Nonlinear Fitting Algorithm Research Articles

An accurate measurement method of irregular coal gangue volume based on adaptive image restoration and error compensation

To improve the accuracy of volume measurement for irregularly shaped coal gangue, defects in the depth image and various errors in volume measurement are analyzed. The gray difference similarity (Gds) is proposed for pre-classifying defects, and the depth and RGB information are used interactively for adaptive repair. To minimize the impact of abnormal gray distribution and irrelevant information on the repair process, the areas to be repaired are divided into abnormal regions or layers based on gray and distance weights. Taking into account parameters like geometric morphology (GeMo), volume (Ve), and GeMo × Ve, the influence of wrong imaging and gaps is fully considered. The reverse compensation of errors is achieved by applying the principles of mathematical statistics and the nonlinear surface fitting algorithm. The results show that compared with other algorithms, the proposed algorithm has the smallest measurement error of 6.614 % and is not easily affected by external factors.

Efficient Modeling of Distributed Energy Resources’ Impact on Electric Grid Technical Losses: A Dynamic Regression Approach

Technical losses in electrical grids are inherent inefficiencies induced by the transmission and distribution of electricity, resulting in energy losses that can reach up to 40% of the generated energy. These losses pose significant challenges to grid operators regarding energy sustainability, reliability, and economic viability. Distributed Energy Resources (DERs) offer promising solutions to lower technical losses by decentralizing energy generation and consumption, reducing the need for long-distance transmission and optimizing grid operation. Hence, estimating the impact of DERs on grid technical losses becomes paramount for grid operators and planners. In response, this article proposes the application of regression modeling and nonlinear curve fitting algorithms to provide a more nuanced understanding and better characterize the intricate interplay between DER deployment and technical losses. Through a comprehensive case study based on more than 1080 computer simulations, we demonstrate the effectiveness of our proposed dynamic polynomial varying coefficient regression model in estimating the impact of DERs on technical losses within electrical grids. The proposed model offers a simple and effective methodology that allows grid operators to gain insights into the nonlinear dynamics of DER integration and make quicker and more informed decisions regarding grid management strategies, infrastructure investments, and policy interventions. Also, this research contributes to advancing the field of grid optimization by offering a simple equation that enhances our ability and haste to assess and mitigate technical losses in the context of an evolving energy landscape characterized by increasing DER adoption.

Predicting Fine Dead Fuel Load of Forest Floors Based on Image Euler Numbers

The fine dead fuel load on forest floors is the most critical classification feature in fuel description systems, affecting several parameters in the manifestation of wildland fires. An accurate determination of this fine dead fuel load contributes substantially to effective wildland fire prevention, monitoring, and suppression. This study investigated the viability of incorporating image Euler numbers into predictive models of fine dead fuel load via the taking photos method. Pinus massoniana needles and Quercus fabri broad leaves—typical fuel types in karst areas—served as the research subjects. Accurate field data were collected in the Tianhe Mountain forests, China, while artificial fine dead fuelbeds of differing loads were constructed in the laboratory. Images of the artificial fuelbeds were captured and uniformly digitized according to various conversion thresholds. Thereafter, the Euler numbers were extracted, their relationship with fuel load was analyzed, and this relationship was applied to generate three load-prediction models based on stepwise regression, nonlinear fitting, and random forest algorithms. The Euler number had a significant relationship with both P. massoniana and Q. fabri fuel loads. At low conversion thresholds, the Euler number was negatively correlated with fuel load, whereas a positive correlation was recorded when this threshold exceeded a certain value. The random forest model showed the best prediction performance, with mean relative errors of 9.35% and 14.54% for P. massoniana and Q. fabri, respectively. The nonlinear fitting model displayed the next best performance, while the stepwise regression model exhibited the largest error, which was significantly different from that of the random forest model. This study is the first to propose the use of image features to predict the fine fuel load on a surface. The results are more objective, accurate, and time-saving than current fuel load estimates, benefiting fuel load research and the scientific management of wildland fires.

Wavelet-based saturated absorption line detection for laser frequency locking

Owing to the presence of noise and the Doppler background, accurate saturated absorption (SA) peak automatic identification technology poses a significant challenge for laser frequency tuning and locking. To address this issue, a novel peak identification algorithm for the SA spectrum is proposed. First, a Gaussian filter based on a Gaussian continuous wavelet transform is proposed to mitigate the spectral high-frequency noise. Subsequently, a hybrid method combining a first-order Gaussian continuous wavelet transformation and adaptive threshold judgment was designed for multi-peak boundary segmentation. Finally, we obtained the target peak and its sweeping voltage based on an adaptive nonlinear fitting algorithm, which was almost unaffected by the peak asymmetry caused by the Doppler background.

A CNN-assisted mid-infrared high-sensitivity exhaled ammonia sensor based on cavity ring-down spectroscopy

The cavity ring-down spectroscopy (CRDS) is becoming increasingly important in sensitive gas detection for atmospheric pollutant detection, greenhouse gas monitoring, human respiratory gas analysis, and measurement of specific gases in industrial processes. However, the accuracy and sensitivity of CRDS are greatly limited by noise and ring-down time extraction algorithms. To solve this problem, a CNN-assisted high-sensitivity exhaled ammonia sensor based on cavity ring-down spectroscopy was developed in this paper, which is the first time to introduce the convolutional neural network to cavity ring-down spectroscopy. A CNN filter and a neural network-based ring-down time extraction algorithm trained by two different datasets were applied to the sensor, solving the shortcomings of the traditional CRDS. Among several filters, the CNN filter achieves the best performance and the SNR is improved by 3.4 times. Compared to traditional nonlinear fitting algorithm, a sensitivity enhancement factor of 3.48 was obtained and a sub-ppb detection limit can be achieved by using Allan deviation analysis. The experimental results prove the feasibility of deep learning for improving the performance of cavity ring-down spectroscopy gas sensor.

Thermal radiation correction formula of the scaling criteria for film cooling of turbine blades

Adiabatic effectiveness (η) is the most important parameter for evaluating film cooling capacity. For turbine blades, it is usually based on the scaling criteria to achieve the mapping of effectiveness from low temperature conditions in the laboratory to real application scenarios. However, with the increase of gas temperature and humidity, the thermal radiation effect is obvious, resulting in the inapplicability of the traditional scaling criteria. In this study, a radiation correction formula was proposed to modify the scaling criteria. Firstly, based on the wide band K-distribution (WBK) model, the absorption coefficients of typical aviation kerosene gas products were calculated. Secondly, the dataset was constructed based on computational fluid dynamics (CFD) assisted design, and Python codes were introduced to automate the post-processing of coefficients. Thirdly, radiation related dimensionless parameters (εw, Tbi, TR, mCO2, mH2O, mO2, mN2) were selected as independent variables. Finally, an explicit function between based on a nonlinear fitting algorithm was obtained. The correlation formula of the scaling criteria proposed was compatible with reasonable flow parameters and model parameters. Compared with the traditional approach, which must be tested at high temperature to fully consider the effects of radiation, the formula proposed in this study is energy-saving and innovative.

Sub-micron weak phase particle characterization using the reconstructed volume intensities from in-line digital holography microscopy

Digital holography microscopy is a powerful technique for retrieving particle properties that are often challenging to obtain with other methods. However, analyzing holographic data using non-linear fitting algorithms and machine learning is difficult without prior information. In this paper, we present a novel technique for sizing and determining the refractive index of sub-micron, weak phase, spherical particles using the Rayleigh-Sommerfeld diffraction theory. Our method involves reconstructing the volume of synthetic holograms using the HoloPy software for particles of different sizes and material properties. We then fit a Gaussian function at the point of numerical re-focus, as given by the first local minima after the Gouy-phase shift, for size and sub-pixel position estimates. By retrieving the magnitude and location of the maximum scattered intensity, we build a scattered interpolant that relates all the parameters of interest. We demonstrate that our technique had a mean error in particle refractive index of 1.24 ± 1.74% with synthetic data and accurately estimates the size and refractive index of similar-sized nanoparticles in experiments. Compared to least-squares fitting, our method performs similarly with synthetic data but outperformed it with experimental data, showcasing its superior accuracy and reliability. Furthermore, we use our technique combined with function-fitting approaches. This hybrid method uses our proposed technique to approximate the initial conditions of non-linear fitting algorithms, leading to improved accuracy. Finally, we explore the potential of using the intensity cubes as well-defined thresholds to differentiate particles from interference caustics in a reconstructed volume. Overall, our results demonstrate the efficacy and accuracy of our technique for retrieving particle properties from holographic data, even when prior information was not available. This technique could have broad applications in the field of nanoparticle characterization.

DFT-Based Tight-binding model of vdW bilayer χ3 and β12 borophene

In this work, a tight-binding (TB) model with the Slater–Koster (SK) approximation is presented to describe the electronic properties of vdW bilayer χ3 and β12 borophene with AA stack. This model is created by using four orbitals of S, Px, Py, and Pz for each boron atom. By fitting the results of the TB model and density functional theory (DFT) calculations using the least-squares method and the Levenberg-Marquardt nonlinear fitting algorithm, the optimal Hamiltonian and the overlap matrix are calculated. This TB model well describes energy bands around high-symmetry k-points, by considering three nearest neighbors in each layer and a non-orthogonal basis set.

Development and Temperature Correction of Piezoelectric Ceramic Sensor for Traffic Weighing-In-Motion.

Weighing-In-Motion (WIM) technology is one of the main tools for pavement management. It can accurately describe the traffic situation on the road and minimize overload problems. WIM sensors are the core elements of the WIM system. The excellent basic performance of WIMs sensor and its ability to maintain a stable output under different temperature environments are critical to the entire process of WIM. In this study, a WIM sensor was developed, which adopted a PZT-5H piezoelectric ceramic and integrated a temperature probe into the sensor. The designed WIM sensor has the advantages of having a small size, simple structure, high sensitivity, and low cost. A sine loading test was designed to test the basic performance of the piezoelectric sensor by using amplitude scanning and frequency scanning. The test results indicated that the piezoelectric sensor exhibits a clear linear relationship between input load and output voltage under constant environmental temperature. The linear correlation coefficient R2 of the fitting line is up to 0.999, and the sensitivity is 4.04858 mV/N at a loading frequency of 2 Hz at room temperature. The sensor has good frequency-independent characteristics. However, the temperature has a significant impact on it. Therefore, the output performance of the piezoelectric ceramic sensor is stabilized under different temperature conditions by using a multivariate nonlinear fitting algorithm for temperature compensation. The fitting result R2 is 0.9686, the root mean square error (RMSE) is 0.2497, and temperature correction was achieved. This study has significant implications for the application of piezoelectric ceramic sensors in road WIM systems.

Interdependency of Core Temperature and Glabrous Skin Blood Flow in Human Thermoregulation Function: A Pilot Study.

Human thermoregulation is governed by a complex, nonlinear feedback control system. The system consists of thermoreceptors, a controller, and effector mechanisms for heat exchange that coordinate to maintain a central core temperature. A principal route for heat flow between the core and the environment is via convective circulation of blood to arteriovenous anastomoses located in glabrous skin of the hands and feet. This paper presents new human experimental data for thermoregulatory control behavior along with a coupled, detailed control system model specific to the interdependent actions of core temperature and glabrous skin blood flow (GSBF) under defined transient environmental thermal stress. The model was tuned by a nonlinear least-squared curve fitting algorithm to optimally fit the experimental data. Transient GSBF in the model is influenced by core temperature, nonglabrous skin temperature, and the application of selective thermal stimulation. The core temperature in the model is influenced by integrated heat transfer across the nonglabrous body surface and GSBF. Thus, there is a strong cross-coupling between GSBF and core temperature in thermoregulatory function. Both variables include a projection term in the model based on the average rates of their change. Six subjects each completed two thermal protocols to generate data to which the common model was fit. The model coefficients were unique to each of the twelve data sets but produced an excellent agreement between the model and experimental data for the individual trials. The strong match between the model and data confirms the mathematical structure of the control algorithm.

Temperature-Dependent Characterization of Power Amplifiers Using an Efficient Electrothermal Analysis Technique

In this paper, we propose an efficient methodology for the electrothermal characterization of power amplifier (PA) integrated circuits. The proposed electrothermal analysis method predicts the effect of temperature variations on the key performances of PAs, such as gain and linearity, under realistic dynamic operating conditions. A comprehensive technique for identifying an equivalent compact thermal model, using data from 3-D finite element method thermal simulation and nonlinear curve fitting algorithms, is described. Two efficient methods for electrothermal analysis applying the developed compact thermal model are reported. The validity of the methods is evaluated using commercially available electrothermal computer-aided design (CAD) tools and through extensive pulsed RF signal measurements of a PA device under test. The measurement results confirm the validity of the proposed electrothermal analysis methods. The proposed methods show significantly faster simulation speed comparing to available CAD tools for electrothermal analysis. Moreover, the results reveal the importance of electrothermal characterization in the prediction of the temperature-aware PA dynamic operation.

Research on preparation process of ethanol and C4 olefin based on linear and nonlinear regression fitting algorithm

First of all, aiming at studying the relationship between ethanol conversion, C4 olefin selectivity and temperature for each catalyst using the knowledge of fitting arbitrary data and adopting the basic idea of control variable method, linear regression equation and nonlinear regression equation model are established. Aiming at the solution of linear regression and non-linear regression model, this paper uses the fitting algorithm to calculate the functional relationship between the two variables, and uses Matlab to solve the specific function expression and draw the function relation diagram to further solve the relationship between catalyst combination, temperature and ethanol conversion and C4 olefin selectivity.

MRI diffusion phantoms: ADC and relaxometric measurement comparisons between polyacrylamide and agarose gels

PurposeThe aim of this study is to compare polyacrylamide and agarose gels, as components of a simple MRI phantom, for the measurements of Apparent Diffusion Coefficient (ADC), T1 and T2 relaxation times. Materials and methodsFive (5) test tubes with polyacrylamide gels of different monomer concentrations and six (6) test tubes of different agarose gel concentrations were used as a phantom for ADC, T1 and T2 measurements, which were expressed as 2D color parametric maps, on a 1.5 T clinical MRI system. ADC and T2 maps were calculated utilizing a Weighted Linear (WL) regression fitting algorithm. T1 maps were calculated utilizing a standard non-linear fitting algorithm. ResultsIn agarose gels, ADC measurements are independent of the agarose concentration, whereas the T1 and T2 relaxation times decrease with increasing agarose concentration. On the contrary, in polyacrylamide gels, ADC measurements decrease quadratically while increasing the monomer concentration, whereas the T1 and T2 relaxation times reveal a linear decrease with increasing monomer concentration. ConclusionPolyacrylamide gels can serve as a better means for simulating ADC values, as compared with the agarose gels used in this study.

Assessment of shifted excitation Raman difference spectroscopy in highly fluorescent biological samples.

Shifted excitation Raman difference spectroscopy (SERDS) can be used as an instrumental baseline correction technique to retrieve Raman bands in highly fluorescent samples. Genipin (GE) cross-linked equine pericardium (EP) was used as a model system since a blue pigment is formed upon cross-linking, which results in a strong fluorescent background in the Raman spectra. EP was cross-linked with 0.25% GE solution for 0.5 h, 2 h, 4 h, 6 h, 12 h, and 24 h, and compared with corresponding untreated EP. Raman spectra were collected with three different excitation wavelengths. For the assessment of the SERDS technique, the preprocessed SERDS spectra of two excitation wavelengths (784 nm-786 nm) were compared with the mathematical baseline-corrected Raman spectra at 785 nm excitation using extended multiplicative signal correction, rubberband, the sensitive nonlinear iterative peak and polynomial fitting algorithms. Whereas each baseline correction gave poor quality spectra beyond 6 h GE crosslinking with wave-like artefacts, the SERDS technique resulted in difference spectra, that gave superior reconstructed spectra with clear collagen and resonance enhanced GE pigment bands with lower standard deviation. Key for this progress was an advanced difference optimization approach that is described here. Furthermore, the results of the SERDS technique were independent of the intensity calibration because the system transfer response was compensated by calculating the difference spectrum. We conclude that this SERDS strategy can be transferred to Raman studies on biological and non-biological samples with a strong fluorescence background at 785 nm and also shorter excitation wavelengths which benefit from more intense scattering intensities and higher quantum efficiencies of CCD detectors.

Validación de un algoritmo de obtención de biomarcadores de imágenes dinámicas de perfusión en tomografía computarizada

A partir del análisis de las imágenes dinámicas de perfusión de contraste en tomografía computarizada, se pueden obtener parámetros que miden características fisiológicas relacionadas con la permeabilidad de los tejidos. Puesto que no existen elementos patrón con los que realizar calibraciones de los conjuntos de herramientas de adquisición y procesado, es necesario hacer una validación de los resultados obtenidos con el algoritmo aplicado a imágenes sintéticas. En este texto se estudia el desempeño en condiciones ideales y en presencia de ruido de un algoritmo de ajuste no lineal para la obtención de parámetros del modelo de Tofts extendido para imágenes de perfusión dinámica. En las pruebas se utiliza como fuente de datos unas imágenes sintéticas formadas a partir de valores conocidos de los parámetros del modelo.

Adaptive modal decomposition based overlapping-peaks extraction for thickness measurement in chromatic confocal microscopy.

Accurate overlapping-peaks extraction plays a critical role in chromatic confocal thickness measurement of ultra-thin transparent film. However, the current algorithms usually appear as a perceptible extraction error resulting from the disturbing influence among peaks in the process of fitting the spectral axial response signal (sARS) of the two measuring surfaces. In this paper, we propose an adaptive modal decomposition method to extract multi peaks for the ultra-thin materials. With this method, the sARS can be firstly decomposed into several sub-modes, which can be used to obtain the peak wavelength of each measuring surface by the existing single peak extraction algorithms, such as the centroid method and Gauss fitting method. Monte Carlo simulations and experimental tests demonstrate that the proposed algorithm has significant improvements over the existing nonlinear fitting algorithms in terms of peak extraction accuracy and precision.

Modelling of the electrocardiographic signal during an angioplasty procedure in the right coronary artery

Dynamical models are useful tools to generate sets of varied morphological signals by synthesizing human electrocardiograms (ECGs). These signals are used for testing and improving algorithms of ECG delineation, patient monitoring and heart disease detection. This work presents a procedure based on the ECGSYN model to synthesize ECG morphological changes induced by a percutaneous transluminal coronary angioplasty (PTCA) procedure in the right coronary artery. We provide a set of parameters to be used in ECGSYN and generate heartbeats with altered ST-T complexes. These characteristic model parameters were obtained through a non-linear fitting algorithm applied to every available heartbeat. To extend these parameters, normal distributions were generated with their means and standard deviations obtained from the STAFF III database. Parameters were presented for P, QRS and T-waves at leads II, III and aVF. The synthesis procedure shows an average correlation and positive predictive value of 92.2% and 88.2%, respectively. In conclusion, we provide a technique capable of synthesizing electrocardiographic ischemic morphology with physiological plausibility. Then, the generation of data sets for algorithm testing can benefit from this system of ECG signal synthesis.

Effect of atmospheric oxygen on the kinetic parameters of thermal degradation of pine branch particles

Thermal degradation of forest combustibles plays an important role in the ignition and spread of wildland fires. Atmospheric oxygen affects thermal degradation mechanisms. In this paper, the thermal degradation behavior of pine branch (PB) particles of Pinus Sylvestris is investigated by using a thermogravimetric analyzer under inert and oxidative atmospheres. Results indicate that the thermal degradation process of PB particles in nitrogen differs from that in oxidative atmospheres, except for the initial stage from room temperature to 250 °C. Comparison between DTG and DSC curves under atmospheres with oxygen concentrations 5%–21% indicates that thermal degradation is promoted by increasing atmospheric oxygen. A unified scheme composed of four first-order reactions is used for kinetic analysis by simulating TG data with heating rates of 10, 15, 20, and 25 °C/min simultaneously. Kinetic parameters and reaction rate coefficients have been calculated based on multi-heating rate data, by the combined use of Genetic algorithm (GA) and nonlinear fitting algorithm. It is shown that the unified scheme is capable of capturing the characteristics of thermal degradation reactions under all heating rates and oxygen concentrations. It is found that the activation energies of four reactions first increase with oxygen concentration increasing from 0% to 15%, and then remain constant with oxygen concentration increasing from 15% to 21% except for reaction 2. The reaction rate coefficients of reactions 1, 3 and 4 obviously increase with oxygen concentration, while that of reaction 2 does not depend on oxygen concentration.

A new high-precision sphere-fitting method with small segment angles

Measuring a spherical surface with small segment angle (e.g. 1°) precisely is a big challenge in scientific research and engineering applications. To fit sphere surfaces with small segment angles with high precision, a five-parameter constrained nonlinear least square fitting (CNLSF) method is presented in this work, where an Adam optimization algorithm with a prominent anti-interference ability is employed. We discuss various factors which influence the final uncertainty evaluation of the sphere’s radius. A Monte Carlo simulation is conducted by superimposing Gaussian noise on the ideal spherical data to simulate practical instrument errors, then the relationship between the fitting bias of the sphere’s radius and noise the level, the number of sampling points and the segment angle is investigated by comparing the performance of the linear least square fitting algorithm, the nonlinear least square fitting algorithm and the CNLSF algorithm. Finally, the simulated and experimental results show that the CNLSF method performs more precisely and robustly than the other algorithms, even when the corresponding segment angle approaches 1°, which illustrates that it is a promising and practical method in the real measurement world.

Multi-Task Learning for Multi-Dimensional Regression: Application to Luminescence Sensing

The classical approach to non-linear regression in physics is to take a mathematical model describing the functional dependence of the dependent variable from a set of independent variables, and then using non-linear fitting algorithms, extract the parameters used in the modeling. Particularly challenging are real systems, characterized by several additional influencing factors related to specific components, like electronics or optical parts. In such cases, to make the model reproduce the data, empirically determined terms are built in the models to compensate for the difficulty of modeling things that are, by construction, difficult to model. A new approach to solve this issue is to use neural networks, particularly feed-forward architectures with a sufficient number of hidden layers and an appropriate number of output neurons, each responsible for predicting the desired variables. Unfortunately, feed-forward neural networks (FFNNs) usually perform less efficiently when applied to multi-dimensional regression problems, that is when they are required to predict simultaneously multiple variables that depend from the input dataset in fundamentally different ways. To address this problem, we propose multi-task learning (MTL) architectures. These are characterized by multiple branches of task-specific layers, which have as input the output of a common set of layers. To demonstrate the power of this approach for multi-dimensional regression, the method is applied to luminescence sensing. Here, the MTL architecture allows predicting multiple parameters, the oxygen concentration and temperature, from a single set of measurements.