Multi-probe linear fitting and time of arrival linear correction method to analyze blade vibration based on blade tip timing without once-per-revolution

Blade vibration monitoring can ensure the safe operation of aeroengine rotor blades.Among the methods of blade vibration monitoring,Blade Tip Timing(BTT)method has attracted more and more attention because of its advantages of non-contact measurement.However,it is difficult to install the Once-Per-Revolution(OPR)probe in the confined space of aeroengine,and the failure and instability of the OPR signal will reduce the reliability of the blade vibration analysis results,which directly affects the accuracy of the blade vibration parameters identification.The Multi-Probe linear fitting and Time of Arrival(ToA)Linear Correction method based on the BTT(MP-LC-BTT)without OPR is proposed to reduce the errors of single probe linear fitting method for blade vibration displacement analysis.The proposed method can also correct the calculation error of blade vibration displacement due to the nonlinear change of rotation speed,which can improve the analysis accuracy of the blade vibration displacement.A new blade vibration model conforming to the actual vibration characteristics is established,and the effectiveness of the proposed method is verified by numerical simulation.Finally,the reliability and accuracy of the MP-LC-BTT method have been verified by the experiments which include two high-speed blade test-benches and an industrial axial fan.This method can be used in the actual aero-engine monitoring instead of the BTT method with OPR.

Linear-fitting-based similarity coefficient map for tissue dissimilarity analysis in T2^＊-w magnetic resonance imaging

Similarity coefficient mapping（SCM） aims to improve the morphological evaluation of T＊2weighted magnetic resonance imaging（T＊2-w MRI）. However, how to interpret the generated SCM map is still pending. Moreover, is it probable to extract tissue dissimilarity messages based on the theory behind SCM？ The primary purpose of this paper is to address these two questions. First, the theory of SCM was interpreted from the perspective of linear fitting. Then, a term was embedded for tissue dissimilarity information. Finally, our method was validated with sixteen human brain image series from multiecho T＊2-w MRI. Generated maps were investigated from signal-to-noise ratio（SNR） and perceived visual quality, and then interpreted from intra- and inter-tissue intensity. Experimental results show that both perceptibility of anatomical structures and tissue contrast are improved. More importantly, tissue similarity or dissimilarity can be quantified and cross-validated from pixel intensity analysis. This method benefits image enhancement, tissue classification, malformation detection and morphological evaluation.

Estimation of mass transfer coefficient in ozone absorption by linear least square fitting and Simplex search methods

For physical ozone absorption without reaction,two parametric estimation methods,i.e.the common linear least square fitting and non-linear Simplex search methods,were applied,respectively,to determine the ozone mass transfer coefficient during absorption and both methods give almost the same mass transfer coefficient.While for chemical absorption with ozone decomposition reaction,the common linear least square fitting method is not applicable for the evaluation of ozone mass transfer coefficient due to the difficulty of model linearization for describing ozone concentration dissolved in water.The nonlinear Simplex method obtains the mass transfer coefficient by minimizing the sum of the differences between the simulated and experimental ozone concentration during the whole absorption process,without the limitation of linear relationship between the dissolved ozone concentration and absorption time during the initial stage of absorption.Comparison of the ozone concentration profiles between the simulation and experimental data demonstrates that Simplex method may determine ozone mass transfer coefficient during absorption in an accurate and high efficiency way with wide applicability.

The Parameters Fitting in High-strength Concrete Mix Proportion Experiment

Parameters that need to be fitted in High-Strength concrete mix proportion expe riment and two equation models that are referenced in the experiment are discuss ed. The reasoning and implement of the corresponding linear fitting algorithm ar e demonstrated.Parmeter fitting is realized by value estimate method of mathemat ical statistics.This paper combines mathematical statisitics,linear equations an d template thought together successfully and discussed an efficient parameter fi tting method based on strength equation model and water consumption equation mod el.

An Interesting Fitting Formula of Quark Masses

We show an interesting empirical formula of quark masses here, which is obtained by implementing the east squares fit. In this formula the measured QCD coupling is almost a ＂best fitting coupling＂.

A self-adaptive linear evolutionary algorithm for solving constrained optimization problems

In many real-world applications of evolutionary algorithms,the fitness of an individual requires a quantitative measure.This paper proposes a self-adaptive linear evolutionary algorithm （ALEA） in which we introduce a novel strategy for evaluating individual＇s relative strengths and weaknesses.Based on this strategy,searching space of constrained optimization problems with high dimensions for design variables is compressed into two-dimensional performance space in which it is possible to quickly identify ＇good＇ individuals of the performance for a multiobjective optimization application,regardless of original space complexity.This is considered as our main contribution.In addition,the proposed new evolutionary algorithm combines two basic operators with modification in reproduction phase,namely,crossover and mutation.Simulation results over a comprehensive set of benchmark functions show that the proposed strategy is feasible and effective,and provides good performance in terms of uniformity and diversity of solutions.

High temperature and high pressure rheological properties of high-density water-based drilling fluids for deep wells

To maintain tight control over rheological properties of high-density water-based drilling fluids, it is essential to understand the factors influencing the theology of water-based drilling fluids. This paper examines temperature effects on the rheological properties of two types of high-density water-based drilling fluids （fresh water-based and brine-based） under high temperature and high pressure （HTHP） with a Fann 50SL rheometer. On the basis of the water-based drilling fluid systems formulated in laboratory, this paper mainly describes the influences of different types and concentration of clay, the content of a colloid stabilizer named GHJ-1 and fluid density on the rheological parameters such as viscosity and shear stress. In addition, the effects of aging temperature and aging time of the drilling fluid on these parameters were also examined. Clay content and proportions for different densities of brine-based fluids were recommended to effectively regulate the rheological properties. Four theological models, the Bingham, power law, Casson and H-B models, were employed to fit the rheological parameters. It turns out that the H-B model was the best one to describe the rheological properties of the high-density drilling fluid under HTHP conditions and power law model produced the worst fit. In addition, a new mathematical model that describes the apparent viscosity as a function of temperature and pressure was established and has been applied on site.

Forward modeling and inversion of the relation model between the gas content of plume and its seismic attribute

The methane bubble plume attracts interest because it offers direct evidence of seafloor gas leakage and plays an indirect role in the exploration and identification of natural gas hydrate.In this study,based on established plume models and their migration sections,three amplitude-class attributes were extracted from three formations for the migration sections of five plumes,and the correlation between the gas content and seismic attribute was obtained.As the gas content increases,the amplitude attribute correspondingly increases,and the linear correlation is relatively good.Moreover,correlation coefficients between gas content and amplitude attributes are close to 1.0.By using linear fitting,the relation model between the gas content of the plume and the seismic attribute was obtained.The relation model was subsequently used to invert the gas content from a real databearing plume.Comparison of the gas content section of the plume with the attribute section and real seismic section reveals common distribution characteristics,namely,the color of the section in the lower right corner is dark.If the amplitude value is large in the seismic section of the real plume,the amplitude attribute value is also large in the corresponding attribute section,and the inverted value of the gas content is also large(because gas content and amplitude are linearly correlated),which indicates that the plume bubbles of the section in the lower right corner is intensively distributed.Finally,the obtained gas content section of the plume can reflect the distribution of the plume bubble content more simply and intuitively,from which the distribution law of seafloor bubbles can be deduced,and this lays a foundation for the further estimation of the gas content of the plume and hydrate reserves.

Methods of de-noising the low frequency electromagnetic data

The quality of the low frequency electromagnetic data is affected by the spike and the trend noises.Failure in removal of the spikes and the trends reduces the credibility of data explanation.Based on the analyses of the causes and characteristics of these noises,this paper presents the results of a preset statistics stacking method(PSSM)and a piecewise linear fitting method(PLFM)in de-noising the spikes and trends,respectively.The magnitudes of the spikes are either higher or lower than the normal values,which leads to distortion of the useful signal.Comparisons have been performed in removing of the spikes among the average,the statistics and the PSSM methods,and the results indicate that only the PSSM can remove the spikes successfully.On the other hand,the spectrums of the linear and nonlinear trends mainly lie in the low frequency band and can change the calculated resistivity significantly.No influence of the trends is observed when the frequency is higher than a certain threshold value.The PLSM can remove effectively both the linear and nonlinear trends with errors around 1% in the power spectrum.The proposed methods present an effective way for de-noising the spike and the trend noises in the low frequency electromagnetic data,and establish a research basis for de-noising the low frequency noises.

A Simple Approach to Compute Interatomic Force Constant for Mono and Diatomic Semiconductors

In this paper, a mathematical relation was found between interatomic Hooke’s force constant and both the bulk modulus and interatomic distance in solid crystals, considering that the forces which have effect on an atom are only those resulted from the neighboring atoms, and the forces are subject to Hooke’s law as the deflections of atoms from their equilibrium positions are very small. This work has been applied on some solid semiconducting crystals of diatomic primitive cell, including crystals of mono-atomic primitive cell automatically, by using linear statistical fitting with computer programming and, then, using mathematical analysis, proceeding from the vibrational dispersion relation of solid linear lattice, these two methods have been used in the process in order to support each other and for the result to be satisfying and reasonable. This is a contribution to the process of using computer programming in physics to facilitate mathematical analyses and obtain the required relations and functions by designing and developing appropriate computer programs in line with the macro and micro natures of materials. The importance of this is in enhancing our understanding of the interatomic actions in cells and of the crystal structure of materials in general and semiconductors in particular, as it is a step of the initial steps to facilitate the process of calculating energies and extracting mathematical relations between correlation energy and temperature as well as between sub-fusion and fusion energies with temperature.

About the Optimized Design of the Parking Space on the Campus of a College

In recent years, with the large increase in the number of motor vehicles in colleges and universities and the lag in campus planning, the relative shortage of parking spaces on campus has become increasingly serious. Taking Baoding College as an example, this article analyzes the current situation of static traffic on campus and finds out the problem of parking on campus through questionnaire surveys and field surveys. Analyze the growth trend of the number of motor vehicles based on the data, use the GM (1, 1) model and the linear fitting model to predict the number of motor vehicles in the future, and determine the size and layout of the parking lot based on the campus size, functional zoning, and road layout. The big campus-based parking system planning method based on big data can effectively solve the problems of small sample data, low accuracy, and poor timeliness of traditional methods, which improves the practicability and scientificity of planning results.

Characterization of plasma current quench during disruption in EAST tokamak

A preliminary analysis of plasma current quenching is presented in this paper based on the disruption database.It demonstrates that 26.8%of discharges have been disrupted in the last 2012 campaign,in addition,the plasma disruptive rate grows with the increase of plasma current.The best-fit linear and instantaneous plasma current quench rate is extracted from the recent EAST disruptions,showing that an 80%-30%interval of the maximum plasma current is well fit for the EAST device.The lowest area-normalized current quench time is 3.33 ms/m;with the estimated plasma electron temperature being 7.3 eV;9.5 eV.In the disruption case the maximum eddy current goes up to 400 kA,and a fraction of currents are respectively driven on the upper and lower outer plate with nearly 100 MPa-200 MPa stress in the leg.

Instantaneous frequency estimation of multi-component Chirp signals in noisy environments

A classical time-varying signal, the multi-component Chirp signal has been widely used and the ability to estimate its instantaneous frequency （IF） is very useful. But in noisy environments, it is hard to estimate the 1F of a multi-component Chirp signal accurately. Wigner distribution maxima （WDM） are usually utilized for this estimation. But in practice, estimation bias increases when some points deviate from the true IF in high noise environments. This paper presents a new method of multi-component Chirp signal 1F estimation named Wigner Viterbi fit （WVF）, based on Wigner-Ville distribution （WVD） and the Viterbi algorithm. First, we transform the WVD of the Chirp signal into digital image, and apply the Viterbi algorithm to separate the components and estimate their IF. At last, we establish a linear model to fit the estimation results. Theoretical analysis and simulation results prove that this new method has high precision and better performance than WDM in high noise environments, and better suppression of interference and the edge effect. Compared with WDM, WVF can reduce the mean square error （MSE） by 50% when the signal to noise ration （SNR） is in the range of-15dB to -11dB. WVF is an effective and promising 1F estimation method.

An Improved Power Flow Method to Cope with Non-smooth Constraints of Integrated Energy Systems

Integrated energy system applications can significantly improve energy efficiency.In this paper,we establish an integrated energy system containing heat,electricity and gas.The existing power flow(PF)calculation method applied to integrated energy systems(IESs)does not consider non-smooth constraints,such as the piecewise pipeline friction coefficient and generator buses reactive power limits,etc.Mixed integer nonlinear programming(MINLP)is conventionally used to deal with piecewise pipeline friction coefficients in gas network parts,but it is both complex and inefficient.Hence,we develop a piecewise linear function-based fitting method that can reduce the number of integer variables and enhanced the computational efficiency.In the electric network part,if the reactive power of the PV bus violates limits,it will be converted into a PQ bus,which is a non-differentiable and non-smooth constraint.Mixed complementarity problems are conventionally introduced to represent the PV-PQ buses type switching relationship and are addressed by the Newton-Raphson(NR)method.However,the above method is sensitive to the initial point.Here,we introduce a robust projected Levenberg-Marquardt(PLM)algorithm to cope with this issue.We demonstrate the advantages of our method and validate it both in a small-scale system and largescale network test cases.

Analysis of Depth-Diameter Relationship of Craters around Oceanus Procellarum Area

Studying the depth-diameter relationship of impact craters around the Oceanus Procellarum area together with values for simple crater,complex crater and basin confirms two inflections in the depth/diameter （d/D） curve.We classify impact craters to three types,which are simple crater,complex crater and basin.Using the most ＇pristine＇ or deepest craters in the data,three kinds of depth-diameter relationships are determined：the linear fit for simple crater is d=0.126D＋0.490 2;the best empirical power fit for complex crater is d=0.327 3D0.625 2;the best empirical power fit for basin is d=0.300 4D0.463 3,where d is the depth of the crater and D is the diameter of the crater,both in kilometers.The depth-diameter relationship for basin is characterized by a lower slope than that for complex craters,demonstrating that this morphologic transition corresponds to a further decrease in the depth of an impact structure relative to its diameter with increasing size.These relationships can then be used to estimate the theoretical depth of any impact radius,and therefore can be used to estimate the pristine shape of the crater around the Oceanus Procellarum area.The study of Oceanus Procellarum will help humankind to learn more about the origin and evolution of the moon.

Influence of accelerated curing on the compressive strength of polymer-modified concrete

In recent building practice,rapid construction is one of the principal requisites.Furthermore,in designing concrete structures,compressive strength is the most significant of all parameters.While 3-d and 7-d compressive strength reflects the strengths at early phases,the ultimate strength is paramount.An effort has been made in this study to develop mathematical models for predicting compressive strength of concrete incorporating ethylene vinyl acetate(EVA)at the later phases.Kolmogorov-Smirnov(KS)goodness-of-fit test was used to examine distribution of the data.The compressive strength of EVA-modified concrete was studied by incorporating various concentrations of EVA as an admixture and by testing at ages of 28,56,90,120,210,and 365 d.An accelerated compressive strength at 3.5 hours was considered as a reference strength on the basis of which all the specified strengths were predicted by means of linear regression fit.Based on the results of KS goodness-of-fit test,it was concluded that KS test statistics value(D)in each case was lower than the critical value 0.521 for a significance level of 0.05,which demonstrated that the data was normally distributed.Based on the results of compressive strength test,it was concluded that the strength of EVA-modified specimens increased at all ages and the optimum dosage of EVA was achieved at 16%concentration.Furthermore,it was concluded that predicted compressive strength values lies within a 6%difference from the actual strength values for all the mixes,which indicates the practicability of the regression equations.This research work may help in understanding the role of EVA as a viable material in polymer-based cement composites.

Design and characteristics of a non-contact rotational sensor based on a fiber Bragg grating

We propose a novel non-contact rotational sensor based on a fiber Bragg grating(FBG) packaged in a core of a magnetic head, which converts the introduced strain from the circular magnetic railings ruler into the rotational information. A mathematical model is built for processing the data obtained by an interrogator, and the accuracy and resolution of the measurements are analyzed by altering the radius and period of the circular magnetic railings ruler, as well as the dimension of the sensor. The experimental results show that it is in good accordance with the theoretical analysis on rotational angle, and the fitting results indicate that the results obtained from the rotational sensor match very well with the real rotational velocity with a linearity of 0.998 and a standard error of about 0.01.