CN116558406A - GNSS-accelerometer integrated bridge deformation monitoring abrupt fault detection method based on state domain - Google Patents

GNSS-accelerometer integrated bridge deformation monitoring abrupt fault detection method based on state domain Download PDF

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CN116558406A
CN116558406A CN202211732154.0A CN202211732154A CN116558406A CN 116558406 A CN116558406 A CN 116558406A CN 202211732154 A CN202211732154 A CN 202211732154A CN 116558406 A CN116558406 A CN 116558406A
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state
gnss
value
bridge
data
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胡锦民
张云龙
何义磊
陈旭升
齐春雨
谭兆
张冠军
石德斌
梁永
洪江华
杨云洋
杨双旗
房博乐
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China Railway Design Corp
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B7/00—Measuring arrangements characterised by the use of electric or magnetic techniques
    • G01B7/16—Measuring arrangements characterised by the use of electric or magnetic techniques for measuring the deformation in a solid, e.g. by resistance strain gauge
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/32—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring the deformation in a solid
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Abstract

The invention discloses a GNSS-accelerometer integrated bridge deformation monitoring abrupt fault detection method based on a state domain, which comprises the following steps: s1, arranging a base station at a clear place which is close to a bridge and has good observation conditions, arranging a monitoring point at a bridge midspan, acquiring GNSS/accelerometer data at the monitoring point, and determining initial parameters; s2, establishing a Kalman filtering state equation and an observation equation, updating an observation value, and calculating a state prediction value and an observation quantity residual; s3, based on observed quantity residues, carrying out abrupt fault detection based on a state domain; and S4, completing filtering calculation through a self-adaptive Kalman filtering algorithm. The invention can detect inaccurate dynamic model and random information in the Kalman filtering process, and realize accurate detection of system faults, thereby ensuring the reliability and precision of the GNSS/accelerometer fusion system in the deformation monitoring process.

Description

GNSS-accelerometer integrated bridge deformation monitoring abrupt fault detection method based on state domain
Technical Field
The invention belongs to the technical field of bridge deformation monitoring, and particularly relates to a GNSS/accelerometer integrated bridge deformation monitoring abrupt fault detection algorithm based on a state domain.
Background
Deformation is one of basic measurement values for measuring bridge performance and reliability, and is widely applied to bridge load test and structural loss evaluation. Dynamic displacement signals of the bridge under normal operation conditions, particularly pseudo-static and low-order vibration components, provide important information for real-time bearing conditions and long-term operation states of the bridge.
Bridge deformation monitoring is widely applied to dynamic deformation monitoring besides monitoring by a GNSS technology. However, the acceleration must be subjected to two integrations to obtain a displacement, in the process, accumulated errors are inevitably generated, and static displacement is difficult to recover from the acceleration, and the acceleration is insensitive to low-frequency vibration lower than 0.2 Hz; while GNSS is difficult to recognize high-frequency vibrations above 2Hz, but is sensitive to low-frequency vibrations, and accurate three-dimensional displacement can be obtained. Therefore, the GNSS and the accelerometer are fused and complemented, and the high-low frequency vibration extraction can be simultaneously satisfied, so that the accuracy and the integrity of deformation monitoring are ensured.
Many students at home and abroad have conducted intensive studies on GNSS/accelerometer fusion and application in structural building deformation monitoring, and many studies show that the fusion of two sensors through Kalman filtering can obtain millimeter-level precision deformation and provide information for long-term bridge deformation monitoring. However, in the process of applying the kalman filter, the dynamic model and the random information provided to the filter must be accurate to realize the optimal performance of the kalman filter, otherwise, the filtering result may generate undesirable conditions such as abrupt failure, so as to cause the misalignment of the monitoring effect.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides the GNSS-accelerometer integrated bridge deformation monitoring abrupt fault detection method which can detect inaccurate dynamic models and random information in the Kalman filtering process and ensure the reliability and the accuracy of a GNSS and accelerometer fusion system in the deformation monitoring process.
For this purpose, the invention adopts the following technical scheme:
a GNSS-accelerometer integrated bridge deformation monitoring abrupt fault detection method based on a state domain comprises the following steps:
s1, data preprocessing: determining displacement and acceleration of the GNSS in each direction, acquiring original data of the GNSS displacement and the accelerometer, and removing zero drift of the acceleration data through recursive high-pass filtering to obtain high-quality data;
s2, updating the observed value, and calculating a state predicted value and an observed value residual: firstly, establishing a Kalman filtering state equation and an observation equation:
based on the establishment of a Kalman filtering equation, performing a time updating process and a measurement updating process of a GNSS/accelerometer integrated system based on the adaptive Kalman filtering to obtain t k State parameter vector predictive value corresponding to moment
Predicting observationsThe method comprises the following steps:
the observed quantity residual is a predicted observed valueGNSS observations and accelerometer raw data Z measured with bridge k A difference between;
s3, abrupt fault detection based on state domains: detection of abrupt faults in bridge monitoring systems using statistical hypothesis testing, wherein the original hypothesis B 0 If the result is error-free, the GNSS displacement/acceleration fusion estimation value is consideredAnd covariance matrix thereof->No error exists; alternative hypothesis B 1 Checking for errors;
s4, performing self-adaptive Kalman filtering, and performing iterative calculation according to the self-adaptive factors, wherein the method comprises the following steps:
s41, judging whether only acceleration data exist, if so, calculating an adaptive factor, and continuing filtering; if not, directly calculating and storing the state estimation value and the covariance matrix thereof;
s42, calculating an adaptive factor:
adaptive factor a k Is counted by a state disagreement valueFor judgment, three sections of calculation functions are listed to determine the adaptive factor a k The method is characterized by comprising the following steps:
wherein ,c0 ＝1.0～1.5，c 1 ＝3.0～8.0； wherein ,/>For the state vector reference value, +.>For the state vector predictor, then +.>For its two norms, get the adaptive factor a k In the range of 0 to 1, wherein the state vector reference value +.>The calculation formula of (2) is as follows:
s43, calculating and storing state estimation values and covariance matrixes thereof: in the time update process and the measurement update process based on the adaptive Kalman filtering, t k Time of day state parameter estimationMetering valueAnd state parameter estimation value->Covariance matrix of (2)The following are provided:
and then willAnd->Substituting k+1 epoch calculation until the filtering is finished.
In the step S1, the method for removing the null shift of the acceleration data by the recursive high-pass filtering is as follows:
(1) Hypothesized state variablesWith a known prior gaussian probability density function:
wherein ,to obey mean +.>Covariance->Is a normal distribution of (c). At the same time, this state is obtained by observing the amount +.>Indirectly, there are:
Z＝h(X)+V
wherein h (X) is defined byA known nonlinear function; v is a probability density functionMeasurement noise in (a); the state variable X is unknown, while the observed quantity Z is known;
(2) Calculating a posterior estimation value of the state vector according to the Bayesian theorem:
where p (z|x) is the unique measured probability density function associated with the observation equation z=h (X) +v; delta denotes dirac delta function, with:
p(Z|X)＝∫∫δ(Z-h(X)-V)p(X)p(V)dXdV。
in the step S2, the process of calculating the state prediction value and the observed quantity residual is as follows:
based on the establishment of a Kalman filtering equation, the time updating process and the measurement updating process of the GNSS/accelerometer integrated system based on the adaptive Kalman filtering are carried out:
in the formula ：
k represents t k Moment, observation variance coefficient matrix
At t k-1 From time to t k A system state transition matrix at a moment;
is a noise driving matrix;
W k-1 for system excitation noise, the acceleration disturbance is regarded as a covariance matrix delta 2 I Gaussian white noise, W k Covariance matrix of (2)
At t k A time state parameter estimation value; k (K) k Is a gain matrix; />Estimated value +.>Is a covariance matrix of (a); />Predicted value +.>Is a covariance matrix of (a); />For predicting observations +.>Is a covariance matrix of (a); r is R k Measuring a noise covariance matrix; Δt represents the sampling rate; />At t k State parameter vector predictive value corresponding to time, predictive observation value +.>GNSS observations and accelerometer raw data Z measured with bridge k The difference is the observed quantity residual;
the step S3 includes the following sub-steps:
s31, constructing state domain mutation fault detection statistics: will be at time t 0 By time t k Chi-square variable based on error square sumThe following definitions are made:
in the formula ,Zi For i time observation quantity, H i For the coefficient matrix at instant i, R i For the measurement noise covariance matrix at time i,the fusion estimated value at the moment i;
will be at time t k Chi-square delta at this point is defined as:
obtainingIs in the form of a recurrence:
wherein ,
let the predicted observed valueFrom the original observed value Z k The difference between them is e k Then in original hypothesis B 0 Under the condition that e k Following gaussian white noise emissions for which mathematical expectations are 0, there are:
the variance is:
thenThe simplification is as follows:
when abrupt failure occurs, e k No longer obeys the gaussian white noise distribution of 0, which is expected mathematically, by detecting e k The statistical characteristics of the bridge monitoring data are used for carrying out mutation fault detection on the bridge monitoring data, and measuring test statistics are calculated:
wherein ,for chi-square increment, e k For observing residual->E is k Is a variance of (2);
if the original assumption B 0 Correct, probability density functionApproximately coincident with degree of freedom n z Chi-square distribution of n z To measure the dimension of the domain.
S32, calculating a detection threshold under the corresponding false alarm rate: defining a false alarm probability P FA And calculate the corresponding P FA The threshold values of (2) are:
wherein ,is about->The operator inf represents the infinit, the cumulative distribution function of +.>Consider as a fault detection threshold;
s33, judging the size of the detection statistic and the detection threshold value: will measure the test statisticsAnd threshold valueComparison is performed: if->Then the bridge actual measurement data is considered to have no fault, and the calculation of the step state estimation value and the covariance matrix in the step S43 is continued; if->Then the bridge measured data is considered to have abrupt fault, and an alarm is sent out.
In step S42, the calculated state vector reference value is improved in deformation monitoring of bridge or dam engineeringThe method of (1) is as follows:
will a k Substituting the calculated state estimation value and the covariance matrix.
The GNSS data is divided into base station data and monitoring station data, and the sampling rate is preferably set to 10hz.
Preferably, the base station is arranged in an open place close to the bridge and good in observation condition; arranging monitoring points on a bridge midspan to obtain obvious displacement change; the accelerometer data is high frequency data of 200hz.
The method can be applied to monitoring the deformation of the structures, in particular to monitoring the deformation of bridges. Compared with the prior art, the detection method has the following beneficial effects:
1. according to the invention, the reliability of monitoring is improved in a mode of combining GNSS data and accelerometer multi-source data; the stability of the filtering process is improved by removing the zero drift of the acceleration data through pretreatment;
2. the invention effectively improves the effectiveness of bridge structure detection by using the self-adaptive Kalman filtering method, and aims at solving the problem that the calculated self-adaptive factor is inaccurate due to serious satellite signal shielding or serious multipath influence during bridge monitoring, and provides an improved state vector reference value calculation method, thereby further improving the detection precision;
3. the abrupt fault detection algorithm provided by the invention aims at the application characteristics of the bridge, is based on the observation quantity residual detection in the self-adaptive Kalman filtering process, can effectively detect inaccurate dynamic models and random information in the filtering process, realizes the accurate detection of system faults, and improves the reliability of bridge structure monitoring.
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FIG. 1 is a flow chart of a GNSS/accelerometer integrated bridge deformation monitoring abrupt fault detection method of the present invention.
Detailed Description
The GNSS-accelerometer integrated bridge deformation monitoring abrupt fault detection algorithm based on the state domain of the invention is described in detail below with reference to the accompanying drawings.
Referring to fig. 1, the state-domain-based GNSS/accelerometer integrated bridge deformation monitoring abrupt fault detection method of the present invention includes the following steps:
s1, data preprocessing: and determining initial parameters and obtaining an observation value. The method comprises the following steps:
s11, initial parameters such as displacement, acceleration and the like of the GNSS in all directions are determined.
S12, obtaining observed values, namely GNSS displacement and accelerometer original data:
preferably, the receiver model is Tianbao R10, GNSS displacement data is divided into base station data and monitoring station data, and the sampling rate is set to be 10hz. In order to obtain more accurate GNSS displacement, the base station is arranged at a clear place which is close to a bridge and has good observation conditions; and arranging monitoring points on the midspan of the bridge to obtain obvious displacement change. The GNSS monitoring receiver and the accelerometer are installed at a monitoring point.
Preferably, the IMU model of the accelerometer is SPAN-IGM-A1, and the data sampling rate is 200hz.
S13, removing the zero drift of the acceleration data through recursive high-pass filtering to obtain high-quality data so as to improve the filtering and resolving effects. The method comprises the following steps:
(1) The GNSS-accelerometer integrated system abrupt fault detection method applied to bridge deformation monitoring is established based on Gaussian assumption and statistical assumption inspection. Thus, assume a state variableThe probability density function (probability density function, PDF) with a known prior gaussian is:
wherein ,to obey mean +.>Covariance->Is a normal distribution of (c). At the same time, this state is obtained by observing the amount +.>Indirectly, there are:
Z＝h(X)+V
wherein h (X) is defined byKnown as nonlinear function, V is a probability density functionIn (a) measurement noise in (b). The state variable X is unknown and the observed quantity Z is known.
(2) Calculating a posterior estimation value of the state vector according to the Bayesian theorem:
where p (z|x) is the unique measured probability density function associated with the observation equation z=h (X) +v, δ represents the dirac delta function:
p(Z|X)＝∫∫δ(Z-h(X)-V)p(X)p(V)dXdV。
s2, updating the observed value, and calculating the state predicted value and the observed value residual. The method comprises the following steps:
s21, establishing a Kalman filtering state equation and an observation equation:
s22, on the basis of the establishment of a Kalman filtering equation, performing a time updating process and a measurement updating process of the GNSS/accelerometer integrated system based on the adaptive Kalman filtering:
wherein k represents t k Moment, observation variance coefficient matrixAt t k-1 From time to t k A system state transition matrix at a moment; />Is a noise driving matrix; w (W) k-1 For system excitation noise, the acceleration disturbance is regarded as a covariance matrix delta 2 I Gaussian white noise, W k Covariance matrix of (2) At t k A time state parameter estimation value; k (K) k Is a gain matrix; />Estimated value +.>Covariance matrix of>Predicted value +.>Covariance matrix of>To predict observed valuesIs a covariance matrix of (a); r is R k Measuring a noise covariance matrix; Δt represents the sampling rate; />At t k State parameter vector predictive value corresponding to time, predictive observation value +.>GNSS observations and accelerometer raw data Z measured with bridge k The difference is the observed quantity residual.
S3, abrupt fault detection based on state domains: detection of abrupt faults in bridge monitoring systems using statistical hypothesis testing, where the original hypothesis B 0 Is error-free, i.e. considered GNSS displacement/acceleration fusion estimationCovariance matrixNo error exists; alternative hypothesis B 1 The test is needed to check for errors. The fault detection method carries out mutation fault detection based on observed quantity residues, and comprises the following steps:
s31, constructing state domain mutation fault detection statistics: first, the time t 0 By time t k Chi-square variable based on error square sumThe following definitions are made:
in the formula ,Zi For i time observation quantity, H i For the coefficient matrix at instant i, R i For the measurement noise covariance matrix at time i,the fusion estimate at time i.
Will be at time t k Chi-square delta at this point is defined as:
then it can be obtainedIn the form of recursion of:
wherein
However, in practical applications, if the above formula is deducedAs an index of fault detection, when a sudden fault occurs, the state estimation value +.>And covariance matrix thereof->Errors occur and no recursion can be performed to obtain the state estimate for the next time. Therefore, to ensure->The accuracy of the index is obtained before the status update>Substituting the state predictive value updated in step 2 +.>To indicate t k Time->And observed residual:
the above-mentioned materials are mixedSubstituting the observed quantity residue into->The method can obtain:
step 2 updated predicted observationsLet->From the original observed value Z k The difference between them is e k Then in original hypothesis B 0 Under the condition that e k The gaussian white noise release should be obeyed with a mathematical expectation of 0, namely:
the variance is:
thenCan be simplified into:
when abrupt failure occurs, e k The gaussian white noise distribution with mathematical expectations of 0 is no longer obeyed. Thus, by detecting e k The statistical characteristics of the bridge monitoring data can be used for carrying out mutation fault detection, and the measurement test statistics are calculated as follows:
in the formula ,is the covariance matrix of the predicted observations.
If the original assumption B 0 Is correct, probability density functionApproximately coincident with degree of freedom n z Chi-square distribution of n z To measure the dimension of the domain.
S32, calculating a detection threshold under the corresponding false alarm rate: defining a false alarm probability P FA And calculate the corresponding P FA The threshold values of (2) are:
wherein ,is about->The operator inf represents the infinit, the cumulative distribution function of +.>Considered as a fault detection threshold.
S33, judging the size of the detection statistic and the detection threshold value:
will measure the test statisticsAnd threshold->Comparison is performed: if->Then considering that the bridge measured data has no fault, and continuing to calculate the state estimation value and the covariance matrix of the step (3) in the step 4; if it isThen the bridge measured data is considered to have abrupt fault, and an alarm is sent out.
S4, self-adaptive Kalman filtering. The adaptive Kalman filtering is calculated according to the iteration of the adaptive factor, and comprises the following steps:
s41, judging whether only acceleration data exist, if so, calculating an adaptive factor, and continuing filtering; if not, directly calculating and storing the state estimation value and the covariance matrix thereof.
S42, calculating an adaptive factor:
adaptive factor a k Is counted by a state disagreement valueFor judgment, three sections of calculation functions are listed to determine the adaptive factor a k The method is characterized by comprising the following steps:
wherein ,c0 ＝1.0～1.5，c 1 ＝3.0～8.0。
wherein ,for the state vector reference value, +.>For the state vector predictor, then +.>Is a binary norm thereof, thereby obtaining an adaptive factor a k In the range of 0 to 1.
Wherein the state vector parameterTest valueThe calculation formula of (2) is as follows:
in the formula For the observation value equivalent weight matrix,/for the observation value equivalent weight matrix>The calculated state vector reference valueIn the bridge deformation monitoring, satellite signal shielding is serious or the satellite signal is greatly influenced by multiple paths, so that the calculated adaptive factor is inaccurate, the method is improved, and the state vector reference value is calculated>The new method of (2) is as follows:
will a k Substituting the state estimation value and the covariance matrix of the state estimation value in the step (3).
S43, calculating and storing state estimation values and covariance matrixes thereof:
in the time update process and the measurement update process based on the adaptive Kalman filtering, t k Time state parameter estimation valueAnd state parameter estimation value->Covariance matrix>The following are provided:
and then willAnd->Substituting k+1 epoch calculation until the filtering is finished.
In addition to the methods described above, embodiments of the present application may also be a computer program product comprising computer program instructions which, when executed by a processor, cause the processor to perform steps in a method according to various embodiments of the present application described in the above "exemplary methods" section of the present specification.
The computer program product may write program code for performing the operations of embodiments of the present application in any combination of one or more programming languages, including an object oriented programming language such as Java, C++ or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code may execute entirely on the user's computing device, partly on the user's device, as a stand-alone software package, partly on the user's computing device, partly on a remote computing device, or entirely on the remote computing device or server.
Furthermore, embodiments of the present application may also be a computer-readable storage medium, having stored thereon computer program instructions, which when executed by a processor, cause the processor to perform steps in a method according to various embodiments of the present application described in the above section "exemplary method" of the present specification.
The computer readable storage medium may employ any combination of one or more readable media. The readable medium may be a readable signal medium or a readable storage medium. The readable storage medium may include, for example, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or a combination of any of the foregoing. More specific examples (a non-exhaustive list) of the readable storage medium would include the following: an electrical connection having one or more wires, a portable disk, a hard disk, random Access Memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.
The basic principles of the present application have been described above in connection with specific embodiments, it should be noted that the advantages, benefits, effects, etc. mentioned in the present application are merely examples and are not to be considered as limiting, which are necessarily possessed by the various embodiments of the present application. Furthermore, the specific details disclosed herein are for purposes of illustration and understanding only, and are not intended to be limiting, as the application is not intended to be limited to the details disclosed herein as such. Any environmental, material changes or simple combinations within the technical scope of the invention are within the scope of the invention.

Claims (8)

1. A GNSS-accelerometer integrated bridge deformation monitoring abrupt fault detection method based on a state domain comprises the following steps:
s1, data preprocessing: determining displacement and acceleration of the GNSS in each direction, acquiring original data of the GNSS displacement and the accelerometer, and removing zero drift of the acceleration data through recursive high-pass filtering to obtain high-quality data;
s2, updating the observed value, and calculating a state predicted value and an observed value residual: firstly, establishing a Kalman filtering state equation and an observation equation:
based on the establishment of a Kalman filtering equation, performing a time updating process and a measurement updating process of a GNSS/accelerometer integrated system based on the adaptive Kalman filtering to obtain t k State parameter vector predictive value corresponding to moment
Predicting observationsThe method comprises the following steps:
the observed quantity residual is a predicted observed valueGNSS observations and accelerometer raw data Z measured with bridge k A difference between;
s3, abrupt fault detection based on state domains: detection of abrupt faults in bridge monitoring systems using statistical hypothesis testing, wherein the original hypothesis B 0 If the result is error-free, the GNSS displacement/acceleration fusion estimation value is consideredAnd covariance matrix thereof->No error exists; alternative falseLet B 1 Checking for errors;
s4, performing self-adaptive Kalman filtering, and performing iterative calculation according to the self-adaptive factors, wherein the method comprises the following steps:
s41, judging whether only acceleration data exist, if so, calculating an adaptive factor, and continuing filtering; if not, directly calculating and storing the state estimation value and the covariance matrix thereof;
s42, calculating an adaptive factor:
adaptive factor a k Is counted by a state disagreement valueFor judgment, three sections of calculation functions are listed to determine the adaptive factor a k The method is characterized by comprising the following steps:
wherein ,c0 ＝1.0～1.5，c 1 ＝3.0～8.0； wherein ,/>For the state vector reference value, +.>For the state vector predictor, then +.>For its two norms, get the adaptive factor a k In the range of 0 to 1, wherein the state vector reference value +.>The calculation formula of (2) is as follows:
s43, calculating and storing state estimation values and covariance matrixes thereof: in the time update process and the measurement update process based on the adaptive Kalman filtering, t k Time state parameter estimation valueAnd state parameter estimation value->Covariance matrix>The following are provided:
and then willAnd->Substituting k+1 epoch calculation until the filtering is finished.
2. The state-domain-based GNSS-accelerometer integrated bridge deformation monitoring abrupt fault detection method according to claim 1, wherein in step S1, the method for removing the zero drift of the acceleration data by recursive high-pass filtering is as follows:
(1) Hypothesized state variablesWith a known prior gaussian probability density function:
wherein ,to obey mean +.>Covariance->Is a normal distribution of (c). At the same time, this state is obtained by observing the amount +.>Indirectly, there are:
Z＝h(X)+V
wherein h (X) is defined byA known nonlinear function; v is a probability density functionMeasurement noise in (a); the state variable X is unknown, while the observed quantity Z is known;
(2) Calculating a posterior estimation value of the state vector according to the Bayesian theorem:
where p (z|x) is the unique measured probability density function associated with the observation equation z=h (X) +v; delta denotes dirac delta function, with:
p(Z|X)＝∫∫δ(Z-h(X)-V)p(X)p(V)dXdV。
3. the method for detecting the abrupt fault of the state-domain-based GNSS-accelerometer integrated bridge deformation monitoring according to claim 2, wherein the process of calculating the state prediction value and the observed quantity residual in step S2 is as follows:
based on the establishment of a Kalman filtering equation, the time updating process and the measurement updating process of the GNSS/accelerometer integrated system based on the adaptive Kalman filtering are carried out:
in the formula ：
k represents t k Moment, observation variance coefficient matrix
At t k-1 From time to t k A system state transition matrix at a moment;
is a noise driving matrix;
W k-1 for system excitation noise, the acceleration disturbance is regarded as a covariance matrix delta 2 I Gaussian white noise, W k Covariance matrix of (2)
At t k A time state parameter estimation value; k (K) k Is a gain matrix; />Estimated value +.>Is a covariance matrix of (a);predicted value +.>Is a covariance matrix of (a); />For predicting observations +.>Is a covariance matrix of (a); r is R k Measuring a noise covariance matrix; Δt represents the sampling rate; />At t k Corresponding to the momentState parameter vector predictor, predictive observer +.>GNSS observations and accelerometer raw data Z measured with bridge k The difference is the observed quantity residual.
4. The state-domain-based GNSS-accelerometer-integrated bridge deformation monitoring abrupt fault detection method according to claim 3, wherein step S3 comprises the following sub-steps:
s31, constructing state domain mutation fault detection statistics: will be at time t 0 By time t k Chi-square variable based on error square sumThe following definitions are made:
in the formula ,Zi For i time observation quantity, H i For the coefficient matrix at instant i, R i For the measurement noise covariance matrix at time i,the fusion estimated value at the moment i;
will be at time t k Chi-square delta at this point is defined as:
obtainingIs in the form of a recurrence:
wherein ,
let the predicted observed valueFrom the original observed value Z k The difference between them is e k Then in original hypothesis B 0 Under the condition that e k Following gaussian white noise emissions for which mathematical expectations are 0, there are:
the variance is:
thenThe simplification is as follows:
when abrupt failure occurs, e k No longer obeys the gaussian white noise distribution of 0, which is expected mathematically, by detecting e k The statistical characteristics of the bridge monitoring data are used for carrying out mutation fault detection on the bridge monitoring data, and measuring test statistics are calculated:
wherein ,for chi-square increment, e k For observing residual->E is k Is a variance of (2);
if the original assumption B 0 Correct, probability density functionApproximately coincident with degree of freedom n z Chi-square distribution of n z To measure the dimension of the domain.
S32, calculating a detection threshold under the corresponding false alarm rate: defining a false alarm probability P FA And calculate the corresponding P FA The threshold values of (2) are:
wherein ,is about->The operator inf represents the infinit, the cumulative distribution function of +.>Consider as a fault detection threshold;
s33, judging the size of the detection statistic and the detection threshold value: will measure the test statisticsAnd threshold->Comparison is performed: if->Then the bridge actual measurement data is considered to have no fault, and the calculation of the step state estimation value and the covariance matrix in the step S43 is continued; if->Then the bridge measured data is considered to have abrupt fault, and an alarm is sent out.
5. The method for detecting abrupt fault in state-domain-based GNSS-accelerometer integrated bridge deformation monitoring according to claim 1, wherein in step S42, the state vector reference value is calculated in an improved manner in deformation monitoring of bridge or dam engineeringThe method of (1) is as follows:
will a k Substituting the calculated state estimation value and the covariance matrix.
6. The state-domain-based GNSS-accelerometer integrated bridge deformation monitoring abrupt fault detection method of claim 1, wherein: the GNSS data is divided into base station data and monitoring station data, and the sampling rate is set to 10hz.
7. The state-domain-based GNSS-accelerometer integrated bridge deformation monitoring abrupt fault detection method of claim 1, wherein: the base station is arranged at a vacant place which is close to the bridge and has good observation conditions; and arranging monitoring points on the midspan of the bridge to obtain obvious displacement change.
8. The state-domain-based GNSS-accelerometer integrated bridge deformation monitoring abrupt fault detection method of claim 1, wherein: the accelerometer data is high frequency data of 200hz.
CN202211732154.0A 2022-12-30 2022-12-30 GNSS-accelerometer integrated bridge deformation monitoring abrupt fault detection method based on state domain Pending CN116558406A (en)

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Publication number Priority date Publication date Assignee Title
CN117723782A (en) * 2024-02-07 2024-03-19 山东大学 Sensor fault identification positioning method and system for bridge structure health monitoring

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117723782A (en) * 2024-02-07 2024-03-19 山东大学 Sensor fault identification positioning method and system for bridge structure health monitoring
CN117723782B (en) * 2024-02-07 2024-05-03 山东大学 Sensor fault identification positioning method and system for bridge structure health monitoring

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