scholarly journals A Weighted Linear Least Squares Location Method of an Acoustic Emission Source without Measuring Wave Velocity

Sensors ◽  
2020 ◽  
Vol 20 (11) ◽  
pp. 3191 ◽  
Author(s):  
Zilong Zhou ◽  
Yichao Rui ◽  
Xin Cai ◽  
Ruishan Cheng ◽  
Xueming Du ◽  
...  
Keyword(s):  
Acoustic Emission ◽  
Least Squares ◽  
Wave Velocity ◽  
Linear Equations ◽  
Linear Least Squares ◽  
Governing Equations ◽  
Traditional Methods ◽  
Location Method ◽  
Reference Equation ◽  
The Mean

The location of an acoustic emission (AE) source is crucial for predicting and controlling potential hazards. In this paper, a novel weighted linear least squares location method for AE sources without measuring wave velocity is proposed. First, the governing equations of each sensor are established according to the sensor coordinates and arrival times. Second, a mean reference equation is established by taking the mean of the squared governing equations. Third, the system of linear equations can be obtained based on the mean reference equation, and their residuals are estimated to obtain their weights. Finally, the AE source coordinate is obtained by weighting the linear equations and inserting the parameter constraint. The AE location method is verified by a pencil lead break experiment, and the results show that the locating accuracy of the proposed method is significantly higher than that of traditional methods. Furthermore, the simulation test proves that the proposed method also has a better performance (location accuracy and stability) than the traditional methods under any given scale of arrival errors.

Boundary Extension Technique for HHT Based on Response Surface Method

2012 ◽  
Vol 256-259 ◽  
pp. 2854-2862
Author(s):  
Ling Bai ◽  
Jin Zhao Liu ◽  
Ai Min Xu ◽  
Xing Fang
Keyword(s):  
Least Squares ◽  
Response Surface ◽  
Response Surface Method ◽  
Linear Equations ◽  
Hessian Matrix ◽  
Extension Problem ◽  
Boundary Extension ◽  
Linear Least Squares ◽  
Least Squares Problem ◽  
Surface Method

HHT is widely used to analyze nonlinear and non-stationary signals. But how to extend boundaries of signals in decomposition processes is a key problem of HHT. A new technique based on response surface method (RSM), which establishes the recursive relations between sample points of signals, is presented to deal with this difficult problem. Besides, the boundary extension problem arising from HHT can be described by mathematical least squares problem but traditional gradient algorithms may diverge when the Hessian matrix of the object function of the least squares problem is non-positive. It has been proved that the generalized inverse of the linear equations (derived from the linear least squares problem) by singular value decomposition is the solution of original linear least squares problems. Thereby the divergence problem is also solved. Analysis results with respect to simulation signals and measured signals show that the method with new boundary extension technique performs successfully for HHT.

scholarly journals A Closed-Form Method of Acoustic Emission Source Location for Velocity-Free System Using Complete TDOA Measurements

Sensors ◽  
2020 ◽  
Vol 20 (12) ◽  
pp. 3553
Author(s):  
Zilong Zhou ◽  
Yichao Rui ◽  
Xin Cai ◽  
Riyan Lan ◽  
Ruishan Cheng
Keyword(s):  
Acoustic Emission ◽  
Closed Form ◽  
Linear Equations ◽  
Source Location ◽  
Acoustic Velocity ◽  
Simulation Test ◽  
Traditional Methods ◽  
Free System ◽  
Location Accuracy ◽  
Influence Of Noise

A closed-form method of acoustic emission (AE) source location for a velocity-free system using complete time difference of arrival (TDOA) measurements is proposed in this paper. First, this method established the governing equation of unknown acoustic velocity for each sensor; then, the governing equations of each of the three sensors were transformed into a linear equation, which can form a system of linear equations with the complete TDOA measurements. Third, the least squares solutions of the AE source coordinate and acoustic velocity were separately solved by an orthogonal projection operator. The proposed method was verified by the pencil-lead break experiment, and the results showed that the location accuracy and stability of the proposed method were better than those of traditional methods. Moreover, a simulation test was carried out to investigate the influence of noise scales on the location accuracy, and the results further prove that the proposed method holds higher noise immunity than the traditional methods.

The Estimation of Blood Platelet Survival

1972 ◽  
Vol 28 (03) ◽  
pp. 447-456 ◽  
Author(s):  
E. A Murphy ◽  
M. E Francis ◽  
J. F Mustard
Keyword(s):  
Standard Deviation ◽  
Least Squares ◽  
Experimental Error ◽  
Blood Platelet ◽  
Least Squares Estimation ◽  
Systematic Relationship ◽  
Platelet Survival ◽  
The Mean ◽  
Normally Distributed

SummaryThe characteristics of experimental error in measurement of platelet radioactivity have been explored by blind replicate determinations on specimens taken on several days on each of three Walker hounds.Analysis suggests that it is not unreasonable to suppose that error for each sample is normally distributed ; and while there is evidence that the variance is heterogeneous, no systematic relationship has been discovered between the mean and the standard deviation of the determinations on individual samples. Thus, since it would be impracticable for investigators to do replicate determinations as a routine, no improvement over simple unweighted least squares estimation on untransformed data suggests itself.

scholarly journals Prediction of shallow bit position based on vibration signal monitoring of bit broken rock

2021 ◽  
Vol 17 (1) ◽  
pp. 155014772199170
Author(s):  
Jinping Yu ◽  
Deyong Zou
Keyword(s):  
Acoustic Emission ◽  
Time Domain ◽  
Vibration Signal ◽  
Rock Breaking ◽  
Drill String ◽  
Mean Square ◽  
Drilling Force ◽  
Emission Signal ◽  
Force Signal ◽  
The Mean

The speed of drilling has a great relationship with the rock breaking efficiency of the bit. Based on the above background, the purpose of this article is to predict the position of shallow bit based on the vibration signal monitoring of bit broken rock. In this article, first, the mechanical research of drill string is carried out; the basic changes of the main mechanical parameters such as the axial force, torque, and bending moment of drill string are clarified; and the dynamic equilibrium equation theory of drill string system is analyzed. According to the similarity criterion, the corresponding relationship between drilling process parameters and laboratory test conditions is determined. Then, the position monitoring test system of the vibration bit is established. The acoustic emission signal and the drilling force signal of the different positions of the bit in the process of vibration rock breaking are collected synchronously by the acoustic emission sensor and the piezoelectric force sensor. Then, the denoised acoustic emission signal and drilling force signal are analyzed and processed. The mean value, variance, and mean square value of the signal are calculated in the time domain. The power spectrum of the signal is analyzed in the frequency domain. The signal is decomposed by wavelet in the time and frequency domains, and the wavelet energy coefficients of each frequency band are extracted. Through the wavelet energy coefficient calculated by the model, combined with the mean, variance, and mean square error of time-domain signal, the position of shallow buried bit can be analyzed and predicted. Finally, by fitting the results of indoor experiment and simulation experiment, it can be seen that the stress–strain curve of rock failure is basically the same, and the error is about 3.5%, which verifies the accuracy of the model.

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