CN112034048A - Beam structure crack positioning method based on multiple frequency response function estimation - Google Patents

Beam structure crack positioning method based on multiple frequency response function estimation Download PDF

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CN112034048A
CN112034048A CN201910409482.9A CN201910409482A CN112034048A CN 112034048 A CN112034048 A CN 112034048A CN 201910409482 A CN201910409482 A CN 201910409482A CN 112034048 A CN112034048 A CN 112034048A
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crack
beam structure
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罗柏文
刘双奇
蒋勉
王昭文
邝应炜
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Hunan University of Science and Technology
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    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
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    • G01—MEASURING; TESTING
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Abstract

The invention discloses a beam structure crack positioning method based on multiple frequency response function estimation, wherein equidistant mark points are arranged on a beam structure, and the positions of the mark points are determined; respectively obtaining vibration response signals of each set mark point when the beam structure has no cracks and cracks by adopting a non-contact measurement method under the premise of adding excitation input; performing multiple frequency response function estimation on vibration transfer characteristics between input and output position points based on excitation input and vibration signals output by any marking point; comparing the changes of the frequency response function between the corresponding input and output positions of the beam structure when no crack exists and the beam structure has a crack to establish a corresponding crack identification index; and finally, realizing accurate positioning of the crack region of the beam structure by identifying the maximum position of the frequency response function change value. The invention uses the damage detection method based on the frequency response function, has strong anti-interference capability, is sensitive to the damage of the structure and can accurately position the crack position.

Description

Beam structure crack positioning method based on multiple frequency response function estimation
Technical Field
The invention belongs to the technical field of beam structure crack detection, and particularly relates to a beam structure crack positioning method based on multiple frequency response function estimation.
Background
At present, in practical application, many mechanical engineering structural components can be simplified into beam structures, and the health state of the beam structures is directly related to the safe operation of the whole system. Under the long-term action of alternating load, random load and natural environment factors, the beam structure is easy to generate cracks to influence the service life and the safe and reliable operation of the beam structure, even serious failure accidents can be caused, and huge loss is directly caused. Therefore, the crack damage position of the beam-shaped structure is accurately judged, and the method has important significance for realizing rapid and accurate maintenance treatment, preventing serious accidents and the like.
Among many fault detection and diagnosis technologies, the vibration detection method has the characteristics of high diagnosis speed, high accuracy, accurate diagnosis part, capability of realizing on-line monitoring and the like, is widely applied to the field of structural crack detection, and generally adopts methods based on frequency, vibration mode, frequency response function and the like. The detection method adopting the natural frequency has lower sensitivity to the cracks, and generally, the cracks can be accurately identified only when the damages are serious; the damage identification method based on the vibration mode also faces the problems of incomplete measurement of the vibration mode and insensitive indexes; the damage detection method utilizing the frequency response function is wide in application, the frequency response function is used for describing the vibration transfer characteristic of the structure, the anti-interference capability is strong, and the damage to the structure is sensitive, so that the positioning accuracy of the crack position of the beam structure is low.
Disclosure of Invention
In order to solve at least one of the above technical problems, the present invention provides a method for positioning cracks of a beam structure based on multiple frequency response function estimation.
The purpose of the invention is realized by the following technical scheme:
the method for positioning the cracks of the beam structure based on the multiple frequency response function estimation is characterized by comprising the following steps of:
s1, arranging a plurality of marking points which are distributed at equal intervals on the beam structure, and determining the positions of the marking points;
s2, inputting a vibration excitation signal to the same beam structure under the same working condition aiming at the same beam structure, and collecting vibration response signals output by the beam structure when each mark point position has no cracks or cracks;
s3, according to the vibration excitation signal and the vibration response signal, describing the vibration transfer characteristics of each mark point of the beam structure when no crack exists or a crack exists by adopting a frequency response function;
s4, establishing a crack identification and positioning index model of each mark point position according to the change of the frequency response function of each corresponding mark point before and after the generation of the beam structure crack;
and S5, determining whether the beam structure has cracks and the crack positions according to the crack identification and positioning index model under the same working condition aiming at the beam structure with the unknown crack positions.
As a further improvement, in the step S2, a machine vision non-contact measurement method is adopted to collect, for the same beam structure, the vibration response signals X output from the positions of the mark points when the beam structure is crack-free1，X2，X3，K，XLCollecting vibration response signals output by the positions of the mark points when the beam structure has cracks
Figure BDA0002062340580000021
As a further improvement, in the step S3, the vibration excitation signal F inputted by actual measurement and the crack-free vibration response signal X outputted by actual measurement of the ith mark point are calculatediCross spectral mean of
Figure BDA0002062340580000022
Calculating self-spectrum mean value P of actually measured input vibration excitation signalFF(f)；
By the formula
Figure BDA0002062340580000023
Calculating to obtain a frequency response function of the ith mark point;
vibration excitation signal F input by the crack-free beam structure and crack-free vibration response signal X of each mark point position1，X2，X3，K，XLCalculating the frequency response function R of each mark point1(f)，R2(f)，R3(f)，...，RL(f)；
Vibration excitation signal F input by the cracked beam structure and cracked vibration response signal of each mark point position
Figure BDA0002062340580000024
Calculating the frequency response function of each mark point
Figure BDA0002062340580000025
As a further improvement, in the step S4, comparing the frequency response functions of the corresponding mark points of the non-cracked beam and the cracked beam, calculating error quantization values of the frequency response functions of the corresponding mark points of the non-cracked beam and the cracked beam, averaging the error quantization values through N experiments, eliminating error factors, and obtaining an error index
Figure BDA0002062340580000036
Figure BDA0002062340580000031
L error indexes can be obtained by L marking points along the beam direction
Figure BDA0002062340580000032
Value of
Figure BDA0002062340580000033
Applying a normalization formula:
Figure BDA0002062340580000034
corresponding the L marking points to an error index
Figure BDA0002062340580000035
Normalizing to obtain damage index corresponding to L marking points1，2，…，L}。
As a further improvement, in step S4, a damage index value histogram corresponding to each mark point is drawn along the beam structure direction, the mark point corresponding to the maximum damage index value is found, and the mark point is seti＝max{1，2，…，LPosition the crack at point [ x ]i-1，xi]And determining the crack identification and positioning index model of each marking point position.
The invention provides a beam structure crack positioning method based on multiple frequency response function estimation, which comprises the following steps: s1, arranging a plurality of marking points which are distributed at equal intervals on the beam structure, and determining the positions of the marking points; s2, inputting a vibration excitation signal to the beam structure aiming at the same beam structure, and collecting vibration response signals output by the beam structure when each mark point position has no crack or cracks; s3, according to the vibration excitation signal and the vibration response signal, describing the vibration transfer characteristics of each mark point of the beam structure when no crack exists or a crack exists by adopting a frequency response function; s4, establishing a crack identification and positioning index model of each mark point position according to the change of the frequency response function of each corresponding mark point before and after the generation of the beam structure crack; and S5, determining whether the beam structure has cracks and the crack positions according to the crack identification and positioning index model aiming at the beam structure with the unknown crack positions. The invention has the following beneficial effects:
1. the damage detection method based on the frequency response function is strong in anti-interference capability, sensitive to structural damage and capable of accurately positioning crack positions;
2. the invention realizes the large-span measurement of the mark points by using a machine vision non-contact measurement method, and the measurement method is variable without influencing the actual vibration characteristics of the structure.
3. The position of the crack in the beam structure can be found and determined in time, so that the beam structure can be maintained in time, waste caused by premature replacement of the beam structure is reduced, and the material utilization rate is improved;
4. the method avoids safety accidents caused by failure of timely discovering of crack damage of the beam structure, and provides guarantee for the safety of the engineering structure.
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The invention is further illustrated by means of the attached drawings, but the embodiments in the drawings do not constitute any limitation to the invention, and for a person skilled in the art, other drawings can be obtained on the basis of the following drawings without inventive effort.
Fig. 1 is a schematic diagram of the positions of the mark points of the beam structure provided by the present invention.
FIG. 2 is a schematic diagram of an experimental structure based on machine vision measurement provided by the present invention; wherein, 1 is a blade; 2, a base; 3, a vibration exciter; 4-an industrial camera; 5-a bar light source; 6-vibration exciter control system; 7-a power amplifier; 8-an acceleration sensor; and 9, an image acquisition system.
FIG. 3 is a flow chart of a beam structure crack location positioning detection method provided by the present invention;
FIG. 4 is a diagram of crack identification and positioning index distribution of crack damage at each measuring point between 7 and 8 measuring points of the beam structure under the second-order natural frequency excitation condition of the beam structure provided by the invention.
FIG. 5 is a diagram of crack identification and positioning indexes of crack damage at each measuring point between 5 and 6 measuring points of the beam structure under the second-order natural frequency excitation condition of the beam structure.
FIG. 6 is a crack identification and positioning index distribution diagram of crack damage at each measuring point between 7 and 8 measuring points of the beam structure and under the condition of input excitation frequency 42 HZ.
FIG. 7 is a crack identification and positioning index distribution diagram of crack damage at each measuring point between the measuring points 7 and 8 of the beam structure and under the condition of input excitation frequency 62 HZ.
Detailed Description
In order to make those skilled in the art better understand the technical solution of the present invention, the following detailed description of the present invention is provided with reference to the accompanying drawings and specific embodiments, and it is to be noted that the embodiments and features of the embodiments of the present application can be combined with each other without conflict.
The invention has the core that the invention provides a beam structure crack positioning method based on multiple frequency response function estimation, which carries out multiple frequency response function estimation and describes the vibration transfer characteristics between input and output position points based on excitation input and vibration signals output by any marking point; comparing the changes of the frequency response function between the corresponding input and output positions of the beam structure when no crack exists and the beam structure has a crack to establish a corresponding crack identification index; and finally, realizing accurate positioning of the crack region of the beam structure by identifying the maximum position of the frequency response function change value. Specifically, marking points with equal intervals are arranged on a beam structure, and the positions of the marking points are determined; respectively obtaining vibration response signals of each set mark point when the beam structure has no cracks and cracks by adopting a non-contact measurement method under the premise of adding excitation input; performing multiple frequency response function estimation on vibration transfer characteristics between input and output position points based on excitation input and vibration signals output by any marking point; comparing the changes of the frequency response function between the corresponding input and output positions of the beam structure when no crack exists and the beam structure has a crack to establish a corresponding crack identification index; and finally, realizing accurate positioning of the crack region of the beam structure by identifying the maximum position of the frequency response function change value.
According to the method for positioning the cracks of the beam structure based on the multiple frequency response function estimation, provided by the embodiment of the invention, two small beam structures in normal states and at different positions of crack damage are manufactured by measuring multi-position point vibration response data, and for accurately obtaining vibration response signals of multi-position points of the beam structure under the same condition, position mark points are arranged on a side surface middle line of the beam structure and are horizontally arranged at equal intervals, and the number of the position mark points is 15, as shown in figure 1; the multi-position point vibration response signals are collected through a machine vision measuring device, the schematic diagram of the experimental device is shown in figure 2, the root end of a beam structure 1 is fixed on a base 2, and the other end of the beam structure is in a free state; the beam structure 1 is fixedly connected with the vibration exciter 3 through an adhesion thimble, and an acceleration sensor is pasted near the connection part of the beam structure for real-time vibration feedback; the industrial camera 4 is fixed on a tripod and horizontally placed right in front of the beam structure 1, and the two strip-shaped light sources 5 are placed in front of the side of the beam structure to ensure uniform illumination of a measuring point; an excitation signal is sent by a built-in vibration controller of a computer vibration exciter control system 6 and is transmitted to a power amplifier 7, then the excitation signal is transmitted to an excitation rod of a vibration exciter 3 by the power amplifier 7 to drive the beam structure 1 to vibrate, an acceleration sensor 8 arranged at the tail end of the excitation rod feeds back a vibration signal to the vibration exciter control system 6 so as to ensure the precision of the excitation signal generated by the vibration exciter 3, the beam structure 1 is subjected to vibration test by the vibration exciter 3, and meanwhile, an image acquisition system 9 is used for carrying out continuous image acquisition on the vibration process of the beam structure 1. And subsequently acquiring a multi-position point vibration response signal of the beam structure through image processing.
As shown in fig. 3, a method for positioning a crack of a beam-like structure based on multiple frequency response function estimation provided by an embodiment of the present invention includes the following steps:
and S1, arranging a plurality of marking points which are distributed at equal intervals on the beam structure, and determining the positions of the marking points. Specifically, the beam structure is marked, the number L of the marking points is set, and the positions of the L marking points are determined. And arranging position marking points which are arranged at equal intervals on the edge section of the beam structure, and identifying the vibration image marking points of the beam structure without cracks and with cracks in the same working state in a machine vision non-contact distributed measurement mode.
And S2, inputting a vibration excitation signal to the beam structure under the same working condition aiming at the same beam structure, and collecting vibration response signals output by the beam structure when each mark point position has no cracks or cracks. Specifically, under the same working state and the same input vibration excitation signal F, aiming at the same beam structure, crack-free vibration response signals X of the mark points of the beam structure at the crack-free position are collected when the beam structure is crack-free1，X2，X3，K，XLAnd crack vibration response signals for each of said mark point positions when said beam structure has a crack
Figure BDA0002062340580000061
And S3, according to the vibration excitation signal and the vibration response signal, describing the vibration transmission characteristics of each mark point of the beam structure when no crack exists or a crack exists by adopting a frequency response function. Specifically, calculating the frequency response function R of each output mark point relative to the input point according to the crack-free beam structure input signal and the output vibration signal of any mark point1(f)，R2(f)，R3(f)，...，RL(f) (ii) a Calculating the frequency response function of each output mark point relative to the input point according to the input signal of the cracked beam structure and the output vibration signal of any mark point
Figure BDA0002062340580000062
Calculating the measured input signal F and the measured output signal X at the ith pointiCross spectral mean of
Figure BDA0002062340580000063
Calculating the self-spectral mean P of the measured input signalFF(f)。
By the formula
Figure BDA0002062340580000064
And calculating to obtain the frequency response function of the ith point relative to the input point.
Inputting a signal F from a crack-free beam structure and a crack-free vibration response signal X at each of the mark point positions1，X2，X3，K，XLCalculating the frequency response function R of each output mark point relative to the input point1(f)，R2(f)，R3(f)，...，RL(f)。
Inputting signal F by the crack-free beam structure and crack-free vibration response signal of each mark point position
Figure BDA0002062340580000065
Calculating the frequency response function of each output mark point relative to the input point
Figure BDA0002062340580000066
And S4, establishing a crack identification and positioning index model of each mark point position according to the change of the frequency response function of each corresponding mark point before and after the generation of the beam structure crack. Specifically, frequency response functions of corresponding mark points of the non-cracked beam and the cracked beam are compared, error quantification values of the frequency response functions of the corresponding mark points of the non-cracked beam and the cracked beam are calculated, averaging is carried out through N times of experiments, error factors are eliminated, and an error index is obtained
Figure BDA0002062340580000077
Figure BDA0002062340580000071
Then L error indexes can be obtained by L marking points along the beam direction
Figure BDA0002062340580000072
Value of
Figure BDA0002062340580000073
Using normalisation formulae
Figure BDA0002062340580000074
Will be provided with
Figure BDA0002062340580000075
Normalized to obtain damage index1，2，…，L}；
Drawing a histogram of normalized damage index values corresponding to the mark points along the beam structure direction, finding out the mark point corresponding to the maximum damage index value, and settingi＝max{1，2，…，LPosition the crack at point [ x ]i-1，xi]In the meantime.
And S5, determining whether the beam structure has cracks and the crack positions according to the crack identification and positioning index model under the same working condition aiming at the beam structure with the unknown crack positions.
In order to explain the feasibility of the method, the effect of crack position identification under the conditions of different crack positions under the second-order natural frequency excitation frequency of the beam structure, the same crack position and different input excitation frequencies is verified through experiments, and the specific verification process is as follows:
1. crack position change verification experiment
And performing a frequency sweep experiment on the beam structure through the vibration exciter to obtain the second-order natural frequency 46HZ of the beam structure.
1) The crack position is between 7 and 8 points: setting crack positions on the beam between 7 and 8 points, applying 46HZ sinusoidal fixed frequency excitation to the beam structure through a vibration exciter, and acquiring crack-free vibration response signals X at the positions of the mark points when the beam structure is crack-free aiming at the same beam structure under the same working state and the same input signal F1，X2，X3，K，XLAnd crack vibration response signals for each of said mark point positions when said beam structure has a crack
Figure BDA0002062340580000076
Calculating the frequency response function R of each output mark point relative to the input point according to the input signal of the crack-free beam structure and the output vibration signal of any mark point by a formula (1)1(f)，R2(f)，R3(f)，...，RL(f) Calculating the frequency response function of each output mark point relative to the input point according to the input signal of the cracked beam structure and the output vibration signal of any mark point
Figure BDA0002062340580000081
The damage index values corresponding to the mark points of the beam structure are calculated by the formulas (2) and (3), a value histogram 4 is drawn along the mark points on the beam, and the maximum value of the mark point No. 8 can be known from the value histogram 4, so that the crack position area can be determined to be between 7 and 8, and the crack position area obtained by the experimental result is consistent with the actually set crack area position.
2) The crack position is between 5 and 6 points: setting crack position on the beam between 5 and 6 points, applying sinusoidal fixed frequency excitation to the beam structure 46HZ by the vibration exciter, and working in the same stateUnder the same state and the same input signal F, aiming at the same beam structure, acquiring crack-free vibration response signals X of the mark point positions when the beam structure has no cracks1，X2，X3，K，XLAnd crack vibration response signals for each of said mark point positions when said beam structure has a crack
Figure BDA0002062340580000082
Calculating the frequency response function R of each output mark point relative to the input point according to the input signal of the crack-free beam structure and the output vibration signal of any mark point by a formula (1)1(f)，R2(f)，R3(f)，...，RL(f) Calculating the frequency response function of each output mark point relative to the input point according to the input signal of the cracked beam structure and the output vibration signal of any mark point
Figure BDA0002062340580000083
The damage index values corresponding to the mark points of the beam structure are calculated by the formulas (2) and (3), a value histogram 4 is drawn along the mark points on the beam, and the maximum value of the mark point No. 6 can be known from the graph 5, so that the crack position area can be determined to be between 5 and 6, and the crack position area obtained by the experimental result is consistent with the actually set crack area position.
2. Excitation frequency variation verification experiment
1) Excitation frequency 42 HZ: setting the crack position on the beam between 7 and 8 points, applying 42HZ sinusoidal fixed frequency excitation to the beam structure through a vibration exciter, and acquiring crack-free vibration response signals X at the mark point positions of the same beam structure under the same working state and the same input signal F when the beam structure is crack-free1，X2，X3，K，XLAnd crack vibration response signals for each of said mark point positions when said beam structure has a crack
Figure BDA0002062340580000084
Calculating each output mark point according to the input signal of the crack-free beam structure and the output vibration signal of any mark point by the formula (1)Frequency response function R of relative input point1(f)，R2(f)，R3(f)，...，RL(f) Calculating the frequency response function of each output mark point relative to the input point according to the input signal of the cracked beam structure and the output vibration signal of any mark point
Figure BDA0002062340580000091
The damage index values corresponding to the mark points of the beam structure are calculated and obtained through formulas (2) and (3), a value histogram 6 is drawn along the mark points on the beam, and the maximum value of the mark point No. 8 can be known from the value histogram 6, so that the crack position area can be determined to be between 7 and 8, and the crack position area obtained through experimental results is consistent with the actually set crack area position.
2) Excitation frequency 62 HZ: setting the crack position on the beam between 7 and 8 points, applying 62HZ sinusoidal fixed frequency excitation to the beam structure through a vibration exciter, and acquiring crack-free vibration response signals X at the mark point positions of the same beam structure under the same working state and the same input signal F when the beam structure is crack-free1，X2，X3，K，XLAnd crack vibration response signals for each of said mark point positions when said beam structure has a crack
Figure BDA0002062340580000092
Calculating the frequency response function R of each output mark point relative to the input point according to the input signal of the crack-free beam structure and the output vibration signal of any mark point by a formula (1)1(f)，R2(f)，R3(f)，...，RL(f) Calculating the frequency response function of each output mark point relative to the input point according to the input signal of the cracked beam structure and the output vibration signal of any mark point
Figure BDA0002062340580000093
Calculating to obtain damage index values corresponding to each mark point of the beam structure according to formulas (2) and (3), drawing a value histogram 7 along the mark points on the beam, and finding out that the value of the mark point No. 8 is maximum from the value histogram 7, so that the crack position area can be determined to be between 7 and 8 points, and the crack position obtained by experimental resultsThe region coincides with the actually provided crack region position.
In the description above, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described herein, and therefore should not be construed as limiting the scope of the present invention.
In conclusion, although the present invention has been described with reference to the preferred embodiments, it should be noted that, although various changes and modifications may be made by those skilled in the art, they should be included in the scope of the present invention unless they depart from the scope of the present invention.

Claims (5)

1. A beam structure crack positioning method based on multiple frequency response function estimation is characterized by comprising the following steps:
s1, arranging a plurality of marking points which are distributed at equal intervals on the beam structure, and determining the positions of the marking points;
s2, inputting a vibration excitation signal to the same beam structure under the same working condition aiming at the same beam structure, and collecting vibration response signals output by the beam structure when each mark point position has no cracks or cracks;
s3, according to the vibration excitation signal and the vibration response signal, describing the vibration transfer characteristics of each mark point of the beam structure when no crack exists or a crack exists by adopting a frequency response function;
s4, establishing a crack identification and positioning index model of each mark point position according to the change of the frequency response function of each corresponding mark point before and after the generation of the beam structure crack;
and S5, determining whether the beam structure has cracks and the crack positions according to the crack identification and positioning index model under the same working condition aiming at the beam structure with the unknown crack positions.
2. The method for positioning cracks of beam-like structure based on multiple frequency response function estimation of claim 1, wherein in step S2, a machine vision non-contact measurement method is adopted for the same beam junctionA structure for collecting crack-free vibration response signals X output by the positions of the mark points when the beam structure has no cracks1，X2，X3，K，XLCollecting crack vibration response signals output by the positions of the mark points when the beam structure has cracks
Figure FDA0002062340570000011
3. The method for positioning cracks of beam-like structures based on multiple frequency response function estimation as claimed in claim 2, wherein in step S3, the measured input vibration excitation signal F and the measured output crack-free vibration response signal X of the ith mark point are calculatediCross spectral mean of
Figure FDA0002062340570000012
Calculating self-spectrum mean value P of actually measured input vibration excitation signalFF(f)；
By the formula
Figure FDA0002062340570000013
Calculating to obtain a frequency response function of the ith mark point;
vibration excitation signal F input by the crack-free beam structure and crack-free vibration response signal X of each mark point position1，X2，X3，K，XLCalculating the frequency response function R of each mark point1(f)，R2(f)，R3(f)，...，RL(f)；
Vibration excitation signal F input by the cracked beam structure and cracked vibration response signal of each mark point position
Figure FDA0002062340570000021
Calculating the frequency response function of each mark point
Figure FDA0002062340570000022
4. The method for positioning cracks of beam-like structures based on multiple frequency response function estimation as claimed in claim 3, wherein in step S4, the frequency response functions of the corresponding mark points of the crack-free beam and the crack-containing beam are compared, the error quantization values of the frequency response functions of the corresponding mark points of the crack-free beam and the crack-containing beam are calculated, the average is performed through N times of experiments, the error factors are eliminated, and the error index is obtained
Figure FDA0002062340570000023
Figure FDA0002062340570000024
L error indexes can be obtained by L marking points along the beam direction
Figure FDA0002062340570000025
Value of
Figure FDA0002062340570000026
Applying a normalization formula:
Figure FDA0002062340570000027
corresponding the L marking points to an error index
Figure FDA0002062340570000028
Normalizing to obtain damage index corresponding to L marking points1，2，…，L}。
5. The method as claimed in claim 4, wherein in step S4, a histogram of damage index values corresponding to each mark point is plotted along the beam structure direction, a mark point corresponding to the maximum damage index value is found, and the mark point is seti＝max{1，2，…，LPosition the crack at point [ x ]i-1，xi]And determining the crack identification and positioning index model of each marking point position.
CN201910409482.9A 2019-05-17 2019-05-17 Beam structure crack positioning method based on multiple frequency response function estimation Withdrawn CN112034048A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113591014A (en) * 2021-07-15 2021-11-02 桂林电子科技大学 Crack area identification method for space balance truss plate girder
CN114295726A (en) * 2022-01-07 2022-04-08 中国船舶重工集团公司第七一一研究所 Heat exchanger plate crack detection device and crack detection method thereof

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113591014A (en) * 2021-07-15 2021-11-02 桂林电子科技大学 Crack area identification method for space balance truss plate girder
CN113591014B (en) * 2021-07-15 2024-03-29 桂林电子科技大学 Crack area identification method for space balance truss plate girder
CN114295726A (en) * 2022-01-07 2022-04-08 中国船舶重工集团公司第七一一研究所 Heat exchanger plate crack detection device and crack detection method thereof

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