CN107356417B - A kind of bolted joint damnification recognition method merging Time-Series analysis and comentropy - Google Patents
A kind of bolted joint damnification recognition method merging Time-Series analysis and comentropy Download PDFInfo
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Abstract
The invention discloses a kind of bolted joint damnification recognition methods for merging Time-Series analysis and comentropy, comprising the following steps: 1) arranges multiple acceleration transducers in bolted joint structure to survey the acceleration responsive sequence of corresponding measuring point；2) standard deviation of all measuring point acceleration responsive sequences in structure is calculated, using standard deviation maximum value as normalized parameter, normalize actual measureed value of acceleration response, the characteristics of being responded according to actual measureed value of acceleration selects suitable time series models to carry out data fitting in AR model, arma modeling and MA model；3) residual sequence between actual measureed value of acceleration response data and model of fit is calculated, using residual sequence standard deviation as structural response feature；4) relationship that comentropy quantifies the residual sequence standard deviation of adjacent two measuring point is introduced, the structural damage sensitive indicator under state to be measured is calculated, identifies the damage of bolted joint structure.This method can accurately identify engaging portion faulted condition, meet the requirement monitored to bolted joint connection status.
Description
Technical field
The present invention relates to monitoring structural health conditions fields, and in particular to a kind of fusion Time-Series analysis is in conjunction with the bolt of comentropy
Portion's damnification recognition method.
Background technique
For engineering structure health monitoring system, the monitoring of bolted joint connection status is extremely important, it is connection
The key component that load is transmitted between part, affects the operational safety of structure.However, since the bolted joint mechanism of action is complicated,
It is very difficult that the true mechanical behavior of engaging portion is described by nonlinear theory or linear theory, and model expend compared with
High cost.In this context, the model-free methods for studying bolted joint non-destructive tests just seem particularly significant.The nothing being previously mentioned
Model method refers to: without establishing engaging portion mechanical model, structural response signal is obtained by the sensor being mounted in structure,
And structure feature is extracted from structural response, the damage of identification engaging portion.
Currently, bolted joint Study on Damage Identification has been achieved with many achievements, be broadly divided into " having model method " with
" model-free methods ".Entitled " diagnostic method that a kind of spatial mesh structure node bolt loosens damage ", patent application
Number be 201310006366.5 Chinese invention patent, by obtain bolt ball connection moment of flexure-rotation curve, will connection make
With being equivalent to straight-bar.[Li Ling, Cai Anjiang, Cai Ligang, Guo Tieneng, the Ruan Xiaoguang bolted joint dynamic characteristic identification side such as Li Ling
Method [J] mechanical engineering journal, 2013,49 (7): 168-175.] from macroscopic aspect, engaging portion connection function is expressed as
The spring connection of limited point, obtains the equivalent linear model of bolted joint on joint face.The mechanics of connector interaction
Model is complicated, and influence factor is numerous, it is difficult to the accurate mechanical model of engaging portion is established from constitutive relation level.Modeling is complicated, no
Accurately, so that there is model method to expend higher cost during bolted joint non-destructive tests, and model error reduces
The reliability of non-destructive tests result.
Model-free methods do not need to establish engaging portion model, directly judge engaging portion state by structural response feature, keep away
Model error is exempted from.There are mapping relations for configuration state and its response sequence data rule, theoretical based on time series analysis, from
Autocorrelation angles analyze the rule of data, its statistical nature are obtained, to identify structural damage.Time Series Analysis Method only needs to measure
Structure time response series, measurement are easily achieved, convenient for application.Common analysis model has AR model, MA model, arma modeling
Deng.The key for accurately identifying engaging portion damage is to construct the damage locating index that can really reflect structural damage situation
(Damage sensitive feature,DSF).Someone is with the AR model residual sequence standard under state to be measured and normal condition
The ratio between difference is damage locating index, and also someone constructs damage using the higher order statistical square (kurtosis, the degree of bias) of AR model residual sequence
Sensitive indicator.The building thought of existing index usually investigates the degree that structure condition responsive to be measured deviates normal condition, but nothing
It will cause configuration state by connector damage or engaging portion damage and deviate normal condition, thus be easy the damage of erroneous judgement engaging portion.
Summary of the invention
The purpose of the present invention is in view of the above shortcomings of the prior art, provide a kind of fusion Time-Series analysis and comentropy
Bolted joint damnification recognition method, this method does not need to establish engaging portion mechanical model, merely with the acceleration responsive of structure
Time-histories sequence just can complete engaging portion non-destructive tests, and the method damages sensitivity to engaging portion, can accurately identify engaging portion
Damage meets the requirement monitored to bolted joint connection status.
The purpose of the present invention can be achieved through the following technical solutions:
A kind of bolted joint damnification recognition method merging Time-Series analysis and comentropy, the method includes following steps
It is rapid:
1) arrange exciting bank for giving structure white-noise excitation, while the cloth in structure in bolted joint structure
Set the acceleration responsive sequence that multiple acceleration transducers are used to survey structurally corresponding measuring point；
2) standard deviation of all measuring point acceleration responsive sequences in structure is calculated, is normalization ginseng with standard deviation maximum value
The characteristics of number, normalization actual measureed value of acceleration is responded, responded according to actual measureed value of acceleration, is selected in AR model, arma modeling and MA model
It selects suitable time series models and carries out data fitting；
3) residual sequence between actual measureed value of acceleration response data and model of fit is calculated, is knot with residual sequence standard deviation
Structure response characteristic；
4) relationship for quantifying the residual sequence standard deviation of two neighboring measuring point by introducing comentropy, calculates under state to be measured
Structural damage sensitive indicator, identify bolted joint structure damage.
Further, in step 1), the multiple acceleration transducer is arranged in each connector of bolted joint structure
Two sides.
Further, the bolted joint damnification recognition method of a kind of fusion Time-Series analysis and comentropy specifically includes
Following steps: N number of measuring point is arranged altogether in each connector two sides of bolted joint structure, white noise is measured by acceleration transducer
Acceleration responsive sequence { the x of measuring point is corresponded under acoustically-driveni, sequence { xiIndicate that measuring point i is acquired at same time separation delta t
The orderly acceleration responsive sequences of n, the acceleration responsive sequence initial data maximum standard deviation max acquired with N number of measuring point
(σi) it is normalized parameter, carry out data normalization:
In formulaIt is measuring point i acceleration responsive sequence { xiMean value,It is measuring point i original in t moment acceleration responsive
Data xi,tValue after normalization calculates the auto-correlation coefficient and partial correlation coefficient of each measuring point:
In formulaIt is acceleration responsive value of the measuring point i in t+k time Δt, ρi(k) the k rank auto-correlation of measuring point i is indicated
Coefficient, the k rank partial correlation coefficient of measuring point i and the value of k-th of autoregressive coefficient of AR (k) model are equal, can be in MATLAB work
It is obtained after AR (k) model parameter of tool case estimation response sequence, according to the property of auto-correlation coefficient and partial correlation coefficient, selects AR
Suitable time series models carry out data fitting in model, arma modeling or MA model:
In formulaRespectively indicate acceleration responsive value of the measuring point i in t- time Δt, measuring point i
In acceleration responsive value of acceleration responsive value ... the measuring point i in t-p time Δt of t-2 time Δt, εt、εt-1……εt-qPoint
Not Biao Shi the residual error of t moment, t- time Δt residual error ... t-q time Δt residual error,Respectively indicate
One autoregressive coefficient, second autoregressive coefficient ..., p-th of autoregressive coefficient, θ1、θ2……θnRespectively indicate first cunning
Dynamic regression coefficient, second sliding regression coefficient ..., n-th of sliding regression coefficient, subscript p, q respectively indicate in model comprising p
Rank autoregressive coefficient and q rank slide regression coefficient；After selecting suitable time series models, complete to join using the tool box MATLAB
Number estimation, when parameter Estimation, first setting models order comprehensively considers fitting degree using BIC criterion and from becoming using posteriority method
Number is measured, an optimal models are selected in numerous valid models:
N is sample size in formula,It is residual sequence variance, m is the known variables number in model, confirms shape to be measured
The optimal models of state and each measuring point data of normal condition simultaneously estimate its parameter, calculate each measuring point actual measureed value of acceleration response data
Residual sequence between model of fit:
Using the residual sequence between each measuring point actual measureed value of acceleration response data and model of fit as each Measuring Point Structure
Response characteristic, introduces the relationship that comentropy quantifies the residual sequence standard deviation of two neighboring measuring point, and the structural damage of building is sensitive
Index is the sum of the absolute value of the comentropy subitem difference of state to be measured and normal condition:
Ui=-pi log pi
σ in formulai(ε) and σi+1(ε) respectively indicates the acceleration responsive residual sequence standard deviation of measuring point i and measuring point i+1, UiTable
Show the comentropy subitem value constructed by measuring point i and measuring point i+1, wherein Uj testAnd Uj refRespectively indicate state and normal condition to be measured
Comentropy subitem, DSF (i) indicate by measuring point i and measuring point i+1 acceleration responsive data calculate damage locating index value,
If state to be measured carrys out self-structure normal condition, two adjacent measuring points of state and normal condition to be measured respond residual sequence standard deviation
The comentropy subitem of composition is identical, then DSF (i) is close to zero；If state to be measured includes bolted joint faulted condition, bolt
Engaging portion region DSF (i) variation is much larger than other regional changes, so as to identify that bolted joint is damaged.
Further, if the auto-correlation coefficient of each measuring point trails, partial correlation coefficient truncation selects AR model；If each
The auto-correlation coefficient truncation of measuring point, partial correlation coefficient hangover then select MA model；If the auto-correlation coefficient of each measuring point trails, partially
Related coefficient hangover then selects arma modeling.
Further, a kind of bolted joint damnification recognition method merging Time-Series analysis and comentropy, when utilization
Between series analysis model fitting white-noise excitation under bolted joint structure acceleration responsive data, pass through introduce comentropy amount
Change the relationship between the two neighboring measuring point of bolted joint structure, with the comentropy of state to be measured and normal condition acceleration responsive
The sum of absolute value for difference of itemizing is used as damage locating index.
Compared with the prior art, the invention has the following advantages and beneficial effects:
The present invention has merged that Time-Series analysis is theoretical and information entropy theory, proposes a kind of fusion Time-Series analysis and comentropy
Bolted joint damnification recognition method, this method does not need to establish engaging portion mechanical model, merely with the acceleration responsive of structure
Time-histories sequence just can complete the non-destructive tests of engaging portion, and the method damages sensitivity to engaging portion, can accurately identify engaging portion damage
Wound meets the requirement monitored to bolted joint connection status.
Detailed description of the invention
Fig. 1 is the reality of the bolted joint damnification recognition method of a kind of fusion Time-Series analysis of the embodiment of the present invention and comentropy
Alms giver's flow chart.
Fig. 2 is the experimental provision schematic diagram of the embodiment of the present invention.
Fig. 3 (a) is free beam of embodiment of the present invention damage setting schematic diagram, and Fig. 3 (b) is the damage of cantilever beam of the embodiment of the present invention
Schematic diagram is set.
Fig. 4 is the specific recognition result figure of the embodiment of the present invention.
Specific embodiment
Present invention will now be described in further detail with reference to the embodiments and the accompanying drawings, but embodiments of the present invention are unlimited
In this.
Embodiment:
A kind of bolted joint damnification recognition method for merging Time-Series analysis and comentropy is present embodiments provided, master is implemented
Flow chart is as shown in Figure 1, comprising the following steps:
1) arrange exciting bank for giving structure white-noise excitation, while the cloth in structure in bolted joint structure
Set the acceleration responsive sequence that multiple acceleration transducers are used to survey structurally corresponding measuring point；
2) standard deviation of all measuring point acceleration responsive sequences in structure is calculated, is normalization ginseng with standard deviation maximum value
The characteristics of number, normalization actual measureed value of acceleration is responded, responded according to actual measureed value of acceleration, is selected in AR model, arma modeling and MA model
It selects suitable time series models and carries out data fitting；
3) residual sequence between actual measureed value of acceleration response data and model of fit is calculated, is knot with residual sequence standard deviation
Structure response characteristic；
4) relationship for quantifying the residual sequence standard deviation of two neighboring measuring point by introducing comentropy, calculates under state to be measured
Structural damage sensitive indicator, identify bolted joint structure damage.
Specifically includes the following steps: arranging N number of measuring point altogether in each connector two sides of bolted joint structure, pass through acceleration
Acceleration responsive sequence { the x of measuring point is corresponded under degree sensor measurement white-noise excitationi, sequence { xiIndicate measuring point i when identical
Between acquire under separation delta t n orderly acceleration responsive sequences, the acceleration responsive sequence initial data acquired with N number of measuring point
Maximum standard deviation max (σi) it is normalized parameter, carry out data normalization:
In formulaIt is measuring point i acceleration responsive sequence { xiMean value,It is measuring point i original in t moment acceleration responsive
Data xitValue after normalization calculates the auto-correlation coefficient and partial correlation coefficient of each measuring point:
In formulaIt is acceleration responsive value of the measuring point i in t+k time Δt, ρi(k) the k rank auto-correlation of measuring point i is indicated
Coefficient, the k rank partial correlation coefficient of measuring point i and the value of k-th of autoregressive coefficient of AR (k) model are equal, can be in MATLAB work
It is obtained after AR (k) model parameter of tool case estimation response sequence, according to the property of auto-correlation coefficient and partial correlation coefficient, if each
The auto-correlation coefficient of measuring point trails, and partial correlation coefficient truncation then selects AR model；If the auto-correlation coefficient truncation of each measuring point, partially
Related coefficient hangover then selects MA model；If the auto-correlation coefficient of each measuring point trails, partial correlation coefficient hangover selects ARMA
Model.Suitable time series models in AR model, arma modeling or MA model are selected to carry out data fitting:
In formulaRespectively indicate acceleration responsive value of the measuring point i in t- time Δt, measuring point i
In acceleration responsive value of acceleration responsive value ... the measuring point i in t-p time Δt of t-2 time Δt, εt、εt-1……εt-qPoint
Not Biao Shi the residual error of t moment, t- time Δt residual error ... t-q time Δt residual error,Respectively indicate
One autoregressive coefficient, second autoregressive coefficient ..., p-th of autoregressive coefficient, θ1、θ2……θnRespectively indicate first cunning
Dynamic regression coefficient, second sliding regression coefficient ..., n-th of sliding regression coefficient, subscript p, q respectively indicate in model comprising p
Rank autoregressive coefficient and q rank slide regression coefficient；After selecting suitable time series models, complete to join using the tool box MATLAB
Number estimation, when parameter Estimation, first setting models order comprehensively considers fitting degree using BIC criterion and from becoming using posteriority method
Number is measured, an optimal models are selected in numerous valid models:
N is sample size in formula,It is residual sequence variance, m is the known variables number in model, confirms shape to be measured
The optimal models of state and each measuring point data of normal condition simultaneously estimate its parameter, calculate each measuring point actual measureed value of acceleration response data
Residual sequence between model of fit:
Using the residual sequence between each measuring point actual measureed value of acceleration response data and model of fit as each Measuring Point Structure
Response characteristic, introduces the relationship that comentropy quantifies the residual sequence standard deviation of two neighboring measuring point, and the structural damage of building is sensitive
Index is the sum of the absolute value of the comentropy subitem difference of state to be measured and normal condition:
Ui=-pi log pi
σ in formulai(ε) and σi+1(ε) respectively indicates the acceleration responsive residual sequence standard deviation of measuring point i and measuring point i+1, UiTable
Show the comentropy subitem value constructed by measuring point i and measuring point i+1, wherein Uj testAnd Uj refRespectively indicate state and normal condition to be measured
Comentropy subitem, DSF (i) indicate by measuring point i and measuring point i+1 acceleration responsive data calculate damage locating index value,
If state to be measured carrys out self-structure normal condition, two adjacent measuring points of state and normal condition to be measured respond residual sequence standard deviation
The comentropy subitem of composition is identical, then DSF (i) is close to zero；If state to be measured includes bolted joint faulted condition, bolt
Engaging portion region DSF (i) variation is much larger than other regional changes, so as to identify that bolted joint is damaged.
The bolted joint structure that the present embodiment form using cantilever beam and free beam as object, damage by description bolted joint
Identification process, for experimental provision schematic diagram as shown in Fig. 2, experiment cantilever beam length is 800mm, sectional dimension is 50mm × 10mm；From
It is 400mm by beam length, sectional dimension is 50mm × 10mm；Material is steel；Contact length is 50mm, and connection bolt is
M14 plain bolt.Bolted joint non-destructive tests specific implementation step is as follows:
(1) excitation and response measuring device are installed in bolted joint structure, exciting bank is exciting in the present embodiment
Device, response measuring device are acceleration transducer, provide white-noise excitation by vibration excitor, 7 acceleration are arranged in structure
Sensor (P1, P2……P7, as shown in Figure 2), structure is divided into 6 region (P1~P2For first area R1, P2~P3It is
Two region R2... ... P6~P7For the 6th region R6), bolted joint is in third region R3, in measurement process, sample frequency is
1024Hz, when sampling a length of 4s.
(2) the structural response data under 3 kinds of operating conditions are measured in the present embodiment, are normal condition, engaging portion damage shape respectively
State and connector and engaging portion faulted condition simultaneously.Engaging portion damage, spiral shell under normal condition are realized by release bolt pretightning force
Bolt pretightning force is 24Nm, and bolt pretightening is 7Nm under the faulted condition of engaging portion, and connector damage is cantilever beam and free beam
It damages simultaneously, wherein cantilever beam damage occurs at from fixing end 30cm (in second area), as shown in Fig. 3 (b), free beam damage
Wound occurs at from fixing end 98cm, i.e., from (in the 5th region), as shown in Fig. 3 (a), passing through sand at free beam aperture end 23cm
Turbine is respectively cut into the crack that depth is 10mm in beam two sides, achievees the purpose that injury region Stiffness degradation.
(3) the measuring point response under different operating conditions is normalized, calculates auto-correlation coefficient hangover, partial correlation coefficient
Truncation selects AR model to carry out data fitting, determines optimal models order according to BIC criterion, obtain the time sequence of measurement data
Column model.The residual sequence between measured data and model of fit is calculated, using residual sequence standard deviation as structural response feature.
(4) relationship for quantifying the residual sequence standard deviation of two neighboring measuring point by introducing comentropy, calculates state to be measured
Under structural damage sensitive indicator, identification bolted joint damage.
Bolted joint non-destructive tests result is as shown in figure 4, a kind of fusion Time-Series analysis and comentropy as can be seen from Figure 4
Bolted joint damnification recognition method, in this specific embodiment contain only engaging portion damage the case where and in engaging portion and company
Fitting under degree of impairment, can accurately identify that engaging portion is damaged simultaneously.
It is contemplated that by conjunction with specific bolted joint structure and further being improved and being developed,
When it is of the present invention it is a kind of fusion Time-Series analysis and comentropy bolted joint damnification recognition method in monitoring structural health conditions
When field is widely applied, generated engineering application value will be huge.Simultaneously in structural healthy monitoring system, bolt is added
Connect engaging portion connection status monitoring modular, can engineering technology conversion in get the mastery, generate huge economic benefit and
Commercial value.
The above, only the invention patent preferred embodiment, but the scope of protection of the patent of the present invention is not limited to
This, anyone skilled in the art is in the range disclosed in the invention patent, according to the present invention the skill of patent
Art scheme and its patent of invention design are subject to equivalent substitution or change, belong to the scope of protection of the patent of the present invention.
Claims (4)
1. a kind of bolted joint damnification recognition method for merging Time-Series analysis and comentropy, which is characterized in that the method packet
Include following steps:
1) exciting bank is arranged in bolted joint structure, and for giving structure white-noise excitation, while in structure, arrangement is more
A acceleration transducer is used to survey the acceleration responsive sequence of structurally corresponding measuring point；
2) standard deviation for calculating all measuring point acceleration responsive sequences in structure is returned using standard deviation maximum value as normalized parameter
One selects to close in AR model, arma modeling and MA model the characteristics of changing actual measureed value of acceleration response, responded according to actual measureed value of acceleration
Suitable time series models carry out data fitting；
3) residual sequence between actual measureed value of acceleration response data and model of fit is calculated, is rung by structure of residual sequence standard deviation
Answer feature；
4) relationship for quantifying the residual sequence standard deviation of two neighboring measuring point by introducing comentropy, with state to be measured and benchmark shape
The sum of the absolute value of the comentropy subitem difference of state acceleration responsive is used as damage locating index, identification bolted joint structure
Damage.
2. a kind of bolted joint damnification recognition method for merging Time-Series analysis and comentropy according to claim 1,
Be characterized in that: in step 1), the multiple acceleration transducer is arranged in the two sides of each connector of bolted joint structure.
3. a kind of bolted joint damnification recognition method for merging Time-Series analysis and comentropy according to claim 1,
It is characterized in that, the method specifically includes the following steps: arrange N number of survey in each connector two sides of bolted joint structure altogether
Point measures the acceleration responsive sequence { x that measuring point is corresponded under white-noise excitation by acceleration transduceri, sequence { xiIndicate to survey
The orderly acceleration responsive sequence of n that point i is acquired at same time separation delta t, the acceleration responsive sequence acquired with N number of measuring point
Column initial data maximum standard deviation max (σi) it is normalized parameter, carry out data normalization:
In formulaIt is measuring point i acceleration responsive sequence { xiMean value,It is measuring point i in t moment acceleration responsive initial data
xi,tValue after normalization calculates the auto-correlation coefficient and partial correlation coefficient of each measuring point:
In formulaIt is acceleration responsive value of the measuring point i in t+k time Δt, ρi(k) the k rank auto-correlation coefficient of measuring point i is indicated,
The k rank partial correlation coefficient of measuring point i and the value of k-th of autoregressive coefficient of AR (k) model are equal, can estimate in the tool box MATLAB
Obtained after counting AR (k) model parameter of response sequence, according to the property of auto-correlation coefficient and partial correlation coefficient, select AR model,
Suitable time series models carry out data fitting in arma modeling or MA model:
In formulaMeasuring point i is respectively indicated in the acceleration responsive value of t- time Δt, measuring point i in t-2
Acceleration responsive value of acceleration responsive value ... the measuring point i of time Δt in t-p time Δt, εt、εt-1……εt-qTable respectively
Show the residual error of the residual error of t moment, residual error ... the t-q time Δt of t- time Δt,Respectively indicate first
Autoregressive coefficient, second autoregressive coefficient ..., p-th of autoregressive coefficient, θ1、θ2……θnFirst is respectively indicated to slide back
Return coefficient, second sliding regression coefficient ..., n-th of sliding regression coefficient, subscript p, q respectively indicate in model comprising p rank from
Regression coefficient and q rank slide regression coefficient；After selecting suitable time series models, parameter is completed using the tool box MATLAB and is estimated
Meter, when parameter Estimation, first setting models order comprehensively considers fitting degree and independent variable using BIC criterion using posteriority method
Number selects an optimal models in numerous valid models:
N is sample size in formula,It is residual sequence variance, m is the known variables number in model, confirms state to be measured and base
The optimal models of the quasi- each measuring point data of state simultaneously estimate its parameter, calculate each measuring point actual measureed value of acceleration response data and fitting
Residual sequence between model:
It is responded using the residual sequence between each measuring point actual measureed value of acceleration response data and model of fit as each Measuring Point Structure
Feature introduces the relationship that comentropy quantifies the residual sequence standard deviation of two neighboring measuring point, the structural damage sensitive indicator of building
For the comentropy of state to be measured and normal condition itemize difference the sum of absolute value:
Ui=-pilog pi
σ in formulai(ε) and σi+1(ε) respectively indicates the acceleration responsive residual sequence standard deviation of measuring point i and measuring point i+1, UiIndicate by
The comentropy subitem value of measuring point i and measuring point i+1 building, wherein Uj testAnd Uj refRespectively indicate the letter of state and normal condition to be measured
Entropy subitem is ceased, DSF (i) indicates the damage locating index value calculated by the acceleration responsive data of measuring point i and measuring point i+1, if
State to be measured carrys out self-structure normal condition, and two adjacent measuring point response residual sequence standard deviations of state and normal condition to be measured are constituted
Comentropy subitem it is identical, then DSF (i) is close to zero；If state to be measured includes bolted joint faulted condition, combination is bolted
Portion region DSF (i) variation is much larger than other regional changes, so as to identify that bolted joint is damaged.
4. a kind of bolted joint damnification recognition method for merging Time-Series analysis and comentropy according to claim 3,
Be characterized in that: if the auto-correlation coefficient of each measuring point trails, partial correlation coefficient truncation selects AR model；If each measuring point from
Related coefficient truncation, partial correlation coefficient hangover then select MA model；If the auto-correlation coefficient of each measuring point trails, partial correlation coefficient
Hangover then selects arma modeling.
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| CN109088770B (en) * | 2018-08-21 | 2020-03-31 | 西安交通大学 | Electromechanical system interactive network modeling method based on self-adaptive symbol transfer entropy |
| CN111832188B (en) * | 2020-07-24 | 2023-10-03 | 重庆大学 | Nonlinear structure damage identification method based on GARCH-M model |
| CN113094987B (en) * | 2021-04-06 | 2023-05-23 | 南京市特种设备安全监督检验研究院 | Bolt pretightening force identification method based on AR model vector and response surface |
| CN112733410B (en) * | 2021-04-06 | 2021-07-06 | 南京市特种设备安全监督检验研究院 | Bolt pretightening force identification method based on model correction and AR model |
| CN114791928A (en) * | 2022-04-13 | 2022-07-26 | 河海大学 | Time domain information entropy driven boundary self-adaptive structure fatigue damage detection method |
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