Envelope Fitting Research Articles

Interpretation of complex x-ray photoelectron peak shapes. II. Case study of Fe 2p3/2 fitting applied to austenitic stainless steels 316 and 304

In this paper, a review of the analysis of Fe 2p3/2 peak and other transition metals in the austenitic stainless steel literature is presented. It reveals the significant shortcomings of the most widely used approaches, based on the principle of “chemistry fitting,” where single symmetric peaks are used to represent either individual oxidation states or specific compounds. No meaningful conclusions can be drawn from these commonly employed two- or three-component peak fitting (2C and 3C) approaches; the implication being that a large portion of the literature that relies on this approach is flawed. As a significantly more accurate and reliable alternative to “chemistry fitting,” we also assess “envelope fitting” (using empirical multiplet structures) and examine its limitations when applying the approach to austenitic stainless steel data. A detailed comparison of these two fitting approaches is described in Part I. For other elements such as Cr 2p, the problems associated with using single components to represent oxidation states or compounds are not as severe. It was found that it does not impact binding energy measurements, but does influence relative intensities, which will have a flow-on effect for oxide thickness calculations and obtaining a correct understanding of the surface more broadly.

Identification of Damping of Spruce Wood (Picea abies) under Various Levels of Moisture Content Using Time-Scale Decomposition.

The damping of spruce wood is analysed at different moisture content levels for the first three vibration modes of tangentially and radially vibrating samples. Two methods were used to determine the damping. The first was the vibration envelope fitting as an improved version of the well-known logarithmic decrement, and the second was the newer and recently increasingly used wavelet transform. Both methods showed that the damping of spruce wood first decreases and then increases with moisture content, with the damping in the first vibration mode being about 9% higher in the radial direction than in the tangential direction. In the second and third vibration modes, the damping in the tangential direction was higher than in the radial direction by about 10% and 8.8%, respectively. The measured damping factors from the envelope fitting had, on average, 15.9% higher values than those from the wavelet transform. It can be concluded from the results that the wavelet transform is more accurate for determining the damping factor, as it enables the decoupling of multi-degree of freedom systems if mode coupling is present.

Envelope fitting for real-time cascaded microring resonator’s output spectrum

Envelope fitting for real-time cascaded microring resonator’s output spectrum

Parallel unambiguous generalized phase-shifting and T-spline fitting algorithms for optical micro-structured surface 3D topography metrology.

3D topography metrology of optical micro-structured surfaces is critical for controlled manufacturing and evaluation of optical properties. Coherence scanning interferometry technology has significant advantages for measuring optical micro-structured surfaces. However, the current research faces difficulties of designing high accuracy and efficient phase shifting, and characterization algorithms for optical micro-structured surface 3D topography metrology. In this paper, parallel unambiguous generalized phase-shifting and T-spline fitting algorithms are proposed. To avoid phase ambiguity and improve the accuracy of the phase-shifting algorithm, the zero-order fringe is determined by the iterative envelope fitting with Newton's method, and the accurate zero optical path difference is determined by a generalized phase-shifting algorithm. In particular, the calculation procedures of the multithreading iterative envelope fitting with Newton's method and generalized phase shifting are optimized with the graphics processing unit-Compute Unified Device Architecture kernel function. Additionally, to fit the base form of optical micro-structured surfaces and characterize the surface texture and roughness, an effective T-spline fitting algorithm is proposed by optimizing the preimage of the T-mesh with image quadtree decomposition. Experimental results show that the surface reconstruction of optical micro-structured surfaces using the proposed algorithm is more accurate, and the efficiency is 10 times higher than that of current algorithms; the time of the surface reconstruction is less than 1s. Compared with the current B-spline method, the accuracy of roughness characterization using the proposed T-spline algorithm is improved by more than 10%.

Nonequal arm surface measurement of femtosecond optical frequency combs using the Savitzky-Golay filtering algorithm.

In precision machining, the surface geometry of a device is one of the important parameters that directly affects the device performance. This paper proposes nonequal arm surface measurement of femtosecond optical frequency combs (OFCs) using the Savitzky-Golay filtering algorithm, which uses the high spatial coherence of OFCs to realize high-precision, nonequal surface measurements. The Savitzky-Golay filtering algorithm and a high-order polynomial envelope fitting algorithm are used to smooth and denoise the interference signals to improve signal quality and measurement accuracy. The experiments are carried out under the condition of nonequal arms, and the results show that the repeatability is 28.6nm for 20 consecutive measurements on the step surface of a 0.5mm gauge block. The frosted glass surface is measured 20 times, and the measurement repeatability at the center position is 89.6nm, which verified the system capability of nonequal arm high-precision measurement under different reflective surfaces.

Estimation of EMD Envelope Based on MQ Interpolation

Empirical modal decomposition (EMD) is a data-driven signal analysis method that can effectively decompose signals into components of different scales. However, there are still key issues such as endpoint effects, envelope fitting and theoretical foundation improvement that need to be solved. In this paper, we introduce Multi-Quadratic (MQ) fitting interpolation to estimate the envelope in the empirical modal decomposition, which is an efficient, high-precision and conformal fitting method without solving the system of equations.

An improved empirical wavelet transform and sensitive components selecting method for bearing fault

The empirical wavelet transform (EWT) has made outstanding contributions in the field of fault diagnosis. However, when EWT processes complex signals, there may be modal aliasing or meaningless components. In order to solve the spectral segmentation defect of the EWT method and improve its ability to extract bearing fault features, this paper proposes a new algorithm to improve EWT. In order to weaken the influence of extreme points in the complex Fourier spectrum on modal differentiation, the cycle envelope spectral segmentation method is proposed. The maximum envelope fitting method not only reduces the number of useless extreme points, but also highlights each mode. The number of filters is reduced while suppressing the interference of noise on the modal. The components that contain similar information in the result will be merged based on their correlation. Then sensitive IMFs assessing index (SIAI) is proposed to combine correlation and symmetry of the signal, and obtains the characteristics of time domain, frequency domain, and amplitude domain to extract fault information. Locomotive bearing and wind turbine gearbox bearing fault data verified the effectiveness of the method.

An adjustable envelope based EMD method for rolling bearing fault diagnosis

Empirical mode decomposition (EMD) can decompose complex non-stationary signals into the sum of several intrinsic mode functions (IMF), and it is widely used in fault diagnosis of mechanical devices. In order to solve the mode mixing problem and enhance the fault feature extraction ability, an adjustable envelope based EMD (AE-EMD) method was proposed. Firstly, the envelope fitting method is replaced by rational Hermite interpolation, which can effectively avoid the outstanding over and undershoot problem in the conventional fitting curve. Secondly, the optimal parameter in the AE-EMD is searched by grey wolf optimizer (GWO) using the maximum Kurtosis index as the objective function. Then, the AE-EMD method combined with the Hilbert envelope spectrum is employed to extract the fault characteristic frequency. Case study demonstrates that AE-EMD can restrain the mode mixing effectively, and it also has better fault feature extraction ability compared with the conventional EMD. This proposed method has potential significance to the fault diagnosis and condition-based maintenance (CBM) of rolling bearings in the large and complex equipment.

Design of an Acoustic-Based Nondestructive Test (NDT) Instrument to Predict the Modulus of Elasticity of Wood

Modulus of elasticity (E) can predict the mechanical characteristics, as well as grade the quality of wood. The Destructive Test (DT) method is the more commonly used, where the wood sample is split up when being tested. This research used the NDT method based on the longitudinal stress wave method (LSWM) whilst utilizing handheld instruments. The calculated E-dynamic (Ed) from the NDT method was compared with the E-static (Es) from the DT method to validate the technique. Six different wood types were tested with ten samples of each kind. An average R-value of 0.898 was obtained, indicating a high correlation between the Ed values and Es values. The LSWM method requires reliable hardware and software to record the impulse response. It starts by hitting the wood with a hammer to create an impulse, finding the resonance frequency (f0), and later calculating the Ed. A more practical and easy-to-use handheld mobile instrument was developed using a Raspberry Pi-2 microcomputer as the signal processor, an LCD touchscreen, a USB soundcard, and a dynamic microphone that covers 0.1-5kHz and -64 ± 3dB. An internal telecommunication system is provided to support measurements conducted at lumber mills. The software includes band-pass filtering of the recorded spectrum where the f0 is depicted. A time-domain envelope fitting is then applied to the filtered spectrum to obtain the R2envelope. A low R2envelope value indicates an inadequate impulse response, and therefore, the test should be redone.

Mode Mixing Suppression Algorithm for Empirical Mode Decomposition Based on Self-Filtering Method

The Hilbert-Huang transform (HHT) is a classic method in time-frequency analysis field which was proposed in 1998. Since it is not limited by signal type, it is generally applied in medicine, target detection and so on. Empirical mode decomposition (EMD) is a pre-processing part of HHT. However, EMD still has many imperfect aspects, such as envelope fitting, the endpoint effect, mode mixing and other issues, of which the most important issue is the mode mixing. This paper proposes a mode mixing suppression algorithm based on self-filtering method using frequency conversion. The proposed algorithm focuses on the instantaneous frequency estimation and the false components removing procedures, which help the proposed algorithm to update or purify the designated intrinsic mode function (IMF). According the simulation results, the proposed algorithm can effectively suppress the mode mixing. Comparing with ensemble empirical mode decomposition (EEMD) and mask method, the suppression performance is increased by 26%.

Absolute Single Cavity Length Interrogation of Fiber-Optic Compound Fabry⁻Perot Pressure Sensors Through a White Light Non-Scanning Correlation Method.

A white light non-scanning correlation interrogation system was proposed and built to interrogate absolute length of the air cavity of fiber-optic compound Fabry–Perot pressure sensors for the extraction of pressure value. By carefully choosing thickness range and tilt angle of the optical wedge used for cavity length matching, correlation interferometric signal of the basal cavity can be naturally filtered out. Based on peak positioning by Fourier transform, bandpass filtering in frequency domain, inverse Fourier transform back to time domain, envelope fitting and zero fringe finding through a gravity center method, cavity length can be determined with an accuracy of 0.04%. The system was used for the interrogation of a fiber-optic compound Fabry–Perot pressure sensor under different pressures. For a pressure range of 0.1~2.9 Mpa, the linear relationship between the air cavity length and the gas pressure imposed was successfully extracted.

Echo signal envelope fitting based signal processing methods for ultrasonic gas flow-meter

The echo signal of the ultrasonic gas flow-meter is difficult to locate, and the computation of signal processing methods proposed by others is extensive which affects the meter’s real-time performance. Aiming at solving these problems the echo signal envelopes under different flow rates are analyzed. And three kinds of signal processing methods based on echo signal envelope fitting are proposed. The shape of the echo signal remains the “approximate spindle shape” as the flow rate increases, and the envelope gradient of the middle parts of the upper envelope’s rising section and the lower envelope’s falling section remains the same at different flow rates, so the mathematical models of the two sections are established to obtain the envelope gradient curves of the two sections. With the envelope gradient curves, the ranges of envelope and peak points that linearly distributed are obtained. The least squares fitting is performed on those peak points to obtain two feature straight lines for respectively representing the upper envelope’s rising section and the lower envelope’s falling section. According to the spatial characteristics of the feature straight lines, the points on the feature straight lines are selected as the feature points for quickly locating the echo signal. According to the offline verification and comparison, the best one of three kinds of signal processing methods is selected, and realized on the hardware system of the two-channel ultrasonic gas flow-meter. The transmitter of two-channel ultrasonic gas flow-meter is developed based on FPGA & DSP dual core structure. It utilizes the parallel processing capacity and logic control ability of FPGA to realize the controlling of the high-speed ADC & DAC and the storage of the data. At the same time, it adopts the high-speed computing capacity of DSP to implement the digital signal processing method. The gas flow calibration experiments were carried out in a national accredited testing agency to verify the effectiveness of the signal processing methods and system. The experimental results show that the improved signal processing method based on echo signal upper and lower envelope fitting can quickly and accurately locate the echo signal. And the measurable range of the ultrasonic gas flow meter based on this signal processing method is broadened to 10 m3/h to 1,300 m3/h, and the turndown ratio is broadened to 1:130.

Top-Down Hydrogen-Deuterium Exchange Analysis of Protein Structures Using Ultraviolet Photodissociation.

Top-down hydrogen-deuterium exchange (HDX) analysis using electron capture or transfer dissociation Fourier transform mass spectrometry (FTMS) is a powerful method for the analysis of secondary structure of proteins in solution. The resolution of the method is a function of the degree of fragmentation of backbone bonds in the proteins. While fragmentation is usually extensive near the N- and C-termini, electron capture (ECD) or electron transfer dissociation (ETD) fragmentation methods sometimes lack good coverage of certain regions of the protein, most often in the middle of the sequence. Ultraviolet photodissociation (UVPD) is a recently developed fast-fragmentation technique, which provides extensive backbone fragmentation that can be complementary in sequence coverage to the aforementioned electron-based fragmentation techniques. Here, we explore the application of electrospray ionization (ESI)-UVPD FTMS on an Orbitrap Fusion Lumos Tribrid mass spectrometer to top-down HDX analysis of proteins. We have incorporated UVPD-specific fragment-ion types and fragment-ion mixtures into our isotopic envelope fitting software (HDX Match) for the top-down HDX analysis. We have shown that UVPD data is complementary to ETD, thus improving the overall resolution when used as a combined approach.

An improved inverse method by envelope fitting for prediction of contact stresses in strip rolling

An improved inverse method by envelope fitting approach has been developed to improve prediction accuracy of contact stresses in strip rolling. By comparisons of the simulation data with theoretical results predicted by different inverse methods, it can be found that the improved inverse method by envelope fitting has a better predictive effect than the old method, in particular for the friction stress. And then, a rolling experiment is developed to validate the industrial feasibility of the improved inverse method. Comparing the results predicted by FEM and different inverse methods, it is also demonstrated that the improved inverse method is better than the old method in the rolling test. It is believed that the improved inverse method by envelope fitting approach would have great potential for industrial rolling.

Research of the indirect friction sensor for prediction of contact stress by improved inverse method in strip rolling

In order to avoid strip marks or perturbation of local lubricant flow at the interface between strip and work roll in strip rolling, an indirect friction sensor has been designed. This sensor is based on the inverse method improved by envelope fitting method, which utilizes strain gage to measure strains at one point inside the work roll to evaluate the contact stress in roll gap. Then several cold rolling tests have been performed at different reductions to demonstrate the rational and the validity of this indirect friction sensor. Comparing the results evaluated by finite element method with the results reconstructed by different inverse methods, it is found that the improved inverse method leads to a better solution to evaluation of the contact stress, in particular for prediction of shear stress. In addition, reasonable prediction is obtained for large reduction but not for small reduction (only the order of magnitude is obtained). It is believed that this research has a strategic importance for practical application.

Hidden defect recognition based on the improved ensemble empirical decomposition method and pulsed eddy current testing

This article presents a new approach for recognizing hidden defects in conductive structures based on the improved ensemble empirical decomposition (IEEMD) and the pulsed eddy current (PEC) testing technique. First, the ensemble empirical mode decomposition (EEMD) method is improved in terms of envelope fitting, end effects and false components. Then, feature vector composed of the principal marginal spectrum peaks are extracted by the help of Hilbert weighted frequencies and characteristic frequencies. It has been verified by simulation signals that the IEEMD method can obtain more accurate intrinsic mode function components (IMFs). The proposed feature extraction method may recognize various hidden defect in the rail specimen with satisfying accuracy and robustness to such disturbances as noise and liftoff.

Robust stability analysis of machining operations

Prediction of machine tool chatter requires the characterization of dynamic of the machine-tool-workpiece system by means of frequency response functions (FRFs). Uncertainties of the measured FRFs result in uncertainties of the calculated stability diagrams, therefore robustness of stability prediction against parameter perturbations is of high importance. Although there exist methods to determine robust stability in terms of stability radii, these methods either give a conservative estimate of the real uncertainties or are limited to perturbations of a few modal parameters, only. In this paper, a frequency-domain approach is presented to determine robust stability boundaries using the measured FRFs directly without any modal parameter identification. The method is based on an envelope fitting around the measured FRFs combined with some considerations of the single-frequency method. The application of the method is demonstrated in case of a turning operation, where the machine tool structure is characterized by a series of FRF measurements.

Robust Stability of Machining Operations in Case of Uncertain Frequency Response Functions

Prediction of machine tool chatter requires a dynamic characterization of the machine-tool-workpiece system by means of frequency response functions (FRFs). Stability lobe diagrams are sensitive to the uncertainties of the measured FRF, which reduces the reliability of their industrial application. In this paper, a frequency-domain method is presented to determine robust stability boundaries with respect to the uncertainties of the FRF. The method is based on an envelope fitting around the measured FRFs combined with some considerations of the single-frequency method. The application of the method is validated on a turning operation characterized by a series of FRF measurements. It is shown that stability analysis using the averaged FRF may considerably overestimate the region of robust stability.

Improved Empirical Mode Decomposition Algorithm of Processing Complex Signal for IoT Application

Hilbert-Huang transform is widely used in signal analysis. However, due to its inadequacy in estimating both the maximum and the minimum values of the signals at both ends of the border, traditional HHT is easy to produce boundary error in empirical mode decomposition (EMD) process. To overcome this deficiency, this paper proposes an enhanced empirical mode decomposition algorithm for processing complex signal. Our work mainly focuses on two aspects. On one hand, we develop a technique to obtain the extreme points of observation interval boundary by introducing the linear extrapolation into EMD. This technique is simple but effective in suppressing the error-prone effects of decomposition. On the other hand, a novel envelope fitting method is proposed for processing complex signal, which employs a technique of nonuniform rational B-splines curve. This method can accurately measure the average value of instantaneous signal, which helps to achieve the accurate signal decomposition. Simulation experiments show that our proposed methods outperform their rivals in processing complex signals for time frequency analysis.

Decoding 3D Disk Structure and Dynamics Using Doppler Tomography

AbstractWe demonstrate a method to measure both rotation curves and 3D ISM structure in edge-on galaxies. Two-dimensional spectral coverage of edge-on galaxies reveals substantial deviations in emission line shapes from a purely gaussian profile that vary with radius and height. Non-gaussianity is quantified using statistical moments to third order. We infer the 3D density distribution by comparing the measured line profiles to synthetic line-of-sight velocity distributions from a suite of three-dimensional galaxy models with different 3D distributions of dust and gas and different rotation curve shapes and amplitudes. We apply this method using multi-position longslit data of nearby edge-on galaxy ESO 435-G25 and find our derived rotation curve matches measured HI rotation from envelope fitting but requires a flared dust disk to accurately describe the radial and vertical trends in the measured statistical moments. Our results are consistent with dynamical expectations for constant pressure support in a disk with exponentially declining surface-density.