CN111351438B - Estimation method and monitoring system for horizontal dynamic displacement of high-rise structure - Google Patents
Estimation method and monitoring system for horizontal dynamic displacement of high-rise structure Download PDFInfo
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Abstract
The invention provides an estimation method and a monitoring system for horizontal translational displacement of a high-rise structure, belonging to the technical field of monitoring of horizontal dynamic displacement of the structured(x, t) and the inclination angle uθ(x, t), the horizontal dynamic displacement of the structure under the action of wind load is dominant by the contribution of a first-order mode, and the horizontal dynamic displacement u under the first-order mode is respectively obtainedd1(x, t) and the inclination angle uθ1(x, t) satisfies ud1(x,t)＝β×uθ1(x, t); curve fitting horizontal dynamic displacement ud1(x, t) and the inclination angle uθ1(x, t) gives the linear coefficient β. Under other wind loads, particularly extreme wind loads, only the inclination angle u of the x point of the measured structure, which changes along with the time t, is measuredθS(x, t) and retaining its first order modal contribution signal uθS1(x, t) obtaining real-time horizontal dynamic displacement u of the x point of the structure along with the change of the time tdS1(x, t), approximating the true horizontal motional displacement u of the structuredS(x, t), real-time dynamic monitoring, convenient calculation, higher precision, no interference of environmental factors such as weather, noise and the like, and improved monitoring structure accuracy.
Description
Technical Field
The invention relates to the technical field of structure horizontal dynamic displacement monitoring, in particular to a method for estimating horizontal dynamic displacement of a high-rise structure and a monitoring system thereof.
Background
With the progress of society, a large number of super high-rise buildings with novel structures and complex shapes are continuously emerging, and in order to ensure safe and reliable operation of the structures, a certain method is adopted to monitor and control the internal force change and deformation of the structures. The dynamic displacement is an important index for reflecting the performance and safety of the structure, and the displacement is the basic monitoring content no matter the structure construction control or the structure health monitoring.
The existing high-rise structure horizontal dynamic displacement monitoring technology mainly adopts an acceleration sensor quadratic integral method, GPS system measurement, total station measurement and the like, but all the measurement methods have defects during measurement, for example, the acceleration sensor quadratic integral method obtains the horizontal dynamic displacement of the structure by measuring the floor horizontal acceleration of the structure, but the precision is lower; the GPS system is susceptible to electromagnetic interference and the like, and cannot monitor the change of the horizontal dynamic displacement of the structure in real time under the condition of severe weather; the total station has high measurement precision, generally needs manual reading, has human errors, has short measurement distance, cannot carry out multi-point real-time and synchronous measurement, and cannot carry out long-time continuous measurement in extreme weather.
Disclosure of Invention
The invention aims to provide an estimation method and a monitoring system for horizontal translational displacement of a high-rise structure, which can monitor the horizontal translational displacement of the structure under any wind load in real time, have higher precision and have no influence on the monitoring result by the environment.
The embodiment of the invention is realized by the following steps:
one aspect of the embodiments of the present invention provides a method for estimating horizontal translational displacement of a high-rise structure, which includes measuring horizontal translational displacement u at a structure x point along with time t in a period of time t for multiple times in a synchronous mannerd(x, t) and the inclination u at the point of the structure x as a function of the time tθ(x, t); according to the horizontal dynamic displacement ud(x, t) and the angle of inclination uθ(x, t) respectively obtaining the horizontal dynamic displacement u in the first-order moded1(x, t) and the inclination angle uθ1(x, t) satisfying: u. ofd1(x,t)＝β×uθ1(x, t); moving the horizontal motion by ud1(x, t) and the angle of inclination uθ1(x, t) fitting a curve to obtain a linear coefficient beta; real-time measurement of the inclination u of a point x of a structure as a function of time tθS(x, t) and obtaining the dip angle u in the first-order modeθS1(x, t); according to the formula: u. ofd1(x,t)＝β×uθ1(x, t) isReal-time horizontal dynamic displacement u of x point of structure along with time tdS1(x, t) according to udS1(x,t)≈udS(x, t), estimating the horizontal dynamic displacement udS(x,t)。
Optionally, the synchronous multiple measurements are performed on the horizontal dynamic displacement u of the structure x point along with the time t within the time td(x, t) and the inclination u at the point of the structure x as a function of the time tθ(x, t) includes: obtaining a displacement time domain signal at the x point of the structure to obtain the horizontal dynamic displacement u of the x point of the structure along with the change of time td(x, t); acquiring a dip angle time domain signal at the point x of the structure to obtain a dip angle u at the point x of the structure which changes along with time tθ(x,t)。
Optionally, said moving according to said horizontal motion ud(x, t) and the angle of inclination uθ(x, t) respectively obtaining the horizontal dynamic displacement u in the first-order moded1(x, t) and the inclination angle uθ1(x, t) includes: converting the displacement time domain signal at the x point of the structure into a displacement frequency domain signal; converting the dip angle time domain signal at the structure x point into a dip angle frequency domain signal; respectively carrying out band-pass filtering on the displacement frequency domain signal at the structure x point and the inclination angle frequency domain signal at the structure x point, and respectively reserving the displacement first-order frequency domain signal at the structure x point and the inclination angle first-order frequency domain signal at the structure x point; respectively transforming the displacement first-order frequency domain signal at the structure x point and the inclination first-order frequency domain signal at the structure x point to respectively obtain a displacement first-order time domain signal at the structure x point and an inclination first-order time domain signal at the structure x point, namely, the horizontal translation displacement u under a first-order moded1(x, t) and the inclination angle uθ1(x,t)。
Optionally, said displacing said horizontal movement ud1(x, t) and the angle of inclination uθ1(x, t) the curve fitting to obtain the linear coefficient β includes: and performing curve fitting on the displacement first-order time domain signal at the structural x point and the inclination first-order time domain signal at the structural x point to obtain the linear coefficient beta.
Optionally, the conversion of the displacement time domain signal into the displacement frequency domain signal and the conversion of the tilt time domain signal into the tilt frequency domain signal are both fourier transforms; and respectively transforming the displacement first-order frequency domain signal at the structure x point and the inclination first-order frequency domain signal at the structure x point into inverse Fourier transform.
Optionally, said displacing said horizontal movement ud1(x, t) and the angle of inclination uθ1The (x, t) curve fit is a least squares curve fit.
Optionally, a laser vibration meter is used for acquiring a time domain signal and a frequency domain signal of the displacement measuring point, and an inclinometer is used for acquiring a time domain signal and a frequency domain signal of the inclination measuring point.
According to another aspect of the embodiments of the present invention, a system for monitoring horizontal translational displacement of a high-rise structure is provided, which includes a measuring module for measuring horizontal translational displacement u at an x point of the structuredAnd the inclination u at the point x of the structureθ(ii) a A data processing module for establishing a horizontal dynamic displacement curve function u along with the change of time td(x, t) and the dip curve function uθ(x, t); preserving the horizontal displacement u by bandpass filteringd(x, t) and the inclination angle uθFirst order modal contribution u of (x, t)d1(x, t) and uθ1(x, t), horizontal dynamic displacement u under curve fitting first-order moded1(x, t) and the inclination angle uθ1(x, t) obtaining a linear coefficient beta, and calculating the horizontal dynamic displacement u of the point x of the structure along with the change of the time t according to the linear coefficient betadS1(x, t) satisfying: u. ofd1(x,t)＝β×uθ1(x, t); and the master controller is electrically connected with the measuring module and the data processing module respectively.
Optionally, the measurement module comprises a laser vibrometer and an inclinometer, and the laser vibrometer is used for measuring horizontal translational displacement udThe inclinometer is used for measuring an inclination angle uθ。
Optionally, the master controller is electrically connected to the measurement module and the data processing module through a communication bus respectively.
The embodiment of the invention has the beneficial effects that:
according to the estimation method and the monitoring system for the horizontal translation displacement of the high-rise structure, provided by the embodiment of the invention, under normal wind load of a good environment, the change of the x point of the structure along with the time t within a period of time t is synchronously measured for multiple timesHorizontal dynamic displacement u ofd(x, t) and the inclination u at the point of the structure x as a function of the time tθ(x, t) and then according to the horizontal dynamic displacement ud(x, t) and the inclination angle uθ(x, t) respectively obtaining the horizontal dynamic displacement u in the first-order moded1(x, t) and the inclination angle uθ1(x, t) which satisfies ud1(x,t)＝β×uθ1(x, t), then curve fitting the horizontal kinetic displacement ud1(x, t) and the inclination angle uθ1(x, t) to obtain a linear coefficient beta, wherein the linear coefficient beta is only related to the first-order mode of the structure intrinsic property and is not influenced by external load. Under other wind loads, particularly extreme wind loads, the horizontal dynamic displacement of the structure cannot be directly tested by equipment due to the limitation of environmental conditions, so that the change of the inclination angle u of the x point of the structure along with the time t is only measuredθS(x, t) and retaining its first order modal contribution to obtain signal uθS1(x, t), according to the identified linear coefficient beta and the formula, the real-time horizontal dynamic displacement u of the structure x point changing with the time t can be calculateddS1(x, t). Under the action of wind load, no matter under the action of extreme wind load or normal wind load, the horizontal dynamic displacement of the structure is dominant by first-order modal contribution, so udS1(x,t)≈udS(x, t) according to the inclination uθS1(x, t) calculating out horizontal translation displacement udS1(x, t), approximating the true horizontal motional displacement u of the structuredS(x, t). In this way, it is possible to determine the inclination u only from a continuous test under any wind loadθ(x, t) estimating the horizontal dynamic displacement u of the structured(x, t), the purpose of monitoring the horizontal translation displacement of the structure in real time is achieved, and particularly, the structure can reflect the safety and the comfort of the structure and play a role in early warning while realizing real-time dynamic monitoring on high-rise and super high-rise structures under extreme wind loads. The method is a new method for monitoring the horizontal translation displacement of the structure, is convenient to calculate, has high precision, is not interfered by environmental factors such as weather, noise and the like, and improves the accuracy of the monitoring structure.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.
Fig. 1 is a flowchart of a method for estimating horizontal displacement of a high-rise structure according to an embodiment of the present invention;
FIG. 2 is a second flowchart of a method for estimating horizontal displacement of a high-rise structure according to an embodiment of the present invention;
FIG. 3 is a diagram of an original time domain signal of a displacement measurement point of a 4-layer frame according to an embodiment of the present invention;
FIG. 4 is an original time domain signal diagram of a tilt angle measurement point of a 4-layer frame provided in an embodiment of the present invention;
FIG. 5 is a diagram of an original frequency domain signal of a displacement measurement point of a 4-layer frame according to an embodiment of the present invention;
FIG. 6 is a diagram of an original frequency domain signal of a tilt angle measurement point of a 4-layer frame according to an embodiment of the present invention;
FIG. 7 is a diagram illustrating the cumulative contribution of mode displacement of a 4-layer frame according to an embodiment of the present invention;
FIG. 8 is a graph of a time domain signal after curve fitting for a 4-layer framework provided by an embodiment of the present invention;
FIG. 9 is a graph of frequency domain signals after curve fitting for a 4-layer frame according to an embodiment of the present invention;
FIG. 10 is a simplified schematic illustration of a proof test of a 4-layer frame according to an embodiment of the present invention;
FIG. 11 is a simplified schematic diagram of a validation test of building A according to an embodiment of the present invention;
FIG. 12 is a diagram of an original time domain signal of a displacement measurement point of a building A according to an embodiment of the present invention;
FIG. 13 is a diagram of an original time domain signal of a dip measurement point of a building A according to an embodiment of the present invention;
FIG. 14 is a diagram of an original frequency domain signal of a displacement measurement point of a building A according to an embodiment of the present invention;
FIG. 15 is a diagram of an original frequency domain signal of a dip measurement point of a building A according to an embodiment of the present invention;
FIG. 16 is a time domain signal diagram of a building A after first-order processing of the measuring points;
FIG. 17 is a frequency domain signal diagram of a building A after first-order processing of a measuring point;
FIG. 18 is a graph of a time domain signal after curve fitting for building A according to an embodiment of the present invention;
fig. 19 is a frequency domain signal diagram after curve fitting of the a-building according to the embodiment of the present invention.
Icon: 10-laser vibrometer; 20-inclinometer.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures.
Example one
Along with social development, super high-rise building structure systems gradually develop towards complication. A large number of super high-rise buildings adopt a structural system of 'a frame, a core tube and an outrigger truss', and the structural system is mainly characterized in that a reinforcing layer is arranged in the structure, so that the integral rigidity of the structure is increased, and the interlayer displacement angle and the horizontal dynamic displacement of the structure are controlled. Super high-rise structures are more sensitive to horizontal loads, such as wind loads, which can cause excessive deformation of the structure, leading to comfort and safety issues. Therefore, monitoring and control of the horizontal dynamic displacement of the structure under wind load is one of the key issues for health monitoring of super high-rise structures. The method monitors the horizontal displacement of the super high-rise structure under different wind loads in real time, and plays a key role in the safety evaluation and vibration control of the structure.
The existing high-rise structure horizontal dynamic displacement monitoring technology mainly comprises the following steps: the method comprises the following steps that (1) an acceleration sensor secondary integration, a GPS system, a total station and a laser displacement sensor are adopted, but the monitoring technologies have different defects, for example, the acceleration sensor secondary integration method is used for measuring the floor horizontal acceleration of a structure, the measured acceleration is subjected to two-time integration to obtain the horizontal dynamic displacement of the structure, but under the action of a horizontal load, an integral constant item is difficult to determine, the error is large after the two-time integration, and the precision is low; the GPS system performs real-time phase differentiation by receiving the carrier phase of the navigation satellite, thereby measuring the dynamic displacement of the structure in real time. However, the GPS is susceptible to electromagnetic interference, multipath effect, satellite visual conditions, and the like, and cannot guarantee real-time monitoring of changes in the horizontal dynamic displacement of the structure under severe weather conditions; the total station has higher measurement precision, the existing measurement technology is mature, the application is wide, but manual reading is generally needed, human errors exist, the measurement distance is short, multi-point real-time and synchronous measurement cannot be carried out, and long-time continuous measurement cannot be carried out in extreme weather; the laser displacement sensor has high precision, is used for measuring the accurate displacement of a small structure, can hardly find an immovable reference point for a large structure, can not be overlong in wiring, and is limited in monitoring distance.
The existing monitoring method has advantages and disadvantages, and cannot meet the monitoring requirements of high precision and no environmental influence. On the basis, the embodiment provides an estimation method of the horizontal displacement of the high-rise structure, which is based on the rechecking of the laser vibration meter 10 (laser displacement sensor), and the structure horizontal displacement under the wind load is monitored in real time by using the inclinometer 20. The method has high precision, is not influenced by environment change, and can continuously monitor the horizontal dynamic displacement of the structure under the action of typhoon particularly in coastal areas so as to achieve the purpose of real-time early warning.
In the estimation method for the horizontal translational displacement of the high-rise structure provided by the embodiment, the structure is dynamically monitored in the same time period, and the horizontal translational displacement u changing with the time t at the x point of the structure under the normal wind load condition is synchronously measured for multiple timesd(x, t) and the inclination u at the point of the structure x as a function of the time tθ(x, t) preserving the horizontal translational displacement u by means of band-pass filtering techniquesd(x, t) and the inclination angle uθFirst order modal contribution u of (x, t)d1(x, t) and uθ1(x, t) satisfying: u. ofd1(x,t)＝β×uθ1(x, t); and obtaining a linear coefficient beta through curve fitting of the time domain signal, wherein the linear coefficient beta is only related to the natural vibration mode of the structure and is not influenced by external load. By means of the identified linear coefficient beta and the formula, when monitoring is carried out on the high-rise structure operation state in the future, only the inclinometer 20 is used for measuring the inclination angle u in real timeθS(x, t) and by bandpass filtering retaining its first order modal contribution to obtain signal uθS1(x, t) multiplied by the identified linear coefficient beta, the horizontal dynamic displacement u of the higher-level structure can be estimateddS1(x, t) u, since the horizontal dynamic displacement of the structure under wind loading dominates with first order modal contributiondS1(x,t)≈udS(x, t), the horizontal dynamic displacement u can be estimateddS(x, t), the purpose of monitoring horizontal dynamic displacement in real time is achieved.
As shown in fig. 1, the method specifically includes:
s100: synchronously and repeatedly measuring the horizontal dynamic displacement u of the point x of the structure along with the change of the time t within a period of time td(x, t) and the inclination u at the point of the structure x as a function of the time tθ(x,t)。
Under normal wind load, the horizontal dynamic displacement u at the x point of the structure is measured by the laser vibrometer 10dThe laser vibration meter 10 outputs a displacement time domain signal, and establishes a horizontal dynamic displacement curve function u along with the change of time td(x,t)。
On the other hand, the displacement time domain signal needs to be converted into a displacement frequency domain signal through Fourier transform for subsequent filtering.
In addition, before the displacement time domain signal is collected, the sensitivity coefficient of the laser vibration meter 10 can be adjusted, so that the measured data is more accurate.
Within the same period of time t, the inclination angle u of the structure x point changing along with the time is synchronously measured for multiple timesθ(x,t)。
It is emphasized that the time-dependent horizontal dynamic displacement u at the x-point of the structure is measured several timesd(x, t) and multiple measurements of the tilt u at the x point of the structure as a function of timeθThe (x, t) must be accurately synchronized within the same time t, and can be achieved by a time synchronization technology.
Inclination uθThe angle of the measurement point with respect to the earth's gravity reference line is measured by the inclinometer 20θThe inclinometer 20 outputs an inclination time domain signal, and establishes an inclination curve function u along with the change of time tθ(x,t)。
And on the other hand, the tilt time domain signal is converted into a tilt frequency domain signal through Fourier transform for subsequent filtering.
Similarly, before collecting the time domain tilt angle signals, the sensitivity coefficient of the inclinometer 20 can be adjusted to make the obtained tilt angle data more accurate.
S110: according to horizontal dynamic displacement ud(x, t) and the inclination angle uθ(x, t) respectively obtaining the horizontal dynamic displacement u in the first-order moded1(x, t) and the inclination angle uθ1(x, t) satisfying:
ud1(x,t)＝β×uθ1(x,t) (1)；
preserving horizontal motion u by band-pass filtering techniqued(x, t) and the inclination angle uθFirst order modal contribution u of (x, t)d1(x, t) and uθ1(x, t) and satisfies the above formula (1).
Specifically, as shown in fig. 2, S200: converting the displacement time domain signal at the x point of the structure into a displacement frequency domain signal; and converting the tilt angle time domain signal at the x point of the structure into a tilt angle frequency domain signal.
S210: and respectively carrying out band-pass filtering on the displacement frequency domain signal at the structure x point and the inclination angle frequency domain signal at the structure x point, and respectively reserving the displacement first-order frequency domain signal at the structure x point and the inclination angle first-order frequency domain signal at the structure x point.
S220: respectively transforming the displacement first-order frequency domain signal at the structure x point and the inclination first-order frequency domain signal at the structure x point to respectively obtain a displacement first-order time domain signal at the structure x point and an inclination first-order time domain signal at the structure x point, namely obtaining the horizontal dynamic displacement u only considering the contribution of a first-order moded1(x, t) and the inclination angle uθ1(x,t)。
The frequency domain signal is converted to a time domain signal by an inverse fourier transform.
S120: will move horizontally by ud1(x, t) and the inclination angle uθ1And (x, t) curve fitting to obtain a linear coefficient beta.
And performing curve fitting on the displacement first-order time domain signal at the point x of the structure and the inclination first-order time domain signal at the point x of the structure to obtain the linear coefficient beta.
The curve fitting method includes many methods such as a least square method, a minimum absolute residual method, a bi-level method, and the like. The least square method is adopted in the embodiment, the sum of the squares of the difference between the fitting value and the true value of the polynomial of single fitting is taken to be the minimum, the fitting result precision is good, and the requirement can be met.
And fitting the displacement first-order time domain graph at the structure x point and the inclination first-order time domain graph at the structure x point obtained after inverse Fourier transform, wherein each measuring point can obtain a linear coefficient beta. And fitting the displacement first-order time domain graph and the inclination first-order time domain graph, and analyzing the fitted frequency domains again to obtain that the frequency domains of the displacement first-order time domain graph and the inclination first-order time domain graph are nearly consistent from the aspect of amplitude and trend.
After each group of data is processed, a linear coefficient beta can be obtained, the coefficient can be regarded as a coefficient obtained by curve fitting after high-order interference is removed based on band-pass filtering and only first-order modal contribution in original displacement and inclination angle signals is reserved.
S130: real-time measurement of the inclination u of a point x of a structure as a function of time tθS(x, t) and obtaining the dip angle u in the first-order modeθS1(x,t)。
Under any wind load, especially extreme windUnder load, the inclination u is measured directly by the inclinometer 20 in the case where it is not possible to test the horizontal kinematic displacement of the structure directly by the equipment, due to the constraints of the environmental conditionsθS(x, t) and then the signal u is obtained by bandpass filtering with the first order modal contribution preservedθ1(x,t)。
S140: according to the formula: u. ofd1(x,t)＝β×uθ1(x, t) deriving the real-time horizontal dynamic displacement u at the x-point of the structure as a function of time tdS1(x,t)，udS1(x,t)≈udS(x, t), the horizontal dynamic displacement u can be estimateddS(x,t)。
According to the identified linear coefficient beta and the formula (1), the horizontal dynamic displacement u of the structure at the x point along with the change of the time t under the extreme wind load is obtaineddS1(x, t). Because under the action of wind load, no matter under the action of extreme wind load or normal wind load, the structural displacement is dominant by the contribution of a first-order mode, u isdS1(x,t)≈udS(x, t), and approximately estimating the true horizontal translational displacement u of the structuredS(x,t)。
It should be noted that once the linear coefficient β is identified, the inclination response u can be determined only from the continuously tested inclination under any wind loadθ(x, t) estimating the horizontal dynamic displacement u of the structured(x,t)。
The method for estimating the horizontal translational displacement of the high-rise structure provided by the embodiment of the invention synchronously measures the horizontal translational displacement u of the structure x point changing along with the time t for multiple times under the normal wind load of a good environmentd(x, t) and the inclination u at the point of the structure x as a function of the time tθ(x, t) and then according to the horizontal dynamic displacement ud(x, t) and the inclination angle uθ(x, t) respectively obtaining the horizontal dynamic displacement u in the first-order moded1(x, t) and the inclination angle uθ1(x, t) which satisfies ud1(x,t)＝β×uθ1(x, t), then curve fitting the horizontal kinetic displacement ud1(x, t) and the inclination angle uθ1(x, t) yields a linear coefficient β which is related only to the natural mode shape of the structure and is not affected by external loads. Under other wind loads, especially extreme wind loads, it has not been possible to test the horizontal dynamic displacement of the structure directly by the equipment due to environmental conditions, and thereforeBy measuring only the angle of inclination u at the x point of the structure as a function of time tθS(x, t) and retaining its first order modal contribution to obtain signal uθS1(x, t), according to the identified linear coefficient beta and the formula, the real-time horizontal dynamic displacement u of the structure x point changing with the time t can be calculateddS1(x, t). Under the action of wind load, no matter under the action of extreme wind load or normal wind load, the horizontal dynamic displacement of the structure is dominant by first-order modal contribution, so udS1(x,t)≈udS(x, t) according to the inclination uθS1(x, t) calculating out horizontal translation displacement udS1(x, t), approximating the true horizontal motional displacement u of the structuredS(x, t). In this way, it is possible to determine the inclination u only from a continuous test under any wind loadθ(x, t) estimating the horizontal dynamic displacement u of the structured(x, t), the purpose of monitoring the horizontal translation displacement of the structure in real time is achieved, and particularly, the structure can reflect the safety and the comfort of the structure and play a role in early warning while realizing real-time dynamic monitoring on high-rise and super high-rise structures under extreme wind loads. The method is a new method for monitoring the horizontal movement displacement of the structure, only the first-order mode of the structure is considered when the horizontal movement displacement of the structure is estimated, high-frequency interference in the mode of the structure is removed and reflected through fitting, calculation is convenient, precision is high, interference of environmental factors such as weather, noise and the like is avoided, and accuracy of the monitoring structure is improved.
It should be noted that the method deduces an expression of a linear coefficient beta from a basic theory of structure dynamics, and provides a calculation condition that a first-order mode is dominant when calculating the horizontal translational displacement of the structure under the action of wind load, wherein the derivation process of the formula (1) is as follows:
in the equivalent static wind load calculation method, the downwind wind load is divided into an average wind load and a wind vibration force caused by the first-order vibration of the structure, and the fact that the first-order modal contribution rate is the largest under the wind load effect of the structure is explained, and other high-order modal contributions can be not considered. In the wind resistance design of the structure, in the wind vibration response calculation analysis of a common high-rise and high-rise structure, only the effect of the first-order vibration mode of the structure is usually considered, so that the method only considers the estimation method of the horizontal movement displacement of the structure when the structure is mainly in the first-order mode under the wind load effect.
According to the fundamental principle of free vibration of a structural dynamics multi-degree-of-freedom system, the linear multi-degree-of-freedom system with free vibration has an equation:
wherein, M in the formula (2) is a structural total mass matrix; c is a structural total damping matrix; k is a structural total stiffness matrix; p (t) is the external force load applied to the structure.
As can be seen from equation (2): when the structure vibrates, the displacement u (x, t) of the structure is related to the vibration mode and the vibration mode coordinate of the structure, and the vibration mode coordinate are coupled together. Thus, for a structure with an n-order mode, in vibration, the decoupled displacement of the structure can be expressed as the formula:
wherein u (x, t) in the formula (3) is the horizontal dynamic displacement of the structure;
is the nth order vibration mode of the structure; q. q.snAnd (t) is the nth order vibration type coordinate of the structure at the time t.
Firstly, a structural vibration mode coordinate function q is matchednAnd (t) analyzing, and respectively pushing from two aspects of an undamped system and a damped system. And aiming at a damping system, Rayleigh damping is adopted in the theoretical derivation process.
Without damping, qnThe expression of (t) is:
equation (4) is simplified to:
qn(t)＝enωt (5)；
for a damped system, rayleigh damping is known as shown in the following equation:
C＝a0M+a1K (6)；
wherein, a0And a1Is a scaling factor.
The damping affects the natural frequency and the vibration period of the multi-degree-of-freedom system. So when damping ratio ζnUnder 20%, the damping has little influence on the natural frequency and period of the system with multiple degrees of freedom, so the time mode coordinate function q of the system with dampingn(t) the expression is:
wherein, in the formula (5), ω is the frequency of the structural vibration, and e is a natural constant; in the formula (7), α is a coefficient related to the damping ratio.
From the above formula, when there is no damping in the system, the mode shape coordinate function qn(t) is related only to the natural frequency and time of the structure. In other words, the results obtained are consistent regardless of which measurement method is used to measure the natural frequency of the structure. If different measuring methods are measured at the same time, the mode shape coordinate function qn(t) will be uniform.
Let the structural displacement response obtained directly by displacement be ud(x, t) the structural displacement response obtained by the tilt angle is uθ(x, t). Under the condition that only the first-order mode of the structure is considered to be dominant, the following are:
according to the theoretical derivation of this embodiment, combining the structure dynamics theory and the formula, it can be known that, under the excitation of the external environment at the same time for the same structure, the structure displacement obtained by any index should be the same, that is:
ud(x,t)＝uθ(x,t)＝u(x,t) (9)；
therefore, the present embodiment proposes a method for calculating the horizontal translational displacement of the structure by using the tilt angle, which is referred to as a coefficient β method for short, based on the review of the laser vibrometer 10 and considering the field environment. The calculation formula of the method under the condition that only the structure first-order mode is dominant is shown as the following formula:
from equation (10) we can obtain:
the product of the mode shape ratio and the mode shape coordinate ratio in equation (11) is expressed by a linear coefficient β, and the equation can be obtained as follows: u. ofd(x,t)＝β×uθ(x, t). The formula is u in the case of considering only the first-order moded1(x,t)＝β×uθ1(x,t)。
The feasibility of the method proposed in this example was verified experimentally as follows:
as shown in fig. 10, taking a 4-layer frame as an example, the frame spans 1 layer and 4 layers, the span is 1.4m, and the layer height is 0.8 m. In FIG. 10, the total length of the vertical steel plates (columns) is 3.2m, the width is 0.3m, and the thickness is 0.008 m; the horizontal steel plate (beam) is 1.4m long, 0.3m wide and 0.008m thick, and the mass of each layer of the frame is adjusted by changing the weight plates of each layer.
A control system (not shown in figure 10) is arranged on the top of the frame and mainly comprises a control motor, a servo driver, an EtherCAT bus and a computer. The loading system mainly comprises a speed reducer (provided with a frequency converter) and a counterweight block. Wherein the fixed reduction ratio of the speed reducer is 1/15, and the rated power is 2200W; the frequency modulation range of the frequency converter is 0-15 Hz, the speed regulation range of the corresponding speed reducer motor is 0-120 rpm, and the rotating output frequency range is 0-2 Hz.
4 laser vibration meters 10 (laser displacement sensors) and 4 inclinometers 20 are adopted, each layer is provided with one inclinometer 20 along the direction of the weak axis of the frame, and the laser displacement sensors are arranged on parallel iron rods beside the frame at the same horizontal position and simultaneously acquire displacement signals. And selecting different external excitation working conditions by using a speed reducer.
For example, a working condition with an excitation of 5Hz is selected, a group of signals is obtained at the same time, and a mode shape contribution rate and a mode shape displacement contribution rate are compared by selecting a 4-layer frame as an analysis object, as shown in fig. 5, 6 and 7.
From the two power spectral densities, the first-order energy contribution of the structure in the power spectrum measured by the laser vibrometer 10 accounts for more than 98%, the energy of other orders is too small and can be ignored, in the power spectral density measured by the inclinometer 20, the first-order energy accounts for the main part, but the interference of other high-order energy occurs, and the frequency of the structure cannot be ignored.
In the vibration mode displacement accumulated contribution coefficient, the first-order vibration mode contribution rate at the measuring point of the laser vibration meter 10 reaches 93.88 percent, but the first-order vibration mode contribution rate at the measuring point of the inclinometer 20 at the same position only reaches 80 percent, and the second-order vibration mode contribution rate can reach 10 percent.
By comparing the frequency domain graphs of the two with the accumulated contribution rate of the mode displacement, a significant difference exists, and the difference is not negligible. The known laser vibration meter 10 has high precision and high accuracy in measuring the horizontal translation displacement of the structure within a certain distance, and by taking the power spectral density and the vibration mode displacement contribution rate as reference, the following conclusion can be obtained through the above experimental phenomena:
the frame power spectrum measured by the angle meter is compared with the measuring point of the laser vibration meter 10, obvious energy exists in the high order, if the high order energy is not removed, the measuring value of the inclinometer 20 is directly used for calculating the horizontal dynamic displacement of the structure, error interference exists, and the accuracy of the measuring result cannot be judged.
The vibration mode participation coefficient and the vibration mode accumulated displacement contribution coefficient obtained after the analysis of the measured value are both the first-order structure dominance, so that in the data analysis and processing, the inclination angle signal is processed, only the first-order structure mode is reserved, and the high-order interference is removed. The specific data processing method is shown in fig. 1 and fig. 2, and is not described herein again.
A 4-layer frame was chosen and the time domain signal was compared with the frequency domain signal after signal processing and fitting by the laser vibrometer 10 and inclinometer 20 as shown in fig. 3, 4, 5, 6, 8 and 9. After fitting, a set of fitting coefficients is obtained, and the fitting coefficients are linear coefficients beta.
Linear coefficient beta value obtained after signal processing and horizontal dynamic displacement u of 4-layer frame measured by laser vibration meter 10dAnd the 4-layer frame horizontal translation displacement u measured by the caster 20 multiplied by the linear coefficient betadAs shown in table 1 below (coefficient β in table 1 is a linear coefficient β):
TABLE 1
After 4 groups of different working conditions are selected for excitation, the frame structure can be obtained, and after the frame structure is fitted by the laser vibration meter 10 and the inclinometer 20, the linear coefficient beta obtained by different layers can be regarded as a fixed value, the working conditions are shown in table 2, and the coefficients under different working conditions are shown in table 3:
TABLE 2
TABLE 3
In summary, when the horizontal dynamic displacement of the structure is to be obtained under the extreme wind load, only the horizontal dynamic displacement and the inclination angle of the structure under the normal wind load need to be measured, the first-order modal contribution of the structure is retained through band-pass filtering, and the horizontal dynamic displacement and the inclination angle of the first-order modal contribution are fitted through a time domain signal curve to obtain the linear coefficient beta. Under any wind load, particularly under extreme wind load, only the inclination angle of the structure needs to be measured, and the horizontal dynamic displacement of the structure can be obtained through the linear coefficient beta and the formula (1).
To further verify the applicability of the method in the actual high-rise structure, the high-rise building located in the Shenshu university Shenzhen No. 4 (building A) of the Shenzhen industry university (Shenzhen) and the Shenshu Dashenzhen campus of the Shenzhen southern mountain university city is 87.7 meters in total height, 26 layers in total and 4200 square meters in the construction land area, as shown in FIG. 11. The east-west direction of the high-rise building is a weak axial direction, the south-north direction is a strong axial direction, and the strong and weak axial directions are all taken as research objects in the text, so that the weak axial results are intensively researched and explained.
In order to ensure that the laser vibrometer 10 and the inclinometer 20 acquire the accurate modal of the structure, firstly, a distributed acceleration acquisition system is used for carrying out modal analysis on the building No. 4 to acquire the accurate modal information of the structure, and then the result is compared with the results of the laser vibrometer 10 and the inclinometer 20 to ensure the accuracy of the linear coefficient beta. One sensor in each of the east and north directions is arranged in the layers of the structure 6, 10, 14, 18, 22, 26.
And comparing the structural modes measured by the laser vibration meter based on the data of the No. 4 building mode measured by the distributed acceleration as a basis to ensure that the two modes can accurately reflect the structural modes. And then carrying out linear coefficient beta method experimental verification by using a laser vibration meter and an inclinometer to find linear coefficient beta values of the 4 th floor in different directions, thereby researching the change condition and range of the linear coefficient beta.
According to the signal processing method provided by the embodiment, firstly, 23 layers of measuring points are analyzed, the original time domain graphs of laser displacement and inclination angle of the measuring points are shown in fig. 12 and 13, and the frequency domain graphs are shown in fig. 14 and 15; obtaining a time domain and frequency domain diagram after first-order energy of the reserved structure and FFT (fast Fourier transform), as shown in FIGS. 16 and 17; the fitted displacement is a time domain plot and a frequency domain plot as shown in fig. 18 and 19. The fitting process of the 14-layer measuring points and the 23-layer measuring points is the same, and the description is omitted.
Under the action of wind load, no matter 14 or 23 layers, when the laser vibration meter 10 measures the structural displacement, the reflected structural modes include a first-order mode which is dominant, and the structural modes reflected by the inclinometer 20 have obvious high-order modes, and after data processing, the modal distribution when the structural displacement is measured can be correctly reflected by removing the interference of the high-order modes from the signals measured by the inclinometer 20.
After each group of signals are processed and fitted, a linear coefficient beta value can be obtained, data without obvious interference of the signals in two days are selected for 14 and 23 layers, and the obtained experimental beta value (linear coefficient beta) after data processing and fitting is shown in a table 4-1. As can be seen from Table 4-1, the linear coefficient β value has small variation in the magnitude of the different floor values at different times, and the linear coefficient β value of the high-rise structure can be obtained through the following Table 4-2, which is considered as a value between 483-488, and the average value of the two is 485.5 for convenience.
TABLE 4.1 Weak axial Experimental beta values
TABLE 4-2 maximum and minimum ranges of measured beta values
Example two
The embodiment provides a monitoring system for horizontal translational displacement of a high-rise structure, which comprises a measuring module for measuring the horizontal translational displacement u at the x point of the structuredAnd the inclination u at the point x of the structureθ(ii) a A data processing module for establishing a horizontal dynamic displacement curve function u along with the change of time td(x, t) and the dip curve function uθ(x, t); preserving the horizontal displacement u by bandpass filteringd(x, t) and the inclination angle uθFirst order modal contribution u of (x, t)d1(x, t) and uθ1(x, t), horizontal dynamic displacement u under curve fitting first-order moded1(x, t) and the inclination angle uθ1(x, t) obtaining a linear coefficient beta, and calculating the random number at the point x of the structure according to the linear coefficient betaHorizontal dynamic displacement u of time t changedS1(x, t) satisfying: u. ofd1(x,t)＝β×uθ1(x, t); the master controller is electrically connected with the measuring module and the data processing module through the communication bus respectively.
The master controller is used for sending a measurement instruction to the measurement module, the measurement module feeds collected data back to the master controller after collecting the measurement point data, the master controller transmits the collected data to the data processing module, and the data processing module feeds processing results back to the master controller after processing the data so that a user can check and analyze the data conveniently.
The measuring module comprises a laser vibration meter 10 and an inclinometer 20, wherein the laser vibration meter 10 is used for measuring horizontal translational displacement, and the inclinometer 20 is used for measuring an inclination angle.
The monitoring system for the horizontal movement displacement of the high-rise structure has the advantages of high measurement precision, convenience in measurement, simplicity in equipment installation and wiring and convenience in maintenance.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (7)
1. A method for estimating horizontal translation displacement of a high-rise structure is characterized by comprising the following steps:
the real-time horizontal dynamic displacement and the real-time inclination angle at the x point of the structure within a period of time under normal wind load are synchronously measured for multiple times based on a laser vibration meter and an inclinometer respectively so as to obtain the horizontal dynamic displacement u of the x point of the structure along with the change of time td(x, t) and a tilt angle u that varies with time tθ(x,t)；
According to the horizontal dynamic displacement ud(x, t) and the angle of inclination uθ(x, t) respectively obtaining the horizontal dynamic displacement u in the first-order mode through band-pass filteringd1(x, t) and the dip angle u in the first order modeθ1(x,t)；
Translating the horizontal movement u in the first-order moded1(x, t) and the first order modeAngle of inclination uθ1(x, t) curve fitting to obtain a linear coefficient beta, wherein the linear coefficient beta is used for obtaining the linear coefficient beta according to a formula ud1(x,t)＝β×uθ1(x, t) subsequently estimating the horizontal dynamic displacement of the x point of the structure along with the change of the time t;
in the estimation process, the inclination angle u changing with the time t at the point x of the structure is obtained based on the real-time measurement of the inclinometerθS(x, t) and obtaining the dip angle u in the first-order modeθS1(x,t)；
According to said angle of inclination uθS1(x, t) according to said formula ud1(x,t)＝β×uθ1(x, t) obtaining the horizontal dynamic displacement u in the first-order mode of the x point of the structure along with the change of the time tdS1(x, t) according to udS1(x,t)≈udS(x, t), estimating to obtain the actual horizontal dynamic displacement udS(x,t)。
2. The method for estimating horizontal translational displacement of a high-rise structure according to claim 1, wherein the real-time horizontal dynamic displacement and real-time inclination angle at the x point of the structure under normal wind load are measured for a plurality of times in a synchronous manner to obtain the horizontal dynamic displacement u at the x point of the structure which changes along with the time td(x, t) and a tilt angle u that varies with time tθ(x, t) includes:
obtaining a displacement time domain signal at the x point of the structure in real time to obtain the horizontal dynamic displacement u of the x point of the structure along with the change of time td(x,t)；
Acquiring a dip angle time domain signal at the point x of the structure in real time to obtain a dip angle u at the point x of the structure changing along with time tθ(x,t)。
3. Method for estimating the horizontal dynamic displacement of a high-rise structure according to claim 2, characterised in that said horizontal dynamic displacement u is based on said horizontal dynamic displacementd(x, t) and the angle of inclination uθ(x, t) respectively obtaining the horizontal dynamic displacement u in the first-order mode through band-pass filteringd1(x, t) and the dip angle u in the first order modeθ1(x, t) includes:
converting the displacement time domain signal at the x point of the structure into a displacement frequency domain signal; converting the dip angle time domain signal at the structure x point into a dip angle frequency domain signal;
respectively carrying out band-pass filtering on the displacement frequency domain signal at the structure x point and the inclination angle frequency domain signal at the structure x point, and respectively reserving the displacement first-order frequency domain signal at the structure x point and the inclination angle first-order frequency domain signal at the structure x point;
respectively transforming the displacement first-order frequency domain signal at the structure x point and the inclination first-order frequency domain signal at the structure x point to respectively obtain a displacement first-order time domain signal at the structure x point and an inclination first-order time domain signal at the structure x point, namely, the horizontal translation displacement u under a first-order moded1(x, t) and the inclination angle uθ1(x,t)。
4. The method for estimating horizontal translational displacement of high-rise structure according to claim 3, wherein the horizontal translational displacement u in the first-order mode is estimatedd1(x, t) and the angle of inclination u in the first-order modeθ1(x, t) the curve fitting to obtain the linear coefficient β includes:
and performing curve fitting on the displacement first-order time domain signal at the structural x point and the inclination first-order time domain signal at the structural x point to obtain the linear coefficient beta.
5. The method of estimating horizontal translational displacement of a tall structure according to claim 3, wherein the conversion of the displacement time domain signal into the displacement frequency domain signal and the conversion of the tilt time domain signal into the tilt frequency domain signal are both Fourier transforms;
and respectively transforming the displacement first-order frequency domain signal at the structure x point and the inclination first-order frequency domain signal at the structure x point into inverse Fourier transform.
6. Method for estimating horizontal translational displacements of a tall structure according to claim 1, characterized in that said horizontal translational displacements u are displacedd1(x, t) and the angle of inclination uθ1The (x, t) curve fit is a least squares curve fit.
7. A monitoring system for horizontal dynamic displacement of a high-rise structure is characterized by comprising:
a measurement module for measuring the horizontal dynamic displacement u at the x point of the structure under normal wind load for multiple times based on the laser vibration meter and the inclinometerdAnd the inclination u at the point x of the structureθ；
A data processing module for establishing a horizontal translation displacement curve function u along with the change of time td(x, t) and the dip curve function uθ(x, t); according to the horizontal dynamic displacement curve function ud(x, t) and the dip curve function uθ(x, t) respectively obtaining the horizontal dynamic displacement u in the first-order mode through band-pass filteringd1(x, t) and the dip angle u in the first order modeθ1(x, t); translating the horizontal movement u in the first-order moded1(x, t) and the angle of inclination u in the first-order modeθ1(x, t) curve fitting to obtain a linear coefficient beta, wherein the linear coefficient beta is used for obtaining the linear coefficient beta according to a formula ud1(x,t)＝β×uθ1(x, t) subsequently estimating the horizontal dynamic displacement of the x point of the structure along with the change of the time t;
and the master controller is electrically connected with the measuring module and the data processing module through communication buses respectively.
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