Linear and Non-Linear Dynamics of Inertial Waves in a Rotating Cylinder with Antiparallel Inclined Ends

This work is devoted to the experimental study of inertial wave regimes in a non-uniform rotating cylinder with antiparallel inclined ends.In this setting,the cross-section of the cylinder is divided into two regions where the fluid depth increases or decreases with radius.Three different regimes are found:inertial wave attractor,global oscillations(the cavity’s resonant modes)and regime of symmetric reflection of wave beams.In linear wave regimes,a steady single vortex elongated along the rotation axis is generated.The location of the wave’s interaction with the sloping ends determines the vortex position and the vorticity sign.In non-linear regimes several pairs of the triadic resonance subharmonics are detected simultaneously.The instability of triadic resonance is accompanied by the periodic generation of mean vortices drifting in the azimuthal direction.Moreover,the appearance frequency of the vortices is consistent with the low-frequency subharmonic of the triadic resonance.The experimental results shed light on the mechanisms of the inertial wave interaction with zonal flow and may be useful for the development of new methods of mixing.

STRONGLY CONVERGENT INERTIAL FORWARD-BACKWARD-FORWARD ALGORITHM WITHOUT ON-LINE RULE FOR VARIATIONAL INEQUALITIES

This paper studies a strongly convergent inertial forward-backward-forward algorithm for the variational inequality problem in Hilbert spaces.In our convergence analysis,we do not assume the on-line rule of the inertial parameters and the iterates,which have been assumed by several authors whenever a strongly convergent algorithm with an inertial extrapolation step is proposed for a variational inequality problem.Consequently,our proof arguments are different from what is obtainable in the relevant literature.Finally,we give numerical tests to confirm the theoretical analysis and show that our proposed algorithm is superior to related ones in the literature.

A PID Tuning Approach for Inertial Systems Performance Optimization

In the practice of control the industrial processes, proportional-integral-derivative controller remains pivotal due to its simple structure and system performance-oriented tuning process. In this paper are presented two approaches for synthesis the proportional-integral-derivative controller to the models of objects with inertia, that offer the procedure of system performance optimization based on maximum stability degree criterion. The proposed algorithms of system performance optimization were elaborated for model of objects with inertia second and third order and offer simple analytical expressions for tuning the PID controller. Validation and verification are conducted through computer simulations using MATLAB, demonstrating successful performance optimization and showcasing the effectiveness PID controllers’ tuning. The proposed approaches contribute insights to the field of control, offering a pathway for optimizing the performance of second and third-order inertial systems through robust controller synthesis.

Design and Performance Analysis of HMDV Dynamic Inertial Suspension Based on Active Disturbance Rejection Control

This paper addresses the impact of vertical vibration negative effects,unbalanced radial forces generated by the static eccentricity of the hub motor,and road excitation on the suspension performance of Hub Motor Driven Vehicle(HMDV).A dynamic inertial suspension based on Active Disturbance Rejection Control(ADRC)is proposed,combining the vertical dynamic characteristics of dynamic inertial suspension with the features of ADRC,which distinguishes between internal and external disturbances and arranges the transition process.Firstly,a simulation model of the static eccentricity of the hub motor is established to simulate the unbalanced radial electromagnetic force generated under static eccentricity.A quarter-vehicle model of an HMDV with a controllable dynamic inertial suspension is then constructed.Subsequently,the passive suspension model is studied under different grades of road excitation,and the impact mechanism of suspension performance at speeds of 0–20 m/s is analyzed.Next,the three main components within the ADRC controller are designed for the second-order controlled system,and optimization algorithms are used to optimize its internal parameters.Finally,the performance of the traditional passive suspension,the PID-based controllable dynamic inertial suspension,and the ADRC-based controllable dynamic inertial suspension are analyzed under different road inputs.Simulation results show that,under sinusoidal road input,the ADRC-based controllable dynamic inertial suspension exhibits a 52.3%reduction in the low-frequency resonance peak in the vehicle body acceleration gain diagram compared to the traditional passive suspension,with significant performance optimization in the high-frequency range.Under random road input,the ADRC-based controllable dynamic inertial suspension achieves a 29.53%reduction in the root mean square value of vehicle body acceleration and a 14.87%reduction in dynamic tire load.This indicates that the designed controllable dynamic inertial suspension possesses excellent vibration isolation performance.

A Novel Fall Detection Framework Using Skip-DSCGAN Based on Inertial Sensor Data

With the widespread use of Internet of Things(IoT)technology in daily life and the considerable safety risks of falls for elderly individuals,research on IoT-based fall detection systems has gainedmuch attention.This paper proposes an IoT-based spatiotemporal data processing framework based on a depthwise separable convolution generative adversarial network using skip-connection(Skip-DSCGAN)for fall detection.The method uses spatiotemporal data from accelerometers and gyroscopes in inertial sensors as input data.A semisupervised learning approach is adopted to train the model using only activities of daily living(ADL)data,which can avoid data imbalance problems.Furthermore,a quantile-based approach is employed to determine the fall threshold,which makes the fall detection frameworkmore robust.This proposed fall detection framework is evaluated against four other generative adversarial network(GAN)models with superior anomaly detection performance using two fall public datasets(SisFall&MobiAct).The test results show that the proposed method achieves better results,reaching 96.93% and 92.75% accuracy on the above two test datasets,respectively.At the same time,the proposed method also achieves satisfactory results in terms ofmodel size and inference delay time,making it suitable for deployment on wearable devices with limited resources.In addition,this paper also compares GAN-based semisupervised learning methods with supervised learning methods commonly used in fall detection.It clarifies the advantages of GAN-based semisupervised learning methods in fall detection.

Hybrid pedestrian positioning system using wearable inertial sensors and ultrasonic ranging

Pedestrian positioning system(PPS)using wearable inertial sensors has wide applications towards various emerging fields such as smart healthcare,emergency rescue,soldier positioning,etc.The performance of traditional PPS is limited by the cumulative error of inertial sensors,complex motion modes of pedestrians,and the low robustness of the multi-sensor collaboration structure.This paper presents a hybrid pedestrian positioning system using the combination of wearable inertial sensors and ultrasonic ranging(H-PPS).A robust two nodes integration structure is developed to adaptively combine the motion data acquired from the single waist-mounted and foot-mounted node,and enhanced by a novel ellipsoid constraint model.In addition,a deep-learning-based walking speed estimator is proposed by considering all the motion features provided by different nodes,which effectively reduces the cumulative error originating from inertial sensors.Finally,a comprehensive data and model dual-driven model is presented to effectively combine the motion data provided by different sensor nodes and walking speed estimator,and multi-level constraints are extracted to further improve the performance of the overall system.Experimental results indicate that the proposed H-PPS significantly improves the performance of the single PPS and outperforms existing algorithms in accuracy index under complex indoor scenarios.

Weak and Strong Convergence of Self Adaptive Inertial Subgradient Extragradient Algorithms for Solving Variational Inequality Problems

Many solutions of variational inequalities have been proposed,among which the subgradient extragradient method has obvious advantages.Two different algorithms are given for solving variational inequality problem in this paper.The problem we study is defined in a real Hilbert space and has L-Lipschitz and pseudomonotone condition.Two new algorithms adopt inertial technology and non-monotonic step size rule,and their convergence can still be proved when the value of L is not given in advance.Finally,some numerical results are designed to demonstrate the computational efficiency of our two new algorithms.

Free-walking:Pedestrian inertial navigation based on dual foot-mounted IMU

The inertial navigation system(INS),which is frequently used in emergency rescue operations and other situations,has the benefits of not relying on infrastructure,high positioning frequency,and strong real-time performance.However,the intricate and unpredictable pedestrian motion patterns lead the INS localization error to significantly diverge with time.This paper aims to enhance the accuracy of zero-velocity interval(ZVI)detection and reduce the heading and altitude drift of foot-mounted INS via deep learning and equation constraint of dual feet.Aiming at the observational noise problem of low-cost inertial sensors,we utilize a denoising autoencoder to automatically eliminate the inherent noise.Aiming at the problem that inaccurate detection of the ZVI detection results in obvious displacement error,we propose a sample-level ZVI detection algorithm based on the U-Net neural network,which effectively solves the problem of mislabeling caused by sliding windows.Aiming at the problem that Zero-Velocity Update(ZUPT)cannot suppress heading and altitude error,we propose a bipedal INS method based on the equation constraint and ellipsoid constraint,which uses foot-to-foot distance as a new observation to correct heading and altitude error.We conduct extensive and well-designed experiments to evaluate the performance of the proposed method.The experimental results indicate that the position error of our proposed method did not exceed 0.83% of the total traveled distance.

Comparison study on measurement of rail weld joint between inertial reference method and multi-point chord reference method

Purpose – Straightness measurement of rail weld joint is of essential importance to railway maintenance. Dueto the lack of efficient measurement equipment, there has been limited in-depth research on rail weld joint with a5-m wavelength range, leaving a significant knowledge gap in this field.Design/methodology/approach – In this study, the authors used the well-established inertial referencemethod (IR-method), and the state-of-the-art multi-point chord reference method (MCR-method). Two methodshave been applied in different types of rail straightness measurement trollies, respectively. These instrumentswere tested in a high-speed rail section within a certain region of China. The test results were ultimatelyvalidated through using traditional straightedge and feeler gauge methods as reference data to evaluate the railweld joint straightness within the 5-m wavelength range.Findings – The research reveals that IR-method and MCR-method produce reasonably similar measurementresults for wavelengths below 1 m. However, MCR-method outperforms IR-method in terms of accuracy forwavelengths exceeding 3 m. Furthermore, it was observed that IR-method, while operating at a slower speed,carries the risk of derailing and is incapable of detecting rail weld joints and low joints within the track.Originality/value – The research compare two methods’ measurement effects in a longer wavelength rangeand demonstrate the superiority of MCR-method.

Vertical vibration control using nonlinear energy sink with inertial amplifier

To reduce additional mass, this work proposes a nonlinear energy sink(NES)with an inertial amplifier(NES-IA) to control the vertical vibration of the objects under harmonic and shock excitations. Moreover, this paper constructs pure nonlinear stiffness without neglecting the gravity effect of the oscillator. Both analytical and numerical methods are used to evaluate the performance of the NES-IA. The research findings indicate that even if the actual mass is 1% of the main oscillator, the NES-IA with proper inertia angles and mass distribution ratios can still effectively attenuate the steady-state and transient responses of the main oscillator. Nonlinear stiffness and damping also have important effects. Due to strongly nonlinear factors, the coupled system may exhibit higher branch responses under harmonic excitation. In shock excitation environment, the NES-IA with a large dynamic mass can trigger energy capture of both main resonance and high-frequency resonance. Furthermore, the comparison with the traditional NES also confirms the advantages of the NES-IA in overcoming mass dependence.

A RELAXED INERTIAL FACTOR OF THE MODIFIED SUBGRADIENT EXTRAGRADIENT METHOD FOR SOLVING PSEUDO MONOTONE VARIATIONAL INEQUALITIES IN HILBERT SPACES

In this paper,we investigate pseudomonotone and Lipschitz continuous variational inequalities in real Hilbert spaces.For solving this problem,we propose a new method that combines the advantages of the subgradient extragradient method and the projection contraction method.Some very recent papers have considered different inertial algorithms which allowed the inertial factor is chosen in[0;1].The purpose of this work is to continue working in this direction,we propose another inertial subgradient extragradient method that the inertial factor can be chosen in a special case to be 1.Under suitable mild conditions,we establish the weak convergence of the proposed algorithm.Moreover,linear convergence is obtained under strong pseudomonotonicity and Lipschitz continuity assumptions.Finally,some numerical illustrations are given to confirm the theoretical analysis.

Some Possible Solutions of Nonlinear Internal Inertial Gravity Wave Equations in the Atmosphere

In this paper, the nonlinear internal inerntial gravity wave equation is derived by the analysis method of phase plane and is solved by integration method. The results showed that this nonlinear equation not only has ordinary solitary wave solution but also has another extra-ordinary solutions, and the form of solution is related to stratification stability, wave velocity and direction of wave motion.

Diurnal wind and nonlinear interaction between inertial and tidal currents in the South China Sea during the passage of Typhoon Conson

Diurnal wind （DW） and nonlinear interaction between inertial and tidal currents near the Xisha Islands of the South China Sea （SCS） during the passage of Typhoon Conson （2010） are investigated using observational data and a damped slab model. It is found that the DWs, which are dominated by clockwise wind components, are prominent at our observational site. The DWs increase after the passage of the typhoon from 1 to about 4 m/s, which may be due to the decrease of the sea surface temperature caused by the passage of the typhoon. Kinetic energy spectra and bicoherence methods reveal nonlinear interactions between the inertial currents and the 2MK3 tidal constituent at our observational site. The slab damped model reproduces the inertial currents successfully induced by the total observed winds, and it is shown that the inertial currents induced by DWs are positively proportional to the DWs speed. Even though the observed inertial currents are distinct, the proportion of inertial currents induced by DWs to those induced by the total observed winds is just 0.7%/4% before/after the passage of typhoon. This shows that the inertial currents induced by the DWs are unimportant near the Xisha Islands during the typhoon season.

Closed-Loop System Identification Approach of the Inertial Models

The mathematical model that approximates the dynamics of the industrial process is essential for the efficient synthesis of control algorithms in industrial applications. The model of the process can be obtained according to the identification procedures in the open-loop, or in the closed-loop. In the open-loop, the identification methods are well known and offer good process approximation, which is not valid for the closed-loop identification, when the system provides the feedback output and doesn’t permit it to be identified in the open-loop. This paper offers an approach for experimental identification in the closed-loop, which supposes the approximation of the process with inertial models, with or without time delay and astatism. The coefficients are calculated based on the values of the critical transfer coefficient and period of the underdamped response of the closed-loop system with P controller, when system achieves the limit of stability. Finally, the closed-loop identification was verified by the computer simulation and the obtained results demonstrated, that the identification procedure in the closed-loop offers good results in process of estimation of the model of the process.

DOUBLE INERTIAL PROXIMAL GRADIENT ALGORITHMS FOR CONVEX OPTIMIZATION PROBLEMS AND APPLICATIONS

In this paper, we propose double inertial forward-backward algorithms for solving unconstrained minimization problems and projected double inertial forward-backward algorithms for solving constrained minimization problems. We then prove convergence theorems under mild conditions. Finally, we provide numerical experiments on image restoration problem and image inpainting problem. The numerical results show that the proposed algorithms have more efficient than known algorithms introduced in the literature.

Inertial effect on minimum magnetic field for magnetization reversal in ultrafast magnetism

In the field of ultrafast magnetism,i.e.,subpicosecond or femtosecond time scales,the dynamics of magnetization can be described by the inertial Landau-Lifhitz-Gilbert equation.In terms of this equation,the intrinsic characteristics are investigated in detail for the theoretical limit of the magnetization reversal field.We can find that there is a critical value for the inertia parameterτ_(c),which is affected by the damping and anisotropy parameter of the system.When the inertial parameter factorτ<τ_(c),the limit value of the magnetization reversal field under the ultrafast magnetic mechanism is smaller than that of the fast magnetic mechanism.Whenτ>τ_(c),the limit value of the magnetization reversal field will be larger than the limit value under the fast magnetic mechanism.Moreover,it is important to point out that the limit value of the magnetization reversal field under the ultrafast magnetic mechanism decreases with the increasing inertial factor,asτ<τ_(c)/2,which increases with inertial factorτasτ>τ_(c)/2.Finally,with the joint action of damping and anisotropy,compared with fast magnetism,we find that the limit value of the magnetization reversal field has rich variation characteristics,i.e.,there is not only a linear and proportional relationship,but also an inverse relationship,which is very significant for the study of ultrafast magnetism.

The Family of Exponential Attractors and Inertial Manifolds for a Generalized Nonlinear Kirchhoff Equations

In this paper, we study the long-time behavior of a class of generalized nonlinear Kichhoff equation under the condition of n dimension. Firstly, the Lipschitz property and squeezing property of the nonlinear semigroup related to the initial-boundary value problem are proved, and then the existence of its exponential attractor is obtained. By extending the space E0 to Ek, a family of the exponential attractors of the initial-boundary value problem is obtained. In the second part, we consider the long-time behavior for a system of generalized Kirchhoff type with strong damping terms. Using the Hadamard graph transformation method, we obtain the existence of a family of the inertial manifolds while such equations satisfy the spectrum interval condition.

New hybrid inertial CQ projection algorithms with line-search process for the split feasibility problem

In this paper, we propose two hybrid inertial CQ projection algorithms with linesearch process for the split feasibility problem. Based on the hybrid CQ projection algorithm, we firstly add the inertial term into the iteration to accelerate the convergence of the algorithm, and adopt flexible rules for selecting the stepsize and the shrinking projection region, which makes an optimal stepsize available at each iteration. The shrinking projection region is the intersection of three sets, which are the set C and two hyperplanes. Furthermore, we modify the Armijo-type line-search step in the presented algorithm to get a new algorithm.The algorithms are shown to be convergent under certain mild assumptions. Besides, numerical examples are given to show that the proposed algorithms have better performance than the general CQ algorithm.

NCCT for Micropolar Solid and Fluid Media Based on Internal Rotations and Rotation Rates with Rotational Inertial Physics: Model Problem Studies

This paper presents model problem studies for micropolar thermoviscoelastic solids without memory and micropolar thermoviscous fluid using micropolar non-classical continuum theories (NCCT) based on internal rotations and rotation rates in which rotational inertial physics is considered in the derivation of the conservation and balance laws (CBL). The dissipation mechanism is due to strain rates as well as rotation rates. Model problems are designed to demonstrate and illustrate various significant aspects of the micropolar NCCT with rotational inertial physics considered in this paper. In case of micropolar solids, the translational and rotational waves are shown to coexist. In the absence of microconstituents (classical continuum theory, CCT) the internal rotations are a free field, hence have no influence on CCT. Absence of gradients of displacements and strains in micropolar thermoviscous fluid medium prohibits existence of translational waves as well as rotational waves even though the appearance of the mathematical model is analogous to the solids, but in terms of strain rates. It is shown that in case of micropolar thermoviscous fluids the BAM behaves more like time dependent diffusion equation i.e., like heat conduction equation in Lagrangian description. The influence of rotational inertial physics is demonstrated using BLM as well as BAM in the model problem studies.

An Improved Particle Filter Map Matching Algorithm for Personal Inertial Positioning

The current particle filtering map matching algorithm has problems such as low map utilization and poor accuracy of turnoff positioning, etc. This paper proposed an improved particle filtering-based map-matching algorithm for the inertial positioning of personnel. The historical moment position constraint and feasible region constraint of particles were introduced in this paper. A resampling method based on multi-stage backtracking of particles was proposed. Therefore, the effectiveness of newly generated particles could be guaranteed. The utilization rate of map information could be improved, thus enhancing the accuracy of personnel localization. The walking experiment results showed that, compared with the traditional PDR algorithm, the proposed method had higher localization accuracy and better repeatability of the localization trajectory for multi-turn paths. Under the total travel of 480 meters, the deviation of the starting end point was less than 2 meters, which was about 0.4% of the total travel.