CN112667952A - Non-integral reconstruction method for structure dynamic displacement - Google Patents
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Abstract
The invention provides a structure dynamic displacement non-integral reconstruction method, which has higher displacement reconstruction precision. According to the method, the actually measured acceleration signal of the structure is expressed into a fitting signal with the characteristics of the Prony signal, so that the effective stripping of a baseline wandering item, a structural vibration item and a noise item in the actually measured acceleration signal is realized, and the Prony signal sequence of the residual acceleration without the baseline wandering item is obtained. The method deduces and establishes the acceleration-displacement relation based on the pluronic signal parameters, and realizes the accurate reconstruction of the structure speed and the displacement based on the residual pluronic signal sequence. The invention inherits the advantages of the Prony signal to the non-periodic signal representation on the displacement reconstruction, and avoids the drift term error. The invention realizes the displacement reconstruction by establishing the conversion relation between the acceleration and the displacement through the characteristic parameters of the acceleration signal, and avoids the loss of the low-frequency term of the signal existing in the traditional integration and high-pass filtering method.
Description
Technical Field
The invention relates to a structure dynamic displacement non-integral reconstruction method.
Background
The dynamic displacement is one of the most important measurement indexes for describing the dynamic characteristics of the structural engineering, and can be directly converted into the strain and deformation of the structure to provide effective information of the operation of the structure. Especially when the structure has non-linear characteristics or permanent deformations, the dynamic displacement of the structure is of crucial importance. In addition to traditional applications, dynamic displacements caused by structural vibrations are also widely used in engineering, such as in the fields of structural vibration control, health monitoring, system identification, and the like. While displacement is very useful, direct measurement of displacement is often difficult and challenging. This is because the displacement is a relative quantity, and when the displacement measurement is performed by using conventional devices, such as a laser displacement sensor, a linear variable differential transformer, and the like, a static reference point is usually required to support the devices, which is often difficult to be realized in a practical environment. Although the Global Positioning System (GPS) does not require a fixed reference point for measurement, its sampling frequency is low (typically 1hz to 20hz) and accuracy is limited (about 1.0 cm). In addition, the use of GPS also incurs high cost. In addition, GPS recorded signals may lose the necessary information in some cases.
Compared with the measurement of the dynamic displacement of the structure, the acceleration test does not need a fixed reference point, the test is more mature and accurate, and the method is widely applied to the structure test. Based on the advantages of acceleration testing, it is currently more inclined to reconstruct the true dynamic displacement information of the structure from the measured acceleration. Theoretically, due to the strict mathematical transformation relationship between acceleration and velocity, the displacement information of the structure can be reconstructed by quadratic integration. However, direct integration of acceleration is generally not feasible because the initial velocity and initial displacement of the structure are unknown during operation, and there can be severe drift terms in the reconstructed dynamic displacement.
At present, two main methods are provided for solving the problem of drift term in displacement obtained after integration. The first method is to transform the acceleration signal into frequency domain by fourier transform, integrate in the frequency domain, and finally transform the integrated displacement into time domain by transfer function and inverse fourier transform. Since the measured acceleration signal usually hardly satisfies the periodic assumption of fourier transform, the displacement obtained by using the frequency domain integration method inevitably generates a large truncation error. The time domain integration method directly processes the acceleration in the time domain, so that errors caused by Fourier transform are avoided, but drift terms are inevitably generated in reconstruction displacement due to the influence of unknown initial conditions. Therefore, most of the research at present focuses on removing the drift term in the time domain reconstruction displacement. Trifunac and Lee (1973) propose a time-domain displacement reconstruction method in combination with baseline correction and high-pass filtering. Converse and Brady (1992) fill in the beginning and end phases of the acceleration signal and reconstruct the displacement using least squares linear fitting and high-pass filtering. Chiu (1997) achieves displacement reconstruction by least squares fitting and high-pass filtering the acceleration and subtracting the initial velocity therein. Boore et al (2002) perform a least squares fit to the velocity, differentiate the adjustment function and remove it from the acceleration, thereby achieving baseline adjustment. Darragh et al (2004) fit the velocities separately using three functions, linear fitting, bilinear piecewise fitting, and quadratic fitting, and reconstruct the displacements without high-pass filtering. Park et al (2005) effectively achieves the reconstruction of bridge displacement by subtracting the mean of acceleration and velocity to adjust the baseline. However, the above methods all implement displacement reconstruction by using a method combining baseline fitting and high-pass filtering, however, in the filtering process, low-frequency components in signals are inevitably filtered, which may cause inaccuracy of reconstruction displacement.
Disclosure of Invention
The invention aims to provide a non-integral reconstruction method for structure dynamic displacement, which is based on the decomposition and reconstruction of an acceleration signal, characterizes the actually measured acceleration signal into a form meeting the characteristics of a Prony signal, and removes components causing drift. The true velocity and displacement of the structure are then reconstructed by using the remaining pluroni signal parameters and the initial velocity and displacement of the structure are calculated. For the reconstruction of the speed and the displacement, the method is based on the decomposition and reconstruction of the acceleration, establishes the mathematical relationship among the acceleration, the speed and the displacement by using the Prony signal parameters, avoids the error caused by integration, simultaneously overcomes the problem of low frequency term loss in signals caused by the traditional high-pass filtering method, and finally realizes the high-precision reconstruction of the structural displacement.
The invention is realized by adopting the following technical scheme:
a structure dynamic displacement non-integral reconstruction method is characterized by comprising the following specific steps:
(1) decomposing and characterizing the actually measured acceleration signal into a structure real acceleration signal, a noise signal and an acceleration baseline drift signal;
(2) fitting the true acceleration signal, the noise signal and the acceleration baseline drift signal of the structure by using the Prony signal parameters;
(3) obtaining a Porony signal parameter representation form of the actually measured acceleration signal;
(4) solving the Prony signal parameter of the actually measured acceleration signal;
(5) stripping an acceleration baseline drift signal by utilizing the Pornia signal parameter of the actually measured acceleration signal obtained by solving, and removing the acceleration baseline drift signal;
(6) establishing a mathematical relation between the acceleration signal without the baseline wandering term and the real speed of the structure;
(7) obtaining an expression of the real speed of the structure, and solving the initial speed of the structure; integrating the real speed expression of the obtained structure by solving to obtain a real displacement expression of the structure;
(8) obtaining the reconstructed structural displacement and the initial displacement;
further, in steps (1) to (3):
in order to take into account errors in the measured acceleration data due to the effects of testing and noise, the measured acceleration signal is processed
Characterized in that:
in the formula, a (t) is a structure real acceleration signal, epsilon (t) is a noise signal contained in the test signal, u is a baseline drift component in the test acceleration signal, and t represents a corresponding moment.
Assuming that three signal components, namely a structure true acceleration signal a (t), a noise signal epsilon (t) and a baseline drift component u, all satisfy the Prony signal characteristics, and fitting the acceleration by using a Prony signal sequence, the following form can be written:
in the formula, NpRepresenting the number of components in the structural signal, NnRepresenting the number of components in the noise signal, gamma and lambda being the puroni signal parameters for the corresponding components;
the three parts in the above formula are uniformly expressed as
In the formula, Nl+1 represents the number of components in the measured acceleration signal, i.e. Nl＝Np+Nn。
The innovation of the steps (1) to (3) is as follows: in the setting of the acceleration signal, the problems of structural vibration, environmental noise and baseline drift in the test are simultaneously considered. And then dividing the acceleration into a drift item, a structural information item and a noise component item, and fitting the drift item, the structural information item and the noise component item by uniformly using a Prony signal sequence, so that the actually measured acceleration signal is uniformly expressed in a form meeting the characteristics of the Prony signal, and the defect that the traditional Fourier sequence cannot perform high-precision fitting on the drift item and the noise item due to periodic assumption is overcome.
Further, in steps (4) to (5):
solving the formula (3), calculating to obtain the Prony signal parameter and recording the Prony signal parameter
And
it can be distinguished as respectively corresponding to a drift term, a structural component term and a noise component term in the signal; wherein the component frequency representing the baseline shift is much smaller than the frequencies of the structural signal component and the noise signal component (approximately equal to 0), the calculation result
The frequency of the corresponding component can be calculated as follows:
in the formula, img represents taking an imaginary part.
By pairs
Can be judged according to the judgment
And
and screening, so as to reconstruct the acceleration signal by using the remaining Prony signal sequence:
equation (5) represents the acceleration signal contaminated by noise after removing the baseline drift.
The innovation in steps (4) - (5) is represented by: the drift term is removed by combining the fitted Prony signal parameters with the signal characteristics of the drift term, so that the problem that the low-frequency component in the signal is inevitably lost when the drift term is removed by the traditional high-pass filtering method is solved, and the precision of the calculation result is improved.
Further, in (6) to (7):
the expression (5) is integrated to obtain the corresponding expression of the real speed of the structure, namely
The true velocity corresponding to the true acceleration signal of the structure can be found
Comprises the following steps:
meanwhile, the corresponding initial speed can be calculated by the formula (6)
Comprises the following steps:
the steps (6) to (7) are innovatively embodied in that: by using the Prony signal parameters, the mathematical relationship between the acceleration and the speed is established, the problem of noise amplification caused by using integration is solved, meanwhile, the mathematical relationship between the acceleration without the trend term and the initial speed of the structure is established by using the fitted Prony signal parameters, and meanwhile, the initial speed of the structure is directly solved through the acceleration signals.
Further, in (7) to (8):
integrating the true velocity obtained by the solution, i.e.
The reconstructed structure displacement can be obtained
And initial displacement
Namely, it is
And
the steps (7) to (8) are innovatively embodied in that: by using the Prony signal sequence, the mathematical relationship between the actually measured acceleration signal and the real displacement of the structure is established, the displacement drift caused by the unknown initial condition and the acceleration baseline drift problem after the secondary integration is used is avoided, and the problem of low-frequency loss caused by the high-pass filtering in the traditional method is solved. Meanwhile, a mathematical relation between the parameters of the Prony signal for fitting the acceleration signal and the initial displacement of the structure is established, so that when the method is used for reconstructing the real displacement of the structure, the reconstructed displacement result is more accurate.
The invention provides a novel structure dynamic displacement reconstruction method, which is mainly based on the decomposition and reconstruction of acceleration, and establishes the conversion relation between the acceleration and the displacement by using the parameters of a Prony signal on the basis of performing Prony signal characteristic fitting on the acceleration. The method first characterizes the measured acceleration signal in a form that satisfies the pluronic signal characteristics and separates therefrom a pluronic signal sequence representing a drift term. The shift is then reconstructed using the remaining Prony parameters. By using the decomposed Prony parameters, a mathematical relationship between the true velocity and displacement of the structure and the acceleration is established, including an estimation of the initial velocity and displacement values at the start of the measurement. Meanwhile, the method of the invention utilizes the decomposition and reconstruction technology of the acceleration, thereby avoiding the error caused by integral and effectively avoiding the drift problem caused by integral. In addition, the noise contained in the acceleration recording is also decomposed and converted into velocity and displacement reconstruction, so that the method has good robustness. It can be seen from the introduction of the background art that no research work similar to the method exists at present.
In conclusion, compared with the prior art, the invention has the advantages and positive effects that:
1) the method is based on the decomposition and reconstruction of the acceleration signal, establishes the conversion relation between the acceleration and the speed and the displacement by using the acceleration signal obtained by the Prony signal fitting test, avoids the error caused by the integral and has higher precision. Meanwhile, the real initial displacement and speed of the structure can be reconstructed through the acceleration obtained through testing, so that the detailed information of the structure vibration is revealed.
2) According to the method, the actually measured acceleration signal is divided into the drift item, the structural vibration information item and the noise item, so that the problem of poor fitting accuracy caused by the fact that the actually measured signal does not meet the periodic assumption of Fourier transform is solved, the high-accuracy removal of the drift item is realized, and the feasibility and the practicability of the method in the actual engineering structure are improved.
3) The traditional displacement reconstruction method is based on integration and high-pass filtering, but due to the defects of the high-pass filtering, the drift term in the signal can be filtered, and meanwhile, the loss of low-frequency components in the signal can be caused, and errors are caused. Through the method for parameter fitting of the Prony signal, the precise isolation of the drift term in the signal is realized, meanwhile, the mathematical relation between the acceleration and the displacement is established, the error caused by integral is avoided, and the high-precision reconstruction of the dynamic displacement of the structure is realized.
4) In the invention, based on the decomposition and reconstruction of the acceleration signal, the Pornia signal parameters are used for fitting the acceleration signal, thereby removing the drift term caused by integral, establishing the conversion relation between the acceleration and the speed and the displacement, avoiding the problems of high-pass filtering loss and low-frequency term, amplified error of integral and the like, ensuring higher calculation precision of the calculation method, providing a new analysis method for the vibration displacement calculation of an engineering structure in engineering, providing a new technical means for the monitoring, control and other works of related structures and having a certain engineering application prospect.
Drawings
FIG. 1 is a schematic diagram of a test arrangement;
FIG. 2 is a graph of measured signals measured using an acceleration sensor and a laser displacement sensor, wherein (a) is a graph of acceleration signals and (b) is a graph of displacement signals;
FIG. 3 is a graph of the results of a fitting of a pluronic parameter to a measured acceleration, wherein (a) is the result of a fitting of a whole acceleration using a pluronic signal, (b) is the result of a fitting of a 2 to 2.1 second acceleration signal, and (c) is the result of a fitting of a 10 to 10.1 second acceleration signal;
FIG. 4 is a graph of the results of the dynamic displacement of the structure reconstructed by the method of the present invention, wherein (a) is a graph comparing the structure displacement reconstructed by the method of the present invention with the test displacement, and (b) is the result of the 2-3 second displacement reconstruction; (c) the results were reconstructed at 12 to 13 seconds of displacement.
The specific implementation mode is as follows:
the present invention is further described in detail below with reference to the drawings and specific examples to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the specific embodiments and that various changes made to the present invention, which are obvious to those skilled in the art, should be covered by the claims of the present invention as long as they are within the spirit and scope of the present invention defined and determined by the appended claims.
Model information:
in the embodiment, vibration test data of the cantilever beam 2 placed on the hydraulic vibration table 1 are adopted for calculation and analysis, the control table 3 is used for controlling the hydraulic vibration table 1 to generate random vibration in the test, and the acceleration sensor 4 is used for testing acceleration data of the top end of the cantilever beam 2. The cantilever beam 2 is of steel structure, the size is 1.89m multiplied by 40mm multiplied by 20mm, and the elastic modulus is 2.1 multiplied by 1011N/m. To verify the accuracy of the conversion results, the displacement at the center of the acceleration was measured using a laser displacement sensor 5. A schematic of the test run layout is shown in figure 1. The sampling frequency of the laser displacement sensor and the sampling frequency of the acceleration sensor are both set to be 500Hz in the test.
In this embodiment, the x-direction acceleration data of the installed acceleration sensor is selected for analysis, and the acceleration signal and the displacement signal obtained by the test in the experiment are shown in fig. 2(a) and 2 (b). As can be seen from the figure, the test is divided into three stages, namely a pre-test stage, a formal test stage and a test stopping stage. Here, the data of the first two phases are selected for analysis, i.e. the acceleration signal of the first 22s is subjected to displacement reconstruction. Assuming that the acceleration signal of the first 22s satisfies the formula (1), before performing displacement reconstruction using the acceleration signal, the acceleration signal is first fitted using the pluronic signal, that is, the formulas (2) and (3), and the modal order needs to be adjusted in the fitting process to achieve the best fitting effect, in this experiment, the modal order is set to 3000, and the fitting result is shown in fig. 3 (a). Fig. 3(b) and (c) show the fitting results for 2 to 2.1 seconds and 10 to 10.1 seconds. It can be seen that the solved pluronic signal parameters fit well to the test acceleration, which also proves to be representative of the original acceleration signal.
After obtaining the puroni signal parameters that can represent the measured acceleration, the real acceleration of the structure can be reconstructed using equation (5). Since the modal order was set to 3000, a total of 1500 components were fitted. The frequency magnitude corresponding to each component can be calculated by formula (4), and the frequency of 8 components is infinitely close to 0Hz through calculation. After removing the 8 components, the true velocity and the initial velocity of the structure can be solved by using the remaining parameters of the pluronic signal through the equations (6), (7) and (8), and the true displacement and the initial displacement of the structure can be reconstructed through the equations (9), (10) and (11).
And (4) comparing the results:
the reconstructed displacement result is shown in fig. 4(a) by using the decomposed pluronic signal parameters and using the established mathematical relationship between acceleration and displacement. Meanwhile, fig. 4(b) and (c) show the reconstruction results for 2 to 3 seconds and 12 to 13 seconds. As can be seen from the results, the reconstructed result has better consistency with the test result of the laser displacement sensor. This also demonstrates the correctness of the method of the invention.
Claims (5)
1. A structure dynamic displacement non-integral reconstruction method is characterized by comprising the following specific steps:
(1) decomposing and characterizing the actually measured acceleration signal into a structure real acceleration signal, a noise signal and an acceleration baseline drift signal;
(2) fitting the true acceleration signal, the noise signal and the acceleration baseline drift signal of the structure by using the Prony signal parameters;
(3) obtaining a Porony signal parameter representation form of the actually measured acceleration signal;
(4) solving the Prony signal parameter of the actually measured acceleration signal;
(5) stripping an acceleration baseline drift signal by utilizing the Pornia signal parameter of the actually measured acceleration signal obtained by solving, and removing the acceleration baseline drift signal;
(6) establishing a mathematical relation between the acceleration signal without the baseline wandering term and the real speed of the structure;
(7) obtaining an expression of the real speed of the structure, and solving the initial speed of the structure; integrating the real speed expression of the obtained structure by solving to obtain a real displacement expression of the structure;
(8) obtaining the reconstructed structural displacement and the initial displacement.
2. The method for non-integral reconstruction of the dynamic displacement of the structure according to claim 1, wherein the problems of vibration of the structure, environmental noise and baseline drift of the acceleration sensor during the test are simultaneously considered in the steps (1) to (3); in the steps (1) - (3), the acceleration signals are divided into a drift item, a structural information item and a noise component item, the pluronic signal sequences are used for fitting the drift item, the structural information item and the noise component item, and the actually measured acceleration signals are uniformly expressed in a form meeting the characteristics of the pluronic signals.
3. The method of claim 1, wherein the steps (4) - (5) isolate the pluronic signal parameters representing the drift term and reconstruct the acceleration signal using the remaining pluronic signal sequence.
4. The method for non-integral reconstruction of dynamic displacement of a structure according to claim 1, wherein the step (6) establishes a mathematical relationship between the acceleration signal without the drift term and the true velocity of the structure, and solves the initial velocity of the structure by using the mathematical relationship.
5. The method according to claim 1, wherein the steps (7) - (8) are based on the real displacement of the structure and the mathematical relationship between the acceleration and the velocity, and the displacement expression and the initial displacement of the structure are obtained by solving.
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