guideline is developed by first categorizing the channels into four types, followed by performing time‐domain, frequency domain, and closed‐loop tests for all models and channel types. The evaluation of the tests shows that for short and wave‐dominated channels, the Muskingum, Integrator Delay, and Integrator Delay Zero models perform the best, while for longer channels the linear inertial model is the most suitable. Finally, a decision‐tree is presented how to choose the model. Lastly, a decision‐tree is introduced to aid in the selection of the most appropriate model.

Exponential decay of solutions to an inertial model for a wave equation with viscoelastic damping and time varying delay

In the present work, we study the global existence and uniform decay rates of solutions to the initial-boundary value problem related to the dynamic behavior of evolution equations accounting for rotational inertial forces along with a linear time-nonlocal Kelvin-Voigt damping arising in viscoelastic materials. By constructing appropriate Lyapunov functional, we show that the solution converges to the equilibrium state exponentially in the energy space.

High speed impact on granular media: breakdown of conventional inertial drag models.

In this study, we extensively explore the impact process on granular media, particularly focusing on situations where the ratio of impact speed to acoustic speed is on the order of 0.01-1. This range significantly exceeds that considered in existing literature (0.0001-0.001). Our investigation involves a comprehensive comparison between our simulation data, obtained under high-speed conditions, and the established macroscopic drag models. In the high-speed regime, conventional drag force models prove inadequate, and the drag force cannot be separated into a depth-dependent static pressure and a depth-independent inertial drag, as suggested in previous literature. A detailed examination of the impact process in the high-speed limit is also presented, involving the spatio-temporal evolution of the force chain network, displacement field, and velocity field at the particle length scale. Unlike prior works demonstrating the exponential decay of pulses, we provide direct evidence of acoustic pulses propagating over long distances, reflecting from boundaries, and interfering with the original pulses. These acoustic pulses, in turn, induce large scale reorganization of the force chain network, and the granular medium continuously traverses different jammed states to support the impact load. Reorientation of the force chains leads to plastic dissipation and the eventual dissipation of the impact energy. Furthermore, we study the scaling of the early stage peak forces with the impact velocity and find that spatial dimensionality strongly influences the scaling.