CN117171985A - Real-time monitoring method, device and equipment for nonlinear structure and storage medium - Google Patents
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Abstract
The application discloses a real-time monitoring method, device, equipment and storage medium of a nonlinear structure. The method can be used for engineering structures under the action of loads such as earthquakes, so that the health state of the structures can be known in real time, and effective guarantee is provided for structure evaluation.
Description
Technical Field
The present application relates to the field of civil engineering technologies, and in particular, to a method, an apparatus, a device, and a storage medium for monitoring a nonlinear structure in real time.
Background
The unknowns in the structural health monitoring application of an engineering structure are mainly of three types, namely external excitation (such as excitation caused by earthquakes, typhoons, etc.), unknown structural states including velocity and displacement, and unknown structural parameters including stiffness, damping, non-linear parameters, etc. The unknown external excitation effective identification of the engineering structure is a precondition of engineering structure safety evaluation and vibration control, the reliable estimation of the structural state can be used for fatigue damage identification of the structure to be monitored, the structural performance of the engineering structure can be reflected by parameters such as rigidity and damping of the structure, and the health monitoring result can directly reflect the health state of the engineering structure; however, in general, the structural parameters of the engineering structure are unknown, and it is difficult to directly measure all the structural states of a structure and external excitation.
When the engineering structure is subjected to the load actions of earthquake, typhoon and the like and the structure is subjected to large displacement and large deformation, strong nonlinear characteristics can appear, and the nonlinearity can cause more complex dynamic phenomena. At present, most of nonlinear structure identification researches are to identify structural state-structural parameters under the condition that external excitation is known, and the state vector comprises a structural state vector and an unknown structural parameter vector, but in actual engineering, the external excitation is usually difficult to directly measure, so that the structural state vector and the structural parameter vector of an engineering structure are difficult to estimate.
Disclosure of Invention
The present application aims to at least solve the technical problems existing in the prior art. Therefore, the application provides a real-time monitoring method, device and equipment for a nonlinear structure and a storage medium, which can know the health state of the structure in real time and provide effective guarantee for structure evaluation.
According to the real-time monitoring method of the nonlinear structure of the embodiment of the first aspect of the application, the real-time monitoring method of the nonlinear structure comprises the following steps:
collecting partial acceleration response generated by the nonlinear structure under the action of external excitation;
simulating the structural parameters of the nonlinear structure and the external excitation into a random walk model, and constructing an augmented state vector consisting of a structural parameter vector, the external excitation and a state vector of the nonlinear structure according to the random walk model;
and estimating the structural state, structural parameters and the external excitation of the nonlinear structure in real time by adopting unscented Kalman filtering according to the partial acceleration response and the augmented state vector.
The real-time monitoring method of the nonlinear structure provided by the application has at least the following beneficial effects:
the identification research of the nonlinear structure at the present stage is to identify the structural state-structural parameter under the condition that the external excitation is known, and the state vector comprises the structural state vector and the uncertain structural parameter vector, but in actual engineering, the external excitation is generally difficult to directly measure. In the method, unknown external excitation, structural parameters and structural states are combined, and the unknown structural states, structural parameters and external excitation are estimated by adopting unscented Kalman filtering according to partial acceleration response and the augmented state vectors obtained by actual acquisition by constructing the augmented state vectors comprising the unknown external excitation, the structural parameter vectors and the structural state vectors, so that the estimated efficiency and accuracy can be improved. The method can be used for engineering structures under the action of loads such as earthquakes, so that the health state of the structures can be known in real time, and effective guarantee is provided for structure evaluation.
According to some embodiments of the application, a first sigma point set of the augmented state vector is generated by adopting unscented transformation according to state estimation and error covariance at the current moment, and corresponding weights are calculated;
converting the first sigma point set into a state prediction vector, merging the state prediction vector according to the weight to obtain a state estimation of the previous step, and calculating a corresponding error covariance;
generating a second sigma point set of the state prediction vector by adopting unscented transformation according to the state estimation of the previous step and the corresponding error covariance;
converting the second sigma point set into a measurement prediction vector corresponding to a sigma point, and merging the measurement prediction vectors corresponding to the sigma point according to the weight to obtain a measurement prediction;
calculating a measurement prediction covariance and a state-measurement covariance according to the state estimation of the previous step, the state prediction vector, the measurement prediction vector corresponding to the sigma point and the measurement prediction;
calculating a Kalman gain from the measurement prediction covariance and the state-measurement covariance;
calculating a state estimate for a next time based on the state estimate for the previous step, the kalman gain, the partial acceleration response and the measurement prediction to obtain a structural state, structural parameters and external excitation for the next time from the state estimate for the next time; wherein a sampling period is spaced between the current time and the next time.
According to some embodiments of the application, the calculating a measurement prediction covariance and a state-measurement covariance from the state estimate of the previous step, the state prediction vector, the measurement prediction vector, and the measurement prediction comprises:
wherein P is yy，(i+1|i) In order to measure the predicted covariance of the signal,for the measured prediction vector corresponding to the sigma point,for measurement prediction, n is the dimension of the augmented state vector, +.>Weight of covariance, ++>Is that The subscript (i+ 1|i) is the transition from time i to time (i+1), P uy，(i+1|i) For state-measurement covariance, +.>For state prediction vector, ++>For the state estimation of the previous step, R is the covariance matrix of the measurement noise.
According to some embodiments of the application, the calculating the kalman gain from the measurement prediction covariance and the state-measurement covariance comprises:
wherein,for Kalman gain, ++>Is P yy，(i+1|i) Is a matrix of inverse of (a).
According to some embodiments of the application, the calculating the state estimate for the next time from the state estimate for the previous step, the kalman gain, the partial acceleration response and the measurement prediction value comprises:
wherein y is i+1 For the partial acceleration response at time (i + 1),is a state estimate at time (i+1).
According to some embodiments of the application, after the calculating of the state estimate of the next time instant, an error covariance of the next time instant is also calculated by:
wherein,for the error covariance of the next moment, +.>To estimate the corresponding error covariance for the state of the previous step,/->Is->Is a matrix of inverse of (a).
According to some embodiments of the application, the modeling the structural parameters of the nonlinear structure and the external excitation as a random walk model includes:
simulating the external excitation as a random walk model based on the external excitation and a first gaussian white noise;
and determining structural parameters of the nonlinear structure, and simulating the structural parameters into a random walk model according to the structural parameters and second Gaussian white noise.
According to a second aspect of the present application, a real-time monitoring device for a nonlinear structure includes:
the data acquisition unit is used for acquiring partial acceleration response generated by the nonlinear structure under the external excitation action;
a state vector construction unit for simulating the structural parameters of the nonlinear structure and the external excitation into a random walk model, and constructing an augmented state vector composed of the structural parameter vector, the external excitation and the state vector of the nonlinear structure according to the random walk model;
and the recursion solving unit is used for estimating the structural state, the structural parameters and the external excitation of the nonlinear structure in real time by adopting unscented Kalman filtering according to the partial acceleration response and the augmented state vector.
An electronic device according to an embodiment of the third aspect of the present application comprises at least one control processor and a memory for communication connection with the at least one control processor; the memory stores instructions executable by the at least one control processor to enable the at least one control processor to perform the method of real-time monitoring of a nonlinear structure described above.
A computer-readable storage medium according to an embodiment of the fourth aspect of the present application stores computer-executable instructions for causing a computer to perform the real-time monitoring method of a nonlinear structure described above.
Additional features and advantages of the application will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the application.
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The foregoing and/or additional aspects and advantages of the application will become apparent and may be better understood from the following description of embodiments taken in conjunction with the accompanying drawings in which:
FIG. 1 is a flow chart of a method for real-time monitoring of a nonlinear structure according to an embodiment of the present application;
FIG. 2 is a schematic diagram of estimating the structural state, structural parameters and external excitation of a nonlinear structure using unscented Kalman filtering according to an embodiment of the application;
FIG. 3 is a schematic illustration of a five-layer Duffing-type layer shear frame structure in accordance with an embodiment of the present application;
FIG. 4 is a comparison of predicted and true displacement identification for an embodiment of the present application;
FIG. 5 is a graph of predicted and true velocity identification versus an embodiment of the present application;
FIG. 6 is a graph of stiffness parameter estimation results according to an embodiment of the present application;
FIG. 7 is a graph of nonlinear parameter estimation results according to an embodiment of the present application;
FIG. 8 is a graph of damping scaling factor estimation results according to an embodiment of the present application;
FIG. 9 is a graph comparing the results of external stimulus identification according to an embodiment of the present application;
fig. 10 is a schematic structural diagram of an electronic device according to an embodiment of the present application.
Detailed Description
Embodiments of the present application are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are illustrative only and are not to be construed as limiting the application.
Before proceeding to further detailed description of the disclosed embodiments, the terms and terms involved in the disclosed embodiments are described, which are applicable to the following explanation:
(1) The unscented kalman filter algorithm (Unscented Kalman Filter, UKF) is a non-parametric filter algorithm for handling non-linear systems that can infer values of hidden states from observed and measured data. The basic idea of kf is to predict the future state using a series of weighted state estimates based on the state of the state variables and the observations of the measured variables, and correct the predicted values by the observations and measurements. The unscented transformation is to obtain some sampling points in a deterministic sampling mode, so that the statistical property of the sampling points is equal to the mean value and covariance matrix of the Gaussian distribution. After nonlinear transformation, the points are used to obtain the mean and covariance matrix of the new function in a deterministic weighting mode.
(2) Three unknowns and one known amount of nonlinear structure involved in embodiments of the present disclosure:
external excitation, which refers to unknown excitation acting on nonlinear structures, usually generated by typhoons, earthquakes, etc.;
structural states including speed and displacement of the nonlinear structure under external excitation;
structural parameters, typically including mass, stiffness, damping, non-linear parameters, etc. of the non-linear structure;
the partial acceleration response is measured by an acceleration sensor mounted on a partial region of the nonlinear structure.
First embodiment
Referring to fig. 1, an embodiment of the present application provides a real-time monitoring method for a nonlinear structure, including steps S110 to S130:
step S110, collecting partial acceleration response generated by the nonlinear structure under the action of external excitation in real time.
Step S120, simulating structural parameters and external excitation of the nonlinear structure into a random walk model, and constructing an augmented state vector consisting of structural parameter vectors, external excitation and state vectors of the nonlinear structure according to the random walk model.
And step 130, estimating the structural state, structural parameters and external excitation of the nonlinear structure in real time by adopting unscented Kalman filtering according to the partial acceleration response and the augmented state vector.
The identification research of the nonlinear structure at the present stage is to identify the structural state-structural parameter under the condition that the external excitation is known, and the state vector comprises the structural state vector and the uncertain structural parameter vector, but in actual engineering, the external excitation is generally difficult to directly measure.
In this embodiment, based on the prior art, the unknown external excitation, the structural parameters and the structural states are combined, and by constructing an augmented state vector including the unknown external excitation, the structural parameter vector and the structural state vector, according to the partial acceleration response and the augmented state vector obtained by actual acquisition, the estimation of the unknown structural states, the structural parameters and the external excitation is realized by adopting unscented kalman filtering, so that the efficiency and the accuracy of the estimation can be improved. The method can be used for engineering structures under the action of loads such as earthquakes, so that the health state of the structures can be known in real time, and effective guarantee is provided for structure evaluation.
Second embodiment
The present embodiment provides a specific implementation manner of the method shown in the first embodiment, including steps S210 to S240:
step S210, acquiring partial acceleration response of the structure to be monitored under unknown external excitation.
The sensor is arranged in a structure to be monitored (nonlinear structure), and when the structure to be monitored is excited externally, the acceleration response of a part of the structure read by the sensor is obtained. Only a part of the acceleration response is observed in the method, and the actual observed value is used in the following formula (33).
Step S220, establishing a random walk model of external excitation and structural parameters.
The equation of motion of a continuous time system of a structure to be monitored when subjected to external excitation can be expressed as (for example, a Duffing-type layer shear structure):
wherein M is a mass matrix of the structure to be monitored, C is a damping matrix of the structure to be monitored, K is a rigidity matrix of the structure to be monitored, and W is a nonlinear parameter of the structure to be monitored;x (t) represents acceleration, speed and displacement vector of the structure to be monitored, and f (t) is unknown external excitation. It should be noted that the equations of motion are slightly different for different structures.
Defining a state vectorThe equation of motion of formula (1) can be rewritten asThe form of the state space equation is as follows:
wherein θ (t) represents a structural parameter vector of a structure to be monitored, and comprises mass, stiffness, damping and nonlinear parameters, ω (t) represents process noise, ω can be modeled as zero mean, and covariance matrix is Gaussian distribution of Q; g () is a nonlinear function of the state vector χ (t), expressed as follows:
the measurement equation (or observation equation) can be expressed as:
z(t)＝h(χ(t)，θ(t)，f(t))+v(t) (4)
where h (-) is a nonlinear function of the state vector χ (t), v (t) is measurement noise (or observation noise), v can be modeled as a zero-mean, covariance matrix is a gaussian distribution of R. The measurement equation is used to calculate the predicted acceleration response.
Equation of state spaceAnd the measurement equation may be discretized using the sampling period Δt. The discrete state space equation (i.e., discrete equation (2)), the expression at time (i+1) Δt is as follows:
χ i+1 ＝F(χ i ，θ i ，f i )+ω j (5)
where F (-) is the discretized state vector χ i+1 Is a non-linear function of (2). i=0, 1, …, N; n=t/Δt, t being the total duration of the structural acceleration response observation period.
The measurement equation after the discretization (i.e., the discretization equation (4)) is:
the random walk model is used for representing unknown external excitation of a structure to be monitored and change of structural parameters, and a calculation formula of the discrete time system is as follows:
f i+1 ＝f i +ω f，i (8)
θ i+1 ＝θ i +ω θ，i (9)
wherein f i Representing an unknown external stimulus at time i; θ i The unknown structural parameter vector representing the moment i generally comprises a stiffness parameter, a damping parameter and a nonlinear parameter; omega f，i And omega θ，i Is Gaussian white noise with zero mean value, and covariance matrixes of the Gaussian white noise and the Gaussian white noise are P respectively f，i And P θ，i 。
Step S230, introducing an augmented state vector comprising a state vector, a structural parameter vector and an external stimulus.
u i ＝[χ i T ，θ i T ，f i T ] T (10)
Wherein χ is i A state vector representing the moment i, the state vector comprising the displacement and the velocity.
For the problem of external excitation input-structural state-structural parameter identification of the nonlinear structure of the present embodiment, the expression of the augmented state space equation is as follows:
wherein the new process noise eta j ＝[ω j T ω θ，j T ω f，j T ] T ，A new nonlinear equation for new state vectors and process noise is expressed as follows:
wherein G (·) is an augmented state vector u j+1 Is a non-linear function of (2).
The observation equation based on the augmented state vector can be written as:
y j+1 ＝H(u j+1 )+v j+1 (13)
in equation (13), H (·) is a new nonlinear function of the measurement equation.
While the state vector is constructed by using the combination of the structural state and the structural parameters, the application adds external excitation to combine the three parameter vectors of the structural state, the structural parameters and the external excitation.
Step S240, estimating the structural state, structural parameters and external excitation of the structure to be monitored based on the unscented Kalman filtering algorithm through the partial acceleration response of step S210 and the augmented state vector of step S230.
Referring to fig. 2, the step S240 specifically includes the following steps S241 to S248:
firstly, an unscented Kalman filtering algorithm is a recursive algorithm, and an initial state value of the unscented Kalman filtering algorithm is set as follows:
wherein u is 0 An augmented state vector representing the structure to be monitored with an initial zero-time spread,a predicted value representing an augmented state vector; p (P) 0 Error covariance matrix representing initial zero-time augmented state vector,/, for>Representing the predicted value of the error covariance matrix.
In this embodiment, the current time is i time, the next time is (i+1) time, and the calculation process from i time to (i+1) time is described with a sampling time Δt between i time and (i+1) time. Knowing the state estimate and the error covariance at the current instant i, the state estimate and the error covariance at instant i can be deduced according to a similar procedure, since the following steps describe the calculation process from instant i to instant i+1, which will not be described in detail here.
Step S241, according to the state estimation and the error covariance of the current moment, a first sigma point set of the augmented state vector is generated by adopting unscented transformation, and corresponding weights are calculated.
In step S241, the augmented state vector is subjected to an unscented transformation, and its corresponding sigma points are generated (the present embodiment sets (2n+1) points). The above formulas (16) to (18) are processes for obtaining sigma points,the state estimate and the error covariance at time i, respectively.
Weight corresponding to mean value +.>For the weights corresponding to covariance, n is the dimension of the augmented state vector, λ is the scale parameter, λ=α 2 (n+κ) -n, here α=1, β=2, κ=0.
Step S242, the first sigma point set is converted into a state prediction vector, and the state prediction vector is combined according to the weight to obtain the state estimation of the previous step and calculate the corresponding error covariance.
State space equation using the above equation (11)Sigma Point +.>Conversion to a state prediction vectorThen merge the state prediction vector by weight>Obtaining the state estimate of the previous step at instant i +.>And calculates the error covariance of the state estimation in the previous step +.>
Step S243, a second sigma point set of the state prediction vector is generated by adopting unscented transformation according to the state estimation of the previous step and the corresponding error covariance.
Step S243 is a measurement update, i.e. using a state estimate of the previous stepError covariance +>Regenerating a set of sigma points by means of an unscented transformation>
And step S244, converting the second sigma point set into measurement prediction vectors corresponding to the sigma points, and merging the measurement prediction vectors corresponding to the sigma points according to the weight to obtain measurement prediction.
The sigma point is converted into a measurement prediction vector using a nonlinear measurement equation H ()' shown in equation (13) aboveMerge vector->Obtaining a measurement prediction +.for moment (i+1)>
Step S245, calculating measurement prediction covariance and state-measurement covariance of the measurement noise according to the state estimation, the state prediction vector, the measurement prediction vector corresponding to the sigma point and the measurement prediction of the previous step.
Measurement prediction covariance P taking measurement noise into account yy，(i+1|i) And state-measurement covariance P uy，(i+1|i) ：
Step S246, calculating the Kalman gain according to the measurement prediction covariance and the state-measurement covariance.
To perform measurement update of the state, kalman gain is calculated first
Step S247, calculating the state estimation and the corresponding error covariance of the next moment according to the state estimation, the kalman gain, the partial acceleration response and the measurement prediction of the previous step, so as to obtain the structural state, the structural parameter and the external excitation of the next moment from the state estimation.
According to Kalman gainUpdating to obtain the state vector +.i at time (i+1)>
Wherein y is i+1 The partial acceleration response at time i+1 acquired in step S210.
State vector at this timeThe structure state at the moment (i+1), the structure parameters and the external excitation acting on the structure to be monitored at the moment (i+1) are included.
Error covariance at time i+1 obtained in step S247Acting on the recursive process of the next round. It should be noted that the state estimate +.A.of time i can also be inferred from the above formula>Error covariance +>Not described in detail herein.
In the next cycle, i.e., from (i+1) to (i+2), the calculation of the structural state, structural parameters, and external excitation is performed in the next step according to the flow of steps S241 to S247. And (5) finishing all calculation until N moments.
The identification research of the nonlinear structure at the present stage is to identify the structural state-structural parameter under the condition that the external excitation is known, and the state vector comprises the structural state vector and the uncertain structural parameter vector, but in actual engineering, the external excitation is generally difficult to directly measure. In this embodiment, based on the prior art, the unknown external excitation, the structural parameters and the structural states are combined, and by constructing an augmented state vector including the unknown external excitation, the structural parameter vector and the structural state vector, the estimation of the unknown structural states, the structural parameters and the external excitation is realized by adopting unscented kalman filtering according to the partial acceleration response and the augmented state vector obtained by actual acquisition, so that the efficiency and the accuracy of the estimation can be improved. The method can be used for engineering structures under the action of loads such as earthquakes, so that the health state of the structures can be known in real time, and effective guarantee is provided for structure evaluation.
Third embodiment
For ease of understanding by those skilled in the art, a set of embodiments is provided below:
taking a five-layer Duffing-layer shear frame structure as an example, a schematic diagram of the structure is shown in fig. 3, and the structural parameters are respectively as follows: mass m of each layer L =400 kg, layer stiffness k L 320kN/m, l=1, 2, …,5, so the stiffness to mass ratio of each layer is 0.8, nonlinear parameter w=30 kN/m; collectingWith the rayleigh damping model, the damping coefficient is a=0.5996 and b=0.0032, so the first two-order damping ratio ζ is taken to be 5%. The first five natural frequencies of the structure are 1.2813Hz,3.7400Hz,5.8958Hz,7.5739Hz and 8.6358Hz respectively. The structure was subjected to horizontal seismic excitation and the ground acceleration was modeled as a spectral intensity of 0.49m 2 /s 3 Zero mean gaussian white noise of (a); the whole monitoring period t is 300s, acceleration responses of layers 1, 3 and 5 of the nonlinear structure are observed, and the sampling frequency of monitoring data is 1000Hz. And, at 100s, the 1 st and 4 th layer rigidity of the structure is degraded by 10% on the original basis. Taking the influence of observation noise into consideration, gaussian white noise with a signal root mean square value of 5% is added into the observation information; expanding unknown structural parameters and unknown external excitation of a structure into a state vector to obtain an augmented state vector, and carrying out parameterization processing on parameter items in the augmented state vector in order to avoid the influence of calculation rounding errors by considering that the order of magnitude difference between structural response and parameters is larger; the augmented state vector of the unscented Kalman filter algorithm (UKF algorithm) at this time is
Wherein θ k，L Representing the stiffness parameter vector, θ, after parameterization a 、θ b Represents the damping proportionality coefficient, theta, after parameterization w Representing the non-linear parameters after the parameterization process. The method comprises the following steps:
step S310, acquiring acceleration response of the part of the structure under unknown excitation. Sensors are arranged in the structure to obtain acceleration responses of layers 1, 3 and 5 of the structure using accelerometers when the structure is externally excited.
Step S320, establishing a model.
And S321, establishing a mathematical model of the unknown external excitation and the unknown structural parameters.
f i+1 ＝f i +ω f，i (35)
θ i+1 ＝θ i +ω θ，i (36)
Step S322, determining an augmentation state vector:
step S323, establishing an augmentation state equation of system time dispersion containing process noise:
step S324, according to the state vector, the following observation equation can be obtained:
y i+1 ＝H(u i+1 )+v i+1 (39)
step S330, performing real-time joint estimation of the structural excitation-state-parameters (taking i time to (i+1) time as an example).
Step S331, setting a state initial value of a unscented Kalman filtering algorithm:
step S332, state prediction:
2n+1 sampling points (sigma point set) are generated through unscented transformation, and corresponding weights are calculated:
merging vectorsGet forward state estimate +.>Estimated covariance->
Step S333, measurement update:
(2n+1) sample points (sigma point set) are regenerated by unscented transformation:
step S334, measurement prediction:
step S335, measurement prediction covariance P considering measurement noise yy And state measurement covariance P uy ：
Step S336, updating the state;
kalman gain:
state vector update:
error covariance:
step S337, repeating steps S310 to S330 until the time i=n.
It should be noted that the explanation of the above formulas (35) to (60) is shown in the second embodiment, and will not be repeated here.
Fourth embodiment
Referring to fig. 4 to 9, for better illustration, the following experiment was performed in this embodiment:
fig. 4 and 5 compare the actual response and the estimated response of the engineering structure, and the time interval 5s is selected for amplification comparison, so that the state estimated value can be well matched with the actual value. Fig. 6 shows the results of the stiffness parameter estimation, and it can be seen that the initial time can quickly converge to the true value, and the first and fourth layer stiffness can also quickly converge to the true value after the 100s time is degraded. FIGS. 7 and 8 are graphs of nonlinear parameter and damping scaling factor recognition results, wherein the recognition error is greater than the stiffness parameter because the stiffness contributes more to the structural response and is easier to recognize; it can be seen from the figure that the recognition result is included within 95% confidence interval and within acceptable error range. Fig. 9 compares the actual excitation with the estimated excitation, and a comparison plot comparing the time intervals 1s is selected for an enlarged comparison, the comparison result showing that the estimated excitation is very close to the actual excitation.
Fifth embodiment
Some embodiments of the present application provide a real-time monitoring device for a nonlinear structure, the real-time monitoring device for a nonlinear structure including: the data acquisition unit 1100, the state vector construction unit 1200, and the recursive solving unit 1300 specifically include:
the data acquisition unit 1100 is configured to acquire, in real time, a partial acceleration response generated by the nonlinear structure under the external excitation.
The state vector construction unit 1200 is configured to simulate the structural parameters and the external excitation of the nonlinear structure as a random walk model, and construct an augmented state vector composed of the structural parameter vector, the external excitation, and the state vector of the nonlinear structure according to the random walk model.
The recursive solving unit 1300 is configured to estimate the structural state, structural parameters and external excitation of the nonlinear structure in real time by using unscented kalman filtering according to the partial acceleration response and the augmented state vector.
The apparatus in this embodiment and the foregoing method embodiments are based on the same inventive concept, so that the relevant content of the foregoing method embodiments is also applicable to the content of the apparatus, and thus will not be described herein again.
Sixth embodiment
Referring to fig. 10, the embodiment of the application further provides an electronic device, where the electronic device includes:
at least one memory;
at least one processor;
at least one program;
the program is stored in the memory, and the processor executes at least one program to implement the present disclosure to implement the method for real-time monitoring of a nonlinear structure described above.
The electronic device can be any intelligent terminal including a mobile phone, a tablet personal computer, a personal digital assistant (Personal Digital Assistant, PDA), a vehicle-mounted computer and the like.
The electronic device according to the embodiment of the application is described in detail below.
Processor 1600, which may be implemented by a general-purpose central processing unit (Central Processing Unit, CPU), microprocessor, application specific integrated circuit (Application Specific Integrated Circuit, ASIC), or one or more integrated circuits, etc., is configured to execute related programs to implement the technical solutions provided by the embodiments of the present disclosure;
the Memory 1700 may be implemented in the form of Read Only Memory (ROM), static storage, dynamic storage, or random access Memory (Random Access Memory, RAM). Memory 1700 may store an operating system and other application programs, related program code is stored in memory 1700 when the technical solutions provided by the embodiments of the present disclosure are implemented in software or firmware, and the processor 1600 invokes a real-time monitoring method that performs the nonlinear structure of the embodiments of the present disclosure.
An input/output interface 1800 for implementing information input and output;
the communication interface 1900 is used for realizing communication interaction between the device and other devices, and can realize communication in a wired manner (such as USB, network cable, etc.), or can realize communication in a wireless manner (such as mobile network, WIFI, bluetooth, etc.);
bus 2000, which transfers information between the various components of the device (e.g., processor 1600, memory 1700, input/output interface 1800, and communication interface 1900);
wherein processor 1600, memory 1700, input/output interface 1800, and communication interface 1900 enable communication connections within the device between each other via bus 2000.
The disclosed embodiments also provide a storage medium that is a computer-readable storage medium storing computer-executable instructions for causing a computer to perform the method of real-time monitoring of a nonlinear structure described above.
The memory, as a non-transitory computer readable storage medium, may be used to store non-transitory software programs as well as non-transitory computer executable programs. In addition, the memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one magnetic disk storage device, flash memory device, or other non-transitory solid state storage device. In some embodiments, the memory optionally includes memory remotely located relative to the processor, the remote memory being connectable to the processor through a network. Examples of such networks include, but are not limited to, the internet, intranets, local area networks, mobile communication networks, and combinations thereof.
The embodiments described in the embodiments of the present disclosure are for more clearly describing the technical solutions of the embodiments of the present disclosure, and do not constitute a limitation on the technical solutions provided by the embodiments of the present disclosure, and as those skilled in the art can know that, with the evolution of technology and the appearance of new application scenarios, the technical solutions provided by the embodiments of the present disclosure are equally applicable to similar technical problems.
It will be appreciated by those skilled in the art that the technical solutions shown in the figures do not limit the embodiments of the present disclosure, and may include more or fewer steps than shown, or may combine certain steps, or different steps.
The above described apparatus embodiments are merely illustrative, wherein the units illustrated as separate components may or may not be physically separate, i.e. may be located in one place, or may be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment.
Those of ordinary skill in the art will appreciate that all or some of the steps of the methods, systems, functional modules/units in the devices disclosed above may be implemented as software, firmware, hardware, and suitable combinations thereof.
The terms "first," "second," "third," "fourth," and the like in the description of the application and in the above figures, if any, are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used may be interchanged where appropriate such that the embodiments of the application described herein may be implemented in sequences other than those illustrated or otherwise described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
It should be understood that in the present application, "at least one (item)" means one or more, and "a plurality" means two or more. "and/or" for describing the association relationship of the association object, the representation may have three relationships, for example, "a and/or B" may represent: only a, only B and both a and B are present, wherein a, B may be singular or plural. The character "/" generally indicates that the context-dependent object is an "or" relationship. "at least one of" or the like means any combination of these items, including any combination of single item(s) or plural items(s). For example, at least one (one) of a, b or c may represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", wherein a, b, c may be single or plural.
In the several embodiments provided by the present application, it should be understood that the disclosed apparatus and method may be implemented in other manners. For example, the apparatus embodiments described above are merely illustrative, e.g., the division of elements is merely a logical functional division, and there may be additional divisions of actual implementation, e.g., multiple elements or components may be combined or integrated into another system, or some features may be omitted, or not performed. Alternatively, the coupling or direct coupling or communication connection shown or discussed with each other may be an indirect coupling or communication connection via some interfaces, devices or units, which may be in electrical, mechanical or other form.
The units described as separate units may or may not be physically separate, and units shown as units may or may not be physical units, may be located in one place, or may be distributed over a plurality of network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.
In addition, each functional unit in the embodiments of the present application may be integrated in one processing unit, or each unit may exist alone physically, or two or more units may be integrated in one unit. The integrated units may be implemented in hardware or in software functional units.
The integrated units, if implemented in the form of software functional units and sold or used as stand-alone products, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present application may be embodied in essence or a part contributing to the prior art or all or part of the technical solution in the form of a software product stored in a storage medium, including multiple instructions for causing an electronic device (which may be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods of the embodiments of the present application. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (Random Access Memory, RAM), a magnetic disk, an optical disk, or other various media capable of storing a program. The embodiments of the present application have been described in detail with reference to the accompanying drawings, but the present application is not limited to the above embodiments, and various changes can be made within the knowledge of one of ordinary skill in the art without departing from the spirit of the present application.
Claims (10)
1. The real-time monitoring method for the nonlinear structure is characterized by comprising the following steps of:
collecting partial acceleration response generated by the nonlinear structure under the external excitation action in real time;
simulating the structural parameters of the nonlinear structure and the external excitation into a random walk model, and constructing an augmented state vector consisting of a structural parameter vector, the external excitation and a state vector of the nonlinear structure according to the random walk model;
and estimating the structural state, structural parameters and the external excitation of the nonlinear structure in real time by adopting unscented Kalman filtering according to the partial acceleration response and the augmented state vector.
2. The method of claim 1, wherein said estimating in real time the structural state, structural parameters, and external excitation of the nonlinear structure using unscented kalman filtering based on the partial acceleration response and the augmented state vector comprises:
generating a first sigma point set of the augmented state vector by adopting unscented transformation according to the state estimation and the error covariance at the current moment, and calculating a corresponding weight;
converting the first sigma point set into a state prediction vector, merging the state prediction vector according to the weight to obtain a state estimation of the previous step, and calculating a corresponding error covariance;
generating a second sigma point set of the state prediction vector by adopting unscented transformation according to the state estimation of the previous step and the corresponding error covariance;
converting the second sigma point set into a measurement prediction vector corresponding to a sigma point, and merging the measurement prediction vectors corresponding to the sigma point according to the weight to obtain a measurement prediction;
calculating a measurement prediction covariance and a state-measurement covariance according to the state estimation of the previous step, the state prediction vector, the measurement prediction vector corresponding to the sigma point and the measurement prediction;
calculating a Kalman gain from the measurement prediction covariance and the state-measurement covariance;
calculating a state estimate for a next time based on the state estimate for the previous step, the kalman gain, the partial acceleration response and the measurement prediction to obtain a structural state, structural parameters and external excitation for the next time from the state estimate for the next time; wherein a sampling period is spaced between the current time and the next time.
3. The method of real-time monitoring of a nonlinear structure according to claim 2, wherein said calculating a measurement prediction covariance and a state-measurement covariance from the state estimate of the previous step, the state prediction vector, the measurement prediction vector, and the measurement prediction comprises:
wherein P is yy,(i+1|i) In order to measure the predicted covariance of the signal,for the measurement prediction vector corresponding to sigma point, < ->For measurement prediction, n is the dimension of the augmented state vector, +.>Weight of covariance, ++>Is thatThe subscript (i+ 1|i) is the transition from time i to time (i+1), P uy,(i+1|i) For state-measurement covariance, +.>For state prediction vector, ++>For the state estimation of the previous step, R is the covariance matrix of the measurement noise.
4. A method of real-time monitoring of a nonlinear structure according to claim 3, wherein said calculating a kalman gain from said measurement prediction covariance and a state-measurement covariance comprises:
wherein,for Kalman gain, ++>Is P yy,(i+1|i) Is a matrix of inverse of (a).
5. The method according to claim 4, wherein said calculating a state estimate at a next time from the state estimate of the previous step, the kalman gain, the partial acceleration response, and the measurement prediction value comprises:
wherein y is i+1 For the partial acceleration response at time (i + 1),is a state estimate at time (i+1).
6. The method according to claim 5, wherein after calculating the state estimate of the next time, the error covariance of the next time is further calculated by:
wherein,for the error covariance at the next instant,/>to estimate the corresponding error covariance for the state of the previous step,/->Is->Is a matrix of inverse of (a).
7. The method of any one of claims 1 to 6, wherein simulating the structural parameters of the nonlinear structure and the external excitation as a random walk model comprises:
simulating the external excitation as a random walk model based on the external excitation and a first gaussian white noise;
and determining structural parameters of the nonlinear structure, and simulating the structural parameters into a random walk model according to the structural parameters and second Gaussian white noise.
8. A real-time monitoring device for a nonlinear structure, wherein the real-time monitoring device for a nonlinear structure comprises:
the data acquisition unit is used for acquiring partial acceleration response generated by the nonlinear structure under the external excitation action in real time;
a state vector construction unit for simulating the structural parameters of the nonlinear structure and the external excitation into a random walk model, and constructing an augmented state vector composed of the structural parameter vector, the external excitation and the state vector of the nonlinear structure according to the random walk model;
and the recursion solving unit is used for estimating the structural state, the structural parameters and the external excitation of the nonlinear structure in real time by adopting unscented Kalman filtering according to the partial acceleration response and the augmented state vector.
9. An electronic device, characterized in that: comprising at least one control processor and a memory for communication connection with the at least one control processor; the memory stores instructions executable by the at least one control processor to enable the at least one control processor to perform the method of real-time monitoring of a nonlinear structure as claimed in any one of claims 1 to 7.
10. A computer-readable storage medium, characterized by: the computer-readable storage medium stores computer-executable instructions for causing a computer to perform the real-time monitoring method of a nonlinear structure according to any one of claims 1 to 7.
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