CN113533509B

CN113533509B - Method and device for identifying fatigue microcrack position of steel rail

Info

Publication number: CN113533509B
Application number: CN202110726224.0A
Authority: CN
Inventors: 蔡国强; 梁柯欣
Original assignee: Beijing Jiaotong University
Current assignee: Beijing Jiaotong University
Priority date: 2021-06-29
Filing date: 2021-06-29
Publication date: 2022-04-15
Anticipated expiration: 2041-06-29
Also published as: CN113533509A

Abstract

The embodiment of the invention discloses a method and a device for identifying the position of a rail fatigue microcrack, which comprises the steps of firstly, applying a high-frequency lamb wave signal and a mixed signal of the high-frequency lamb wave signal and a low-frequency vibration signal to a rail to be detected, and receiving the two signals by using four sensors arranged on the rail to be detected; secondly, performing mode decomposition, obtaining a time frequency spectrum, subtracting the time frequency spectrum and filtering a low-frequency vibration signal on the two signals received by each sensor to obtain the time frequency spectrum of the damage identification signal corresponding to the four sensors; and thirdly, after the steel rail to be detected has fatigue microcracks, respectively acquiring the time when the damage modulation signal reaches each sensor, and calculating the sound path of the damage modulation signal transmitted to each sensor through the corresponding time. Respectively taking the center point of each sensor as the center of a circle and the corresponding sound path as the radius to make a circle, and calculating the intersection point coordinates of the four circles; and finally, determining the position coordinates of the fatigue microcracks on the steel rail to be detected by using the coordinates of the intersection points.

Description

Method and device for identifying fatigue microcrack position of steel rail

Technical Field

The invention relates to the technical field of railway industry, in particular to a method and a device for identifying a fatigue microcrack position of a steel rail.

Background

At present, the economy of China gradually turns to a high-quality development stage from a high-speed growth stage, and the traffic transportation level is an important foundation for supporting the development of the economy, wherein a railway which is one of main traffic transportation modes is spotlighted by the national public.

Opportunities coexist with challenges, and the blossoming development situation puts more stringent requirements on railway traffic safety. The railway rails are key equipment for directly bearing vehicle loads, and under the background that the current running speed is continuously improved, the vehicle transportation volume is continuously increased, the operation time is continuously increased and long-term passenger and goods of the railway run together, most of the railway rails are in an out-of-service fatigue state, various diseases are increasingly displayed, more forms of contact collision are generated between wheel rails, and the actual working condition becomes abnormal and complex. The rail damage is mainly caused by three reasons of abrasion, fatigue and process (including production process and maintenance process). The fatigue can accelerate the damage expansion process caused by process defects while possibly causing the steel rail to generate fatigue cracks and even causing the fatigue fracture of the steel rail, and the service life of the steel rail is greatly influenced.

In most cases, fatigue cracks are in the form of micro-cracks or closed cracks that are present in the first 80% or so of the time of fatigue development and are hardly discernible purely by human eye observation. Among them, the fatigue cracks having a width of less than 0.5mm are generally called fatigue microcracks by researchers.

In the actual operation process, the steel rail is always subjected to large-amplitude transverse vibration. Once the rail fatigue micro-cracks are formed, the huge transverse acting force between the wheel rails can promote the wheel rails to expand along the transverse direction, and the possibility of rail breakage is greatly increased. Therefore, the micro-cracks of the steel rail, which are initiated in the early fatigue stage, are effectively detected and timely maintained, the steel rail is prevented from continuously expanding into macro-cracks, and the steel rail is prevented from entering the crack instability expansion stage. Therefore, the method has important significance for accurately positioning the fatigue microcracks of the steel rail, preventing major safety production accidents, ensuring safe and reliable service of the steel rail and maintaining the stable safe foundation of railway transportation.

Disclosure of Invention

The embodiment of the invention provides a method and a device for identifying the position of a fatigue microcrack of a steel rail, which are used for solving the problem that the fatigue microcrack on the steel rail is difficult to position in the prior art.

In order to solve the technical problem, the embodiment of the invention discloses the following technical scheme:

a method for identifying the position of a rail fatigue microcrack is characterized in that four sensors are arranged on a rail to be detected, and the four sensors form a square signal receiving array with the side length of a preset length, and the method comprises the following steps:

applying a first signal into the steel rail to be detected, wherein the first signal is a high-frequency lamb wave signal;

applying a second signal into the steel rail to be detected, wherein the second signal is a mixed signal of a high-frequency lamb wave signal and a low-frequency vibration signal which are the same as the first signal;

respectively acquiring a receiving signal when each sensor receives the first signal as a first receiving signal of the corresponding sensor;

respectively acquiring a receiving signal when each sensor receives the second signal, and taking the receiving signal as a second receiving signal of the corresponding sensor;

aiming at the first receiving signal and the second receiving signal of each sensor, the following processing is carried out to obtain a time-frequency spectrum of the damage identification signal corresponding to each sensor:

performing Mode Decomposition on the first received signal and the second received signal respectively by using a Variational Mode Decomposition algorithm (VMD);

respectively acquiring time frequency spectrums of the first receiving signal and the second receiving signal after the mode decomposition is finished through Hilbert Transform (HT);

subtracting the time frequency spectrum of the first receiving signal from the time frequency spectrum of the second receiving signal to obtain a difference signal time frequency spectrum;

filtering a low-frequency vibration signal in a difference signal time frequency spectrum by using a high-pass filter to obtain a time frequency spectrum of the damage identification signal;

after obtaining a time frequency spectrum of the damage identification signal corresponding to each sensor, judging whether the time frequency spectrum of the damage identification signal corresponding to each sensor contains a modulation side frequency component, wherein the modulation side frequency component is a frequency component of a damage modulation signal generated when a second signal passes through fatigue microcracks and reflected on the time frequency spectrum; if so, determining that the steel rail to be detected has fatigue microcracks;

after fatigue microcracks are determined on the steel rail to be detected, acquiring the moment when modulation side frequency components appear in a frequency spectrum when each sensor corresponds to a damage identification signal, and taking the moment when the damage modulation signal reaches the sensor;

after the time when the damage modulation signal reaches each sensor is obtained, calculating the propagation speed of the damage modulation signal by using the time when the damage modulation signal reaches each sensor;

calculating the sound path of the damage modulation signal transmitted to each sensor based on the time when the damage modulation signal reaches each sensor and the transmission speed of the damage modulation signal;

acquiring coordinates of the center point of each sensor, respectively taking the center point of each sensor as a circle center and the corresponding sound path as a radius to make a circle, and calculating coordinates of intersection points of four intersected circles based on the coordinates of the center points of the sensors;

and determining the position coordinates of the fatigue microcracks on the steel rail to be detected by using the coordinates of the intersection points.

Optionally, calculating the propagation velocity of the impairment modulation signal using the time instants at which the impairment modulation signal arrives at each sensor comprises:

recording the central point of the position of the fatigue microcrack as O, recording the four sensors as A, B, C, D respectively in the counterclockwise direction, and recording the preset side length of a square signal receiving array formed by the four sensors as a;

from the geometric relationship, the area of the triangular OBD can be expressed as:

S_OBD＝S_OAB+S_OAD+S_ABD

wherein the area of the triangle ABD is a²/2；

The moment when the high-frequency lamb wave signal in the second signal propagates to the fatigue microcrack is recorded as t₀The propagation velocity of the impairment modulation signal is denoted v, and the time at which each sensor receives the impairment modulation signal is denoted t_A、t_B、t_C、t_DThe acoustic path of the damage modulation signal propagating to each sensor is denoted by OA ═ v (t), respectively_A-t₀)、OB＝v(t_B-t₀)、OC＝v(t_C-t₀)、OD＝v(t_D-t₀)；

Calculating the areas of the triangle OAB and the triangle OAD by utilizing a Helen formula, substituting the calculated areas into the deformation of the triangle OBD area formula, and obtaining a formula I in a simultaneous manner;

the Helen formula is:

wherein s is the area of a triangle; l_a、l_a、l_aThree sides of the triangle are respectively, and p is the half perimeter.

The first formula is as follows:

according to the calculation method, the area of the triangle OBC can be expressed as the sum of the areas of the triangles OAB, OAC and ABC, wherein the area of the triangle ABC is a²And/2, obtaining a formula II by utilizing a Helen formula:

the second formula is:

in formula one and formula two, there is t₀And v two unknowns which can be solved by a simultaneous equation to calculate the propagation velocity v of the damage modulation signal and the time t when the high-frequency lamb wave signal in the second signal propagates to the fatigue microcrack₀。

Optionally, the calculating, based on the time when the impairment modulation signal reaches each sensor and the propagation speed of the impairment modulation signal, a sound path of the impairment modulation signal propagating to each sensor includes:

according to the time when the damage modulation signal reaches each sensor and the propagation speed of the damage modulation signal, calculating the sound path of the damage modulation signal propagating to each sensor according to the following formula:

Oi＝v*(t_i-t₀)；

where Oi is the acoustic path for the damage modulation signal to propagate to sensor i, t_iThe time at which the damage modulation signal propagates to sensor i (i is A, B, C or D).

Optionally, the obtaining the coordinates of the center point of each sensor, making a circle by taking the center point of each sensor as a circle center and the corresponding sound path as a radius, and calculating the coordinates of the intersection point of the four circles based on the coordinates of the center point of each sensor includes:

acquiring sound paths of the damage modulation signals transmitted to each sensor and using the sound paths as the radius of the corresponding circle to enable R to be equal to R_A＝OA，R_B＝OB，R_C＝OC，R_DOD; wherein R is_A、R_B、R_C、R_DThe radii of the corresponding circles for sensor A, B, C, D, respectively;

the equations for the four circles can be expressed as:

formula 1: (x-x1)²+(y-y1)²＝R_A ²

Formula 2 (x-x2)²+(y-y2)²＝R_B ²

Formula 3 (x-x3)²+(y-y3)²＝R_C ²

Formula 4 (x-x4)²+(y-y4)²＝R_D ²

The coordinates of the centers of circles corresponding to the four sensors A, B, C, D are respectively A (x1, y1), B (x2, y2), C (x3, y3), and D (x4, y 4);

optionally, 3 of the four circles form a group, and four combination modes are provided, including: ABC group, ABD group, BCD group and ACD group;

obtaining coordinates of two intersection points by two equations of a joint type 1 and a formula 2; connecting two equations of formula 1 and formula 3, and obtaining coordinates of two intersection points, thereby obtaining coordinates of four intersection points of the ABC group;

obtaining coordinates of two intersection points by two equations of a joint type 1 and a formula 2; connecting two equations of formula 1 and formula 4, and obtaining coordinates of two intersection points, thereby obtaining coordinates of four intersection points of the ABD group;

obtaining coordinates of two intersection points by two equations of a united type 1 and a formula 3; connecting two equations of formula 1 and formula 4, and obtaining coordinates of two intersection points, thereby obtaining coordinates of four intersection points of the ACD group;

obtaining coordinates of two intersection points by two equations of a joint type 2 and a formula 3; and connecting two equations of the formula 2 and the formula 4, and obtaining coordinates of two intersection points, thereby obtaining coordinates of four intersection points of the BCD group.

Optionally, the determining the position coordinates of the fatigue microcracks on the rail to be detected by using the coordinates of the intersection point includes:

aiming at each combination mode of the sensor corresponding to the circle, two closest intersection points in the four intersection points are obtained, and the midpoint of a connecting line between the two intersection points is used as a positioning result of the combination;

acquiring a planar projection of a steel rail to be detected as a monitoring area;

dividing a monitoring area into a plurality of subunits, wherein all subunits are square units with the same area and are orderly arranged;

sequentially calculating the distance between the central point of each subunit and all combined positioning results;

respectively calculating the damage probability of each subunit by using the distance between the central point of each subunit and all combined positioning results;

and taking the center point coordinate of the subunit with the maximum damage probability as the position coordinate of the fatigue microcrack on the steel rail to be detected.

Optionally, sequentially calculating distances between the central point of each subunit and all the combined positioning results includes:

acquiring the coordinate of the central point of each subunit;

obtaining the coordinates of each combined positioning result;

according to the coordinates of the center points of the subunits and the coordinates of the combined positioning result, respectively calculating the distance between the center point of each subunit and the combined positioning result according to the following formula:

wherein, the coordinate of the central point of any subunit is (i, j); s_ABCThe distance between the center point of the subunit and the ABC group positioning result is obtained, and the coordinate of the ABC group positioning result is (x)_ABC,y_ABC)；s_ABDThe distance between the central point of the subunit and the positioning result of the ABD group is shown as the coordinate of the positioning result of the ABD group in (x)_ABD,y_ABD)；s_ACDThe distance between the center point of the subunit and the positioning result of the ACD group is obtained, and the coordinate of the positioning result of the ACD group is (x)_ACD,y_ACD)；s_BCDThe distance between the center point of the subunit and the positioning result of the BCD group is shown, and the coordinate of the positioning result of the BCD group is (x)_BCD,y_BCD)。

Optionally, the calculating the damage probability of each subunit by using the distance between the central point of each subunit and all the combined positioning results includes:

the primary damage probability of each subunit is calculated according to the following formula:

wherein, P_ABC(i, j) is the primary damage probability of any subunit under the combination ABC; p_ABD(i, j) is the primary injury probability of any subunit under the combined ABD; p_ACD(i, j) is the primary damage probability of any subunit under the combined ACD; p_BCD(i, j) is the primary damage probability of any subunit under the combined BCD; σ ═ 1;

respectively calculating the sum of the primary damage probabilities of each subunit under the four combinations as a total primary damage probability;

acquiring the maximum value of the total primary damage probability of all subunits;

and respectively calculating the damage probability of each subunit according to the following formula:

P(i,j)＝P₄(i,j)/max(P₄(i,j))

wherein, P (i, j) is the damage probability of any subunit; p₄(i, j) is the total primary damage probability of any subunit; max (P)₄(i, j)) is the maximum of the total primary damage probabilities for all subunits.

The utility model provides an identify device of rail fatigue microcrack position sets up four sensors on the rail that awaits measuring, four sensors constitute the square signal reception array of length of a side for default length, include:

the first signal applying module is used for applying a first signal into the steel rail to be detected, wherein the first signal is a high-frequency lamb wave signal;

the second signal applying module is used for applying a second signal into the steel rail to be detected, wherein the second signal is a mixed signal of a high-frequency lamb wave signal and a low-frequency vibration signal which are the same as the first signal;

the first receiving signal acquiring module is used for respectively acquiring a receiving signal when each sensor receives the first signal as a first receiving signal of the corresponding sensor;

the second receiving signal acquiring module is used for respectively acquiring the receiving signal when each sensor receives the second signal as the second receiving signal of the corresponding sensor;

the signal processing module is used for processing the first receiving signal and the second receiving signal of each sensor to obtain a time-frequency spectrum of the damage identification signal corresponding to each sensor; the signal processing module comprises a mode decomposition submodule, a time frequency spectrum acquisition submodule, a difference signal time frequency spectrum acquisition submodule and a damage identification signal time frequency spectrum acquisition submodule; wherein:

a Mode Decomposition sub-module for performing Mode Decomposition on the first received signal and the second received signal respectively by using a Variational Mode Decomposition algorithm (VMD);

a time-frequency spectrum obtaining sub-module, configured to obtain time-frequency spectrums of the first received signal and the second received signal after the mode decomposition is completed, respectively, through Hilbert Transform (HT);

the difference signal time frequency spectrum acquisition submodule is used for carrying out subtraction processing on the time frequency spectrum of the first receiving signal and the time frequency spectrum of the second receiving signal to obtain a difference signal time frequency spectrum;

the damage identification signal time frequency spectrum acquisition submodule is used for filtering a low-frequency vibration signal in a difference signal time frequency spectrum by using a high-pass filter to obtain a time frequency spectrum of the damage identification signal;

the judging module is used for judging whether the frequency spectrum of the damage identification signal corresponding to each sensor contains modulation side frequency components after the time frequency spectrum of the damage identification signal corresponding to each sensor is obtained, wherein the modulation side frequency components are frequency components of the damage modulation signal generated when the second signal passes through fatigue microcracks and reflected on the time frequency spectrum; if so, determining that the steel rail to be detected has fatigue microcracks;

the damage modulation signal reaching time acquisition module is used for acquiring the time when the modulation side frequency component appears in a frequency spectrum when each sensor corresponds to a damage identification signal after determining that the steel rail to be detected has fatigue microcracks, and the time is used as the time when the damage modulation signal reaches the sensors;

the propagation speed acquisition module is used for calculating the propagation speed of the damage modulation signal by using the time when the damage modulation signal reaches each sensor after the time when the damage modulation signal reaches each sensor is obtained;

the sensor sound path calculation module is used for calculating the sound path of the damage modulation signal transmitted to each sensor based on the time when the damage modulation signal reaches each sensor and the transmission speed of the damage modulation signal;

the intersection point coordinate acquisition module is used for acquiring the coordinate of the central point of each sensor, making a circle by taking the central point of each sensor as the center of the circle and the corresponding sound path as the radius, and calculating the coordinate of the intersection point of the intersection points of the four circles based on the coordinate of the central point of each sensor;

and the fatigue microcrack positioning module is used for determining the position coordinates of the fatigue microcracks on the steel rail to be detected by utilizing the coordinates of the intersection points.

According to the technical scheme, the method and the device for identifying the position of the fatigue microcrack of the steel rail provided by the embodiment of the invention comprise the steps of firstly applying a high-frequency lamb wave signal and a mixed signal of the high-frequency lamb wave signal and a low-frequency vibration signal to the steel rail to be detected, and receiving the two signals by using four sensors arranged on the steel rail to be detected; secondly, performing mode decomposition, obtaining a time frequency spectrum, subtracting the time frequency spectrum and filtering a low-frequency vibration signal on the two signals received by each sensor to obtain the time frequency spectrum of the damage identification signal corresponding to the four sensors; and thirdly, after the steel rail to be detected has fatigue microcracks, respectively acquiring the time when the damage modulation signal reaches each sensor, and calculating the sound path of the damage modulation signal transmitted to each sensor through the corresponding time. Respectively taking the center point of each sensor as the center of a circle and the corresponding sound path as the radius to make a circle, and calculating the intersection point coordinates of the four circles; and finally, determining the position coordinates of the fatigue microcracks on the steel rail to be detected by using the coordinates of the intersection points.

In the traditional damage detection algorithm based on ultrasonic waves, because the interference of a wave packet aliasing phenomenon on signal processing is considered, only direct waves (namely arrival head waves) are usually intercepted for analysis and research, however, the direct waves only contain structural information on the shortest straight path between an excitation sensor and a receiving sensor or near the path, and the loss of the structural information in a large number of subsequent scattered and refracted signals can be caused by only the direct waves. To compensate for this drawback, the area of the monitoring area is usually increased by increasing the number of sensors and the detection path. The method does not need to increase extra sensor cost, does not need to separate wave packets with different frequencies, fully utilizes modulation side frequency components generated by sound waves at nonlinear cracks, and greatly improves the average effective detection area of a single sensor.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without inventive exercise.

Fig. 1 is a schematic flow chart of a method for identifying a location of a rail fatigue micro crack according to an embodiment of the present invention;

fig. 2 is a schematic flowchart of step S114 in fig. 1 according to an embodiment of the present invention;

fig. 3 is a schematic structural diagram of an apparatus for identifying a location of a rail fatigue micro crack according to an embodiment of the present invention.

Detailed Description

In order to make those skilled in the art better understand the technical solution of the present invention, the technical solution in the embodiment of the present invention will be clearly and completely described below with reference to the drawings in the embodiment of the present invention, and it is obvious that the described embodiment is only a part of the embodiment of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

Fig. 1 is a schematic flow chart of a method for identifying a position of a rail fatigue micro-crack according to the present invention. In the embodiment disclosed by the invention, four sensors are arranged on the steel rail to be detected, and the four sensors form a square signal receiving array with the side length being the preset length. In one embodiment of the present invention, the sensors are piezoelectric ceramic sensors (PZT), which are mainly used for receiving signals transmitted through the steel rail to be measured, and four PZT sensors may be configured into a square receiving array with a side length of 15 mm.

As shown in fig. 1, the method for identifying the position of the rail fatigue microcrack disclosed by the invention comprises the following steps:

step S101: and applying a first signal to the steel rail to be detected.

And applying a first signal into the steel rail to be detected by utilizing a high-frequency ultrasonic excitation sensor, wherein the first signal is a high-frequency lamb wave signal. For example, a high-frequency ultrasonic lamb wave excitation sensor is used for exciting a row of ultrasonic lamb wave signals with the frequency of 180kHz into the steel rail to be measured. The reason for selecting the frequency of 180kHz is as follows: the rail is swept in advance in a high frequency range of 100kHz to 200kHz, and 180kHz which is large in amplitude and sensitive to nonlinear structures (higher harmonic components caused by system nonlinearity and obvious in frequency spectrogram) is selected as high-frequency excitation frequency.

Step S102: and applying a second signal to the steel rail to be detected.

And applying a second signal into the steel rail to be tested by using a vibration exciter and a high-frequency ultrasonic excitation sensor, wherein the second signal is a mixed signal of a high-frequency lamb wave signal and a low-frequency vibration signal which are the same as the first signal. For example, a vibration sine signal with the frequency of 7kHz and an ultrasonic lamb wave signal with the frequency of 180kHz are applied to the steel rail to be measured by an exciter and a high-frequency ultrasonic lamb wave excitation sensor.

In one embodiment of the present disclosure, step S102 includes the following sub-steps:

1) and applying a low-frequency vibration signal to the steel rail to be detected.

And (3) exciting a series of low-frequency vibration signals, such as vibration sine signals with the frequency of 7kHz, into the steel rail to be tested by using a vibration exciter.

2) Judging whether the low-frequency vibration signal forms a stable vibration sound field,

in one embodiment of the present disclosure, a single train of vibratory signals is applied to the rail in advance, the received signal waveform of the vibratory signal is observed, and the time t required for the waveform to stabilize is recorded. And if the time for applying the low-frequency vibration signal in the step 1) reaches t, the low-frequency vibration signal is considered to form a stable vibration sound field.

If the low-frequency vibration signal forms a stable vibration sound field, executing the step 3): and continuously applying a low-frequency vibration signal into the steel rail to be detected, simultaneously applying a high-frequency lamb wave signal which is the same as the first signal into the steel rail to be detected, and taking a mixed signal of the high-frequency lamb wave signal and the first signal as a second signal. For example, a vibration sine signal with the frequency of 7kHz is applied to the steel rail to be measured, and after a stable vibration sound field is formed, a row of ultrasonic lamb wave signals with the frequency of 180kHz are excited.

Step S103: and respectively acquiring a receiving signal when each sensor receives the first signal as the first receiving signal of the corresponding sensor.

And respectively acquiring a receiving signal when each sensor receives the first signal, and taking the receiving signal as the first receiving signal of the sensor, so that each sensor corresponds to an independent first receiving signal in the four sensors. For example, the first signal is an ultrasonic lamb wave signal having a frequency of 180kHz, which is received by the sensor, and the received signal is taken as the first received signal. In the embodiment disclosed in the present invention, the first received signal may be regarded as a noise signal, and the noise signal reflects an ultrasonic lamb wave response caused by structural parameters (such as material nonlinearity, boundary reflection, and the like) of the steel rail to be measured.

Step S104: and respectively acquiring a receiving signal when each sensor receives the second signal as a second receiving signal of the corresponding sensor.

And respectively acquiring a receiving signal when each sensor receives the second signal, and taking the receiving signal as the second receiving signal of the sensor, so that each sensor corresponds to an independent second receiving signal in the four sensors. For example, the second signal is a mixed signal of an oscillating sinusoidal signal having a frequency of 7kHz and an ultrasonic lamb wave signal having a frequency of 180kHz, the mixed signal is received by the sensor, and the received signal is taken as the second received signal. In the embodiment disclosed by the invention, if the rail to be detected has fatigue microcracks, the second received signal simultaneously contains a damage modulation signal and a noise signal, wherein the damage modulation signal and the noise signal are generated when the second signal passes through the fatigue microcracks.

In the disclosed embodiment of the invention, the vibration signal mainly plays a role in promoting the opening and closing movement at the nonlinear microcrack and enhancing the strength of the respiration effect, and the high-frequency lamb wave signal mainly plays a role in high sensitivity to the nonlinear crack structure.

The following steps S105 to S108 are performed on the first received signal and the second received signal of each sensor, so as to obtain a time-frequency spectrum of the damage identification signal corresponding to each sensor.

Step S105: and respectively carrying out mode decomposition on the first received signal and the second received signal by using a variational mode decomposition algorithm.

The VMD algorithm considers that a signal is formed by overlapping sub-signals with different frequencies, is a wiener filter for minimizing mean square estimation error, aims to decompose an input signal into discrete number of sub-signals with specific series sparsity, and determines each mode mu through iteratively searching the optimal solution of a variational model_kAnd its corresponding center frequency omega_k。

The following is a description of the variational mode decomposition algorithm.

The number of sub-signals is set in advance, for example, 5. The variational mode decomposition algorithm will satisfy μ of the corresponding mode_kThe signal is separated from the original signal, each mode is a sub-signal, and the remaining signals are decomposed continuously. In one embodiment of the present disclosure, the first 5 modes are extracted, which include the high-frequency fundamental, the low-frequency fundamental and the modulation side frequency with the strongest energy of order 3.

Calculating each sub-signal according to the following steps:

1) and solving by using Hilbert transform to obtain a single-side frequency spectrum of the modal subsignal.

2) The spectrum of the modal sub-signal is shifted to the estimated center frequency.

3) The bandwidth of the modal subsignal is estimated using the gaussian smoothness of the demodulated signal, and the constraint variation problem thus generated can be expressed as:

wherein, mu_k、ω_kRespectively, the set sequence of all modal subsignals and the set sequence of their center frequencies.

4) And adding a penalty factor a in the minimization target problem to adjust the penalty degree, and introducing a secondary reconstruction constraint for accelerating the convergence process and a Lagrangian multiplier for ensuring that the reconstruction constraint is met.

Therefore, the formula in step 3) is rewritten as:

5) solving the unconstrained minimization problem in the formula in the step 4).

The alternating iteration process of the VMD algorithm is realized by means of an Alternating Direction Multiplier Method (ADMM), iteration is carried out through the following equation, and the saddle point of the augmented Lagrangian function in the formula is gradually solved, so that the optimal solution of the problem is obtained:

wherein the content of the first and second substances,

and

respectively, representing the result of a fourier transform of the corresponding time domain signal.

The iteration stop condition is that N is equal to N (N is the set mode number) and satisfies:

and respectively carrying out mode decomposition on the first receiving signal and the second receiving signal according to the steps to extract a main mode. The method aims to remove noise signal interference, improve the signal-to-noise ratio and the algorithm accuracy of a received signal, eliminate the strict requirement of Hilbert transform on an input signal, and decompose a time domain signal into a plurality of linear stable inherent mode functions.

Step S106: and respectively acquiring time frequency spectrums of the first receiving signal and the second receiving signal after the mode decomposition is finished through Hilbert transform.

The abscissa of the time frequency spectrum is time, the ordinate is frequency, the line color in the drawn contour graph represents amplitude, and from the time frequency spectrum, it can be observed when a signal of a certain frequency propagates to the receiving sensor, and the amplitude of the signal at the frequency.

The nature of HT is that signals with frequencies greater than 0 are phase delayed by 90 degrees. Let the input signal be x (t), and the HT result H [ x (t) ] can be expressed as:

i.e., H [ x (t) ] is the convolution of x (t) and 1/(π t). The following are obtained by a table look-up method:

from this, H [ x (t) ], has a modulus of 1. Order:

by means of Euler's formula

Obtaining by solution:

thus, it is possible to provide

To visually demonstrate the principle of HT demodulation, the presence signal y (t) is set such that:

y(t)＝x(t)+iH[x(t)]

setting the coordinate axes in three-dimensional space as time axis, real axis and imaginary axis, drawing the waveform of modulation signal x (t) in the time axis-real axis plane, drawing the Hilbert transform result H [ x (t) in the time axis-imaginary axis plane]Drawing the waveform of the signal y (t) in three-dimensional space to obtain that the instantaneous amplitude of the signal y (t) at any moment is (x (t))²+H[x(t)]²)^1/2，

Instantaneous frequency tan^-1{x(t)/H[x(t)]The derivative with respect to time, thereby enabling demodulation of amplitude, frequency.

In the prior art, a Hilbert-yellow Transform algorithm is adopted to perform time-frequency analysis on a signal, the Hilbert-yellow Transform algorithm is mainly composed of two parts, the input signal is firstly processed through an Empirical Mode Decomposition (EMD) algorithm proposed by tsuba academy to be decomposed into a plurality of Intrinsic Mode Functions (IMFs), and then Hilbert Transform (HT) is performed to realize time-frequency domain conversion, so as to obtain a time-frequency spectrum of the signal. However, since the frequency components of the mixed signal of the vibration signal and the ultrasonic signal are complex, the decomposition by the EMD causes problems such as mode aliasing and spurious components. In the technical scheme disclosed by the invention, the VMD algorithm is adopted to effectively solve the problems of mode confusion, false components and the like of the EMD algorithm. In addition, the VMD algorithm can effectively overcome the problem of mode aliasing, is different from the mode-by-cycle elimination of IMF components in the EMD, decomposes signals into a plurality of modes with specific sparse properties and simultaneously reproduces input, and the calculation speed of the VMD algorithm is greatly improved compared with that of the EMD algorithm.

Step S107: and carrying out subtraction processing on the time frequency spectrum of the first receiving signal and the time frequency spectrum of the second receiving signal to obtain a difference signal time frequency spectrum.

And correspondingly subtracting the signal amplitudes with the same frequency in the time frequency spectrums of the first received signal and the second received signal to obtain the time frequency spectrums of the difference signals obtained after the subtraction of the two time frequency spectrums. For example, the amplitude of the frequency spectrum of the first received signal at 30kHz is 0.8, the amplitude of the frequency spectrum of the second received signal at 30kHz is 0.5, and the result of subtracting the amplitudes of the two received signals at 30kHz is 0.3, so that the amplitude of the frequency spectrum of the difference signal at 30kHz is 0.3, and the difference signal time spectrum of the first received signal and the second received signal is obtained according to the above method.

A great difficulty of the nondestructive testing method based on ultrasonic signals lies in how to clearly distinguish between material nonlinearity and damage-induced nonlinearity existing in the tested structure. To some extent, nonlinear acoustic effects induced by material nonlinearities can be considered system noise signals. According to the method provided by the embodiment of the invention, the received signal can be denoised through the corresponding subtraction of the time frequency spectrum, and the nonlinearity of the material or the nonlinearity of the system introduced by the coupling agent and the like is filtered, so that the sensitivity of detecting damage is enhanced, and the effective identification of fatigue microcracks is realized.

Step S108: and filtering the low-frequency vibration signal in the time frequency spectrum of the difference signal by using a high-pass filter to obtain the time frequency spectrum of the damage identification signal.

Since the signal changes after being transmitted to the fatigue microcracks, the change is reflected in the received signal, and it is very critical how to accurately extract the change information caused by the fatigue microcracks from the received signal. Therefore, in the embodiment disclosed in the present invention, first, the first received signal (equivalent to the system noise signal) and the second received signal (equivalent to the damage signal caused by fatigue microcracks and the system noise signal) are subjected to time-frequency spectrum subtraction to remove the system noise signal in the second received signal. Then, a high-pass filter is used for filtering out a low-frequency vibration signal in the signal, the rest signal is a damage identification signal, and the time spectrum of the damage identification signal can directly indicate the information of the fatigue microcracks.

Therefore, in the embodiment disclosed in the present invention, the high-pass filter is used to filter the information of the low-frequency vibration signal in the difference signal time frequency spectrum, so as to obtain the damage identification signal time frequency spectrum.

After the processing of steps S104 to S108 is performed on the first received signal and the second received signal of each sensor, the time-frequency spectrum of the damage identification signal corresponding to each sensor can be obtained, and step S109 is continued.

Step S109: and judging whether the frequency spectrum contains modulation side frequency components or not when the damage identification signal corresponding to each sensor is received.

And the modulation side frequency component is a frequency component of a damage modulation signal generated when the second signal passes through the fatigue microcrack, which is reflected on a time frequency spectrum. When the mixed signal of the high-frequency lamb wave signal and the low-frequency vibration signal is simultaneously applied to the steel rail to be detected, if the steel rail to be detected does not contain fatigue microcracks, the second receiving signal is represented by linear superposition of the high-frequency lamb wave signal and the low-frequency vibration signal, and new frequency components cannot be generated by a frequency spectrum when the identification signal is damaged. If the steel rail to be detected contains fatigue microcracks, the mixed signal is modulated, so that waveform distortion occurs in a time domain of the second receiving signal, a modulation side frequency component with the frequency of high-frequency ultrasonic frequency +/-low-frequency vibration frequency is generated in a frequency domain, and the modulation side frequency component can also be reflected in a time frequency spectrum of the damage identification signal, so that whether the fatigue microcracks exist on the steel rail to be detected can be determined by judging the modulation side frequency component in the frequency spectrum when the damage identification signal is damaged.

And judging whether the frequency spectrum contains modulation side frequency components or not when the damage identification signal corresponding to each sensor is received. In one embodiment of the disclosure, the following sub-steps may be adopted to determine whether the spectrum contains a modulation side-frequency component when the impairment recognition signal is received.

1) And calculating a maximum value point in the frequency spectrum when the damage identification signal is received.

In one embodiment of the present disclosure, all maxima in the spectrum at the time of the impairment recognition signal can be calculated by the following method.

Calculating the slope of a line segment formed by a certain point and a preceding point and a subsequent point in the frequency spectrum when the damage identification signal is calculated, wherein if the slope of a connecting line between the certain point and the preceding point is positive and the slope of a connecting line between the certain point and the subsequent point is negative, the certain point is a maximum value point.

2) And judging whether a maximum point pair with the amplitude larger than 0.1 appears in the preset range of the superposition frequency in the frequency spectrum when the damage identification signal appears.

The superposition frequency is the sum of the high-frequency ultrasonic frequency and the integral multiple of the low-frequency vibration frequency, or the difference of the high-frequency ultrasonic frequency and the integral multiple of the low-frequency vibration frequency, namely the superposition frequency is the integral multiple of the high-frequency ultrasonic frequency +/-the low-frequency vibration frequency. The preset range can be 165kHz-200kHz, and if a pair of maximum point pairs with amplitude larger than 0.1 appears in the preset range of the superposition frequency, modulation side frequency components appear in the frequency spectrum when the identification signal is damaged; and if the maximum point pair does not exist, the modulation side frequency component does not exist in the frequency spectrum when the damage identification signal is damaged.

If the frequency spectrum contains modulation side frequency components when the damage identification signal corresponding to each sensor is received, determining that the steel rail to be detected contains fatigue microcracks, and continuing to execute the step S110; and if the frequency spectrum does not contain modulation side frequency components when the damage identification signal corresponding to each sensor does not exist, determining that the steel rail to be detected does not contain fatigue microcracks.

Step S110: and acquiring the time when the modulation side frequency component appears in the frequency spectrum when each sensor corresponds to the damage identification signal as the time when the damage modulation signal reaches the sensor.

And the abscissa in the time frequency spectrum is a time axis, and the central time of a time period covered by the contour line corresponding to the modulation side frequency component in the time frequency spectrum of the damage identification signal corresponding to the sensor is used as the time when the damage modulation signal reaches the sensor, so that the time when the damage modulation signal reaches each sensor is respectively obtained.

After obtaining the time when the damage modulation signal reaches each sensor, step S111 is performed: the propagation velocity of the impairment modulation signal is calculated using the time at which the impairment modulation signal reaches each sensor.

This step can be achieved by the following method:

S_OBD＝S_OAB+S_OAD+S_ABD

wherein the area of the triangle ABD is a²/2；

the Helen formula is:

The first formula is as follows:

the second formula is:

Step S112: and calculating the sound path of the damage modulation signal transmitted to each sensor based on the time when the damage modulation signal reaches each sensor and the transmission speed of the damage modulation signal.

In the specific embodiment disclosed in the present invention, the acoustic path of the damage modulation signal propagating to each sensor is calculated according to the following formula:

Oi＝v*(t_i-t₀)；

Step S113: and acquiring coordinates of the central point of each sensor, respectively taking the central point of each sensor as a circle center and the corresponding sound path as a radius to make a circle, and calculating coordinates of intersection points of four intersected circles based on the coordinates of the central points of the sensors.

the equations for the four circles can be expressed as:

formula 1: (x-x1)²+(y-y1)²＝R_A ²

Formula 2 (x-x2)²+(y-y2)²＝R_B ²

Formula 3 (x-x3)²+(y-y3)²＝R_C ²

Formula 4 (x-x4)²+(y-y4)²＝R_D ²

The coordinates of the center of the circle corresponding to the four sensors A, B, C, D are a (x1, y1), B (x2, y2), C (x3, y3), and D (x4, y 4).

Optionally, 3 of the four circles form a group, and four combination modes are provided, including: the ABC group, the ABD group, the BCD group, and the ACD group are, for example, a combination of A, B, C circles corresponding to three sensors.

Obtaining coordinates of two intersection points by two equations of a joint type 1 and a formula 2; and connecting two equations of the formula 1 and the formula 3, and obtaining coordinates of two intersection points, thereby obtaining coordinates of four intersection points of the ABC group.

Obtaining coordinates of two intersection points by two equations of a joint type 1 and a formula 2; and combining two equations of formula 1 and formula 4 to obtain the coordinates of two intersection points, thereby obtaining the coordinates of four intersection points of the ABD group.

Obtaining coordinates of two intersection points by two equations of a united type 1 and a formula 3; and connecting two equations of the formula 1 and the formula 4, and obtaining coordinates of two intersection points, thereby obtaining coordinates of four intersection points of the ACD group.

Step S114: and determining the position coordinates of the fatigue microcracks on the steel rail to be detected by using the coordinates of the intersection points.

In one embodiment of the present disclosure, as shown in FIG. 2, this step comprises the following substeps.

Step S1141: and aiming at each combination mode of the sensor corresponding to the circle, two closest intersection points in the four intersection points are obtained, and the midpoint of a connecting line between the two intersection points is used as a combined positioning result.

And selecting two closest intersection points from the four intersection points obtained in each combination mode, and taking the midpoint of a connecting line between the two intersection points as a positioning result of the combination.

Step S1142: and acquiring the plane projection of the steel rail to be detected as a monitoring area.

And taking the area of the steel rail to be detected projected on the plane as a monitoring area.

Step S1143: the monitoring area is divided into a plurality of subunits, all the subunits are square units with the same area, and the subunits are orderly arranged.

The monitoring area is divided into grids according to the arrangement sequence from left to right and from top to bottom, wherein each grid represents a subunit, all the subunits are square, have the same area and are arranged in order.

Step S1144: and sequentially calculating the distance between the central point of each subunit and all combined positioning results.

In the embodiment of the present disclosure, this step can be implemented by the following method:

1) coordinates of the center point of each subunit are obtained.

And obtaining the coordinates of the central point of each subunit according to the monitoring area division mode.

2) And acquiring the coordinates of each combined positioning result.

And calculating the coordinates of the positioning result according to the coordinates of the intersection points in the combination.

3) According to the coordinates of the center points of the subunits and the coordinates of the combined positioning result, respectively calculating the distance between the center point of each subunit and the combined positioning result according to the following formula:

wherein, the coordinate of the central point of any subunit is (i, j); s_ABCThe distance between the center point of the subunit and the ABC group positioning result is obtained, and the coordinate of the ABC group positioning result is (x)_ABC,y_ABC)；s_ABDThe distance between the central point of the subunit and the positioning result of the ABD group is shown as the coordinate of the positioning result of the ABD group in (x)^ABD,y^ABD)；s_ACDSetting up ACD for the distance between the center point of the subunit and the positioning result of ACD setThe coordinates of the bit result are (x)^ACD,y^ACD)；s_BCDThe distance between the center point of the subunit and the positioning result of the BCD group is shown, and the coordinate of the positioning result of the BCD group is (x)^BCD,y^BCD)。

Step S1145: and respectively calculating the damage probability of each subunit by using the distance between the central point of each subunit and all combined positioning results.

1) the primary damage probability of each subunit is calculated according to the following formula:

2) and respectively calculating the sum of the primary damage probabilities of each subunit under the four combinations as the total primary damage probability.

The primary damage probabilities of each subunit under the four combinations are added, and the sum obtained is used as the total primary damage probability of the subunit, namely P₄(i,j)＝P_ABC(i,j)+P_ABD(i,j)+P_ACD(i,j)+P_BCD(i, j)), wherein P₄(i, j) is the total primary damage probability of any one subunit.

3) The maximum value of the total primary damage probability of all subunits is obtained.

And comparing the total primary damage probability of all the subunits to obtain the maximum total primary damage probability.

4) And respectively calculating the damage probability of each subunit according to the following formula:

P(i,j)＝P₄(i,j)/max(P₄(i,j))

Step S1146: and taking the center point coordinate of the subunit with the maximum damage probability as the position coordinate of the fatigue microcrack on the steel rail to be detected.

After the damage probability of each subunit is obtained through calculation, the damage probabilities of all the subunits are compared, the center point coordinate of the subunit with the largest damage probability is used as the position coordinate of the fatigue microcrack on the steel rail to be detected, and the position of the fatigue microcrack on the steel rail to be detected can be determined according to the position coordinate.

Fig. 3 is a schematic structural diagram of a device for identifying a rail fatigue microcrack position, in which four sensors are arranged on a rail to be detected, the four sensors form a square signal receiving array with a side length of a preset length, and the device includes the following modules:

the first signal applying module 11 is configured to apply a first signal into the steel rail to be detected, wherein the first signal is a high-frequency lamb wave signal;

a second signal applying module 12 configured to apply a second signal into the steel rail to be tested, where the second signal is a mixed signal of a high-frequency lamb wave signal and a low-frequency vibration signal that are the same as the first signal;

a first received signal acquiring module 13 configured to acquire a first signal received by each sensor as a first received signal of the corresponding sensor, respectively;

a second received signal acquiring module 14 configured to acquire the second signal received by each sensor as a second received signal of the corresponding sensor;

a signal processing module 15 configured to process the first received signal and the second received signal of each sensor to obtain a time-frequency spectrum of the damage identification signal corresponding to each sensor; the signal processing module comprises a mode decomposition submodule, a time frequency spectrum acquisition submodule, a difference signal time frequency spectrum acquisition submodule and a damage identification signal time frequency spectrum acquisition submodule;

a Mode Decomposition sub-module 151 configured to perform Mode Decomposition on the first received signal and the second received signal using a Variational Mode Decomposition algorithm (VMD), respectively;

a time-frequency spectrum obtaining sub-module 152 configured to obtain time-frequency spectrums of the first received signal and the second received signal after the completion of the mode decomposition, respectively, through Hilbert Transform (HT);

a difference signal time spectrum obtaining sub-module 153 configured to subtract the time spectrum of the first received signal from the time spectrum of the second received signal to obtain a difference signal time spectrum;

a damage identification signal time frequency spectrum obtaining sub-module 154 configured to filter the low-frequency vibration signal in the difference signal time frequency spectrum by using a high-pass filter to obtain a time frequency spectrum of the damage identification signal;

the judging module 16 is configured to, after obtaining the time-frequency spectrum of the damage identification signal corresponding to each sensor, judge whether the time-frequency spectrum of the damage identification signal corresponding to any one sensor contains a modulation side-frequency component, where the modulation side-frequency component is a frequency component of a damage modulation signal generated when the second signal passes through the fatigue microcrack and reflected on the time-frequency spectrum; if so, determining that the steel rail to be detected has fatigue microcracks;

the damage modulation signal arrival time obtaining module 17 is configured to obtain, after determining that there is a fatigue microcrack on the steel rail to be measured, a time when the modulation side frequency component appears in a frequency spectrum when each sensor corresponds to the damage identification signal, as a time when the damage modulation signal arrives at the sensor;

a propagation speed acquisition module 18 configured to calculate a propagation speed of the impairment modulation signal using a time at which the impairment modulation signal reaches each sensor after obtaining the time at which the impairment modulation signal reaches each sensor;

a sensor sound path calculation module 19 configured to calculate a sound path of the damage modulation signal propagated to each sensor based on a time at which the damage modulation signal reaches each sensor and a propagation speed of the damage modulation signal;

an intersection point coordinate obtaining module 20 configured to obtain coordinates of a center point of each sensor, make a circle with the center point of each sensor as a circle center and a corresponding sound path as a radius, and calculate coordinates of intersection points of four circular intersections based on the coordinates of the center points of the sensors;

and the fatigue microcrack positioning module 21 is configured to determine the position coordinates of the fatigue microcracks on the steel rail to be detected by using the coordinates of the intersection points.

It is noted that, in this document, relational terms such as "first" and "second," and the like, may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.

The foregoing are merely exemplary embodiments of the present invention, which enable those skilled in the art to understand or practice the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for identifying the position of a rail fatigue microcrack is characterized in that four sensors are arranged on a rail to be detected, and the four sensors form a square signal receiving array with the side length of a preset length, and the method comprises the following steps:

2. The method of claim 1, wherein calculating the propagation velocity of the impairment modulation signal using the time instants at which the impairment modulation signal arrives at each sensor comprises:

S_OBD＝S_OAB+S_0AD+S_ABD

wherein the area of the triangle ABD is a²/2；

Let the moment at which the second signal propagates to the fatigue microcracks be denoted t₀The propagation velocity of the impairment modulation signal is denoted v, and the time at which each sensor receives the impairment modulation signal is denoted t_A、t_B、t_C、t_DThe acoustic path of the damage modulation signal propagating to each sensor is denoted by OA ═ v (t), respectively_A-t₀)、OB＝v(t_B-t₀)、OC＝v(t_C-t₀)、OD＝v(t_D-t₀)；

the Helen formula is:

wherein s is the area of a triangle; l_a、l_a、l_aThree sides of the triangle are respectively long, and p is the half perimeter;

the first formula is as follows:

the second formula is:

in formula one and formula two, there is t₀And v two unknowns which can be solved by simultaneous equations to calculate the propagation velocity v of the damage modulation signal and the propagation of the high-frequency lamb wave signal in the second signalTo the moment t of fatigue microcracking₀。

3. The method of claim 2, wherein calculating the acoustic path of the impairment modulation signal propagating to each sensor based on the time of arrival of the impairment modulation signal at each sensor and the propagation speed of the impairment modulation signal comprises:

Oi＝v*(t_i-t₀)；

4. The method according to claim 3, wherein the obtaining coordinates of the center point of each sensor, making a circle by taking the center point of each sensor as a center and the corresponding sound path as a radius, and calculating coordinates of an intersection point of four circles based on the coordinates of the center points of the sensors comprises:

the equations for the four circles can be expressed as:

formula 1: (x-x1)²+(y-y1)²＝R_A ²

Formula 2 (x-x2)²+(y-y2)²＝R_B ²

Formula 3 (x-x3)²+(y-y3)²＝R_C ²

Formula 4 (x-x4)²+(y-y4)²＝R_D ²

5. The method of claim 4, wherein determining the location coordinates of the fatigue microcracks on the rail under test using the coordinates of the intersection points comprises:

6. The method of claim 5, wherein sequentially calculating the distance between the central point of each sub-unit and all the combined positioning results comprises:

acquiring the coordinate of the central point of each subunit;

obtaining the coordinates of each combined positioning result;

wherein, the coordinate of the central point of any subunit is (i, j); s_ABCThe distance between the center point of the subunit and the ABC group positioning result is obtained, and the coordinate of the ABC group positioning result is (x)_ABC，y_ABC)；s_ABDThe distance between the central point of the subunit and the positioning result of the ABD group is shown as the coordinate of the positioning result of the ABD group in (x)_ABD，y_ABD)；s_ACDSetting up ACD for the distance between the center point of the subunit and the positioning result of ACD setThe coordinates of the bit result are (x)_ACD，y_ACD)；s_BCDThe distance between the center point of the subunit and the positioning result of the BCD group is shown, and the coordinate of the positioning result of the BCD group is (x)_BCD，y_BCD)。

7. The method of claim 6, wherein the step of calculating the damage probability of each subunit separately by using the distance between the central point of each subunit and all the combined positioning results comprises:

P(i，j)＝P₄(i，j)/max(P₄(i，j))

8. The utility model provides an discern device of rail fatigue microcrack position which characterized in that sets up four sensors on the rail that awaits measuring, four sensors constitute the square signal reception array of length of side for default length, include: