Polynomial Fitting Method Research Articles

Rapid Identification Method for CH4/CO/CH4-CO Gas Mixtures Based on Electronic Nose.

The inherent cross-sensitivity of semiconductor gas sensors makes them extremely challenging to accurately detect mixed gases. In order to solve this problem, this paper designed an electronic nose (E-nose) with seven gas sensors and proposed a rapid method for identifying CH4, CO, and their mixtures. Most reported methods for E-nose were based on analyzing the entire response process and employing complex algorithms, such as neural network, which result in long time-consuming processes for gas detection and identification. To overcome these shortcomings, this paper firstly proposes a way to shorten the gas detection time by analyzing only the start stage of the E-nose response instead of the entire response process. Subsequently, two polynomial fitting methods for extracting gas features are designed according to the characteristics of the E-nose response curves. Finally, in order to shorten the time consumption of calculation and reduce the complexity of the identification model, linear discriminant analysis (LDA) is introduced to reduce the dimensionality of the extracted feature datasets, and an XGBoost-based gas identification model is trained using the LDA optimized feature datasets. The experimental results show that the proposed method can shorten the gas detection time, obtain sufficient gas features, and achieve nearly 100% identification accuracy for CH4, CO, and their mixed gases.

Multi-field-sensing metasurface with robust self-adaptive reconfigurability

Abstract The continuous increase in communication capacity is accompanied by an increase in transmission frequency, which creates new demands on the transmission efficiency in modern. Signal relay transmission can increase the transmission distance, however, conventional repeaters relay the signal in a specified direction, which is difficult to accommodate communication when a receiving device suddenly appears around the repeater. In this work, we propose a new signal transmission repeater, which is implemented by an adaptively reconfigurable multi-beam reflective metasurface based on multispectral detection. The reconfigurable metasurface with varactor diodes is designed and the mapping of phase profiles to voltages is established by polynomial fitting method. Visual, laser, infrared and ultrasonic detectors are used to detect targets in different scenarios. Thus, the detection information is fed back to the reconfigurable metasurface for adaptively multi-beam switching. As verification, the adaptive metasurface repeater was fabricated and measured to verify our design. All the results exhibit consistency with theoretical design. Importantly, this work paves a new way to intelligent metasurfaces and may find applications in intelligent communications, smart home, etc.

MARSplines-Based Soil Moisture Sensor Calibration

Soil moisture sensor calibration based on the Multivariate Adaptive Regression Splines (MARSplines) model is studied in this paper. Different from the generic polynomial fitting methods, the MARSplines model is a non-parametric model, and it is able to model the complex relationship between the actual and measured soil moisture. Rao-1 algorithm is employed to tune the hyper-parameters of the calibration model and thus the performance of the proposed method is further improved. Data collected from four commercial soil moisture sensors is utilized to verify the effectiveness of the proposed method. To assess the calibration performance, the proposed model is compared with the model without using the temperature information. The numeric studies prove that it is promising to apply the proposed model for real applications.

Drift calibration method of Fabry-Perot filters using two-stage decomposition and hybrid modeling.

Although tunable Fabry-Perot (F-P) filters are widely acknowledged as fiber Bragg grating (FBG) demodulators, F-P filters exhibit drift error when subjected to ambient temperature and piezo-electrical transducer (PZT) hysteresis. To address the drift issue, the majority of the existing literature makes use of additional devices like the F-P etalon and gas chamber. In this study, a novel drift calibration method based on two-stage decomposition and hybrid modeling is proposed. The initial drift error sequences are broken down into three frequency components using the variational mode decomposition (VMD), and the medium-frequency components are further broken down using the secondary VMD. The initial drift error sequences are significantly simplified by the two-stage VMD. On this foundation, the long short-term memory (LSTM) network and polynomial fitting (PF) are used to forecast the low-frequency and high-frequency drift errors, respectively. The LSTM enables the prediction of intricate nonlinear local behaviors, while the PF method predicts the overall trend. The benefits of LSTM and PF can be effectively utilized in this manner. Compared to the single-stage decomposition, two-stage decomposition achieves superior results. The suggested method is an affordable and effective alternative to the current drift calibration techniques.

Polynomial Fitting and Interpolation Method in TDOA Estimation of Sensors Network

Time difference of arrival (TDOA) estimation is the key part of TDOA positioning technology in sensors network, whose result will directly affect the positioning accuracy of the signal source. Aiming at the problem that the accuracy of TDOA estimation is greatly limited by the system sampling frequency, this article proposes an improved TDOA estimation method combining polynomial fitting and interpolation. Based on the classical generalized cross correlation (GCC) method, the peak location of the correlation function is adjusted slightly by polynomial fitting. Furthermore, linear interpolation is used to process the original signal to improve the time resolution between the samples, so as to improve the system sampling frequency indirectly and promote the estimation accuracy to the subsampling level. At the end of the article, the proposed method is validated by simulation and some measured data from a certain place in Lanzhou. The results show that the polynomial fitting method can precisely determine the peak location of the GCC correlation function, especially after interpolating 2–4 points in the original signal, the overall TDOA estimation accuracy can be improved by 0.2%–3.6%, which may provide good reference information for practical engineering application of TDOA positioning technology.

Nonlinear model order reduction and vibration control of a membrane antenna structure

In this paper, model order reduction (MOR) of the nonlinear dynamic model of a membrane antenna structure is studied. Nonlinear vibration control of the membrane antenna structure by using cable actuators has also been investigated. First, the nonlinear dynamic model of the membrane antenna structure is established by using the nonlinear finite element method. Then, MOR of this nonlinear model is carried out. The vibration modes obtained by the linearized model are used as transformation bases, and the method of polynomial fitting is applied to approximate the nonlinear terms. Based on the reduced nonlinear dynamic model, by using the tension cables as actuators, a vibration controller is proposed to suppress the nonlinear vibration of the structure. The nonlinear vibration of the membrane antenna structure is suppressed by adjusting the tension force in the cable actuators. Numerical simulations show that the reduced dynamic model obtained by the presented MOR method can approximate the original nonlinear model very well meanwhile reduce the calculation cost significantly, and the nonlinear vibration of the structure can be suppressed effectively by the cable actuators with the proposed control law.

Inverse design of programmable Poisson's ratio and in-plane stiffness for generalized four-fold origami

Origami-inspired metamaterials and structures exhibit extraordinary properties, including programmable Poisson's ratio and tunable stiffness. Although some research has achieved the programmability of generalized four-fold origami structures, the proposed formulas of Poisson's ratio and stiffness are complex and difficult to be applied for inverse design of origami engineering. Here, the geometric mechanics of a generalized four-fold origami unit with three angles and two lengths controls are studied. The analytical formulas give a great potential of inverse design for in-plane Poisson's ratio and in-plane stiffness. To realize inverse design, the transcendental equation with uninvertible solution is simplified by polynomial fitting method. Moreover, the results are verified by the classical Miura origami results, the existing Origami Simulator tools and the physical polyethylene models. Finally, to make the proposed inverse design applicable to non-zero thickness origami, it is recommended to adopt carbon fiber reinforced polymer shell as the connection of the panel.

Fatigue of an Aluminum Foam Sandwich Formed by Powder Metallurgy.

In this paper, an aluminum foam sandwich (AFS) was prepared by the rolling composite-powder metallurgy method, and its fatigue properties were studied. It was compared with an AFS made by the adhesive method to study its fatigue properties more directly. In this experiment, the fatigue performance was investigated by studying the microscopic interface, fatigue life, deflection curve, and failure mode. The results show that the fatigue life of an AFS with the rolling composite-powder metallurgy method is much longer than that with the adhesive method. The failure mode of an AFS made by the rolling composite-powder metallurgy method is shear failure, and that of an AFS made by the adhesive method is shear failure and interface debonding. An AFS with the rolling composite-powder metallurgy method has better fatigue properties. This paper also explored the fatigue damage model using the fatigue modulus method, and the polynomial fitting method has a higher fitting degree.

Comparison and Verification of Gas-Bearing Parameter Evaluation Methods for Deep Shale Based on the Pressure Coring Technique

Gas-bearing properties, such as gas-in-place (GIP) content and adsorbed gas ratio (AGR), have drawn considerable attention because they are essential for shale gas resource evaluation and sweet spot forecasting. The above-mentioned metrics have been determined using a variety of approaches, but they lack systematic comparison and accuracy verification, particularly for deep shale gas, where conventional methods frequently fall short. A total of 30 shales were taken for the investigation utilizing pressure and conventional coring methods from Wufeng and Longmaxi Formations in the Sichuan Basin, China. For pressure coring samples, we developed the experimental protocols and a GIP content classification scheme that categorizes the GIP content into four categories: lost gas (estimated using the temperature-corrected pressure-holding ratio), extracted gas from depressurization, degassed gas, and residual gas. The four pressure coring samples from well Y206 with measured GIP content range from 2.84 to 5.58 m3/tonne, with an average of 4.72 m3/tonne. In contrast to the calculated GIP content of the pressure coring samples, the validity of the current GIP content evaluation methodologies has been confirmed. The comparison results demonstrate that the GIP content assessed using the United States Bureau of Mines (USBM) method is frequently underestimated for samples from conventional coring and notably overstated for samples from pressure coring. The polynomial fitting method dramatically overestimated the GIP content. With its accurate time-dependent boundary conditions and strict theoretical foundation, the simplified carbon isotope fractionation (s-CIF) model exhibits the highest level of accuracy in determining GIP content. Additionally, the s-CIF model can find yet another crucial parameter of AGR. Shale samples from well Y206 had an average AGR of 20.4% but a range from 12.2 to 33.2%. The examination of the influencing factors demonstrates that the lost gas ratio, AGR, and diffusion coefficient are responsible for controlling the calculation error of the USBM method. The lost gas ratio prior to core retrieval increases with decreasing AGR (or increasing diffusion coefficient), which increases the computation error of the USBM method.

Waveform Prediction of Blade Tip‐Timing Sensor Based on Kriging Model and Static Calibration Data

Blade tip clearance is an important parameter affecting the efficiency, stability, and safety of aero‐engines. During the high‐speed rotation of the blade, the blade tip clearance changes, which leads to changes in signal amplitude collected by the tip timing sensor. When the rotor is rotating at high speed, it is impractical to measure the tip‐timing signal under each tip clearance. Aiming at the previous problems, a prediction method of blade tip‐timing sensor waveform based on the combination of the Kriging model and static calibration data are proposed. The relationship between the output voltage of the tip timing sensor and the blade tip clearance and the angle of the blade tip cutting magnetic line is obtained by collecting the data of static calibration. Based on the collected static calibration experimental data and compared with the polynomial fit method and the RBF model, the accuracy of the Kriging model in predicting the waveform of the blade tip timing sensor was verified. The results show that the prediction accuracy of the Kriging model is basically the same as that of the RBF model, but the Kriging model has more advantages in predicting the waveform when the blade tip clearance is unknown. In contrast, the prediction accuracy of the polynomial fit is lower than that of the Kriging and RBF models, and the polynomial fit is prone to significant prediction errors.

A Method to Construct Depth Datum Geodesic Height Model for GNSS Bathymetric Survey

Water depth measurement requires the establishment of one or more tidal stations in the survey area for synchronous water level observation, and finally the water depth is estimated to the depth datum. The non-tidal observation measuring has high efficiency and avoids the water level correction error caused by tidal observation in traditional sounding. Therefore, non-tidal observation measuring has become an effective water depth measurement method in offshore and inland water. However, datum conversion in non-tide operation is mostly based on the polynomial fitting method. The accuracy of this method is influenced by the distribution of datum control points, topographic relief and operation ranges. In this paper, we present a method to construct a depth datum geodesic height model, which can directly obtain a bathymetric database of depth data in a GNSS bathymetric survey. The model incorporates the continuous depth datum and the mean sea level of geodetic height in the same area. Through the numerical simulation of tidal wave motion in regional water, the tidal model is obtained. Based on the grid model, the tidal level is extracted from the tidal model for harmonic analysis, and a continuous depth datum model is established. Mean sea level geodetic height is from the CNES-CLS2015 Average Sea Surface Model. In this paper, the model is confirmed in the South Yellow Sea area. The results show that the accuracy of the depth datum model, and the depth datum geodetic height model meets the accuracy requirements of the datum.

Augmented Underwater Acoustic Navigation with Systematic Error Modeling Based on Seafloor Datum Network

Underwater acoustic navigation technology is an important approach to achieving high precision ocean navigation. One of the critical issues of the technology is to correct systematic errors, which are related to time delays and time-varying sound speed errors. In this study, we propose an augmented underwater acoustic navigation with systematic error model based on seafloor datum network. The proposed algorithm first selects data sets of piece-wise systematic error modeling by extracting the main periodic term of systematic errors based on the Fourier transform. Before that, the wavelet transform is used for denoising to better extract the main periodic term. Then the systematic error correction model is constructed by using the polynomial fitting method. After that, an augmented observation equation of underwater acoustic navigation with systematic error correction is constructed. Finally, an adaptive robust Kalman filter is developed for underwater acoustic navigation. The proposed algorithm is verified by an experiment in the South China Sea. The three-dimensional root mean square values of underwater acoustic navigation are 1.010 and 1.502 m in the operating range of 2.7 and 8.7 km. The results demonstrate that the proposed algorithm can efficiently reduce the influence of systematic error, thus improving underwater acoustic navigation accuracy.

Study of timing performance parameters for a SiPM-based digital positron annihilation lifetime spectrometer

Abstract Positron annihilation lifetime spectroscopy (PALS) is a popular method for studying defects in materials. With the development of fast digital oscilloscopes and digitizers, the conventional analog positron annihilation lifetime (PAL) spectrometer is being replaced by a digital PAL spectrometer. Recently, newly conducted research has developed a PAL spectrometer using a silicon photomultiplier (SiPM) instead of a photomultiplier tube (PMT). Timing resolution of PAL spectrometer needs to be improved to identify the lifetimes of positrons. Many parameters affect the timing performance of a SiPM-based digital PAL spectrometer: bias voltage, pulse smoothing, and the constant fraction value of digital constant fraction discrimination (dCFD). Timing resolution depends on the radiation energy, but only a few studies have considered the energy difference of 1274 keV and 511 keV. In this study, we optimized the timing performance parameters of the SiPM-based digital PAL spectrometer by conducting the timing resolution measurements using two γ-ray sources (22Na and 60Co). With a 32 V bias voltage, 5th degree polynomial fitting method, and optimal constant fraction value, we optimized the timing resolution of our SiPM-based digital PAL spectrometer. Furthermore, the optimal constant fraction value depended on the γ-ray energy and we verified it by timing resolution measurement using 207Bi. We studied the reason why performance parameters have optimal conditions and the optimal constant fraction value varies depending on the γ-ray energy. With optimized performance parameters, we measured the lifetime spectrum of pure silicon to confirm the SiPM-based digital PAL spectrometer. The timing resolution function of the SiPM-based digital PAL spectrometer was 185.6 ps.

Calibration approach to quantify nonlinearity of MEMS pore pressure sensors using optimal interpolation

Micro-electro-mechanical system (MEMS)-based instruments have become more attractive in recent years for many industries, particularly geotechnical monitoring owing to their small size and low capital cost. However, overcoming nonlinearity errors is a major concern to ensure accuracy, precision, and repeatability of measurement. Nonlinearity error in measuring instruments can be solved using polynomial function of different degree based on severity of error. In this study, Lagrange polynomial fitting method is applied for nonlinearity calibration of a newly developed MEMS pore pressure sensor by means of optimum calibration points. A procedure for optimum selection of the calibration points to get the best calibration characteristics of a pore pressure sensor is investigated. For this work, the calibration characteristics are evaluated by Lagrange interpolation using special set of Chebyshev nodes, D, A and R-optimum points. The D-A-R optimum points are constructed by imperialist competitive algorithm. The value of the optimal approach is also compared with a uniform approach using equidistant points through actual readings. The results show the increased accuracy and precision of measurement using optimum approach. This increased accuracy allows the application of MEMS to sense smaller changes in pore pressure readings providing unique opportunity for passive estimation of subsurface properties.

A Method for Capture and Detection of Crop Airborne Disease Spores Based on Microfluidic Chips and Micro Raman Spectroscopy.

Airborne crop diseases cause great losses to agricultural production and can affect people's physical health. Timely monitoring of the situation of airborne disease spores and effective prevention and control measures are particularly important. In this study, a two-stage separation and enrichment microfluidic chip with arcuate pretreatment channel was designed for the separation and enrichment of crop disease spores, which was combined with micro Raman for Raman fingerprinting of disease conidia and quasi identification. The chip was mainly composed of arc preprocessing and two separated enriched structures, and the designed chip was numerically simulated using COMSOL multiphysics5.5, with the best enrichment effect at W2/W1 = 1.6 and W4/W3 = 1.1. The spectra were preprocessed with standard normal variables (SNVs) to improve the signal-to-noise ratio, which was baseline corrected using an iterative polynomial fitting method to further improve spectral features. Raman spectra were dimensionally reduced using principal component analysis (PCA) and stability competitive adaptive weighting (SCARS), support vector machine (SVM) and back-propagation artificial neural network (BPANN) were employed to identify fungal spore species, and the best discrimination effect was achieved using the SCARS-SVM model with 94.31% discrimination accuracy. Thus, the microfluidic-chip- and micro-Raman-based methods for spore capture and identification of crop diseases have the potential to be precise, convenient, and low-cost methods for fungal spore detection.

Optimized CT-TDLAS reconstruction performance evaluation of least squares with the polynomial-fitting method

Computed tomography-tunable diode laser absorption spectroscopy (CT-TDLAS) has been widely used in the diagnosis of the combustion flow field. Several optimized CT reconstruction algorithms such as iteration methods, transformation methods, and nonlinear least squares were applied. Considering the industrial application background, the performances of algebraic iteration reconstruction with the simultaneous algebra reconstruction technique (SART), Tikhonov regularization, and least squares with the polynomial fitting method were discussed in this study. For the mentioned algorithm, identical simulated reconstruction parameters that contained 32-path laser structures, assumed temperature distribution, and absorption databases were adopted to evaluate the reconstruction performance including accuracy, efficiency, and measurement of environment applicability. In this study, different CT reconstruction algorithms were also used to calculate the temperature distribution of the Bunsen burner flame. The different reconstruction results were compared with thermocouple detection data. With the theoretically simulated and experimental analysis, the least squares with the polynomial fitting technique has advantages in reconstruction accuracy, calculation efficiency, and laser path applicability for the measurement condition. It will be helpful in enhancing CT-TDLAS technique development.

Optimal Energy Storage Operation Chart and Output Distribution of Cascade Reservoirs Based on Operating Rules Derivation

An energy storage operation chart (ESOC) is one of the most popular methods for conventional cascade reservoir operation. However, the problem of distributing the total output obtained from the ESOC has not yet been reasonably solved. The discriminant coefficient method is a traditional method for guiding the output distribution by determining the order of reservoir supply or storage; however, it cannot quantify the water used in operation. Thus, this study develops a new output distribution model using a polynomial fitting method and an artificial neural network to express the functional relationship derived from the deterministic optimization results of long-term runoff series to maximize power generation. Cascade reservoirs of the lower reaches of the Jinsha River in China were selected for the case study. Compared to the discriminant coefficient method, the proposed method can rationally distribute the total output, thus avoiding the problem of concentrated deserting water in downstream reservoirs that occurs in the discriminant coefficient method. In general, this study proposes an effective alternative method to guide cascade reservoir operation.

Shape from focus using gradient of focus measure curve

Finding the best focused position is the key to shape from focus (SFF). Focus measure (FM) operators, sampling step, especially various noises usually cause unstable focused position searching and reduce the accuracy of SFF. Traditional methods usually use specific functions like Gaussian function and polynomial function to fit the focus measure curve and take the position of the peak of the fitting curve as the best focused position. However, due to the complexity of the imaging process and the noise, a fixed function is difficult to describe the focus measure curve. In this paper, a robust SFF method is proposed. In the process of finding the best focused position, the signal-to-noise ratio (SNR) of the values near the peak of the focus measure curve is relatively low, which usually leads to incorrect result. However, the rising and falling parts of the focus measure curve are more robust than the low SNR region, so we calculate the gradient of the focus measure curve with an adaptive derivative step. With the derivative step, we can reduce the influence of the SNR region. Then the zero point of the gradient curve and the derivative step are used to find the best focused position. Without any additional pre-work or constraints, our method can achieve high accuracy and strong robustness simultaneously. The effectiveness of the proposed method is evaluated by the simulated objects and real objects with different shapes. The 3D shape recovery results show that the proposed method is a superior alternative to enhance the focus volume in SFF. The RMSE of simulated objects is reduced by more than 25% when the proposed method is applied. For real objects, the RMSE of our method is 36%, 53% lower, compared with the Gaussian interpolation method and the polynomial fitting method, respectively.

Ballistic Object Trajectory and Impact Point Estimation in the Reentry Phase From a Moving Passive Sensor

This article considers the problem of estimating the trajectory of a ballistic target in the reentry phase using 2-D measurements (azimuth and elevation angles) from a moving passive sensor. Previous works investigated the estimation problem of an object in the thrusting and initial ballistic phase from a single fixed passive sensor. This article shows that the 3-D trajectory in the reentry phase can be obtained by estimating the target’s state at the end of the observation interval. The 7-d motion parameter vector (velocity azimuth angle, velocity elevation angle, drag coefficient, target speed, and 3-D position) is estimated by the maximum likelihood (ML) estimator with numerical search. Then we can predict the future position at an arbitrary time and the impact point of the target. The observability of the system for a sensor on a fast aircraft moving with constant velocity or maneuvering is verified via the invertibility of the Fisher information matrix. This is a major extension of the applicability of the recent observability proof for a stationary passive sensor observing a target in a gravitational field. The Cramer–Rao lower bound for the estimated parameters is evaluated and it shows that the estimates are statistically efficient. The angle estimation performance for the ML estimator is also compared with that of the polynomial fitting method. Simulation results illustrate the effectiveness of the proposed method.

Application of Orthogonal Polynomial Fitting Method to Extract Gravity Wave Signals From AIRS Data Related to Typhoon Deep Convection

AbstractGravity waves can influence weather and climate patterns on various temporal and spatial scales in the atmosphere. Despite their recognized importance, there are clearly a lack of sufficient and accurate observations from currently available satellite observing systems to satisfy the requirements of many satellite users. Common method to detect gravity waves is to measure brightness temperature (BT) anomalies, which rely on an initial efficient background removal method. Before gravity waves can be extracted from Atmospheric Infrared Sounder raw radiances, Hoffmann and Alexander (2010, http://doi.org/10.1029/2010jd014401) used a fourth‐order polynomial fitting (4PF) method to remove the background variations. In this study, we propose a new strategy, an optimal orthogonal polynomial fitting (OPF) method using Chebyshev Polynomials as basis functions, to remove the background variations and estimate BT perturbations. By extending the classic 4PF method to the fifth‐order polynomial fitting (5PF) method and combining the Cressman interpolation method, some experiments are designed to validate the feasibility and superiority of the OPF method. The results show that OPF is the optimal method to remove the limb‐brightening effect in the extraction of gravity wave signals generated by typhoons. In addition, what we noticed is that an appropriate fitting orders have to be selected to get more accurate BT anomalies signals in the experiments to extract gravity wave signals.