Inertial Model Research Articles

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.

First-Principle Validation of Fourier's Law: One-Dimensional Classical Inertial Heisenberg Model.

The thermal conductance of a one-dimensional classical inertial Heisenberg model of linear size L is computed, considering the first and last particles in thermal contact with heat baths at higher and lower temperatures, Th and Tl (Th>Tl), respectively. These particles at the extremities of the chain are subjected to standard Langevin dynamics, whereas all remaining rotators (i=2,⋯,L-1) interact by means of nearest-neighbor ferromagnetic couplings and evolve in time following their own equations of motion, being investigated numerically through molecular-dynamics numerical simulations. Fourier's law for the heat flux is verified numerically, with the thermal conductivity becoming independent of the lattice size in the limit L→∞, scaling with the temperature, as κ(T)∼T-2.25, where T=(Th+Tl)/2. Moreover, the thermal conductance, σ(L,T)≡κ(T)/L, is well-fitted by a function, which is typical of nonextensive statistical mechanics, according to σ(L,T)=Aexpq(-Bxη), where A and B are constants, x=L0.475T, q=2.28±0.04, and η=2.88±0.04.

Directed circulating flows in tanks of moving objects

The results of liquid fuel inertial flows numerical modeling in the tanks of the spacecraft during its maneuvering in the Earth's orbit are given. It is shown that the circulations that occur when internal guiding devices are used in the form of widely spaced rigid baffles can be deformed and affect the flow space not covered by them. In addition, the circular moments of inertia of the liquid on the baffles can be controlled by means of the appropriate location of the guide devices in terms of width and distance from the tank wall. The force effects calculation of the moving fluid on the walls and internal structures makes it possible to fairly correctly present the hydrodynamic picture of the of inertial flows development, as well as predict the methods and means of compensation for such disturbances. According to the obtained results of the specified processes simulation in the tanks, it can be stated that the inertial flows of the liquid in the tanks are strongly nonlinear, the properties of which depend on the geometry, the initial conditions for the generation of peak force effects tank on the tank walls and bottoms. The use of internal guiding devices in the flow significantly changes the geometry of wave formations, corrects the coordinates and duration of resonant currents in the tank. The main task is to minimize the mass and dimensions of the baffles with a simultaneous increase in the damping efficiency of resonant flows. In addition, the determination of the power parameters real distribution contributes to the development of the latest, more effective designs of baffles, which will allow more reliable influence on uncontrolled inertial flows in tanks.

Autonomous method for a strapdown inertial navigation system calibration in operation in operation

Strapdown inertial navigation systems (SINS) are widely used in modern air transport. The service life of such systems is decades. During this time, the characteristics of such systems may deteriorate due to the degradation of inertial sensors - gyroscopes and accelerometers. Under these conditions, in order to maintain the required accuracy of the SINS during the entire period of operation, it is necessary either to periodically carry out routine maintenance with the onboard system, or to continuously adapt the used sensor measurement model in terms of compensating for errors that arise. The second direction, which we will call calibration, has the advantage over the first one that it is carried out automatically by the system itself and does not require any additional equipment or additional maintenance work. The known method of SINS recalibration is based on the integration of information from the SINS and from the receiver of satellite radio navigation signals (SRNS). Such calibration, firstly, significantly depends on the availability and quality of satellite information, and secondly, it is possible only for integrated navigation systems in which the inertial subsystem is supplemented by a SRNS receiver. In contrast to the known method, this article solves the problem of autonomous SINS calibration, which is carried out after each flight. The solution is based on a linearized inertial navigation error model based on the boundary conditions of the state vector (at the beginning and end of the flight). The external information used consists only of the initial values of the coordinates and the current measurements of the baroaltimeter. As a result of the decision at the end of the flight, the errors of gyroscopes and accelerometers are determined, as well as the error in determining the final values of latitude and longitude in the SINS. Sensor errors can be used in subsequent system activations, which improves the accuracy of its operation as a whole. The analysis of the suitability and effectiveness of the developed methodology was carried out on a typical flight simulation program.

Abstract 17220: Mathematical Modeling of Echocardiographic Underestimation of Right Ventricular Systolic Pressure in Severe Tricuspid Regurgitation

Background: Echocardiography approximates right ventricular systolic pressure (RVSP) by the simplified Bernoulli Equation (SBE), adding mean right atrial pressure (mRA) to convective pressure (4v 2 ), where v is maximal tricuspid regurgitant (TR) velocity. As TR worsens, the inertance of TR flow increases which may cause TR peak velocity to lag behind the maximal RVSP time point. As a result, using SBE may underestimate RVSP in patients with significant TR. Currently, inertance is not measurable by echo, but theory suggests it is linearly related to regurgitant orifice diameter (3 X ROD). We sought to confirm the principle of RVSP underestimation in ≥severe TR by comparing a lumped parameter model (LPM) of the heart to cath/echo data. Methods: In MATLAB, the LPM uses time-varying elastance of atria/ventricles and the complete Bernoulli equation to model pressure and flow in all chambers/vascular beds. LPM parameters for trace and torrential TR cases yielded convective, inertial, RA and RV pressure curves and critical TR variables: TR volume, mRA, and TR velocity, which were compared to simultaneous cath/echo data in clinical patients. Results: Trace TR pressure curves aligned with RVSP and convective pressure peaks, and near perfect echo prediction. Torrential TR pressure curves show earlier peak RVSP with up to 20mmHg of inertial pressure, resulting in predicted 3.1mmHg underestimation, closely matching the observed underestimation of 3.6mmHg. For modeling demonstration, we show (from 90 subjects) 1 patient with trace TR (ROD 1.1mm), A, and 1 patient with torrential TR (ROD=11.3mm), B, in Figure 1. Conclusions: Our analysis shows the importance of inertial pressure in ≥severe TR: earlier peak RVSP congruent with accelerating increased regurgitant mass and improved approximation of RVSP by inertial pressure quantification modeling. Further clinical study of RVSP underestimation in cases of ≥severe TR and its correction by including inertial forces is recommended.

Diffusive–inertial droplet separation model from two-phase flow

Diffusive–inertial droplet separation model from two-phase flow

Minimum inertial demand estimation of renewable energy considering new power system frequency constraints using sparrow search algorithm

With the proposal of a "dual carbon strategy " and the rising share of renewable energy sources, the resulting low-inertia problem has seriously affected the frequency stability of new power systems. This paper proposes a minimum inertial demand estimation of renewable energy considering new power system frequency constraints to enhance the power system inertia situational awareness and clarify the system operation boundary. Firstly, the frequency response model with multi-source renewable energy units and the time-domain mathematical expressions are established, and the frequency constraints and inertial demand of new power systems are given. The minimum inertial demand estimation model is constructed on this basis, which can be solved by the sparrow search algorithm (SSA). Ultimately, the applicability and practicality of the suggested approach are demonstrated and verified in IEEE 39-bus system. The case study results demonstrate the process can accurately calculate the inertial demand of renewable energy side considering system frequency constraints and give guidance for the stable operation of new power systems.

Optimal swimming locomotion of snake-like robot in viscous fluids

Snake-like robots have several joints that enable them to swim in various types of viscous fluids such as water, mud, and clay by varying the undulation. Because the optimal swimming motion is assumed to be different in fluids with different viscosities, we constructed an equation of motion for a snake-like robot swimming in viscous fluids and attempted to find the optimal swimming motion via numerical analysis. We constructed a snake-like robot comprising eight links in this study that could swim in four fluids with different kinematic viscosities, and measured their joint positions and relative angles during swimming. Accordingly, we proposed a method for identifying multiple unknown parameters of fluid forces acting on a body using the unscented Kalman filter, which could determine the unknown added mass and drag coefficient. Subsequently, we clarified that the inertial drag model is effective in water (small viscosity, μ∼1mPas), while the friction drag model is effective in oil (large viscosity, μ>100mPas). By considering the increase in frictional drag due to boundary layer thinning in the proposed model, we identified the constant drag coefficient regardless of the swimming frequency. Next, we employed the constructed numerical model to explore the trade-off relationship between consumed power and velocity during swimming using exhaustive search. Consequently, we confirmed that the swimming frequency decreased as the fluid viscosity increased under the same swimming power consumption. Moreover, the wavelength of undulation was confirmed to be between half and one wavelength, regardless of the viscosity.

Online Self-Calibration for Visual-Inertial Navigation: Models, Analysis, and Degeneracy

As sensor calibration plays an important role in visual-inertial sensor fusion, this article performs an in-depth investigation of online self-calibration for robust and accurate visual-inertial state estimation. To this end, we first conduct complete observability analysis for visual-inertial navigation systems (VINS) with full calibration of sensing parameters, including inertial measurement unit (IMU)/camera intrinsics and IMU-camera spatial-temporal extrinsic calibration, along with readout time of rolling shutter (RS) cameras (if used). We study different inertial model variants containing intrinsic parameters that encompass most commonly used models for low-cost inertial sensors. With these models, the observability analysis of linearized VINS with full sensor calibration is performed. Our analysis theoretically proves the intuition commonly assumed in the literature—that is, VINS with full sensor calibration has four unobservable directions, corresponding to the system's global yaw and position, while all sensor calibration parameters are observable given fully excited motions. Moreover, we, for the first time, identify degenerate motion primitives for IMU and camera intrinsic calibration, which, when combined, may produce complex degenerate motions. We compare the proposed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">online</i> self-calibration on commonly used IMUs against the state-of-art <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">offline</i> calibration toolbox Kalibr, showing that the proposed system achieves better consistency and repeatability. Based on our analysis and experimental evaluations, we also offer practical guidelines to effectively perform online IMU-camera self-calibration in practice.

On an incompressible inertial nematic electrolyte model of liquid crystal flow

ABSTRACT We study the Cauchy problem of the new model of the three dimensional inertial nematic electrolyte, which models the N-species charged particles diffuse and advect in the nematic liquid crystalline matrix. This new model was proposed by [Calderer MC, Golovaty D, Lavrentovich O, et al. Modeling of nematic electrolytes and nonlinear electroosmosis. SIAM J Appl Math. 2016;76:2260–2285. doi: 10.1137/16M1056225]. The inertial effect is such that the system involves a hyperbolic feature. We first derive the local existence in large initial data when the flow is isotropy, i.e. λ = 1 . For the anisotropy case ( λ > 0 , λ ≠ 1 ), we obtain small data local solutions. Then, by seeking some further dissipative mechanisms from the elliptic structures, the local solution can be extended globally near the constant states with electro-neutrality condition.

A single inertial measurement unit-based deep learning model for predicting knee angles during running

A single inertial measurement unit-based deep learning model for predicting knee angles during running