Perturbation Analysis Method Research Articles

A Method for Retrieving the Ground Flash Fraction and Flash Type from Satellite Lightning Mapper Observations

AbstractAn analytic perturbation method is introduced for retrieving the lightning ground flash fraction in a set of N lightning flashes observed by a satellite lightning mapper. The value of N must be large, typically in the thousands, and the satellite lightning optical observations consist of the maximum group area (MGA) produced by each flash. Moreover, the method subsequently determines the flash type (ground or cloud) of each of the N flashes. Performance tests of the method were conducted using simulated observations that were based on Optical Transient Detector (OTD) and Lightning Imaging Sensor (LIS) data. It is found that the mean ground flash fraction retrieval errors are below 0.04 across the full range 0–1 under the nominal conditions defined. In general, it is demonstrated that the retrieval errors depend on many factors (i.e., the number N of satellite observations, the magnitude of random and systematic instrument measurement errors, the ground flash fraction itself, and the number of samples used to form certain climate distributions employed in the method). The fraction of flashes accurately flash typed by the method averaged better than 78%. Overall, the accuracy of ground flash fraction and flash-typing retrievals degrade as the simulated population ground and cloud flash MGA distributions become more identical. Finally, because the analytic perturbation method was found to be quite robust (i.e., it performed well for several arbitrary underlying MGA distributions), it is not restricted to the lightning problem studied here but can be applied to any inverse problem having a similar problem statement.

Acoustic assessment of erygmophonic speech of Moroccan laryngectomized patients.

IntroductionAcoustic evaluation of alaryngeal voices is among the most prominent issues in speech analysis field. In fact, many methods have been developed to date to substitute the classic perceptual evaluation. The Aim of this study is to present our experience in erygmophonic speech objective assessment and to discuss the most widely used methods of acoustic speech appraisal. through a prospective case-control study we have measured acoustic parameters of speech quality during one year of erygmophonic rehabilitation therapy of Moroccan laryngectomized patients.MethodsWe have assessed acoustic parameters of erygmophonic speech samples of eleven laryngectomized patients through the speech rehabilitation therapy. Acoustic parameters were obtained by perturbation analysis method and linear predictive coding algorithms also through the broadband spectrogram.ResultsUsing perturbation analysis methods, we have found erygmophonic voice to be significantly poorer than normal speech and it exhibits higher formant frequency values. However, erygmophonic voice shows also higher and extremely variable Error values that were greater than the acceptable level. And thus, live a doubt on the reliability of those analytic methods results.ConclusionAcoustic parameters for objective evaluation of alaryngeal voices should allow a reliable representation of the perceptual evaluation of the quality of speech. This requirement has not been fulfilled by the common methods used so far. Therefore, acoustical assessment of erygmophonic speech needs more investigations.

Vortex Street in Homogeneous Dense Dusty Magnetoplasma

For studying the vortex structure in uniform dense dusty astrophysical conditions, a two-dimensional nonlinear equation is derived employing the quantum magnetoplasma hydrodynamic model and considering the strong collisional effect. The coherent vortex solution is obtained by perturbation analysis method. It is shown that the distribution of the electrostatic potential forms spatially a periodic vortex street, and is controlled temporally by the arbitrary function of time that may lead to abundant spacial distributions. It is found that the dust charge number, collision frequency, electron Fermi wavelength and quantum correction all play significant roles to the spatial distribution of vortex street.

Potential Function for Acoustic Multipole Logging on Guided Waves in Transversely Isotropic Medium

A new and effective analytical perturbation method is presented for the multipole acoustic logging in a transversely isotropic medium (TIM) whose symmetric principal axis is parallel to the borehole axis although the exact solutions could be found. In this paper, the new perturbation method is adopted to simulate the dispersion characteristic in a borehole surrounded by a TIM for the first time. The TIM is regarded as a reference unperturbed isotropic state added to the perturbations, and three perturbation quantities about moduli deviated from the isotropic medium are introduced. By selecting a group of displacement potentials and a cylindrical coordinate system oriented along the borehole axis, the zero-, first-order and second-order perturbation solutions of the multipole acoustic field are derived for the weak transversely isotropic elastic solid which has its symmetric principal axis parallel to the borehole axis. It is found that the dispersion characteristic by the perturbation method inside the borehole excited by monopole, dipole sources and quadrupole source are similar to obtained by the exact solution.

Dispersion Correction for Acoustic Multipole Logging on Guided Waves in Transversely Isotropic Medium

A new and effective analytical perturbation method is presented for the multipole acoustic logging in a transversely isotropic medium (TIM) whose symmetric principal axis is parallel to the borehole axis although the exact solutions could be found. In this paper, the new perturbation method is adopted to simulate the dispersion characteristic in a borehole surrounded by a TIM for the first time. The TIM is regarded as a reference unperturbed isotropic state added to the perturbations, and three perturbation quantities about moduli deviated from the isotropic medium are introduced. By selecting a group of displacement potentials and a cylindrical coordinate system oriented along the borehole axis, the zero-, first-order and second-order perturbation solutions of the multipole acoustic field are derived for the weak transversely isotropic elastic solid which has its symmetric principal axis parallel to the borehole axis. The acoustic fields inside and outside the borehole excited by a multipole source are investigated. The dispersion characteristics in the borehole are numerically simulated by the perturbation method in the range of the second perturbation solutions. It is found that the dispersion characteristic by the perturbation method inside the borehole excited by monopole, dipole sources and quadrupole source are similar to obtained by the exact solution.

Full waveform investigation of a perturbation method for acoustical multipole logging in transversely isotropic medium

A new and effective analytical perturbation method is presented for the multipole acoustic logging in a transversely isotropic medium (TIM), whose symmetric principal axis is parallel to the borehole axis and the exact solutions could be found. TIM is regarded as a reference unperturbed isotropic state added to the perturbations, and three perturbation quantities about elastic modulus deviated from the isotropic medium are introduced. By searching for the zero, the first, and the second order of perturbation solutions, the multipole acoustic fields inside and outside the borehole are derived and obtained. The full waveforms in the borehole excited by a monopole, dipole, and quadrupole sources are numerical simulated by perturbation and exact solutions. It is found that the full waveforms are close to the exact solution when the first order perturbation is considered and more close to the exact solution when the second order perturbation is considered. The numerical simulation confirms that the perturbation method is a feasible method for complicated anisotropic medium in acoustic logging.

Analytical perturbation methods for studying a transversely isotropic medium in multipole acoustic logging

A new analytical perturbation method is developed in this study to investigate the general reflection coefficients in the frequency-wavenumber domain of the acoustic field in a fluid-filled borehole surrounded by a transversely isotropic medium (TIM). The transversely isotropic medium with a symmetric axis parallel to the borehole axis, which is usually called a VTI medium, was adopted because its exact solutions exists, and a corresponding isotropic medium was adopted as a reference state of perturbation solution. The general reflection coefficients were originally calculated by using the perturbation method and were compared with the analytical solutions. The zero-, first- and second-order perturbation solutions for the general reflection coefficients excited by monopole, dipole and quadrupole sources were investigated for a transversely isotropic elastic solid. The results showed that the general reflection coefficients obtained by using the perturbation solutions and the analytical solutions were similar for all three sources. In summary, our study demonstrated that the perturbation method is valid and effective in acoustical logging. This work provided a theoretical foundation for extending perturbation analyses to complicated anisotropic acoustical logging applications.

SU‐E‐T‐517: Analytic Formalism to Compute in Real Time Dose Distributions Delivered by HDR Units

Purpose:Develop an analytical algorithm to compute the dose delivered by Ir‐192 dwell positions with high accuracy using the 3‐dimensional (3D) dose distribution of an HDR source. Using our analytical function, the dose delivered by an HDR unit as treatment progresses can be determined using the actual delivered temporal and positional data of each individual dwell. Consequently, true delivered dose can be computed when each catheter becomes active. We hypothesize that the knowledge of such analytical formulation will allow developing HDR systems with a real time treatment evaluation tool to avoid mistreatments.Methods:In our analytic formulation, the dose is computed by using the full anisotropic function data of the TG 43 formalism with 3D ellipsoidal function. The discrepancy between the planned dose and the delivered dose is computed using an analytic perturbation method over the initial dose distribution. This methodology speeds up the computation because only changes in dose discrepancies originated by spatial and temporal deviations are computed. A dose difference map at the point of interest is obtained from these functions and this difference can be shown during treatment in real time to examine the treatment accuracy.Results:We determine the analytical solution and a perturbation function for the 3 translational 3 rotational, and 1D temporal errors in source distributions. The analytic formulation is a sequence of simple equations that can be processed in any modern computer in few seconds. Because computations are based in an analytical solution, small deviations of the dose when sub‐millimeter positional changes occur can be detected.Conclusions:We formulated an analytical method to compute 4D dose distributions and dose differences based on an analytical solution and perturbations to the original dose. This method is highly accurate and can be

The influence of surface roughness on conductor at terahertz frequencies

In this paper, a theoretical study of the influence of surface roughness on conductor is proposed at terahertz frequencies. By using the analytic small perturbation method, the effects of a random rough surface on the absorption by a metallic surface at terahertz frequencies are analyzed. And the effect of rough surface on reflectivity and power spectral density are also demonstrated. The numerical results are very useful for the development of terahertz devices and terahertz material.

Energy Harvester Synthesis Via Coupled Linear-Bistable System With Multistable Dynamics

In this research we study the dynamics of a coupled linear oscillator-bistable energy harvester system. The method of harmonic balance and perturbation analysis are used to predict the existence and stability of the bistable device interwell vibration. The influences of important parameters on tailoring the coupled system response are investigated to determine strategies for improved energy harvesting performance. We demonstrate analytically that for excitation frequencies in a bandwidth less than the natural frequency of the uncoupled linear oscillator having net mass that is the combination of the bistable and linear bodies, the bistable harvester dynamics may be substantially intensified as compared to a single (individual) bistable harvester. In addition, the linear-bistable coupled system may introduce a stable out-of-phase dynamic around the natural frequency of the uncoupled linear oscillator, enhancing the performance of the harvester by providing a second interwell response not possible when using a single bistable harvester. Key analytical findings are confirmed through numerical simulations and experiments, validating the predicted trends and demonstrating the advantages of the coupled system for energy harvesting.

Equilibrium in Wholesale Energy Markets: Perturbation Analysis in the Presence of Renewables

One of the main challenges in the emerging smart grid is the integration of renewable energy resources (RER). The latter introduces both intermittency and uncertainty into the grid, both of which can affect the underlying energy market. An interesting concept that is being explored for mitigating the integration cost of RERs is demand response (DR). Beginning with an overall model of the major market participants with RER and DR, together with the constraints of transmission and generation, we analyze the energy market in this paper and derive conditions for existence and uniqueness of the competitive market equilibrium using standard Karush-Kuhn-Tucker (KKT) criteria. The effect of wind uncertainty on the competitive market equilibrium is then quantified. Perturbation analysis methods are used to compare the equilibria in the nominal and perturbed markets. This analysis is used to quantify the effect of RERs uncertainty and its possible mitigation using DR. Finally numerical studies are reported using an IEEE 30-bus to validate the theoretical results.

Perturbation analysis for optimal production planning of a manufacturing system with influence machine degradation

Abstract In this paper, we considered a failure-prone manufacturing system composed by a single-product machine, a stock and a customer who demands a stochastic quantity of product. To describe the proposed manufacturing system, a discrete flow model is adopted and which takes into account machine failure, lost demands and machine degradation. The goal of this paper is to determine the optimal production planning taken into account service level by minimizing the sum of production, inventory, lost sales and degradation costs. Perturbation analysis method is applied to the discrete flow model for optimizing the proposed system. Then the trajectories of production rate, stock level, degradation rate, and lost demands are studied and the perturbation analysis estimators are determined. These estimators are shown to be unbiased and then they are implanted in an optimization algorithm which determines the optimal production planning in the presence of service level.

Simple and accurate approach for solving of nonlinear heat convective-radiative equation in fin by using the collocation method and comparison with HPM and VIM

Collocation Method (CM) such as analytical technique, which does not need small parameters is here used to evaluate the analytical approximate solutions of the nonlinear heat transfer equation. The obtained results from Collocation Method are compared with other analytical techniques such as Homotopy Perturbation Method (HPM) and Variation Iteration Method (VIM). Also, boundary value problem (BVP) is applied as a numerical method for validation. The results reveal that the Collocation Method is very effective, simple and more accurate than other techniques. Also, it is found that this method is a powerful mathematical tool and can be applied to a large class of linear and nonlinear problems arising in different fields of science and engineering especially at some heat transfer equations.

Hydraulic testing of low-permeability Silurian and Ordovician strata, Michigan Basin, southwestern Ontario

• Hydraulic testing of Silurian and Ordovician sediments – eastern Michigan Basin. • Test equipment, methods and analysis specifically adapted for low-permeability rock. • Parameter perturbation analysis method allows quantification of uncertainty. • K values range from 4E−14 to 4E−8 m/s (Silurian) and 2E−16 to 2E−10 m/s (Ordovician). • Scaled Ordovician K values consistent with laboratory and natural analog estimates. Straddle-packer hydraulic testing was performed in 31 Silurian intervals and 66 Ordovician intervals in six deep boreholes at the Bruce nuclear site, located near Tiverton, Ontario, as part of site-characterization activities for a proposed deep geologic repository (DGR) for low- and intermediate-level radioactive waste. The straddle-packer assembly incorporated a hydraulic piston to initiate in situ pulse tests within low hydraulic conductivity (<1E−10 m/s) test intervals. Pressure transient data collected during the hydraulic tests were analyzed using the well-test simulator nSIGHTS to estimate the hydraulic properties specified as fitting parameters for the tested intervals, quantify parameter uncertainty, and define parameter correlations. Horizontal hydraulic conductivities of the Silurian test intervals range from approximately 4E−14 to 4E−8 m/s. The average horizontal hydraulic conductivities of the Ordovician intervals range from 2E−16 to 2E−10 m/s. The Lower Member of the Cobourg Formation, the proposed host formation of the DGR between 660 and 688 meters below ground surface, was found to have a horizontal hydraulic conductivity of 4E−15 to 3E−14 m/s. The formation pressures inferred from the hydraulic testing, confirmed by long-term monitoring, show that the Upper Ordovician and Middle Ordovician Trenton Group are significantly underpressured relative to a density-compensated hydrostatic condition and relative to the overlying Silurian strata and underlying Black River Group and Cambrian strata. These underpressures could not persist if hydraulic conductivities were not as low as those measured.

Resolution performance analysis of cumulants-based rank reduction estimator in presence of unexpected modeling errors

Compared to the rank reduction estimator (RARE) based on second-order statistics (called SOS-RARE), the RARE employing fourth-order cumulants (referred to as FOC-RARE) is capable of dealing with more sources and mitigating the negative influences of the Gaussian colored noise. However, in the presence of unexpected modeling errors, the resolution behavior of the FOC-RARE also deteriorate significantly as SOS-RARE, even for a known array covariance matrix. For this reason, the angle resolution capability of the FOC-RARE was theoretically analyzed. Firstly, the explicit formula for the mathematical expectation of the FOC-RARE spatial spectrum was derived through the second-order perturbation analysis method. Then, with the assumption that the unexpected modeling errors were drawn from complex circular Gaussian distribution, the theoretical formulas for the angle resolution probability of the FOC-RARE were presented. Numerical experiments validate our analytical results and demonstrate that the FOC-RARE has higher robustness to the unexpected modeling errors than that of the SOS-RARE from the resolution point of view.

Hypernormal Form at Cubic of Honeycomb Sandwich Plate Dynamics Model

Honeycomb sandwich plate have been widly applied in industry design in recent years. In this paper, we study the cubic hypernormal form (the simplest normal form and the unique normal form) for honeycomb sandwich plate dynamics model with the help of Maple symbolic computation. Firstly, we get the average equation of four dimensional cartesian form by using the method of multiple scales perturbation analysis. Based on the method combined new grading function with multiple Lie brackets, we obtain the hypernormal form of cubic truncated. The results will further enrich the research for dynamics of honeycomb sandwich plate model, and is also the basis for higher order normal form research.

THE RELAXATION OF TWISTED CHIRAL NEMATIC LIQUID CRYSTALS WITH SIDE-CHAIN POLYMERIC LAYER

A generalized form of surface dissipation function, for the description of the relative motion of the nematic director with respect to the polymer side chains in twisted chiral nematic samples is proposed, and the relaxation time of such samples are investigated, using the perturbation analysis method proposed by Alexe-Ionescu et al. Our results show that the presence of both the surface dissipation and the polymer side chains increase the relaxation time.

Nonlinear oscillations following the Rayleigh collapse of a gas bubble in a linear viscoelastic (tissue-like) medium

In a variety of biomedical engineering applications, cavitation occurs in soft tissue, a viscoelastic medium. The present objective is to understand the basic physics of bubble dynamics in soft tissue. To gain insights into this problem, theoretical and numerical models are developed to study the Rayleigh collapse and subsequent oscillations of a gas bubble in a viscoelastic material. To account for liquid compressibility and thus accurately model large-amplitude oscillations, the Keller-Miksis equation for spherical bubble dynamics is used. The most basic linear viscoelastic model that includes stress relaxation, viscosity, and elasticity (Zener, or standard linear solid) is considered for soft tissue, thereby adding two ordinary differential equations for the stresses. The present study seeks to advance past studies on cavitation in tissue by determining the basic effects of relaxation and elasticity on the bubble dynamics for situations in which compressibility is important. Numerical solutions show a clear dependence of the oscillations on the viscoelastic properties and compressibility. The perturbation analysis (method of multiple scales) accurately predicts the bubble response given the relevant constraints and can thus be used to investigate the underlying physics. A third-order expansion of the radius is necessary to accurately represent the dynamics. Key quantities of interest such as the oscillation frequency and damping, minimum radius, and collapse time can be predicted theoretically. The damping does not always monotonically decrease with decreasing elasticity: there exists a finite non-zero elasticity for which the damping is minimum; this value falls within the range of reported tissue elasticities. Also, the oscillation period generally changes with time over the first few cycles due to the nonlinearity of the system, before reaching an equilibrium value. The analytical expressions for the key bubble dynamics quantities and insights gained from the analysis may prove valuable in the development and optimization of certain biomedical applications.

Nonlinear analysis of a pulse combustor model with exhaust decoupler and vent pipe

A nonlinear pulse combustor model with an exhaust decoupler and vent pipe was solved using the Poincaré–Lindstedt perturbation analysis method. The solutions included expressions for the pressure in the combustion chamber and the exhaust decoupler respectively. Experiments were made to validate the theoretical analysis; results showed that an exhaust decoupler and a vent pipe can affect the frequency of the pulse combustor and the pressure in the exhaust decoupler (both amplitude and phase). There are five main dimensionless parameters: dimensionless exhaust decoupler volume v, dimensionless vent pipe length l, dimensionless vent pipe area s and dimensionless enthalpy ht0, hd0. Following the values of these five parameters, the working domain of the pulse combustor was divided into three parts: the inphase zone, critical interval and antiphase zone. In the critical interval domain, the pulse combustor cannot work stable. To make a pulse combustor work at the antiphase zone (recommended in engineering applications), a large exhaust decoupler volume, and fairly long vent pipe with a proper cross-section area are required.

Pulsational instability of supergiant protostars: do they grow supermassive by accretion?

Supermassive stars (SMSs; M>10^5 Msun) and their remnant black holes are promising progenitors for supermassive black holes (SMBHs) observed in the early universe at z>7. It has been postulated that SMSs forms through very rapid mass accretion onto a protostar at a high rate exceeding 0.01 Msun/yr. According to recent studies, such rapidly accreting protostars evolve into "supergiant protostars", i.e. protostars consisting of a bloated envelope and a contracting core, similar to giant star. However, like massive stars as well as giant stars, both of which are known to be pulsationally unstable, supergiant protostars may also be also unstable to launch strong pulsation-driven outflows. If this is the case, the stellar growth via accretion will be hindered by the mass loss. We here study the pulsational stability of the supergiant protostars in the mass range M<10^3 Msun through the method of the linear perturbation analysis. We find that the supergiant protostars with M>600 Msun and very high accretion rate Mdot>1.0 Msun/yr are unstable due to the kappa mechanism. The pulsation is excited in the He^+ ionization layer in the envelope. Even under a conservative assumption that all the pulsation energy is converted into the kinetic energy of the outflows, the mass-loss rate is ~10^-3 Msun/yr, which is lower than the accretion rate by more than two orders of magnitude. We thus conclude that the supergiant protostars should grow stably via rapid accretion at least in the mass range we studied. As long as the rapid accretion is maintained in the later stage, protostars will become SMSs, which eventually produce seeds for the high-z SMBHs.