Parametric Analytical Model Research Articles

Parametric Analytical Modulation Transfer Function Model in Turbid Atmosphere with Application to Image Restoration

To address the issues of image blurring and color distortion in hazy conditions, an image restoration method based on a parametric analytical modulation transfer function model is proposed under turbid atmospheric conditions. A source database is established using a numerical radiative transfer method based on discrete ordinate. Through multivariate nonlinear fitting and linear interpolation, the quantitative relationships among critical spatial frequency, turbid atmospheric MTF, and key atmospheric optical parameters—such as optical thickness, single scattering albedo, and asymmetry factor—are examined. A fast and efficient parametric analytical MTF model for turbid atmospheres is developed and applied to restore images affected by fog. The results demonstrate that, within the applicable range of the model, the model’s maximum mean relative error and the root mean square error are 7.16% and 0.0454, respectively. The computational speed is nearly a thousand times faster than that of the numerical radiative transfer method, achieving high accuracy and ease of application. Images restored using this model exhibit enhanced clarity and quality, effectively compensating for the degradation in image quality caused by turbid atmospheres. This approach represents a novel solution to the challenges of image processing in complex atmospheric environments.

Feasibility of ultrasonic non-destructive testing of ancient funerary urns: Experimental and analytical parametric model

Non-invasive modalities are being developed as the computer tools and industrial non-destructive testing capabilities become more widespread. Using the same investigation methods as those applied to modern objects, we seek to study ancient funerary urns containing human bones. The exploration of ancient urns is key to increasing our understanding of the practices of burial and cremation in archaeo-anthropology. But those urns present at archaeological sites are exposed to diversified environments (wet, temperate or dry environment), and can be subjected to chemical or mechanical destructive actions over time. As ancient funeral urns containers are sometimes made of lead, stone or ceramic, the use of X-ray scanners is difficult or even impossible for in situ control. In this work, we propose an engineering technique based on ultrasonic non-destructive testing and wave propagation in urns. An analytical parametric model is developed using mathematical signal processing tools and validated by means of laboratory experiments under controlled conditions of propagation through reproductions of ancient urns for two ultrasonic frequencies (500 kHz and 1 MHz). The aim is to characterise an ancient urn by creating an analytical model, and to use a parametric identification algorithm to determine the presence or absence of bone fragments. The parametric identification algorithm based on the Levenberg–Marquardt method makes it possible to determine the geometrical (thickness) and physical (wave velocity and attenuation, mass density) parameters when the urn is filled with water, with water and bones, and with water, bones and sand. We show that the model makes it readily (processing time ≈15 sec) possible to find the different times of flight between the transducer and the different walls of the urn and the parameters with an accuracy less than 10%.

A new analytical model of the cosmic-ray energy flux for Galactic diffuse radio emission

Low-frequency radio observations of diffuse synchrotron radiation offer a unique vantage point from which to investigate the intricate relationship between gas and magnetic fields in the formation of structures within the Galaxy, spanning from the diffuse interstellar medium (ISM) to star-forming regions. Achieving this pivotal objective hinges on a comprehensive understanding of cosmic-ray properties; these dictate the effective energy distribution of relativistic electrons, which are primarily responsible for the observable synchrotron radiation. Notably, cosmic-ray electrons (CRe) with energies of between 100 MeV and 10 GeV play a crucial role in determining the majority of the sky brightness below the GHz range. However, their energy flux (je) remains elusive because of solar modulation. We propose a way to derive observational constraints on this energy gap of interstellar CRe through the brightness temperature spectral index of low-frequency radio emission, here denoted βobs. We introduce a new parametric analytical model that fits available data for je in accordance with the βobs values measured in the literature between 50 MHz and 1 GHz for diffuse emission in the Milky Way. Our model accounts for multiple observations considering magnetic-field strengths consistent with existing measurements below 10 μG. We present a first all-sky map of the average component of the magnetic field perpendicular to the line of sight and validate our methodology against state-of-the art numerical simulations of the diffuse ISM. This research makes headway in modeling Galactic diffuse emission with a practical, parametric form. It provides essential insights that will help preparations for the imminent arrival of the Square Kilometre Array.

A model for the rapid prediction of small feature width producible by Metal AM

In this paper, an analytical parametric model is presented for the swift prediction of small features producible in the X-Y plane through the Metal AM Laser Powder Bed Fusion (LPBF) process. This model can be employed to design and create surface textures on Additive Manufactured parts without the need for costly post-processing steps. The Rosenthal equation is the basis for the model, which considers both the build parameters of the LPBF process and the thermo-physical properties of the materials. The initial model was constructed and assessed using one LPBF machine followed by the implementation of a tuning method utilizing the Limited Memory Algorithm for Bound Constrained Optimization to enhance the model’s accuracy. Overall, the findings suggest that with a simple optimization step based on a single printed tuning sample, precise analytical models can be established for specific LPBF machines and materials combinations.

ANALYSIS OF SiC GRINDING WHEEL WEAR AND SURFACE ROUGHNESS IN MACHINING OF Al2O3 ADVANCED CERAMIC USING REGRESSION MODEL

Presently, there are more new kinds of requirements for the production of advanced ceramic elements in the engineering field. These ceramic elements are to be machined for a better surface roughness value. Surface roughness of the machined elements is one of the main machining characteristics which play a vital role in determining the high quality of advanced ceramic elements in engineering. In this work, some machining tests were done on the advanced aluminum oxide (Al2O[Formula: see text] ceramic work material using a silicon carbide (SiC) grinding wheel under different process parameters. A parametric analytical model was developed using the method of regression analysis by taking into account of four process parameters, such as depth of cut, feed, grain size and spindle speed. The effectiveness of the model is evaluated based on the comparison of experimental results with the regression analysis. The predicted values of surface roughness ([Formula: see text] and wheel wear ([Formula: see text] with minimum average error are in line to the results of the acquired experiment.

Parametric prediction model and periodic fluctuation interpretation of unidirectional CFRP edge milling force

With the the excellent material properties, carbon fiber reinforced polymer (CFRP) composites have been widely accepted in many fields. Edge milling is indispensable for final shape and assembly requirements. However, it's difficult to predict the machining forces due to the anisotropy and inhomogeneity of CFRP. In order to solve this problem, this paper proposed an analytical parametric model for machining force prediction based on the energy balance in unidirectional CFRP edge milling. The involved energies can be divided into five categories: energy consumed for formation of two new surfaces, friction energy at the tool-chip interface, fracture energy for chip formation, energy consumption for subsurface damage and the kinetic energy of flying chip. Experimental results show that the peak of the edge milling force fluctuates periodically. The relation between feed per tooth and the representative volume element (RVE) is analyzed to interpret the fluctuation phenomenon. In addition, the numerical simulation for CFRP milling is also implemented for verification of the fluctuation phenomenon. In calculation, the effect of strain rate on material parameters (such as the engineering moduli and the dominated strengths) is taken into account. In milling tests, in order to obtain the actual forces, the frequency response functions (FRF) are measured by impact tests for milling force compensation. Finally, the predicted milling forces have a good agreement with experimental observations.

Validated Analytical Model of 8/6 and 10/8 Switched Reluctance Motors

The aim of this work was to develop a parameterized analytical and FEM (Finite Element Method) model of a switched reluctance motor. The developed analytical model was used to assess the performance of these types of motors, and is determined to be a tool for comparing and evaluating switched reluctance motors of various designs. The aim of the work was also the systematization of knowledge related to the operation, structure and methods of determining the static electromagnetic torque generated by switched reluctance motors. The FEM model (ANSYS) was, also, made in order to verify physical phenomena occurring during operation of these motors. Four laboratory tests were executed as part of the work prototypes of switched reluctance motors built at Warsaw University of Technology. A parameterized analytical model was developed and implemented in MATLAB. The model operation tests were conducted and as a result, the characteristics describing the dependence of the electromagnetic torque as a function of the current and the position of the rotor were obtained. The model was validated by confronting the analytical calculations supported by FEM simulation results with the measurement results. The usefulness of the results obtained with the use of the procured models was assessed.

Analytical solution of tokamak vibrations during axisymmetric plasma disruptions

Tokamaks are structures containing a massive supporting structure housing a vacuum vessel with hot plasma. Due to the vacuum vessel heating and temperatures up to 500 ⁰C as for the COMPASS-U, flexible connections need to be used between the main support and the vacuum vessel to accommodate the thermal expansion. Large electromagnetic forces are generated during plasma disruption events, such as Vertical Displacement Events (VDE), inside the vacuum vessel and in the coil system: Central Solenoid (CS), Poloidal Field (PF) coils and Toroidal Field (TF) coils directly attached to the support. In the present paper a parametric analytical model of tokamak vibrations due to axisymmetric plasma disruptions was presented, allowing predictions of the vacuum vessels and the main tokamak structure displacements, velocities and accelerations as well as the dynamic forces transmitted to the foundations. A tokamak was modelled as a 2 DOF dynamic system, including the mass of the main support and the vacuum vessel and the axial stiffnesses and damping values of their supports. A close-form analytical solution was found assuming proportional (Rayleigh) damping for the most general shape of the force functions – described with a series of piecewise linear functions. The electromagnetic forces during axisymmetric VDE were derived from a dedicated 3D model. Detailed solution for the most recent design of the COMPASS-U tokamak was presented, as well as a number of parametric studies checking the sensitivity to the design parameters. The conditions at which large part of the electromagnetic force is transmitted to the concrete foundations were identified. The accuracy of the derived analytical solution was verified with direct numerical integration of the equations of motion.

A lumped parametric analytical model for predicting molten pool temperature and clad geometry in pre-placed powder laser cladding

Pre-placed powder laser cladding is one of the simplest laser-based deposition techniques, having high material usage efficiency and capable to provide sound clad quality. However, the quality along with the geometrical aspects of the deposited layer depends on various energy transfer mechanisms controlled by process parameters. Energy transfer phenomena include the partial absorption of the laser radiation by metal powder layer, melting of the powder layer and transmission of energy to the substrate, along with the losses, like convective heat transfer to the atmosphere and conductive heat transfer to the bulk material. Theses phenomena all together defines the molten pool temperature, which needs to be analyzed to control the geometrical features of the clad and dilution by optimizing the process parameters. Therefore, a lumped parametric analytical model has been formulated and presented in this work for the pre-placed laser cladding process considering energy transfer and loss mechanisms along with the surface tension phenomena of the molten material to predict the molten pool temperature, clad geometry and substrate dilution. The developed model is validated using the experimental results of molten pool temperature of the clad layer, clad width and height as well as the percentage dilution. A continuous mode Yb-Fiber laser system with maximum available laser power of 220 W is used for the deposition of Inconel 625 powder on AISI 304 stainless steel substrate.

УДОСКОНАЛЕННЯ ПОБУДОВИ ТРИВИМІРНИХ МОДЕЛЕЙ ПРУЖИН РОЗТЯГАННЯ ДЛЯ ВИКОНАННЯ ЇХ КРЕСЛЕНИКІВ В ПАКЕТІ AUTODESK INVENTOR

The work proposes developments to improve the modeling of parametric spatial models of tension springs, complementing the functionality of the Autodesk Inventor package to reduce design time and execution of drawings in accordance with the current standard (GOST 2.401-68). The solution to the problem was carried out using the capabilities of the Autodesk Inventor package and the modified theory of circular helical surfaces, which considers the issue of tangency and intersection, methods of forming such surfaces with detailed coverage of their properties and geometric parameters. At the same time, the theory of helical lines with circular helical surfaces, obtained on the basis of helical lines and a circle as a generatrix, with a deep study of the geometric properties of helical lines with a monotonically variable pitch and with a circular pitch, is distinguished by its generality in the approach, the mathematical rigor of the proofs of the theory. The work provides for the possibility of modeling parametric spatial models of tension springs for building drawings, and for carrying out studies of the stress-strain state. It is also possible to change the position of the hooks and the two transitions between the hooks and the spring relative to the spring axis. New algorithms and approaches are proposed that make it possible to significantly expand the range of possible changes in the information of the analytical and geometric parametric spatial model of the tension spring. At the same time, the design time for three-dimensional models of tension springs is reduced, their drawings are made in accordance with applicable standards. The method of modeling the parametric spatial model of the tension spring has been tested and introduced into the educational process and can be applied in production to optimize the development of design documentation at the design stage. Key words: tools, parameterization, hook, transition, work coils, intersection of coils, circular helical surfaces, tension spring, design documentation, Autodesk Inventor.

Modeling of battery pack sizing for electric vehicles

The paper presents the mathematical modeling for battery pack sizing to evaluate the vehicle energy consumption by using the derivation from Parametric Analytical Model of Vehicle Energy Consumption (PAMVEC) by Simpson in R Studio. The assess of storage batteries for electric vehicles (EVs) application is presented in this paper. The main source of power in EVs are batteries and to properly optimize their use in them, a parametric vehicle dynamic model is created and factors like battery mass, energy needed for the EV etc. are predicted using inputs such as battery specific energy, range etc. An assessment of output parameters is performed by using different batteries and compared to determine best battery for EV application.

Quantifying Location-Specific Impacts of Pavement Albedo on Radiative Forcing Using an Analytical Approach

High-albedo materials reflect more solar radiation and, thereby, alter the earth's radiative balance. Increasing pavement albedo, therefore, has been considered as a technological strategy to mitigate global warming. Previous studies have evaluated this strategy using global average models. To factor this effect into life cycle assessments, location-specific models of the albedo effect for pavements are required. A parametric analytical model is developed to estimate the radiative forcing (RF) using a novel model form and an iterative solution approach. The new model is extended to estimate the corresponding global warming potential (GWP) over an analysis period of 50 years for an albedo change in a pavement surface. This was applied to quantify the GWP impacts of increasing pavement albedo in 14 cities across various climate zones in the US. For the United States, the GWP in kg CO2 equivalent per square meter of altered surface ranges from 0.8 to 1.6 per 0.01 change in albedo, a range of more than 40%. Analysis of a hypothetical albedo change to all darker pavements in the US would produce a negative RF of a magnitude equivalent to that associated with a reduction in CO2 emissions of more than 17 Mton per year.

Supernova Photometric Classification Pipelines Trained on Spectroscopically Classified Supernovae from the Pan-STARRS1 Medium-deep Survey

Abstract Photometric classification of supernovae (SNe) is imperative as recent and upcoming optical time-domain surveys, such as the Large Synoptic Survey Telescope (LSST), overwhelm the available resources for spectrosopic follow-up. Here we develop a range of light curve (LC) classification pipelines, trained on 513 spectroscopically classified SNe from the Pan-STARRS1 Medium-Deep Survey (PS1-MDS): 357 Type Ia, 93 Type II, 25 Type IIn, 21 Type Ibc, and 17 Type I superluminous SNe (SLSNe). We present a new parametric analytical model that can accommodate a broad range of SN LC morphologies, including those with a plateau, and fit this model to data in four PS1 filters (g P1 r P1 i P1 z P1). We test a number of feature extraction methods, data augmentation strategies, and machine-learning algorithms to predict the class of each SN. Our best pipelines result in ≈90% average accuracy, ≈70% average purity, and ≈80% average completeness for all SN classes, with the highest success rates for SNe Ia and SLSNe and the lowest for SNe Ibc. Despite the greater complexity of our classification scheme, the purity of our SN Ia classification, ≈95%, is on par with methods developed specifically for Type Ia versus non-Type Ia binary classification. As the first of its kind, this study serves as a guide to developing and training classification algorithms for a wide range of SN types with a purely empirical training set, particularly one that is similar in its characteristics to the expected LSST main survey strategy. Future work will implement this classification pipeline on ≈3000 PS1/MDS LCs that lack spectroscopic classification.

Modal interactions in the nonlinear dynamics of a beam–cable–beam

Quadratic and cubic modal interactions characterize the geometrically nonlinear dynamics of a parametric analytical model composed by two cantilever beams connected by a suspended shallow cable. The natural frequencies and modes of the linearized model are determined exactly, by solving the integral–differential eigenproblem governing the undamped free oscillations. Interesting phenomena of linear cable–beam interaction (frequency veering and modal hybridization) are recognized in the spectrum. Global and local modes are distinguished by virtue of the two localization factors measuring the modal kinetic energy stored in the beams and cable, respectively. The localization level is also put in relation to the magnitude of the quadratic and cubic nonlinearities. Therefore, the exact linear eigensolution is employed to formulate a nonlinearly coupled two-degrees-of-freedom model, defined in the reduced space of the modal amplitudes corresponding to a global and a local mode. The modal interactions between the two modes are analyzed, with focus on the autoparametric excitation mechanisms that can be favored by the occurrence of integer frequency ratios (1:2 and 2:1). Such internal resonance conditions enable significant transfers of mechanical energy—essentially governed by the quadratic coupling terms—from the small amplitudes of the externally excited global mode to the high amplitudes of the autoparametrically excited local mode. Different regimes of periodic and quasi-periodic oscillations are identified.

Study the Sound Insulation of Elastically Restrained Panel

Experimental determination of the acoustic characteristics of a sound insulation panel often requires a standard measurement suite consisting two rooms connected via a window onto which the panel is mounted. While such a facility is quite expensive to build and maintain, the measurement results can show a significant variance, especially at low frequencies. The potential causes may include the characteristics of the rooms, the placement of the sound source(s), the installment of the panels, etc. To better understand the variance of the results and identify the directions for improving the sound insulation designs and applications, a virtual testing capability is developed based on an analytical parametric model. This model consists of a source room, a receiving room, and a partition wall with a mounting window. The sound insulation structures can represent a simple panel or a complex structure with various structural and/or acoustical design features. This model can be effectively used to virtually test the acoustic performance of sound insulation designs under different environments and application conditions.

Biological Optical-to-Chemical Signal Conversion Interface: A Small-Scale Modulator for Molecular Communications

Although many exciting applications of molecular communication (MC) systems are envisioned to be at microscale, the MC testbeds reported in the literature so far are mostly at macroscale. This may partially be due to the fact that controlling an MC system at microscale is challenging. To link the macroworld to the microworld, we propose and demonstrate a biological signal conversion interface that can also be seen as a microscale modulator. In particular, the proposed interface transduces an optical signal, which is controlled using a light-emitting diode, into a chemical signal by changing the pH of the environment. The modulator is realized using Escherichia coli bacteria as microscale entity expressing the light-driven proton pump gloeorhodopsin from Gloeobacter violaceus. Upon inducing external light stimuli, these bacteria locally change their surrounding pH level by exporting protons into the environment. To verify the effectiveness of the proposed optical-to-chemical signal converter, we analyze the pH signal measured by a pH sensor, which serves as a receiver. We develop an analytical parametric model for the induced chemical signal as a function of the applied optical signal. Using this model, we derive a training-based channel estimator that estimates the parameters of the proposed model to fit the measurement data based on a least square error approach. We further derive the optimal maximum likelihood detector and a suboptimal low-complexity detector to recover the transmitted data from the measured received signal. It is shown that the proposed parametric model is in good agreement with the measurement data. Moreover, for an example scenario, we show that the proposed setup is able to successfully convert an optical signal representing a sequence of binary symbols into a chemical signal with a bit rate of 1 bit/min and recover the transmitted data from the chemical signal using the proposed estimation and detection schemes. The proposed modulator may form the basis for future MC testbeds and applications at microscale.

First Principle Based Control Oriented Gasoline Engine Model Including Lumped Cylinder Dynamics

A novel first principle based control oriented model of a gasoline engine is proposed which also carries diagnostic capabilities. Unlike existing control oriented models, the formulated model reflects dynamics of the faultless as well as faulty engine with high fidelity. In the proposed model, the torque production subsystem is obtained by integration of further two subsystems that is model of a single cylinder torque producing mechanism and an analytical gasoline engine cylinder pressure model. Model of a single cylinder torque producing mechanism is derived using constrained equation of motion (EOM) in Lagrangian mechanics. While cylinder pressure is evaluated using a closed form parametric analytical gasoline engine cylinder pressure model. Novel attributes of the proposed model include minimal usage of empirical relations and relatively wider region of model validity. Additionally, the model provides model based description of crankshaft angular speed fluctuations and tension in the rigid bodies. Capacity of the model to describe the system dynamics under fault conditions is elaborated with case study of an intermittent misfire condition. Model attains new capabilities based on the said novel attributes. The model is successfully validated against experimental data.

Nonlinear dynamics of a parametric analytical model for beam-cable-beam structures

A parametric model is proposed to analytically describe the nonlinear dynamics of the structural system composed by two vertical cantilever beams connected by a suspended sagged cable. Focus is made on the geometric nonlinearities that characterize the boundary interactions between the linear beams and the nonlinear Irvine cable. The closed form solution of the linear eigenproblem governing the undamped small-amplitude vibrations enables – first – the clear distinction between global modes, dominated by the beam dynamics, and local modes, dominated by the cable vibrations, and – second – the parametric assessment of some parameter combinations corresponding to integer frequency ratios (1:1, 2:1) between global and local modes. Such internal resonances open the way to different phenomena of linear and nonlinear interactions, which can sustain the transfer of mechanical energy between the interacting modes and, consequently, the onset of high amplitude local oscillations. After the reduction to a single mode basis, the qualitative and quantitative relevance of the system nonlinearities is analyzed. In particular, the effects of the global, local, hybrid nature of the modal shapes on the softening/hardening behavior of the frequency response are investigated.

Structural health monitoring of suspension bridges with features affected by changing wind speed

Tools based on multivariate statistical analysis are becoming very popular for automatically revealing the existence of damage in structures using vibration data under changing environmental and operational conditions (typically temperature, humidity and traffic intensity). In this paper, methods of multivariate statistical analysis are newly applied for monitoring the structural health state of the main cables of suspension bridges, with the main contribution of removing non-linear aeroelastic correlations between dynamic features and wind speed.Considering natural frequencies as damage-sensitive features, an analytical parametric model of suspension bridge with damage in one main cable and subjected to wind loading is formulated, at first, as an extension of previous work. Model predictions demonstrate that apparent frequency variations caused by changes in incoming wind speed can likely be more significant than those produced by a small damage. A technique based on principal component analysis and novelty detection is adopted to cope with this issue and its application to long-term pseudo-experimental buffeting response data, generated by means of the analytical model, is presented. The results demonstrate the feasibility of permanent monitoring systems to reveal the existence of damages in wind-excited long-span bridges producing relative variations in the most sensitive natural frequency smaller than 0.1%.

Analytical parametric model used to study the influence of electrostatic force on surface coverage during electrospinning of polymer fibers

Electrospinning (ES) can readily produce polymer fibers with cross-sectional dimensions ranging from tens of nanometers to tens of microns. Qualitative estimates of surface area coverage are rather intuitive. However, quantitative analytical and numerical methods for predicting surface coverage during ES have not been covered in sufficient depth to be applied in the design of novel materials, surfaces, and devices from ES fibers. This article presents a modeling approach to ES surface coverage where an analytical model is derived for use in quantitative prediction of surface coverage of ES fibers. The analytical model is used to predict the diameter of circular deposition areas of constant field strength and constant electrostatic force. Experimental results of polyvinyl alcohol fibers are reported and compared to numerical models to supplement the analytical model derived. The analytical model provides scientists and engineers a method for estimating surface area coverage. Both applied voltage and capillary-to-collection-plate separation are treated as independent variables for the analysis. The electric field produced by the ES process was modeled using comsol Multiphysics software to determine a correlation between the applied field strength and the size of the deposition area of the ES fibers. matlab scripts were utilized to combine the numerical comsol results with derived analytical equations. Experimental results reinforce the parametric trends produced via modeling and lend credibility to the use of modeling techniques for the qualitative prediction of surface area coverage from ES.