CN114383834A - Ocean engineering structure micro-damage judgment method - Google Patents

Ocean engineering structure micro-damage judgment method Download PDF

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CN114383834A
CN114383834A CN202210036234.6A CN202210036234A CN114383834A CN 114383834 A CN114383834 A CN 114383834A CN 202210036234 A CN202210036234 A CN 202210036234A CN 114383834 A CN114383834 A CN 114383834A
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王树青
蒋玉峰
徐明强
郭建
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Ocean University of China
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Abstract

The invention provides a method for judging tiny damage of an ocean engineering structure, which comprises the following steps: measuring the dynamic response time-course data of the intact ocean engineering structure for multiple times; determining the former n-order modal frequency according to the dynamic response time-course data based on a modal parameter identification method; combining modal frequencies obtained by each test to obtain a perfect frequency matrix; obtaining a frequency matrix to be tested of the ocean engineering structure to be tested by adopting the same method; performing linear discrimination analysis on the intact frequency matrix and the frequency matrix to be detected to obtain an intact frequency residual error and a frequency residual error to be detected; and determining whether the ocean engineering structure to be detected is damaged or not based on a hypothesis testing technology. The original frequency matrix is processed by using a linear discriminant analysis method, the influence of environmental factor change on the structural vibration characteristic is effectively eliminated, the frequency residual error reflecting structural health information is obtained, and the accurate judgment on the micro-damage state of the structure is realized by matching with a statistical hypothesis testing technology.

Description

Ocean engineering structure micro-damage judgment method
The application is a divisional application of a patent application named as a method for determining the tiny damage of the ocean engineering structure, wherein the application date of the original application is 09, 14 and 2020, and the application number is 202010960246.9.
Technical Field
The invention relates to the field of ship and ocean engineering, in particular to a method for judging tiny damage of an ocean engineering structure under the conditions of environmental factors and noise interference.
Background
Ocean engineering structures such as ocean platforms and offshore wind turbines are basic facilities for ocean oil gas and wind energy resource development, and are in severe ocean environments for a long time, fatigue accumulation damage is easy to occur, structure failure is caused, and huge economic loss is caused. Therefore, the method is very important for carrying out damage detection on the ocean engineering structure.
The common method for detecting the structural damage of the ocean engineering at the present stage can be summarized into local detection and overall detection, wherein the local detection method starts earlier and develops relatively mature; for example, magnetic particle inspection, ray inspection, ultrasonic guided wave inspection and the like are adopted, but the method is only limited to a local area of the structure and is difficult to reflect the whole state information of the structure; in addition, the local detection position needs to be determined in advance, and the detection efficiency is extremely low when the damage position is unknown. In contrast, the integral detection method based on the structural vibration characteristics can completely reflect the integral state information of the structure, can provide enough structural performance evolution and degradation information, is particularly suitable for monitoring the ocean engineering structure in real time, and can provide certain guiding significance for the structure life evaluation and maintenance reinforcement decision. The basic principle is as follows: the damage of the structure can cause the change of the physical characteristics of the structure, thereby changing the modal parameters of the structure; and the overall state information of the structure is inverted by obtaining the modal parameters reflecting the physical characteristics of the structure. Common modal parameters are frequency, mode shape, damping ratio, and multi-parameter derivatives.
With the rapid improvement of computer level and data acquisition capability, the overall detection method based on modal parameters is greatly developed. It is noted that most of these methods do not consider the influence of changes in marine environmental factors on the performance of damage detection. The change of the marine environmental factors such as temperature, marine organism attachment, basic scouring and the like can also cause the change of the physical characteristics of the structure, influence the change of the modal parameters of the structure, and even cover the change of the modal parameters caused by the real damage of the structure, especially for early/micro damage. The detection of the tiny damage of the ocean engineering structure considering environmental factors and noise pollution is a difficult problem to be solved urgently at present.
The early detection and diagnosis of the early/small damage of the structure are carried out, the effective structural operation state evaluation is carried out, and the method has important practical value for the safe operation guarantee of the ocean engineering structure.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a method for judging the micro-damage of the ocean engineering structure, which realizes the judgment of the micro-damage of the ocean engineering structure under the environment and noise pollution and has certain guiding significance for early warning and maintenance reinforcement decision of the structure.
In order to achieve the purpose, the invention provides the following scheme:
a method for judging tiny damage of an ocean engineering structure comprises the following steps:
in an actual operation environment, measuring the dynamic response time-course data of the intact ocean engineering structure for multiple times by using a sensor;
determining the first n-order modal frequency of the intact ocean engineering structure according to the dynamic response time-course data of the intact ocean engineering structure based on a modal parameter identification method;
combining modal frequencies obtained by each test to obtain a perfect frequency matrix;
in an actual operation environment, measuring the dynamic response time-course data of the ocean engineering structure to be measured by using a sensor for multiple times;
determining the front n-order modal frequency of the ocean engineering structure to be detected according to the dynamic response time course data of the ocean engineering structure to be detected based on a modal parameter identification method;
combining modal frequencies obtained by each test to obtain a frequency matrix to be tested;
performing linear discrimination analysis on the intact frequency matrix and the frequency matrix to be detected, and solving the projection direction with optimized classification performance of the intact frequency matrix and the frequency matrix to be detected to obtain an intact frequency residual error and a frequency residual error to be detected;
and determining whether the ocean engineering structure to be detected is damaged or not according to the intact frequency residual error and the frequency residual error to be detected based on a hypothesis testing technology.
Optionally, the number of sensors is one.
Optionally, the sensor is an acceleration sensor or a displacement sensor.
Optionally, the good frequency matrix is:
Figure BDA0003468350150000031
wherein, ω ishIs a perfect frequency matrix, h represents a perfect ocean engineering structure, m is the total times of vibration tests,
Figure BDA0003468350150000032
for the first n-order modal frequency of the intact ocean engineering structure obtained for the j-th measurement,
Figure BDA0003468350150000033
and obtaining the ith order modal frequency of the intact ocean engineering structure for the jth measurement.
Optionally, the frequency matrix to be measured is:
Figure BDA0003468350150000034
wherein, ω iscIs a frequency matrix to be tested, c represents the ocean engineering structure to be tested, m is the total times of vibration tests,
Figure BDA0003468350150000035
for the first n-order modal frequency of the ocean engineering structure to be measured obtained by the jth measurement,
Figure BDA0003468350150000036
and obtaining the ith order modal frequency of the ocean engineering structure to be measured for the jth measurement.
Optionally, performing linear discriminant analysis on the perfect frequency matrix and the frequency matrix to be measured, and solving a projection direction with optimized classification performance of the perfect frequency matrix and the frequency matrix to be measured to obtain a perfect frequency residual error and a frequency residual error to be measured, which specifically includes:
respectively carrying out averaging treatment on the intact frequency matrix and the frequency matrix to be detected to obtain a modal frequency matrix of the intact ocean engineering structure and a modal frequency matrix of the ocean engineering structure to be detected;
determining the intra-class variance of the modal frequency matrix of the intact ocean engineering structure according to the modal frequency matrix of the intact ocean engineering structure;
determining the intra-class variance of the modal frequency matrix of the ocean engineering structure to be detected according to the modal frequency matrix of the ocean engineering structure to be detected;
determining an intra-class variance sum according to the intra-class variance of the modal frequency matrix of the intact ocean engineering structure and the intra-class variance of the modal frequency matrix of the ocean engineering structure to be tested;
determining the optimal classification performance projection vector of the intact frequency matrix and the frequency matrix to be detected according to the intra-class variance;
and according to the optimal classification performance projection vector, carrying out projection and dimension reduction treatment on the intact frequency matrix and the frequency matrix to be detected to obtain corresponding intact frequency residual error and frequency residual error to be detected.
Optionally, the modal frequency matrix of the intact ocean engineering structure is:
Figure BDA0003468350150000041
wherein m ishIs a modal frequency matrix of an intact ocean engineering structure,
Figure BDA0003468350150000042
modal frequency matrix m for intact ocean engineering structurehThe average value of the ith row in the test is obtained, and n is the order of the ocean engineering structure to be tested;
the modal frequency matrix of the ocean engineering structure to be tested is as follows:
Figure BDA0003468350150000043
wherein m iscIs a modal frequency matrix of the ocean engineering structure to be measured,
Figure BDA0003468350150000044
modal frequency matrix omega for ocean engineering structure to be measuredcAverage value of the ith row in (1).
Optionally, the intra-class variance sum is determined according to the following formula:
Figure BDA0003468350150000045
Figure BDA0003468350150000046
Figure BDA0003468350150000051
wherein S iswIs the sum of the intra-class variances,
Figure BDA0003468350150000052
is a sound ocean engineering knotThe intra-class variance of the constructed modal frequency matrix,
Figure BDA0003468350150000053
is the intra-class variance of the modal frequency matrix of the ocean engineering structure to be tested, m is the total times of vibration test,
Figure BDA0003468350150000054
for the first n-order modal frequency of the intact ocean engineering structure obtained for the j-th measurement,
Figure BDA0003468350150000055
obtaining the first n-order modal frequency m of the ocean engineering structure to be measured for the jth measurementhModal frequency matrix, m, for a sound marine engineering structurecThe method comprises the following steps that T represents transposition operation of a matrix for a modal frequency matrix of the ocean engineering structure to be detected;
determining an optimal classification performance projection vector according to the following formula:
P＝Sw -1(mh-mc)；
determining a complete frequency residual error and a frequency residual error to be detected according to the following formula;
Figure BDA0003468350150000056
Figure BDA0003468350150000057
wherein the content of the first and second substances,
Figure BDA0003468350150000058
in order to be a good frequency residual,
Figure BDA0003468350150000059
is the frequency residual error to be measured.
Optionally, the determining, based on the hypothesis testing technique, whether the ocean engineering structure to be tested is damaged according to the sound frequency residual and the frequency residual to be tested specifically includes:
calculating a statistical hypothesis test quantity value according to the mean value of the intact frequency residual errors, the mean value of the to-be-tested frequency residual errors, the standard deviation of the intact frequency residual errors and the standard deviation of the to-be-tested frequency residual errors;
calculating a hypothesis test quantity threshold based on the statistical hypothesis test quantity value and the confidence level;
and comparing the absolute value of the hypothesis testing quantity value with the size of the hypothesis testing quantity threshold value, if the absolute value of the hypothesis testing quantity value is smaller than or equal to the hypothesis testing quantity threshold value, judging that the ocean engineering structure to be tested is damaged, and if the absolute value of the hypothesis testing quantity value is larger than the hypothesis testing quantity threshold value, judging that the ocean engineering structure to be tested is not damaged.
Optionally, the statistical hypothesis test magnitude is determined according to the following equation:
Figure BDA0003468350150000061
where t is the statistical hypothesis test quantity, μhIs the mean of the perfect frequency residual, mucIs the mean value, σ, of the frequency residual to be measuredhStandard deviation of perfect frequency residual, σcThe standard deviation of the frequency residual error to be measured is obtained;
the hypothesis test quantity threshold is calculated according to the following formula:
P(t<t*)＝1-α/2；
where α is the confidence level, t*Is a hypothesis test quantity threshold.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the original frequency matrix is processed by using a linear discriminant analysis method, so that the influence of environmental factor change on the structural vibration characteristic is effectively eliminated, a frequency residual capable of reflecting structural health information is obtained, and the accurate judgment on the tiny damage state of the structure is realized by using an effective statistical hypothesis testing technology in a matching manner;
moreover, only the vibration response of the structure needs to be measured, the current environmental factors do not need to be measured, only the intact ocean platform and the damaged ocean platform need to be measured in a short term respectively, and long-term continuous monitoring is not needed; the damage judgment process can be completed by only arranging one sensor, so that the difficulty of damage detection is greatly reduced, and the cost is saved;
the method realizes judgment of the micro damage of the ocean engineering structure under environmental and noise pollution, is beneficial to finding the early damage/micro damage of the structure, and has certain guiding significance for early warning and maintenance reinforcement decision of the structure.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a schematic diagram of a finite element model of an offshore wind turbine structure according to an embodiment of the present invention; (a) the part is a numbering schematic diagram of structural nodes of the offshore wind turbine, (b) the part is a numbering schematic diagram of structural units of the offshore wind turbine, (b) 14 in the part is an inclined strut unit, and 10 is a cross strut unit;
FIG. 2 is a diagram showing the result of the determination of the small damage under the influence of no noise and environmental factors;
fig. 3 is a diagram showing the result of the determination of the micro damage under the influence of 0.15% noise and environmental factors.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the 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.
The invention aims to provide a method for judging the tiny damage of an ocean engineering structure, which is characterized in that an original frequency matrix is processed by using a linear discriminant analysis method, so that the influence of environmental factor change on the vibration characteristic of the structure is effectively eliminated, the damage judgment process can be completed by only arranging one sensor, the difficulty of damage detection is greatly reduced, and the cost is saved.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
A method for judging tiny damage of an ocean engineering structure comprises the following steps:
firstly, carrying out vibration test on a perfect ocean engineering structure in an actual operation environment to obtain a perfect frequency matrix of the structure.
And secondly, performing vibration test on the ocean engineering structure to be tested in the actual operation environment to obtain a frequency matrix to be tested of the structure, wherein whether the ocean engineering structure to be tested is damaged is unknown.
And thirdly, solving the projection direction with the optimized classification performance of the intact frequency matrix to be detected and the frequency matrix to be detected by carrying out linear discrimination analysis on the intact frequency matrix and the frequency matrix to be detected to obtain an intact frequency residual error and a frequency residual error to be detected of the ocean engineering structure.
The fourth step: and carrying out structural damage judgment on the intact frequency residual error and the frequency residual error to be detected by a hypothesis testing technology.
Specifically, the following describes the determination method in detail with reference to specific embodiments:
in the first step, a vibration test is carried out on an intact ocean engineering structure in an actual working environment, and the specific steps of obtaining a frequency matrix of the intact ocean engineering structure are as follows:
(1) in an actual working environment, an acceleration sensor or a displacement sensor is used for measuring the complete dynamic response time-course data of the ocean engineering structure.
(2) Based on a modal parameter identification method, acquiring the first n-order modal frequency of the ocean engineering structure according to the dynamic response time-course data of the intact ocean engineering structure, wherein the jth timeMeasuring the obtained ith order modal frequency to
Figure BDA0003468350150000081
And (4) showing.
(3) And (3) performing m vibration tests in total, combining the frequencies obtained by the tests to construct a complete frequency matrix omega of the structureh
Figure BDA0003468350150000082
In the second step, the marine engineering structure to be tested in the actual operation environment is subjected to vibration test, and the specific steps of obtaining the frequency matrix to be tested of the marine engineering structure are as follows:
the method comprises the steps of carrying out m-time vibration test on a damaged ocean engineering structure, and constructing a frequency matrix omega of the ocean engineering structure to be tested according to the step of obtaining the frequency vibration mode of the intact structure of the ocean engineeringc
Figure BDA0003468350150000083
Wherein the first n-th order modal frequency obtained by the jth measurement is calculated by
Figure BDA0003468350150000084
And (4) showing.
In the third step, the interference of environmental factors is eliminated by performing linear discrimination analysis on the intact frequency matrix and the frequency matrix to be detected, and the concrete steps of obtaining the intact frequency residual error and the frequency residual error to be detected are as follows:
(1) respectively carrying out equalization processing on the intact frequency matrix and the frequency matrix to be measured, wherein
Figure BDA0003468350150000085
And
Figure BDA0003468350150000086
modal frequency moment representing intact ocean engineering structure and ocean engineering structure to be measuredArray omegahAnd ωcAverage value of the ith row in (1).
Figure BDA0003468350150000091
(2) Analyzing to obtain the frequency matrix of the intact ocean engineering structure and the intra-class variance and S of the frequency matrix of the ocean engineering structure to be detectedwWherein
Figure BDA0003468350150000092
And
Figure BDA0003468350150000093
the intra-class variance of the modal frequency matrix expressed as the intact ocean engineering structure and the ocean engineering structure to be measured is as follows:
Figure BDA0003468350150000094
Figure BDA0003468350150000095
Figure BDA0003468350150000096
(3) calculating to obtain the optimal classification performance projection vectors of the intact frequency matrix and the frequency matrix to be measured:
P＝Sw -1(mh-mc) (7)
(4) projecting and reducing the dimension of the frequency matrix of the intact ocean engineering structure and the frequency matrix of the ocean engineering structure to be detected through the projection vector P to obtain corresponding intact frequency residual error and frequency residual error to be detected:
Figure BDA0003468350150000097
Figure BDA0003468350150000098
wherein, formula (8) is the perfect frequency residual, and formula (9) is the frequency residual to be measured.
And in the fourth step, judging the structural damage of the intact frequency residual error and the frequency residual error to be detected by a hypothesis testing technology, and specifically comprising the following steps of:
(1) assuming the mean of the intact frequency residual and the frequency residual to be measured to be equal to the original hypothesis H0The average values are assumed to be unequal H1：
H0:μh＝μc (10)
H1:μh≠μc (11)
(2) Statistical hypothesis test magnitudes were calculated, where μ and σ represent the mean and standard deviation of the frequency residuals:
Figure BDA0003468350150000101
(3) determining a confidence level alpha, calculating a hypothesis testing quantity threshold t*：
P(t<t*)＝1-α/2 (13)
(4) Comparing the hypothesis test magnitude | t | with a test magnitude threshold t*And judging whether the ocean engineering structure is damaged:
Figure BDA0003468350150000102
Figure BDA0003468350150000103
the judgment criterion is as follows: if the hypothesis testing magnitude is larger than the threshold value, rejecting the original hypothesis and considering that the structure is damaged; otherwise, the structure is considered not to be damaged.
To verify the effectiveness of the above method, a typical marine offshore wind turbine structure is illustrated as follows:
firstly, establishing a finite element model:
as shown in fig. 1 (a) and 1 (b), the marine wind turbine structure under simulation study in this embodiment is composed of a support structure and a tower structure, and includes 18 nodes (fig. 1 (a) and 1-18) and 20 units (fig. 1 (b) and 1-20). And (3) writing a finite element program by using MATLAB software, and establishing a finite element model by using a computer to serve as a reference finite element model of an intact ocean platform. And then, simulating different damage working conditions under different working environments to obtain the modal frequency simulating actual measurement. The method simulates various damage working conditions, including damage at different positions and damage in different degrees.
Second, simulation of structural damage and environmental conditions
When the ocean engineering structure is damaged, the overall rigidity of the material is lost, and the material is uniformly simplified into that the elastic modulus on a damaged unit is uniformly weakened. Meanwhile, the overall rigidity of the structure is also affected by changes of environmental conditions, wherein the most typical environmental conditions include temperature, basic scouring and the like, and in the embodiment, temperature factors are selected for simulation. The change of temperature generally causes the change of the elastic modulus of the material, and further influences the rigidity of the ocean platform, and experimental research shows that the elastic modulus and the temperature present a strong linear relationship
E(Tt)＝E(T0)+τ(Tt-T0) (16)
Wherein E (T)0) For the value of the modulus of elasticity in the reference state, the temperature is usually set to 10 ℃ and the corresponding modulus of elasticity is 2.06X 1011Pa; tau is the coefficient of variation of the elastic modulus of steel with temperature and is taken as 1 x 108Pa/℃。
The method is characterized in that the intact and damaged offshore wind turbine structure is supposed to be tested for 1000 times, the temperature difference between the seawater and the air is considered, the temperature in the air is supposed to be subjected to standard normal distribution with the mean value of 10 ℃ and the standard deviation of 8 ℃, and the temperature in the seawater is supposed to be subjected to standard normal distribution with the mean value of 15 ℃ and the standard deviation of 4 ℃.
Thirdly, analyzing damage judgment result
The scheme of the invention is utilized to judge the micro damage of the offshore wind turbine structure, and four working conditions are considered as follows: the working condition I is as follows: the bracing unit is damaged by 1%; working conditions are as follows: 1% of damage to the cross brace unit; working conditions are as follows: the bracing unit is damaged by 3%; working conditions are as follows: 3% of damage to the cross brace unit; and (4) adopting 50 times of repeated tests in each working condition, and calculating the accuracy of judging the tiny damage.
As shown in fig. 2 (a) and 2 (b), the results of the determination of the small damage under the influence of no noise and environmental factors are shown; as shown in fig. 3 (a) and 3 (b), under the influence of no noise, the test statistic of the four damage conditions is assumed to be much larger than the test statistic threshold (1.96), so that the damage determination accuracy of the four damage conditions is 100%; under the influence of 0.15% noise, only 7 times (working condition one) are judged to be healthy by mistake, other 193 times of repeated tests can accurately judge the micro damage of the structure, and the micro damage judgment accuracy rate is 96.5%.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (10)

1. A method for judging the tiny damage of an ocean engineering structure is characterized by comprising the following steps:
in an actual operation environment, measuring the dynamic response time-course data of the intact ocean engineering structure for multiple times by using a sensor;
determining the first n-order modal frequency of the intact ocean engineering structure according to the dynamic response time-course data of the intact ocean engineering structure based on a modal parameter identification method;
combining modal frequencies obtained by each test to obtain a perfect frequency matrix;
in an actual operation environment, measuring the dynamic response time-course data of the ocean engineering structure to be measured by using a sensor for multiple times;
determining the front n-order modal frequency of the ocean engineering structure to be detected according to the dynamic response time course data of the ocean engineering structure to be detected based on a modal parameter identification method;
combining modal frequencies obtained by each test to obtain a frequency matrix to be tested;
performing linear discrimination analysis on the intact frequency matrix and the frequency matrix to be detected, and solving the projection direction with optimized classification performance of the intact frequency matrix and the frequency matrix to be detected to obtain an intact frequency residual error and a frequency residual error to be detected;
and determining whether the ocean engineering structure to be detected is damaged or not according to the intact frequency residual error and the frequency residual error to be detected based on a hypothesis testing technology.
2. The method for determining the minor damage of the oceanographic engineering structure according to claim 1, wherein the number of the sensors is one.
3. The method for determining the minor damage of the oceaneering structure according to claim 2, wherein the sensor is an acceleration sensor or a displacement sensor.
4. The method for determining the micro damage of the ocean engineering structure according to claim 1, wherein the intact frequency matrix is:
Figure FDA0003468350140000011
wherein, ω ishIs a perfect frequency matrix, h represents a perfect ocean engineering structure, m is the total times of vibration tests,
Figure FDA0003468350140000021
for the j measurementThe first n-order modal frequency of the intact ocean engineering structure is obtained,
Figure FDA0003468350140000022
and obtaining the ith order modal frequency of the intact ocean engineering structure for the jth measurement.
5. The method for determining the micro damage of the ocean engineering structure according to claim 1, wherein the frequency matrix to be measured is:
Figure FDA0003468350140000023
wherein, ω iscIs a frequency matrix to be tested, c represents the ocean engineering structure to be tested, m is the total times of vibration tests,
Figure FDA0003468350140000024
for the first n-order modal frequency of the ocean engineering structure to be measured obtained by the jth measurement,
Figure FDA0003468350140000025
and obtaining the ith order modal frequency of the ocean engineering structure to be measured for the jth measurement.
6. The method for determining the micro damage of the ocean engineering structure according to claim 1, wherein the linear discriminant analysis is performed on the intact frequency matrix and the frequency matrix to be measured, and the projection direction with the optimized classification performance of the intact frequency matrix and the frequency matrix to be measured is solved to obtain an intact frequency residual error and a residual error of the frequency to be measured, and the method specifically comprises the following steps:
respectively carrying out averaging treatment on the intact frequency matrix and the frequency matrix to be detected to obtain a modal frequency matrix of the intact ocean engineering structure and a modal frequency matrix of the ocean engineering structure to be detected;
determining the intra-class variance of the modal frequency matrix of the intact ocean engineering structure according to the modal frequency matrix of the intact ocean engineering structure;
determining the intra-class variance of the modal frequency matrix of the ocean engineering structure to be detected according to the modal frequency matrix of the ocean engineering structure to be detected;
determining an intra-class variance sum according to the intra-class variance of the modal frequency matrix of the intact ocean engineering structure and the intra-class variance of the modal frequency matrix of the ocean engineering structure to be tested;
determining the optimal classification performance projection vector of the intact frequency matrix and the frequency matrix to be detected according to the intra-class variance;
and according to the optimal classification performance projection vector, carrying out projection and dimension reduction treatment on the intact frequency matrix and the frequency matrix to be detected to obtain corresponding intact frequency residual error and frequency residual error to be detected.
7. The method for determining the minor damage of the oceaneering structure according to claim 6, wherein the modal frequency matrix of the intact oceaneering structure is:
Figure FDA0003468350140000031
wherein m ishIs a modal frequency matrix of an intact ocean engineering structure,
Figure FDA0003468350140000032
modal frequency matrix m for intact ocean engineering structurehThe average value of the ith row in the test is obtained, and n is the order of the ocean engineering structure to be tested;
the modal frequency matrix of the ocean engineering structure to be tested is as follows:
Figure FDA0003468350140000033
wherein m iscIs a modal frequency matrix of the ocean engineering structure to be measured,
Figure FDA0003468350140000034
modal frequency matrix omega for ocean engineering structure to be measuredcAverage value of the ith row in (1).
8. The method for determining the minor damage of the oceaneering structure according to claim 6, wherein the sum of the intra-class variance is determined according to the following formula:
Figure FDA0003468350140000035
Figure FDA0003468350140000036
Figure FDA0003468350140000037
wherein S iswIs the sum of the intra-class variances,
Figure FDA0003468350140000038
is the intra-class variance of the modal frequency matrix of the intact ocean engineering structure,
Figure FDA0003468350140000041
is the intra-class variance of the modal frequency matrix of the ocean engineering structure to be tested, m is the total times of vibration test,
Figure FDA0003468350140000042
for the first n-order modal frequency of the intact ocean engineering structure obtained for the j-th measurement,
Figure FDA0003468350140000043
obtaining the first n-order modal frequency m of the ocean engineering structure to be measured for the jth measurementhModal frequency matrix, m, for a sound marine engineering structurecModal frequency for ocean engineering structure to be measuredA rate matrix, T representing a transpose operation of the matrix;
determining an optimal classification performance projection vector according to the following formula:
P＝Sw -1(mh-mc)；
determining a complete frequency residual error and a frequency residual error to be detected according to the following formula;
Figure FDA0003468350140000044
Figure FDA0003468350140000045
wherein the content of the first and second substances,
Figure FDA0003468350140000046
in order to be a good frequency residual,
Figure FDA0003468350140000047
is the frequency residual error to be measured.
9. The method for determining the micro damage of the ocean engineering structure according to claim 1, wherein the determining whether the ocean engineering structure to be tested is damaged or not according to the sound frequency residual error and the frequency residual error to be tested based on the hypothesis testing technology specifically comprises:
calculating a statistical hypothesis test quantity value according to the mean value of the intact frequency residual errors, the mean value of the to-be-tested frequency residual errors, the standard deviation of the intact frequency residual errors and the standard deviation of the to-be-tested frequency residual errors;
calculating a hypothesis test quantity threshold based on the statistical hypothesis test quantity value and the confidence level;
and comparing the absolute value of the hypothesis testing quantity value with the size of the hypothesis testing quantity threshold value, if the absolute value of the hypothesis testing quantity value is smaller than or equal to the hypothesis testing quantity threshold value, judging that the ocean engineering structure to be tested is damaged, and if the absolute value of the hypothesis testing quantity value is larger than the hypothesis testing quantity threshold value, judging that the ocean engineering structure to be tested is not damaged.
10. The method for determining the minor damage of the oceanographic engineering structure according to claim 9, wherein the statistical hypothesis test magnitude is determined according to the following formula:
Figure FDA0003468350140000051
where t is the statistical hypothesis test quantity, μhIs the mean of the perfect frequency residual, mucIs the mean value, σ, of the frequency residual to be measuredhStandard deviation of perfect frequency residual, σcThe standard deviation of the frequency residual error to be measured is obtained;
the hypothesis test quantity threshold is calculated according to the following formula:
P(t<t*)＝1-α/2；
where P () is the calculated probability value, α is the confidence level, t*Is a hypothesis test quantity threshold.
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