Polynomial Fitting Method Research Articles

Energy consumption and emission mitigation prediction based on data center traffic and PUE for global data centers

With the rapid development of technologies such as big data and cloud computing, data communication and data computing in the form of exponential growth have led to a large amount of energy consumption in data centers. Globally, data centers will become the world’s largest users of energy consumption, with the ratio rising from 3% in 2017 to 4.5% in 2025. Due to its unique climate and energy-saving advantages, the high-latitude area in the Pan-Arctic region has gradually become a hotspot for data center site selection in recent years. In order to predict and analyze the future energy consumption and carbon emissions of global data centers, this paper presents a new method based on global data center traffic and power usage effectiveness (PUE) for energy consumption prediction. Firstly, global data center traffic growth is predicted based on the Cisco’s research. Secondly, the dynamic global average PUE and the high latitude PUE based on Romonet simulation model are obtained, and then global data center energy consumption with two different scenarios, the decentralized scenario and the centralized scenario, is analyzed quantitatively via the polynomial fitting method. The simulation results show that, in 2030, the global data center energy consumption and carbon emissions are reduced by about 301 billion kWh and 720 million tons CO2 in the centralized scenario compared with that of the decentralized scenario, which confirms that the establishment of data centers in the Pan-Arctic region in the future can effectively relief the climate change and energy problems. This study provides support for global energy consumption prediction, and guidance for the layout of future global data centers from the perspective of energy consumption. Moreover, it provides support of the feasibility of the integration of energy and information networks under the Global Energy Interconnection conception.

Half-life determination of inorganic-organic hybrid nanomaterials in mice using laser-induced breakdown spectroscopy

Inorganic or inorganic-organic hybrid nanomaterials have great potential for applications in the biomedical fields. Biological half-life is an essential pharmacokinetic parameter for these materials to function in vivo. Compared to inductively coupled plasma mass spectrometry (ICP-MS), which is the gold standard, laser-induced breakdown spectroscopy (LIBS) is a faster and more efficient elemental detection method. We investigated an efficient way to quantify the metabolic rate using LIBS. Nanoparticle platforms, such as manganese dioxide-bovine serum albumin (MnO2-BSA) or boehmite-bovine serum albumin (AlO(OH)-BSA) were injected into mice through intravenous administration for LIBS spectrum acquisition. First, the spectral background was corrected using the polynomial fitting method; The spectral interference was eliminated by Lorentz fitting for each LIBS spectrum simultaneously. The support vector regression (SVR) was then used for LIBS quantitative analyses. Finally, the LIBS results were compared with the ICP-MS ones. The half-lives of MnO2-BSA calculated by LIBS and ICP-MS were 2.49 and 2.42 h, respectively. For AlO(OH)-BSA, the half-lives detected by LIBS and ICP-MS were 3.46 and 3.57 h, respectively. The relative error of LIBS is within 5% compared to ICP-MS. The results demonstrate that LIBS is a valuable tool for quantifying the metabolic rates with a high degree of accuracy.

Rapid online analysis of trace elements in steel using a mobile fiber-optic laser-induced breakdown spectroscopy system

A mobile fiber-optic laser-induced breakdown spectrometer (FO-LIBS) prototype was developed to rapidly detect a large quantity of steel material online and quantitatively analyze the trace elements in a large-diameter steel tube. Twenty-four standard samples and a polynomial fitting method were used to establish calibration curve models. The R2 factors of the calibration curves were all above 0.99, except for Cu, indicating the elements’ strong self-absorption effect. Five special steel materials were rapidly detected in the steel mill. The average absolute errors of Mn, Cr, Ni, V, Cu, and Mo in the special steel materials were 0.039, 0.440, 0.033, 0.057, 0.003, and 0.07 wt%, respectively, and their average relative errors fluctuated from 2.9% to 15.7%. The results demonstrated that the performance of this mobile FO-LIBS prototype can be compared with that of most conventional LIBS systems, but the more robust and flexible characteristics of the FO-LIBS prototype provide a feasible approach for promoting LIBS from the laboratory to the industry.

Taylor Polynomial Model of the Geomagnetic Field in an Underground Gas Storage Area

The study of normal geomagnetic background fields is the premise and basis for obtaining local geomagnetic anomalies caused by changes in underground pressure during gas injection and extraction in an underground gas storage (UGS) area. Measurements of the total magnetic field in an array consisting of sixty-three stations were acquired at a UGS and its surrounding areas. We completed field measurements at the stations using proton precession magnetometers (PPMs) with a sensitivity of 0.15 nT @ 1 Hz in April 2017 and March 2018. The geomagnetic background field model of the UGS area is calculated using the Taylor polynomial fitting method based on the data of all measured stations. A fourth-order Taylor polynomial model is appropriate for the UGS area according to a comprehensive comparative analysis of the mean square error and boundary distortion effect. The geomagnetic field distribution in the core area of the UGS can be better described by enlarging the network of repeat stations. The results provide a reference model for extracting the variations in the local magnetic field (LMF) caused by the underground pressure variations in the UGS area.

Robust Algorithms for Digital Image Correlation in the Presence of Displacement Discontinuities

Digital Image Correlation (DIC) is a well-known non-contact experimental technique. Its most common implementation is the subset-based approach, which performs a local least-squares fitting of a simple displacement model — usually an affine transform — to identify the displacement components at the center of the small area under investigation (the subset).Because of the statistical approach, DIC is usually able to provide reliable results even when theoretical prerequisites are not fully satisfied or in the presence of noise. However, the least-squares algorithm is not robust when the data set contains multiple statistical distributions. Indeed, the algorithm does not discriminate between them and process all the input data; thus, the resulting solution is usually unsatisfactory. A typical example implying the described context is the presence of cracks or shear bands inside the subset: as different sections of the inspected area move in different directions, the algorithm is unable to select a solution and the correlation between the reference and the test image is usually poor.This work proposes using RANSAC, a well-known robust algorithm, to select the largest domain of the subset. Because a similar problem has to be faced when computing strain components by the polynomial-fitting method, a simple modification of the main algorithm is suggested to handle also this problem.

Modeling and correction of image pixel hysteresis in atomic force microscopy

In an atomic force microscope (AFM) system, the measurement accuracy in the scan images is determined by the displacement accuracy of piezo scanner. The hysteresis model of piezo scanner displacement is complex and difficult to correct, which is the main reason why the output displacement of the piezo scanner does not have high precision. In this study, an image pixel hysteresis model of the piezo scanner displacement in the AFM system was established. An AFM was used to scan a two-dimensional (2D) grating in the 0 ° and 90 ° directions and a polynomial fitting method was employed to obtain the image pixel hysteresis model parameters of the piezo scanner displacement in the X-direction and Y-direction. The image pixel hysteresis model was applied to correct the AFM scan image of regular octagons. The results showed that the relative measurement error in the X-direction was decreased from 12.47% to 0.52% after the correction and that in the Y-direction decreased from 28.57% to 0.35%. The image pixel hysteresis model can be applied in the post-processing software of a commercial AFM system. The model solves the hysteresis problem of the AFM system and improves the measuring accuracy of AFM in 2 degrees of freedom (2 DOF).

Bisquare robust polynomial fitting method for dimple distortion minimization in surface quality analysis

In this paper, the bisquare robust polynomial fitting (BSRPF) method for surface texture features assessment was proposed. Plateau‐honed cylinder liner bronze surfaces with additionally burnished microcavities (defined as dimple, holes, and/or cavities) were taken into consideration. Analyzed details were measured with stylus (Talyscan 150) or white light interferometer (Talysurf CCI Lite) methods. It was assumed that application of commonly used (in surface contact and noncontact measurement technology) polynomial fitting procedures did not allow to extract required features; distortion of microreservoir dimples for oil consumption assessment was falsely estimated when valleys were near edge or on the edge located. Application of bisquare robust polynomial fitting method caused a minimization of microflattens of dimples irrespective of valley distribution; the biggest degree of polynomial fitting method applied, the minimal distortions of oil reservoirs were noticed. The valley size (depth and width) and valley‐to‐valley distance were also taken into account.

Cut-Edge Detection Method for Rice Harvesting Based on Machine Vision

A cut-edge detection method based on machine vision was developed for obtaining the navigation path of a combine harvester. First, the Cr component in the YCbCr color model was selected as the grayscale feature factor. Then, by detecting the end of the crop row, judging the target demarcation and getting the feature points, the region of interest (ROI) was automatically gained. Subsequently, the vertical projection was applied to reduce the noise. All the points in the ROI were calculated, and a dividing point was found in each row. The hierarchical clustering method was used to extract the outliers. At last, the polynomial fitting method was used to acquire the straight or curved cut-edge. The results gained from the samples showed that the average error for locating the cut-edge was 2.84 cm. The method was capable of providing support for the automatic navigation of a combine harvester.

Multi-class object detection using faster R-CNN and estimation of shaking locations for automated shake-and-catch apple harvesting

In order to address the challenge of labor shortages, and to reduce costs of apple harvesting, a targeted shake-and-catch technique is being developed at Washington State University for fresh market apple harvesting. This technique is showing promising results for some varieties of apples trained to a formal, fruiting wall tree architecture. However, the operators are still required to manually engage the shaker on target branches. To further improve the shake-and-catch apple harvesting system, a multi-class object detection algorithm was developed in this study for automatically detecting apples, branches and trunks in the natural environment using a Faster R-CNN (Regions-Convolutional Neural Network) model. This study deployed transfer learning and fine-tuning for the pre-trained networks (Alexnet, VGG16 and VGG19) and activated the feature of different layers to realize the detection of these objects. The Precision and Recall (PR) curve, F1-score and mean Average Precision (mAP) were used to evaluate the performance of Faster R-CNN in detecting different object classes. VGG19 achieved the highest mAP of 82.4%, which was 10.8% higher than Alexnet and 0.4% higher than VGG16 respectively. The computational time consumed by the entire algorithm was also assessed in this study; Faster R-CNN completed the detection of one image, on average, in 0.45 s. Based on the multi-class object detection results, a polynomial fitting method was used to predict the skeleton equation of branches and trunks. The average Goodness of Fit (R2), Root Mean Squared Error (RMSE) and correlation coefficient (r) between the predicted and reference skeleton were calculated to represent the accuracy of skeleton fitting. VGG16 and VGG19 both achieved higher accuracy than Alexnet for the skeleton fitting of branches and trunks. An algorithm was then developed to estimate shaking locations on the branches using the results of previous steps. Compared with the human experts’ input, a total of 72.7% of shaking locations estimated by the algorithm were considered appropriate. This study provided a foundation and possibility for developing a fully automated shake-and-catch apple harvesting system.

A novel high precise laser 3D profile scanning method with flexible calibration

To improve the accuracy of laser-contour profile devices, we propose a 3D laser scanning system with high accuracy that includes camera and laser plane calibration, and laser-stripe center extraction. First, a calibration device was designed and manufactured, from which the fiducial points can be easily and accurately detected to calibrate the laser plane. Then through the perspective invariance and the projective invariant cross-ratio properties, a flexible and accurate calibration algorithm is presented. A polynomial fitting method is employed to overcome the discontinuity and thickness of the laser stripe center. Finally, a cubic spline interpolation is utilized to restore the continuous gray value of the transitional regions of the light stripe. Experimental results with different test pieces demonstrate that the minimum geometric accuracy is 18µm and the repeatability is less than ± 3µm, which indicates that the proposed method is feasible to be used in industrial high precision measurement.

Dating of an alpine ice core from the interior of the Tibetan Plateau

Accurate archive-based paleoclimate reconstruction requires precise dating. However, the dating of mid- and low-latitude alpine ice cores is in challenge, in particular for the lower parts of ice cores. Here, we present a new dating work for a 109 m ice core collected to bedrock from the Qiangtang No. 1 glacier, central Tibetan Plateau. Annual layer counting based on seasonal indicators, in combination with absolute dating of radioactivity peaks, indicates that the upper part (0–79 m) captures a period of 678 years from 1334–2011 AD, with an uncertainty of ±20 years at 79 m. In the lower part (79–109 m), we dated by visible annual layer thickness-depth relationships and found the lower ice core captures 665 years of deposition and can be dated back to 669 ± 66 AD at 109 m. This new method reduces the ambiguity of utilizing glacier flow models that have been widely used in previous study. On the presence of observable optical annual layers, the polynomial fitting method based on annual layer thickness-depth relationships is a superior method to obtain reliable chronology in the lower parts. Furthermore, this method has the potential to improve the dating of other alpine ice cores with similar settings.

Ultimate Limit State Function and Its Fitting Method of Damaged Ship under Combined Loads

The ultimate limit state function is one of the premises for the assessment of structure strength and the safety of ships under severe conditions. In order to study the residual strength of damaged ships under the combined load of vertical and horizontal bending moments acting on the hull girder, the ultimate limit state function of a damaged ship under combined load, and its fitting methods are investigated in this paper. An improved Smith Method is adopted to calculate the residual load carrying capacity of damage ships, where the rotation and translation of the neutral axis of the damaged cross-section are obtained using a particle swarm optimisation method. Because the distribution curve of the residual load carrying capacity of a damaged ship under combined load is asymmetric, the application of traditional explicit polynomial fitting methods results in poor accuracy. In this study, a piecewise weighted least square fitting method is adopted so as to guarantee the continuity in the transitions, and a method is proposed for fitting the ultimate limit state function of a damaged ship under combined load. Calculations of the residual strength show that the improved Smith Method is more accurate than the original Smith Method for the accurate position of the neutral axis. The error analysis of the fitting methods shows that the ultimate limit state function that is fitted using a piecewise weight least square method is more accurate.

Demagnetization Fault Detection for Double-Sided Permanent Magnet Linear Motor Based on Three-Line Magnetic Signal Signature Analysis

This article investigates a novel demagnetization fault detection method for double-sided permanent magnet synchronous linear motors (DS-PMSLM) that are applied in laser cutting machines. First, a finite-element analysis model of DS-PMSLM is built to preset different demagnetization faults of the permanent magnets (PMs). Second, magnetic intensity distribution signals in air gap region are selected as fault signal for the first time to detect demagnetization faults in DS-PMSLM. Three-line method coupled with self-designed connection structure is originally proposed to obtain and analyze three-line magnetic signals. Simulation comparison with back electromotive force signal validates that three-line magnetic signals are more effective to solve the problem for this double-sided structure PMSLM. Then, continuous wavelet transform (CWT) is innovatively introduced to conduct peak feature extraction for magnetic signals. Comparison experiments between CWT, direct locating method, and polynomial fitting method certify the superiority of CWT. By peak feature analysis, the positions, sides, and severity degrees of PMs' demagnetization faults can be detected accurately. Finally, a prototype is manufactured, and a Gauss meter experimental platform is established to verify the validity and advantages of this method.

Fast Piecewise Polynomial Fitting of Time-Series Data for Streaming Computing

Streaming computing attracts intense attention because of the demand for massive data analyzing in real-time. Due to unbounded and continuous input, the volume of streaming data is so high that all the data cannot be permanently stored. Piecewise polynomial fitting is a popular data compression method that approximately represents the raw data stream with multiple polynomials. The polynomial coefficients corresponding to the best-fitting curve can be calculated by the method of least squares, which minimizes the sum of the squared residuals between observed and fitted values. However, built on several matrix calculations, the method of least squares always leads to high time complexity and is difficult to be applied to streaming computing. This paper puts forward a fast piecewise polynomial fitting for time-series data in streaming computing. The input data stream is dynamically segmented according to a given residual bound. Meanwhile, the data points in each segment are fitted using an improved polynomial fitting method, which has less time overhead than general polynomial fitting by reusing the intermediate calculation results. Experimental results on four time-series datasets show that our algorithm can achieve the highest speedup to the general piecewise polynomial fitting of 2.82x for periodically sampled time-series data and 1.85x for aperiodically sampled time-series data, without affecting the compression ratio and fitting accuracy. Moreover, the event-time latency comparison in a streaming environment indicates that the improved method can endure higher throughput than general piecewise polynomial fitting with the same latency.

An Enhanced INS/GNSS Tightly Coupled Navigation System Using Time-Differenced Carrier Phase Measurement

To enhance the long-term localization accuracy of inertial measurement unit/time-differenced carrier phase (IMU/TDCP) tightly coupled navigation system (TCS), efforts from three aspects have been made in this article. First, we make a comprehensive analysis, which has not been done before, on the errors of TDCP measurement. Then, these errors are modeled and mostly compensated using the polynomial fitting method. Even so, the errors cannot be eliminated completely. Positioning performance will get worse slowly over time due to the error remained in the error-compensated TDCP (CTDCP). Therefore, the final effort has been done in introducing a novel measurement, ionosphere-free wide-lane carrier phase (IFWLCP), to control the deterioration instead of the conventional coarse pseudorange (PR). The CTDCP and IFWLCP are both integrated with IMU measurements using the dual-rate Kalman filter, and the proposed methodology’s effectiveness on improving the positioning accuracy is validated by a road experiment.

Modeling of amplitude-dependent damping characteristics of fiber reinforced composite thin plate

A damping model of fiber reinforced composite thin plate with consideration of amplitude-dependent property is established using the Jones–Nelson nonlinear theory in conjunction with the classical laminated plate theory, polynomial fitting method and strain energy method. In this model, the elastic moduli are expressed as the function of strain energy density and the loss factors in the longitudinal, transverse and shear directions are expressed as the functions of excitation amplitude. Moreover, three TC300 carbon/epoxy composite plates are taken as research objects to carry out a case study. One of them is used to determine the amplitude-dependent coefficients of loss factors in fiber reinforced composites by combining the least square method with polynomial fitting method, and the other two plates are used to verify the correctness of the theoretical model. The results of the developed model considering amplitude dependence and experimental test show a good consistency. It is discovered that the viscoelastic effect of epoxy resin materials will contribute to the increased degree of damping. So, if such plate structures exhibit more pronounced viscoelastic characteristics, there will be more significant in the nonlinear degree of amplitude-dependent damping phenomenon.

Investigation of high-precision algorithm for the spot position detection for four-quadrant detector

In this paper, we propose a new polynomial fitting algorithm to improve the spot position detection accuracy based on four-Quadrant Detector (4QD) when the circular spot with Gaussian energy is used as the incident light model. The traditional polynomial fitting method is difficult to ensure high spot position detection accuracy in a wide detection range. To solve this problem, we analyze and compare the characteristics of different algorithms for spot position detection, and consider the influence of the 4QD gap size in the model. Based on the initial solution of the geometric approximation method, we introduce the error compensation factor function, a new spot position detection model is designed. The results of simulation and experiment show that the new algorithm can greatly reduce the position detection error of 4QD for Gaussian spot. When the radius of incident spot is 0.5 mm and within the detection range of [-0.5 mm∼0.5 mm], the maximum error is 0.001353 mm and the root-mean-square error is 0.0004596 mm with the new five-order polynomial fitting algorithm which are reduced 56.7% and 69.7% than traditional nine-order polynomial fitting algorithm. Moreover, the computational complexity of the new algorithm is much less than traditional algorithm and the new algorithm also has good prospects in laser communication, high energy laser weapons or others.

DEVELOPMENT OF A COMPACT LOWER-LIMB EXOSKELETON FOR WALKING ASSISTANCE: A CASE STUDY

Lower-limb exoskeletons are an effective means to provide paraplegic and hemiplegic individuals with the ability to walk upright. A lot of studies about lower-limb exoskeletons have been developed to assist the impaired populations. However, the existing devices are still too technically complex and expensive for practicality. In this paper, a compact lower-limb exoskeleton for walking assistance is developed, in which a steel-cable actuator is specially designed. In order to accomplish the different tasks presented to gait generation, a control method with multiple stages is employed. In this approach, four basic states and seven intended motions are designed for the finite-state machine. In addition, the reference trajectories of these intended motions are presented and fitted by a modified first-order polynomial-fitting method. Preliminary motion tests of the exoskeleton with three healthy subjects are performed. The results verify the effectiveness of the system design and the gait-generation approach proposed in this paper. The overall exoskeleton system is compact and the corresponding operations are convenient and reliable.

Energy Efficient Control of Parallel Variable-Frequency Pumps in Magnetic Water-Cooling System

Abstract This paper presents an optimal control method for the prediction of parallel centrifugal variable frequency pump performance in any conditions to maximize the total efficiency of the pump system, thereby minimizing energy consumption. First, a theoretical model of parallel water pumping set was established, after which the shaft power model was setup specifically for the off-rating conditions. By combining the typical polynomial fitting method of the efficiency and the shaft power model we brought up, a new optimized control method was proposed. Using this method, the complex optimization task was solved with the optimal control of the operating number selection and speed ratios for parallel variable speed pumps based on the decision-making. The proposed method was subsequently applied to the pumping set of the water-cooling system in High Magnetic Field Facility. The practical testing results of the proposed method showed its superiority over both the primitive and the previous optimal methods, by considerably lowering the power consumption and accurately calculating the performance parameters in any conditions. The method has universality and simplicity for online implementation, which provides a reference for the control methods of parallel centrifugal pumps in variable flow systems with a differential pressure control strategy.

An Electro-Pneumatic Force Tracking System using Fuzzy Logic Based Volume Flow Control

In this paper, a fuzzy logic based volume flow control method is proposed to precisely control the force of a pneumatic actuator in an electro-pneumatic system including four on-off valves. The volume flow feature, which is the relationship between the duty cycle of the pulse width modulation (PWM) period, pressure difference, and volume flow of an on-off valve, is based on the experimental data measured by a high-precision volume flow meter. Through experimental data analysis, the maximum and minimum duty cycles are acquired. A new volume flow control method is introduced for the pneumatic system. In this method, the raw measured data are innovatively processed by a segmented, polynomial fitting method, and a newly designed procedure for calculating the duty cycle is adopted. This procedure makes it possible to combine the original data with fuzzy logic control (FLC). Additionally, the method allows us to accurately control the minimum and maximum opening pulse width of the valve. Several experiments are performed based on the experimental data, instead of the traditional theoretical models. Only 0.141 N (1.41%) overshoot and 0.03 N (0.03%) steady-state error are observed in the step response experiment, and 0.123 N average error is found while tracking the sine wave reference.