CN114383834B - Ocean engineering structure micro damage judging method - Google Patents

Ocean engineering structure micro damage judging method Download PDF

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CN114383834B
CN114383834B CN202210036234.6A CN202210036234A CN114383834B CN 114383834 B CN114383834 B CN 114383834B CN 202210036234 A CN202210036234 A CN 202210036234A CN 114383834 B CN114383834 B CN 114383834B
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engineering structure
ocean engineering
frequency
frequency matrix
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CN114383834A (en
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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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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H17/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves, not provided for in the preceding groups
    • G—PHYSICS
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    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
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    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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    • G06F2111/00—Details relating to CAD techniques
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Abstract

The invention provides a method for judging micro damage of a marine engineering structure, which comprises the following steps: measuring dynamic response time course data of the intact ocean engineering structure for a plurality of times; determining the first n-order modal frequencies according to the dynamic response time course data based on a modal parameter identification method; combining the modal frequencies obtained by each test to obtain a sound frequency matrix; obtaining a frequency matrix to be detected of the ocean engineering structure to be detected by adopting the same method; performing linear discriminant analysis on the perfect frequency matrix and the frequency matrix to be detected to obtain a perfect 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 the hypothesis test technology. The original frequency matrix is processed by using a linear discriminant analysis method, the influence of environmental factor change on structural vibration characteristics is effectively eliminated, the frequency residual error reflecting structural health information is obtained, and the accurate judgment of the micro damage state of the structure is realized by matching with a statistical hypothesis testing technology.

Description

Ocean engineering structure micro damage judging method
The application is a divisional application of a patent application named as a method for judging tiny damage of ocean engineering structure, and the application date of the original application is 09/14/2020/202010960246.9.
Technical Field
The invention relates to the field of ships 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, offshore fans and the like are basic facilities for development of ocean oil gas and wind energy resources, are in severe ocean environments for a long time, are extremely easy to generate fatigue accumulation and damage, lead to structural failure and cause huge economic loss. Therefore, the method is very important for carrying out damage detection on the ocean engineering structure.
The conventional method for detecting the damage of the marine engineering structure at the present stage can be summarized into local detection and overall detection, wherein the local detection method is early in starting and relatively mature in development; for example, magnetic powder detection, ray detection, ultrasonic guided wave detection and the like, but the method is limited to a local area of a structure, so that the whole state information of the structure is difficult to reflect; and the local detection position needs to be predetermined, 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 marine engineering structure in real time, and can provide a certain guiding significance for structural life assessment, maintenance and reinforcement decisions. The basic principle is as follows: the damage to 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 multiparameter derivative parameters.
With the rapid improvement of the computer level and the data acquisition capability, the overall detection method based on the modal parameters is greatly developed. It is worth noting that such methods do not consider the influence of changes in marine environmental factors on the performance of damage detection in large numbers. The change of marine environmental factors such as temperature, marine organism adhesion, basic flushing and the like can also cause the change of physical characteristics of the structure, change of structural modal parameters is affected, and even change of modal parameters caused by real damage of the structure can be covered, especially for early/tiny damage. The detection of the tiny damage of the marine engineering structure by considering environmental factors and noise pollution is a current problem to be solved urgently.
Early detection and diagnosis of early/tiny damage of the structure can be realized, effective structure running state evaluation can be carried out, and the method has important practical value for the safety running guarantee of the ocean engineering structure.
Disclosure of Invention
Aiming at the defects existing 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 above object, the present invention provides the following solutions:
a method for judging the micro damage of a marine engineering structure comprises the following steps:
in an actual operation environment, measuring dynamic response time-course data of a sound ocean engineering structure for a plurality of times by using a sensor;
based on a modal parameter identification method, determining the first n-order modal frequencies of the sound ocean engineering structure according to dynamic response time interval data of the sound ocean engineering structure;
combining the modal frequencies obtained by each test to obtain a sound frequency matrix;
in an actual operation environment, measuring dynamic response time-course data of the ocean engineering structure to be measured for a plurality of times by using a sensor;
based on a modal parameter identification method, determining the first n-order modal frequencies of the ocean engineering structure to be detected according to dynamic response time interval data of the ocean engineering structure to be detected;
combining the modal frequencies obtained by each test to obtain a frequency matrix to be tested;
performing linear discriminant analysis on the perfect frequency matrix and the frequency matrix to be detected, and solving the projection direction of the perfect frequency matrix and the frequency matrix to be detected with optimized classification performance to obtain a perfect frequency residual error and a frequency residual error to be detected;
based on a hypothesis testing technology, determining whether the marine engineering structure to be tested is damaged according to the intact frequency residual error and the frequency residual error to be tested.
Optionally, the number of sensors is one.
Optionally, the sensor is an acceleration sensor or a displacement sensor.
Optionally, the perfect frequency matrix is:
Figure BDA0003468350150000031
wherein omega h For a sound frequency matrix, h represents sound ocean engineering structure, m is the total number of vibration tests,
Figure BDA0003468350150000032
for the first n-order modal frequencies of the intact marine structure obtained by the jth measurement,/th order of the ocean engineering structure>
Figure BDA0003468350150000033
And (3) 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 omega c For the frequency matrix to be measured, c represents the ocean engineering structure to be measured, m is the total number of vibration tests,
Figure BDA0003468350150000035
for the first n-order modal frequencies of the ocean engineering structure to be measured obtained by the jth measurement, ++>
Figure BDA0003468350150000036
And the ith order modal frequency of the ocean engineering structure to be measured is obtained 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 of optimization of classification performance of the perfect frequency matrix and the frequency matrix to be measured to obtain a perfect frequency residual and a frequency residual to be measured, which specifically includes:
respectively carrying out averaging treatment on the sound frequency matrix and the frequency matrix to be detected to obtain a modal frequency matrix of the sound 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 sound ocean engineering structure according to the modal frequency matrix of the sound ocean engineering structure;
determining the intra-class variance of the modal frequency matrix of the ocean engineering structure to be tested according to the modal frequency matrix of the ocean engineering structure to be tested;
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 vectors of the sound frequency matrix and the frequency matrix to be tested according to the intra-class variance sum;
and carrying out projection and dimension reduction processing on the perfect frequency matrix and the frequency matrix to be detected according to the projection vector with the optimal classification performance to obtain corresponding perfect frequency residual errors and frequency residual errors to be detected.
Optionally, the modal frequency matrix of the intact ocean engineering structure is:
Figure BDA0003468350150000041
wherein m is h Mould for intact ocean engineering structureA matrix of the state frequencies,
Figure BDA0003468350150000042
modal frequency matrix m of intact ocean engineering structure h The average value of the ith row in the test, n is the order of the ocean engineering structure to be tested;
the modal frequency matrix of the ocean engineering structure to be detected is as follows:
Figure BDA0003468350150000043
wherein m is c Is a modal frequency matrix of the ocean engineering structure to be measured,
Figure BDA0003468350150000044
the modal frequency matrix omega of the ocean engineering structure to be measured c Average value of row i in (a).
Optionally, the intra-class variance sum is determined according to the following formula:
Figure BDA0003468350150000045
Figure BDA0003468350150000046
Figure BDA0003468350150000051
wherein S is w As the sum of the intra-class variances,
Figure BDA0003468350150000052
intra-class variance of modal frequency matrix for sound ocean engineering structure, +.>
Figure BDA0003468350150000053
The intra-class variance of the modal frequency matrix of the ocean engineering structure to be tested is m is the total secondary of the vibration testCount (n)/(l)>
Figure BDA0003468350150000054
For the first n-order modal frequencies of the intact marine structure obtained by the jth measurement,/th order of the ocean engineering structure>
Figure BDA0003468350150000055
The first n-order modal frequencies, m, of the ocean engineering structure to be measured, which are obtained for the j-th measurement h Mode frequency matrix of intact ocean engineering structure, m c The method is characterized in that the method is a modal frequency matrix of the ocean engineering structure to be detected, and T represents transposition operation of the matrix;
the best classification performance projection vector is determined according to the following formula:
P＝S w -1 (m h -m c )；
determining an intact frequency residual error and a frequency residual error to be measured according to the following formula;
Figure BDA0003468350150000056
Figure BDA0003468350150000057
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA0003468350150000058
for perfect frequency residual, ++>
Figure BDA0003468350150000059
Is the frequency residual to be measured.
Optionally, the determining, based on the hypothesis testing technology, whether the marine engineering structure to be tested is damaged according to the perfect frequency residual error and the frequency residual error to be tested specifically includes:
calculating a statistical hypothesis testing value according to the average value of the perfect frequency residual errors, the average value of the frequency residual errors to be tested, the standard deviation of the perfect frequency residual errors and the standard deviation of the frequency residual errors to be tested;
calculating a hypothesis testing amount threshold according to the statistical hypothesis testing amount value and the confidence level;
and comparing the absolute value of the hypothesis testing magnitude with the hypothesis testing magnitude threshold, if the absolute value of the hypothesis testing magnitude is smaller than or equal to the hypothesis testing magnitude threshold, judging that the ocean engineering structure to be tested is damaged, and if the absolute value of the hypothesis testing magnitude is larger than the hypothesis testing magnitude threshold, judging that the ocean engineering structure to be tested is not damaged.
Optionally, the statistical hypothesis test values are determined according to the following formula:
Figure BDA0003468350150000061
wherein t is the statistical hypothesis test magnitude, μ h Mu, mean of perfect frequency residuals c Sigma, the mean value of the residual error of the frequency to be measured h Standard deviation, sigma, of the perfect frequency residual c Standard deviation of the frequency residual error to be measured;
the hypothesis testing amount 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 amount 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 structural vibration characteristics is effectively eliminated, a frequency residual error capable of reflecting structural health information is obtained, and an effective statistical hypothesis testing technology is matched, so that the accurate judgment of the micro damage state of the structure is realized;
moreover, only the vibration response of the structure is required to be measured, the current environmental factors are not required to be measured, only the intact ocean platform and the damaged ocean platform are required to be measured respectively in a short period, and long-term continuous monitoring is not required to be carried out; the damage judging process can be completed by arranging only one sensor, so that the difficulty of damage detection is greatly reduced, and the cost is saved;
the method realizes the judgment of the micro damage of the marine engineering structure under the environmental and noise pollution, is favorable for finding out the early damage/micro damage of the structure, and has certain guiding significance for early warning, maintenance and 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 of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a finite element model schematic diagram of an offshore wind turbine structure according to an embodiment of the invention; (a) Part is a marine fan structure node numbering schematic diagram, (b) part is a marine fan structure unit numbering schematic diagram, (b) part 14 is a diagonal bracing unit, and 10 is a transverse bracing unit;
FIG. 2 is a graph of the results of a determination of microscopic damage under the influence of noise-free and environmental factors;
FIG. 3 is a graph showing the results of determining the microscopic damage under the influence of 0.15% noise and environmental factors.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims to provide a method for judging the micro damage of a marine 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 structural vibration characteristics is effectively eliminated, the damage judging process can be finished by only arranging one sensor, the difficulty of damage detection is greatly reduced, and the cost is saved.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
A method for judging micro damage of a marine engineering structure comprises the following steps:
and firstly, performing vibration test on the sound ocean engineering structure in the actual operation environment to obtain a sound 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 damage occurs to the ocean engineering structure to be tested is unknown.
Thirdly, linear discriminant analysis is carried out on the perfect frequency matrix and the frequency matrix to be measured, so that projection directions of the perfect frequency matrix to be measured and the frequency matrix to be measured with optimized classification performance are solved, and perfect frequency residual errors and frequency residual errors to be measured of the ocean engineering structure are obtained.
Fourth step: and carrying out structural damage judgment on the perfect frequency residual error and the frequency residual error to be detected by using an assumption checking technology.
Specifically, the following describes the scheme determination method in detail with reference to specific embodiments:
in the first step, vibration test is carried out on the sound ocean engineering structure in the actual operation environment, and the specific steps for obtaining the frequency matrix of the sound ocean engineering structure are as follows:
(1) In an actual working environment, the dynamic response time-course data of the complete ocean engineering structure are measured by using an acceleration sensor or a displacement sensor.
(2) Based on a modal parameter identification method, acquiring the first n-order modal frequencies of the ocean engineering structure according to dynamic response time interval data of the ocean engineering structure, wherein the ith-order modal frequency obtained by the jth measurement is used for obtaining
Figure BDA0003468350150000081
And (3) representing.
(3) Let a total of m vibration tests be performedCombining the frequencies obtained by each test to construct a sound frequency matrix omega of the structure h
Figure BDA0003468350150000082
In the second step, vibration test is carried out on the ocean engineering structure to be tested in the actual operation environment, and the specific steps for obtaining the frequency matrix to be tested of the ocean engineering structure are as follows:
the method comprises the steps of performing m times of vibration test on a damaged ocean engineering structure, referring to the step of obtaining the frequency vibration mode of the ocean engineering sound structure, and constructing a frequency matrix omega of the ocean engineering structure to be detected c
Figure BDA0003468350150000083
Wherein the jth measurement obtains the first n-order modal frequencies
Figure BDA0003468350150000084
And (3) representing.
In the third step, the interference of environmental factors is eliminated by carrying out linear discriminant analysis on the perfect frequency matrix and the frequency matrix to be detected, and the specific steps of obtaining the perfect frequency residual error and the frequency residual error to be detected are as follows:
(1) Respectively carrying out averaging treatment on the sound frequency matrix and the frequency matrix to be measured, wherein
Figure BDA0003468350150000085
And->
Figure BDA0003468350150000086
Modal frequency matrix omega representing intact ocean engineering structure and ocean engineering structure to be detected h And omega c Average value of row i in (a).
Figure BDA0003468350150000091
(2) Analyzing to obtain the intra-class variance and S of the frequency matrix of the sound ocean engineering structure and the frequency matrix of the ocean engineering structure to be tested w Wherein
Figure BDA0003468350150000092
And->
Figure BDA0003468350150000093
The intra-class variance of the modal frequency matrix expressed as a sound marine engineering structure and a marine engineering structure to be measured:
Figure BDA0003468350150000094
Figure BDA0003468350150000095
Figure BDA0003468350150000096
(3) Calculating to obtain the projection vector of the optimal classification performance of the sound frequency matrix and the frequency matrix to be measured:
P＝S w -1 (m h -m c ) (7)
(4) Projecting and dimension-reducing the frequency matrix of the sound ocean engineering structure and the frequency matrix of the ocean engineering structure to be detected through the projection vector P to obtain corresponding sound frequency residual errors and frequency residual errors to be detected:
Figure BDA0003468350150000097
Figure BDA0003468350150000098
wherein, formula (8) is a perfect frequency residual error, and formula (9) is a frequency residual error to be measured.
In the fourth step, structural damage judgment is carried out on the perfect frequency residual error and the frequency residual error to be detected by a hypothesis test technology, and the method specifically comprises the following steps:
(1) Assuming that the average value of the perfect frequency residual error and the frequency residual error to be detected is equal to the original assumption H 0 The preparation is assumed to be mean unequal H 1 ：
H 0 :μ h ＝μ c (10)
H 1 :μ h ≠μ c (11)
(2) Calculating a statistical hypothesis test magnitude, wherein μ and σ represent the mean and standard deviation of the frequency residuals:
Figure BDA0003468350150000101
(3) Determining confidence level alpha, calculating hypothesis testing amount threshold t * ：
P(t<t * )＝1-α/2 (13)
(4) Comparing the hypothesis test magnitude |t| with the test magnitude threshold t * Judging whether the marine engineering structure is damaged:
Figure BDA0003468350150000102
Figure BDA0003468350150000103
wherein the judgment criteria are: 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 damaged.
To verify the effectiveness of the above method, a typical marine offshore wind turbine structure will be described as follows:
1. establishing a finite element model:
as shown in part (a) of fig. 1 and part (b) of fig. 1, the marine fan structure of the simulation study of this embodiment is composed of a support structure and a tower structure, and includes 18 nodes (parts (a) 1 to 18) and 20 units (parts (b) 1 to 20) of fig. 1. And writing a finite element program by utilizing MATLAB software, and establishing a finite element model by a computer to serve as a reference finite element model of the complete ocean platform. Then, under different working environments, different damage working conditions are simulated, and the mode frequency for simulating actual measurement is obtained. This example simulates a variety of damage conditions, including damage at different locations, damage to different degrees.
2. 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 the uniform weakening of the elastic modulus on a damaged unit. Meanwhile, the change of the environmental conditions can influence the overall rigidity of the structure, wherein the most typical environmental conditions are temperature, basic flushing and the like, and in the embodiment, the temperature factors are selected for simulation. The temperature change generally causes the change of the elastic modulus of the material, so as to influence the rigidity of the ocean platform, and experimental research shows that the elastic modulus and the temperature show a strong linear relation
E(T t )＝E(T 0 )+τ(T t -T 0 ) (16)
Wherein E (T) 0 ) The elastic modulus in the reference state is usually set to 10℃and the corresponding elastic modulus is 2.06X 10 11 Pa; t is the coefficient of variation of elastic modulus of steel material with temperature, and is 1×10 8 Pa/℃。
The sound and damaged offshore wind turbine structure is assumed to be tested 1000 times, the difference of the temperature of the sea water and the temperature of the air are considered, the temperature in the air is assumed to be subjected to standard normal distribution with the average value of 10 ℃ and the standard deviation of 8 ℃, and the temperature in the sea water is assumed to be subjected to standard normal distribution with the average value of 15 ℃ and the standard deviation of 4 ℃.
3. Analysis of damage determination results
The method for judging the micro damage of the offshore wind turbine structure is utilized to judge the micro damage of the offshore wind turbine structure, and four working conditions are considered as follows: working condition one: the diagonal bracing unit is damaged by 1%; working condition II: the damage of the transverse support unit is 1%; and (3) working condition III: the diagonal bracing unit is damaged by 3%; and (4) working condition four: 3% of damage to the transverse strut unit; and (5) adopting 50 repeated tests for each working condition, and calculating the accuracy of the micro damage judgment.
As shown in fig. 2 (a) and fig. 2 (b), the determination result of the micro damage under the influence of no noise and environmental factors is shown; as shown in part (a) of fig. 3 and part (b) of fig. 3, under no noise influence, the four damage condition hypothesis test statistics are far greater than the test statistics threshold (1.96), so that the damage judgment accuracy of the four damage conditions is 100%; under the influence of 0.15% noise, only 7 times (working condition one) are misjudged to be healthy, and other 193 repeated tests can accurately judge the tiny damage of the structure, and the tiny damage judging accuracy is 96.5%.
The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to assist in understanding the methods of the present invention and the core ideas thereof; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.

Claims (7)

1. The method for judging the micro damage of the marine engineering structure is characterized by comprising the following steps of:
in an actual operation environment, measuring dynamic response time-course data of a sound ocean engineering structure for a plurality of times by using a sensor;
based on a modal parameter identification method, determining the first n-order modal frequencies of the sound ocean engineering structure according to dynamic response time interval data of the sound ocean engineering structure;
combining the modal frequencies obtained by each test to obtain a sound frequency matrix;
in an actual operation environment, measuring dynamic response time-course data of the ocean engineering structure to be measured for a plurality of times by using a sensor;
based on a modal parameter identification method, determining the first n-order modal frequencies of the ocean engineering structure to be detected according to dynamic response time interval data of the ocean engineering structure to be detected;
combining the modal frequencies obtained by each test to obtain a frequency matrix to be tested;
performing linear discriminant analysis on the perfect frequency matrix and the frequency matrix to be detected, and solving a projection direction of optimization of classification performance of the perfect frequency matrix and the frequency matrix to be detected to obtain a perfect frequency residual and a frequency residual to be detected, wherein the method specifically comprises the following steps:
respectively carrying out averaging treatment on the sound frequency matrix and the frequency matrix to be detected to obtain a modal frequency matrix of the sound 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 sound ocean engineering structure according to the modal frequency matrix of the sound ocean engineering structure;
determining the intra-class variance of the modal frequency matrix of the ocean engineering structure to be tested according to the modal frequency matrix of the ocean engineering structure to be tested;
according to the intra-class variance of the modal frequency matrix of the sound ocean engineering structure and the intra-class variance of the modal frequency matrix of the ocean engineering structure to be detected, determining the intra-class variance and:
Figure FDA0004119433260000011
Figure FDA0004119433260000012
Figure FDA0004119433260000021
wherein S is w As the sum of the intra-class variances,
Figure FDA0004119433260000022
is good toIntra-class variance of modal frequency matrix of marine engineering structure,/->
Figure FDA0004119433260000023
The intra-class variance of the modal frequency matrix of the ocean engineering structure to be tested is m is the total frequency of vibration test,/->
Figure FDA0004119433260000024
For the first n-order modal frequencies of the intact marine structure obtained by the jth measurement,/th order of the ocean engineering structure>
Figure FDA0004119433260000025
The first n-order modal frequencies, m, of the ocean engineering structure to be measured, which are obtained for the j-th measurement h Mode frequency matrix of intact ocean engineering structure, m c The method is characterized in that the method is a modal frequency matrix of the ocean engineering structure to be detected, and T represents transposition operation of the matrix;
and determining the optimal classification performance projection vectors of the sound frequency matrix and the frequency matrix to be tested according to the intra-class variance sum: p=s w -1 (m h -m c )；
According to the projection vector of the optimal classification performance, projecting and dimension-reducing processing is carried out on the perfect frequency matrix and the frequency matrix to be detected, so as to obtain corresponding perfect frequency residual error and frequency residual error to be detected:
Figure FDA0004119433260000026
Figure FDA0004119433260000027
wherein (1)>
Figure FDA0004119433260000028
For perfect frequency residual, ++>
Figure FDA0004119433260000029
The residual error is the frequency to be measured;
based on a hypothesis testing technology, determining whether the marine engineering structure to be tested is damaged according to the perfect frequency residual error and the frequency residual error to be tested, specifically comprises:
calculating a statistical hypothesis testing value according to the average value of the perfect frequency residual errors, the average value of the frequency residual errors to be tested, the standard deviation of the perfect frequency residual errors and the standard deviation of the frequency residual errors to be tested;
calculating a hypothesis testing amount threshold according to the statistical hypothesis testing amount value and the confidence level;
and comparing the absolute value of the hypothesis testing magnitude with the hypothesis testing magnitude threshold, if the absolute value of the hypothesis testing magnitude is smaller than or equal to the hypothesis testing magnitude threshold, judging that the ocean engineering structure to be tested is damaged, and if the absolute value of the hypothesis testing magnitude is larger than the hypothesis testing magnitude threshold, judging that the ocean engineering structure to be tested is not damaged.
2. The method for determining the micro-damage of a marine structure according to claim 1, wherein the number of the sensors is one.
3. The method for determining the micro-damage of the marine engineering 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 marine engineering structure according to claim 1, wherein the perfect frequency matrix is:
Figure FDA0004119433260000031
wherein omega h For a sound frequency matrix, h represents sound ocean engineering structure, m is the total number of vibration tests,
Figure FDA0004119433260000032
for the first n-order modal frequencies of the intact marine structure obtained by the jth measurement,/th order of the ocean engineering structure>
Figure FDA0004119433260000033
And (3) 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 marine engineering structure according to claim 1, wherein the frequency matrix to be measured is:
Figure FDA0004119433260000034
wherein omega c For the frequency matrix to be measured, c represents the ocean engineering structure to be measured, m is the total number of vibration tests,
Figure FDA0004119433260000035
for the first n-order modal frequencies of the ocean engineering structure to be measured obtained by the jth measurement, ++>
Figure FDA0004119433260000036
And the ith order modal frequency of the ocean engineering structure to be measured is obtained for the jth measurement.
6. The method for determining the micro-damage of the marine engineering structure according to claim 1, wherein the modal frequency matrix of the sound marine engineering structure is:
Figure FDA0004119433260000037
wherein m is h Is a modal frequency matrix of a sound ocean engineering structure,
Figure FDA0004119433260000038
modal frequency matrix m of intact ocean engineering structure h The average value of the ith row in the test, n is the order of the ocean engineering structure to be tested;
the modal frequency matrix of the ocean engineering structure to be detected is as follows:
Figure FDA0004119433260000041
wherein m is c Is a modal frequency matrix of the ocean engineering structure to be measured,
Figure FDA0004119433260000042
the modal frequency matrix omega of the ocean engineering structure to be measured c Average value of row i in (a).
7. The method for determining the micro-damage of the marine engineering structure according to claim 1, wherein the statistical hypothesis test value is determined according to the following formula:
Figure FDA0004119433260000043
wherein t is the statistical hypothesis test magnitude, μ h Mu, mean of perfect frequency residuals c Sigma, the mean value of the residual error of the frequency to be measured h Standard deviation, sigma, of the perfect frequency residual c Standard deviation of the frequency residual error to be measured;
the hypothesis testing amount threshold is calculated according to the following formula:
P(t<t * )＝1-α/2；
wherein P () is a calculated probability value, α is a confidence level, t * Is a hypothesis test amount threshold.
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