Exact Analytical Model Research Articles

An exact analytical solution for coupled vibration analysis of a piezoelectric resonator

Abstract Piezoelectric resonators are widely used as the active components in devices such as sensors, actuators, communication filters, and micro/nano-electro-mechanical systems (MEMS / NEMS). Due to the piezoelectric effect, Poisson’s ratio, and its finite dimension, the thickness and lateral vibration modes in a piezoelectric resonator are inevitably coupled. In this paper, an exact analytical model for coupled vibration analysis of a piezoceramic disk is developed based on a new superstition method. The free vibrations are decomposed into thickness and lateral directions in a new form of Fourier-Bessel series and then they are superimposed to satisfy the boundary conditions. To verify the validity of the analytical model proposed here, numerical simulations are performed using COMSOL Multiphysics. An excellent agreement is observed. This analytical model can be applied to the design and optimization of piezoelectric devices.

On-load magnetic field calculation for linear permanent-magnet actuators using hybrid 2-D finite-element method and Maxwell–Fourier analysis

PurposeThe purpose of this study is to present a novel extended hybrid analytical method (HAM) that leverages a two-dimensional (2-D) coupling between the semi-analytical Maxwell–Fourier analysis and the finite element method (FEM) in Cartesian coordinates.Design/methodology/approachThe proposed model is applied to flat permanent-magnet linear electrical machines with rotor-dual. The magnetic field solution across the entire machine is established by coupling an exact analytical model (AM), designed for regions with relative magnetic permeability equal to unity, with a FEM in ferromagnetic regions. The coupling between AM and FEM occurs bidirectionally (x, y) along the edges separating teeth regions and their adjacent regions through applied boundary conditions.FindingsThe developed HAM yields accurate results concerning the magnetic flux density distribution, cogging force and induced voltage under various operating conditions, including magnetic or geometric parameters. A comparison with hybrid finite-difference and hybrid reluctance network methods demonstrates very satisfactory agreement with 2-D FEM.Originality/valueThe original contribution of this paper lies in establishing a direct coupling between the semi-analytical Maxwell–Fourier analysis and the FEM, particularly at the interface between adjacent regions with differing magnetic parameters.

Prediction of Femtosecond Laser Etching Parameters Based on a Backpropagation Neural Network with Grey Wolf Optimization Algorithm.

Investigating the optimal laser processing parameters for industrial purposes can be time-consuming. Moreover, an exact analytic model for this purpose has not yet been developed due to the complex mechanisms of laser processing. The main goal of this study was the development of a backpropagation neural network (BPNN) with a grey wolf optimization (GWO) algorithm for the quick and accurate prediction of multi-input laser etching parameters (energy, scanning velocity, and number of exposures) and multioutput surface characteristics (depth and width), as well as to assist engineers by reducing the time and energy require for the optimization process. The Keras application programming interface (API) Python library was used to develop a GWO-BPNN model for predictions of laser etching parameters. The experimental data were obtained by adopting a 30 W laser source. The GWO-BPNN model was trained and validated on experimental data including the laser processing parameters and the etching characterization results. The R2 score, mean absolute error (MAE), and mean squared error (MSE) were examined to evaluate the prediction precision of the model. The results showed that the GWO-BPNN model exhibited excellent accuracy in predicting all properties, with an R2 value higher than 0.90.

Measuring the viscoelastic relaxation function of cells with a time-dependent interpretation of the Hertz-Sneddon indentation model

The Hertz-Sneddon elastic indentation model is widely adopted in the biomechanical investigation of living cells and other soft materials using atomic force microscopy despite the explicit viscoelastic nature of these materials. In this work, we demonstrate that an exact analytical viscoelastic force model for power-law materials, can be interpreted as a time-dependent Hertz-Sneddon-like model. Characterizing fibroblasts (L929) and osteoblasts (OFCOLII) demonstrates the model's accuracy. Our results show that the difference between Young's modulus EY obtained by fitting force curves with the Hertz-Sneddon model and the effective Young's modulus derived from the viscoelastic force model is less than 3%, even when cells are probed at large forces where nonlinear deformation effects become significant. We also propose a measurement protocol that involves probing samples at different indentation speeds and forces, enabling the construction of the average viscoelastic relaxation function of samples by conveniently fitting the force curves with the Hertz-Sneddon model.

Novel Magnetic Field Modeling Method for a Low-Speed, High-Torque External-Rotor Permanent-Magnet Synchronous Motor

In view of the unstable electromagnetic performance of the air gap magnetic field caused by the torque ripple and harmonic interference of a multi-slot and multi-pole low-speed, high-torque permanent magnet synchronous motor, we propose a simplified model of double-layer permanent magnets. The model is divided into an upper and a lower subdomain, with the upper subdomain being an ideal circular ring and the lower subdomain being a segmented sector ring. Moreover, we develop an exact analytical model of the motor that predicts the magnetic field distribution based on Laplace’s and Poisson’s equations, which is solved using the method of separating variables. Taking a 40p168s low-speed, high-torque permanent magnet synchronous motor as an example, the accuracy of the model is verified by comparison with an ideal circular ring model, a segmented sector ring model, and the finite element method. Based on the proposed simplified model, three combined permanent magnets considering both edge-cutting and polar arc cutting structures are proposed, which are chamfered, rounded, and rectangular combinations. Under the premise of a consistent edge-cutting amount, the electromagnetic characteristics of the three combination types of permanent magnets are compared using the finite element method. The results show that the electromagnetic characteristics of the chamfered combination PM are superior to those of the other two combinations. Finally, a prototype is manufactured and tested to validate the theoretical analysis.

A Review of Research on Diagnosability of Control Systems Based on Structural Analysis

Structural analysis, a model-based fault diagnosis approach, has been extensively highlighted since it does not depend on an exact analytical system model. The structural analysis approach focuses on obtaining the required information for fault detection and fault-tolerant control from the structural model of the control system. Diagnosability is a design attribute that indicates the fault diagnosis capabilities. Diagnosability design not only guarantees that the structure of the control system gives adequate fault information but also that the control system achieves the fault diagnosis with the least cost and the most excellent efficiency. In this paper, in combination with the research progress of structural analysis, the study first designs the structural diagnosability model of the control system based on structural analysis; secondly, the essential techniques of diagnosability evaluation and diagnosability design based on structural analysis are analyzed and summarized, and the diagnosability index system based on structural analysis is designed based on the structural detectability and structural isolation; this lays the foundation for the development of the diagnosability; lastly, the study summarizes the problems of diagnosability research based on structural analysis and the future development direction.

Features of backward waves and negative refraction in absorbing bi-isotropic media and metamaterials

ABSTRACT Conditions of the excitation of backward electromagnetic waves and negative refraction in absorbing bi-isotropic layered media and metamaterials are investigated. Based on the exact analytical model, the features determined by absorption and inhomogeneity of the waves and possible metamaterial properties of the medium are ascertained. It is shown that only simultaneous realization of backward, backward with respect to the boundary between two media, and negative refraction is possible for each of the proper waves in a bi-isotropic layer. The conditions are obtained when two (one transmitted and one reflected waves) or all the four proper waves in the layer are backward and characterized by negative refraction on boundaries. Taking into account the calculation of Pointing’s vector and energy dissipation of the waves, it is shown that the well-known limitations on the chirality and nonreciprocity parameters require a clarification for the considered media.

Application of machine learning methods for the prediction of roll force and torque during plate rolling of micro-alloyed steel

Machine learning technique is extensively used to establish the relationship between non-linear data sets which cannot be described mathematically and thus an exact analytic model is either intractable or too time-consuming to develop. During hot rolling, the effect of process parameters that cannot be captured in mathematical models, such as roll dimensions and its wear, the inter-pass time between rolling passes, temperature variation has been incorporated using multivariate supervised machine learning technique for accurate prediction of roll force and torque during plate rolling of micro-alloyed steel. An ensemble method was used to combine various machine learning techniques and average them to develop one final predictive model. K-cross validation of the model was carried out to validate the results and ensure the model gets the correct pattern of data. Root mean square error of ensemble roll force model was compared with roll force calculation using Sims theory. It was found that the machine learning model can predict the roll force and torque accurately as it takes care of various non-linear process variables which cannot be accounted for mathematically. The R-value of the machine learning model was >98 %, whereas it was 92.2 % for roll force calculation using Sims theory.

Intelligent Modelling of the Real Dynamic Viscosity of Rubber Blends Using Parallel Computing.

Modelling the flow properties of rubber blends makes it possible to predict their rheological behaviour during the processing and production of rubber-based products. As the nonlinear nature of such complex processes complicates the creation of exact analytical models, it is appropriate to use artificial intelligence tools in this modelling. The present study was implemented to develop a highly efficient artificial neural network model, optimised using a novel training algorithm with fast parallel computing to predict the results of rheological tests of rubber blends performed under different conditions. A series of 120 real dynamic viscosity-time curves, acquired by a rubber process analyser for styrene-butadiene rubber blends with varying carbon black contents vulcanised at different temperatures, were analysed using a Generalised Regression Neural Network. The model was optimised by limiting the fitting error of the training dataset to a pre-specified value of less than 1%. All repeated calculations were made via parallel computing with multiple computer cores, which significantly reduces the total computation time. An excellent agreement between the predicted and measured generalisation data was found, with an error of less than 4.7%, confirming the high generalisation performance of the newly developed model.

Deep learning and deep transfer learning-based OPM for FMF systems

Optical performance monitoring (OPM) is indispensable to guarantee stable and reliable operation in few-mode fiber (FMF)-based transmission. OPM consists of measuring optical phenomena such as generalized signal-to-noise ratio (GSNR) based on analytical models. GSNR comprises nonlinear interference (NLI) noise which can be calculated either by exact analytical models e.g., enhanced Gaussian noise (EGN) model which is accurate but computationally complex, or asymptotic analytical models e.g., closed-form EGN model which are approximate but computationally fast. In this paper, we employ deep learning (DL) as an accurate and fast alternative for OPM in FMF-based transmission. However, DL-based OPM requires a large dataset to achieve proper performance whilst it is very difficult and time-consuming to obtain a large field or synthetic dataset. Regarding this issue, we develop deep transfer learning (DTL) for OPM in FMF to realize a fast response requiring a small training dataset and a few training epochs despite various changes in system/link parameters such as launched power, fiber type, and the number of modes. Results show root mean squared error of GSNR estimation is less than 0.02 dB for DL and DTL-based OPM methods. Compared to DL-based OPM, DTL-based OPM records 3 and 5 times reduction in required training dataset size and the number of epochs, respectively which is beneficial for real-time applications

Free Vibration Response of a Steel Liquid Storage Tank with Porous and Perforated Columns via an Exact Continuum Method

The presence of predictable cavities inside a structure is often preferable as it will reduce the vibration amplitude. In this article, inspired by the traditional mass attached to the beam system, in order to solve the problem of free vibration of the steel liquid storage tank with a column made of porous and perforated materials using an exact analytical continuum model is formed. The free vibration response of the mass attached column made of porous materials and holes is established by using a new analytical method known as the Fourier series with Stokes’ transform. The free vibration frequencies are obtained by using an eigen-value approximation, and the influences of the number of holes, filling ratio, porosity and other parameters on the free vibration response are explored. It is shown that an increase in the mass parameter, filling ratio and porosity parameter of the column with an attached mass system could significantly affect the free vibration response of the system.

Failure Modelling of CP800 Using Acoustic Emission Analysis

Advanced high-strength steels (AHHS) are widely used in many production lines of car components. For efficient design of the forming processes, numerical methods are frequently applied in the automotive industry. To model the forming processes realistically, exact material data and analytical models are required. With respect to failure modelling, the accurate determination of failure onset continues to be a challenge. In this article, the complex phase (CP) steel CP800 is characterised for its failure characteristics using tensile tests with butterfly specimens. The material failure was determined by three evaluation methods: mechanically by a sudden drop in the forming force, optically by a crack appearing on the specimen surface, and acoustically by burst signals. As to be expected, the mechanical evaluation method determined material failure the latest, while the optical and acoustical methods showed similar values. Numerical models of the butterfly tests were created using boundary conditions determined by each evaluation method. A comparison of the experiments, regarding the forming force and the distribution of the equivalent plastic strain, showed sufficient agreement. Based on the numerical models, the characteristic stress states of each test were evaluated, which showed similar values for the mechanical and optical evaluation method. The characteristic stress states derived from the acoustical evaluation method were shifted to higher triaxialities, compared to the other methods. Matching the point in time of material failure, the equivalent plastic strain at failure was highest for the mechanical evaluation method, with lower values for the other two methods. Furter, three Johnson–Cook (JC) failure models were parametrised and subsequently compared. The major difference was in the slope of the failure models, of which the optical evaluation method showed the lowest slope. The reasons for the differences are the different stress states and the different equivalent plastic strains due to different evaluation areas.

Deep Neural Network-Based QoT Estimation for SMF and FMF Links

Quality of transmission (QoT) estimation tools for fiber links are the enabler for the deployment of reconfigurable optical networks. To dynamically set up lightpaths based on traffic request, a centralized controller must base decisions on reliable performance predictions. QoT estimation methods can be categorised in three classes: exact analytical models which provide accurate results with heavy computations, approximate formulas that require less computations but deliver a reduced accuracy, and machine learning (ML)-based methods which potentially have high accuracy with low complexity. To operate an optical network in real-time, beside accurate QoT estimation, the speed in delivering results is a strict requirement. Based on this, only the last two categories are candidates for this application. In this paper, we present a deep neural network (DNN) structure for QoT estimation considering both regular single-mode fiber (SMF) and future few-mode fiber (FMF) proposed to increase the overall network capacity. We comprehensively explore ML-based regression methods for estimating generalized signal-to-noise ratio (GSNR) in partial-load SMF and FMF links. Synthetic datasets have been generated using the enhanced Gaussian noise (EGN) model. Results indicate that the proposed DNN-based regressor can provide better accuracy along with less computation complexity, compared with other state-of-the-art ML methods as well as closed-form-EGN and closed-form-GN models.

Exact Analytical Magnetic Field Analysis, Optimization Design and Realization of an Eccentric Magnetic Harmonic Gear

The eccentric magnetic harmonic gear (EMHG) has a high efficiency and high gear ratio capability for large torque transmission. The air gap magnetic field can be calculated using an exact analytical model. The analytical approach is based on the theoretically accurate hyperbolic cotangent transformation method. The relative permeance function, which is derived from the impact of rotor eccentricity, can be used to find the eccentric air gap magnetic field solution. The proposed analytical approach is employed as the basis for a genetic algorithm that is used to develop and optimize the EMHG. The analytical results are in good agreement with the finite element method results, which verifies the correctness and validity of the proposed analytical model. The experimental measurements on the dual-stage EMHG confirm the validity of the analytical prediction.

Probabilistic model to spatially acquire optical links in space under the influence of band-limited beam jitter.

An analytical model is derived for the probability of failure (P-fail) to spatially acquire an optical link with a jittering search beam. The analytical model accounts for an arbitrary jitter spectrum and considers the associated correlations between jitter excursions on adjacent tracks of the search spiral. An expression of P-fail in terms of basic transcendental functions is found by linearizing the exact analytical model with respect to the correlation strength. Predictions from the models indicate a strong decrease of P-fail with increasing correlation strength, which is found to be in excellent agreement with results from Monte Carlo simulations. The dependency of P-fail on the track width and scan speed is investigated, confirming previous assumptions about the impact of correlations. Expressions and applicable constraints are derived for the limits of full and no correlations, and the optimal track width to minimize the acquisition time is computed for a range of scan speeds. The model is applicable to optical terminals equipped with a fast beam steering mirror, as often found for optical communications missions in space.

Theoretical evolution of thermal behaviour of Ti-6Al-4V subjected to selective laser melting: A powder free approach

Additive manufacturing (AM) processes are considered to be the pillar of the next industrial revolution due to their inherent qualities such as design flexibility, the ability to produce complex parts and prototypes, lower cost due to the reduced requirement of materials and curtailed lead time for manufacturing. Selective laser melting (SLM) is one of the most popular metallic AM technologies since it enables accurate control over part dimensions and fabrication of high resolution features. This research paper is aimed to develop an exact analytical model of three-dimensional thermal response captured in SLM of Ti based alloy (Ti-6Al-4V). A physical model has been proposed to predict the temperature profile during the metal additive manufacturing process with consideration of the effect of thermal history developed during moving laser heat source interaction. The corresponding mathematical solution is developed by employing an amalgamation of ‘Duhamel’s theorem’ and ‘Finite Integral Transform method’. The parametric laser-substrate interaction phenomenon is the prime deciding factor for the successful accomplishment of the manufacturing process. This research paper theoretically investigates the thermal characteristics (peak temperature, temperature distribution curvature, pulse time, optical penetration depth, time of laser exposure, laser absorption radius, and so on) by employing Fourier’s heat conduction model with a moving laser heat source. The theoretical estimation has been validated by the existing mathematical as well as experimental research outcomes. Present work might be an asset for deciding the design of process variables and protocols in terms of laser based additive manufacturing specifically the selective laser melting process.

Modeling and Simulation of a Novel Low-Speed High-Torque Permanent Magnet Synchronous Motor with Asymmetric Stator Slots

Focusing on the unstable electromagnetic performance of an air gap magnetic field caused by torque ripple and harmonic interference of a multi-slot and multi-pole low-speed high-torque permanent magnet synchronous motor (LHPMSM), an asymmetric stator slot is proposed to improve the comprehensive electromagnetic performance of the motor. Moreover, this paper develops an exact analytical model which predicts the magnetic field distribution based on Laplace’s and Poisson’s equations. The stator slot asymmetry is introduced into the model and solved by the method of separating variables. Taking a 40p168s LHPMSM as an example, numerical results of the no-load flux density field distributions are obtained by the finite element method (FEM) and employed to validate the analytical model. The influence of stator slot asymmetric structure on electromagnetic characteristics is subsequently analyzed. The results show that, compared with the semi-closed slot model, the asymmetric slot has better torque characteristics, and the electromagnetic characteristics of the motor can be significantly improved by optimizing the stator slot asymmetry. Finally, a prototype is manufactured and tested to validate the theoretical analysis.

Improvement of an Adaptive Robot Control by Particle Swarm Optimization-Based Model Identification

Model-based controllers suffer from the effects of modeling imprecisions. The analytical form of the available model often contains only approximate parameters and can be physically incomplete. The consequences of these effects can be compensated by adaptive techniques and by the improvement of the available model. Lyapunov function-based classic methods, which assume exact analytical model forms, guarantee asymptotic stability by cautious and slow parameter tuning. Fixed point iteration-based adaptive controllers can work without the exact model form but immediately yield precise trajectory tracking. They neither identify nor improve the parameters of the available model. However, any amendment of the model can improve the controller’s operation by affecting its range and speed of convergence. It is shown that even very primitive, fast, and simple versions of evolutionary computation-based methods can produce considerable improvement in their operation. Particle swarm optimization (PSO) is an attractive, efficient, and simple tool for model improvement. In this paper, a PSO-based model approximation technique was investigated for use in the control of a three degrees of freedom PUMA-type robot arm via numerical simulations. A fixed point iteration (FPI)-based adaptive controller was used for tracking a nominal trajectory while the PSO attempted to refine the model. It was found that the refined model still had few errors, the effects of which could not be completely neglected in the model-based control. The best practical solution seems to be the application of the same adaptive control with the use of the more precise, PSO-improved model. Apart from a preliminary study, the first attempt to combine PSO with FPI is presented here.

Intrinsic mode coupling in mirror-symmetric whispering gallery resonators.

Rotationally symmetric micro-cavities with disk, ring or toroidal shape displaying whispering gallery modes (WGMs) play an essential role in modern-day photonics. Due to the reduced symmetry of such resonators compared to spheres, an exact analytical model yielding WGMs as solutions does not exist. The established WGM classification scheme based on approximated analytical solutions is generally useful but neglects a possible interaction between the different modes. In this paper, we assess the limitation of the validity of this established classification based on extensive finite element method (FEM) simulations. We investigate respective mode couplings as well as underlying selection rules based on avoided crossings of the modes' resonance wavelengths. We propose conserved mode properties solely based on true symmetries of the underlying refractive-index distribution and deduce a novel WGM classification scheme.

Quantum simulation of rogue waves in Bose-Einstein condensate: An exact analytical method

A quantum simulator environment is considered in Bose-Einstein condensate under bichromatic optical lattice, manifesting rogue waves. We report an exact analytical model to produce rogue wave excitations, the dynamics of which is investigated by solving the corresponding scalar Gross-Pitaevskii equation. A qualitative understanding of the formation mechanism at various trap parameters is provided by assuming the rogue wave excitation as a mixture of bright and dark solitary waves, which offers a novel illustration of the previous conjecture for rogue waves in Bose-Einstein condensate. We identify the lattice parameters for controlling the spatio-temporal variations of the condensate density. An Anderson-like localization is identified where the condensate is seen to preserve the rogue wave nature at the central frustrated site for larger lattice frustration.