CN110457858B - Method for determining modal vibration main shaft of high-rise building based on double-shaft actual measurement acceleration - Google Patents
Method for determining modal vibration main shaft of high-rise building based on double-shaft actual measurement acceleration Download PDFInfo
- Publication number
- CN110457858B CN110457858B CN201910776761.9A CN201910776761A CN110457858B CN 110457858 B CN110457858 B CN 110457858B CN 201910776761 A CN201910776761 A CN 201910776761A CN 110457858 B CN110457858 B CN 110457858B
- Authority
- CN
- China
- Prior art keywords
- matrix
- vibration
- calculating
- acceleration
- main shaft
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M99/00—Subject matter not provided for in other groups of this subclass
- G01M99/004—Testing the effects of speed or acceleration
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Abstract
The invention relates to a method for determining a modal vibration main shaft of a high-rise building based on double-shaft actually measured acceleration, which comprises the following steps: s1, acquiring an acceleration signal A of a geometric main shaft of a structure; s2, calculating to obtain a whitening matrix W according to the acceleration signal A; s3, solving a whitened input signal Z according to the whitening matrix W and the acceleration signal; s4, calculating a time delay covariance matrix R of the whitened input signal Z z (τ) S5, based on the time-delay covariance matrix R z (τ) calculating an orthogonal matrix V; and S6, solving the vibration mode matrix phi according to the orthogonal matrix V, S7, and solving the deflection angle between the main shaft of the mode vibration and the geometric main shaft according to the vibration mode matrix phi. According to the method, a series of calculations are carried out on the acquired acceleration signals of the geometric main shaft of the structure, and finally the deflection angle between the actual vibration mode of the structure and the geometric main shaft can be accurately obtained, so that the direction of the modal vibration main shaft of the high-rise building can be effectively determined.
Description
Technical Field
The invention relates to the technical field of civil engineering, in particular to a method for determining a modal vibration main shaft of a high-rise building based on double-shaft actually-measured acceleration.
Background
High-rise buildings, particularly super high-rise buildings having a height of more than 300m, are sensitive to wind and seismic loads, and in some cases, dampers such as Tuned Mass Dampers (TMD) or the like are required to be additionally installed at specific floors of the structure in order to reduce the response of the structure to wind or seismic loads. When the damper is mounted, in order to sufficiently suppress the vibration of the main body structure, the mounting position and direction of the damper need to be determined. In order to determine the installation position and the direction of the damper, it is not accurate enough to obtain information such as the structural vibration main shaft by finite element analysis, and the vibration main shaft of the structural main vibration mode is required to be accurately measured. For most buildings with regular body shapes, the main axis of modal vibration is generally very close to the geometric main axis of the structure, and for some buildings with plane asymmetric design, the main axis of modal vibration and the geometric main axis are inclined. In order to measure the vibration principal axis of the structure-dominant vibration mode, the structure needs to be subjected to an acceleration signal test. When performing on-site acceleration signal testing, the x and y axes of the acceleration tester are usually arranged along the geometric main axis direction of the building for the convenience of instrument installation. This results in that the acceleration signals measured by the acceleration tester in the x and y directions are signals obtained by coupling the vibration of the two modal vibration main axes of the structure.
Disclosure of Invention
Aiming at the problem that the measured acceleration signal is inaccurate in the prior art, the invention provides a method for determining a modal vibration main shaft of a high-rise building based on a double-shaft measured acceleration.
The specific scheme of the application is as follows:
a method for determining a modal vibration main shaft of a high-rise building based on a biaxial measured acceleration comprises the following steps:
s1, acquiring an acceleration signal A of a geometric main shaft of a structure;
s2, calculating to obtain a whitening matrix W according to the acceleration signal A;
s3, solving a whitened input signal Z according to the whitening matrix W and the acceleration signal A;
s4, calculating a time delay covariance matrix R of the whitened input signal Z z (τ)；
S5, according to the time-delay covariance matrix R z (τ) calculating an orthogonal matrix V;
s6, solving a vibration mode matrix phi according to the orthogonal matrix V,
and S7, solving a deflection angle between the main shaft of the modal vibration and the geometric main shaft according to the vibration mode matrix phi.
Preferably, step S2 comprises:
s21, calculating covariance matrix R of acceleration signal A A (0)；
S22, for the covariance matrix R A (0) Performing singular value decomposition;
and S23, obtaining a whitening matrix W.
Preferably, S21, a time-delay covariance matrix R of the acceleration signal A is calculated A (0) The method comprises the following steps:
s211, calculating
Wherein superscript T represents a matrix transpose; a (: 1; wherein it is present>
x i 、y i The test values of the acceleration signals of x (t) and y (t) at the ith time point are respectively, and x (t) and y (t) are respectively acceleration signals in x and y directions of a structural geometric main shaft sampled at the time t;
s212, calculating m according to the following formula 1 And m 2 ；
Wherein mean (A (1, 1 n- τ)) represents the average of the 1 st;
s213, calculating
S214, according to
Computing a symmetric delay covariance matrix R A (τ)；/>
S215, let tau =0, obtaining covariance matrix R A (0)。
Preferably, S22, for the covariance matrix R A (0) The formula for singular value decomposition is:
R A (0)＝UλU T ；
where U is a unit matrix in which column vectors are orthogonal to each other, and λ is a diagonal matrix.
Preferably, the whitening matrix W is formulated as:
preferably, in S3, the formula for obtaining the whitened input signal Z according to the whitening matrix W and the acceleration signal a is as follows:
Z＝WA。
preferably, S4, a time-delay covariance matrix R of the whitened input signal Z is calculated z (τ) comprises:
s41, calculating
Wherein superscript T represents a matrix transpose; z (: 1;
s42, calculating m according to the following formula 3 And m 4 ；
Wherein mean (Z (1, 1 n- τ)) represents the average of the 1 st;
s43, calculating
S44, calculating a symmetric time delay covariance matrix:
preferably, S5, according to the time-delay covariance matrix R z (τ) calculating the orthogonal matrix V includes:
s51, respectively aligning the delay covariance matrixes R z Tau of (tau) takes a value delta t,2 delta t z (τ) value; wherein Δ t is the sampling interval of the acceleration test signal;
s52, setting the initial value of the orthogonal matrix V as
S53, according to R z Givens rotation is carried out on the initial value of the (tau) and the initial value of the orthogonal matrix to obtain a rotation matrix, and the rotation matrix is used as the orthogonal matrix V;
s54, updating R in sequence z And (τ) and the orthogonal matrix V, repeating step S53 until the square of the off-diagonal element of the rotation matrix is greater than a preset minimum positive value, and taking the rotation matrix as the final orthogonal matrix V.
Preferably, S6, the equation for solving the oscillation-type matrix Φ according to the orthogonal matrix V is:
Φ＝W -1 V。
preferably, S7, the deriving the deviation angle between the principal axis of the modal vibration and the geometric principal axis according to the mode shape matrix Φ includes: the included angle alpha = arctan (phi) between the vibration main shaft of the first side pendulum and the x axis 21 /φ 11 ) An angle α = arctan (Φ) between the principal axis of vibration of the second side-sway mode and the x-axis 22 /φ 12 ) Wherein
Compared with the prior art, the invention has the following beneficial effects:
according to the scheme, a series of calculations are carried out on the acquired acceleration signals of the geometric main shaft of the structure, and finally the deflection angle between the actual vibration mode of the structure and the geometric main shaft can be accurately obtained, so that the direction of the modal vibration main shaft of the high-rise building can be effectively determined.
Drawings
FIG. 1 is a schematic flow chart of a method for determining a modal vibration principal axis of a high-rise building based on a two-axis measured acceleration according to an embodiment;
FIG. 2 is a schematic diagram of a sensor placement location of an embodiment;
FIG. 3 is a time-course signal in the x-direction of the geometric principal axis of the structure acquired by the sensor according to an embodiment.
FIG. 4 is a time-course signal in the y-direction of the geometric axis of the structure acquired by the sensor according to an embodiment.
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. 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.
Referring to fig. 1, a method for determining a modal vibration main shaft of a high-rise building based on a biaxial measured acceleration includes:
s1, acquiring an acceleration signal A of a geometric main shaft of a structure; the acceleration signal is acquired as
And x (t) and y (t) are acceleration signals in the x direction and the y direction of the geometric main shaft of the structure, which are obtained by sampling at the moment t respectively. The actual sampling signal of the acceleration sensor is a discrete signal, assuming x i 、y i X (t) and y (t) at the ith timeThe test value of the acceleration signal of a point, equation (1) can be written in the form of a discrete signal as:
where n is the sample length.
S2, calculating to obtain a whitening matrix W according to the acceleration signal A; the step S2 comprises the following steps:
s21, calculating a covariance matrix R of the acceleration signal A A (0) (ii) a Further, step S21 includes:
s211, calculating
Wherein superscript T represents a matrix transpose; a (: 1; assume that the delay is set to be τ sample intervals.
S212, calculating m according to the following formula 1 And m 2 ；
Wherein mean (A (1, 1 n- τ)) represents the average of the 1 st;
s213, calculating
S214, according to
Computing a symmetric delay covariance matrix R A (τ)；/>
S215, let tau =0, obtaining covariance matrix R A (0)。
S22, to covariance matrix R A (0) Performing singular value decomposition; the formula for performing singular value decomposition on the covariance matrix C is as follows:
R A (0)＝UλU T ；
where U is a unit matrix in which column vectors are orthogonal to each other, and λ is a diagonal matrix.
And S23, obtaining a whitening matrix W. The whitening matrix W is solved by the formula:
s3, solving a whitened input signal Z according to the whitening matrix W and the acceleration signal; the formula for solving the input signal Z after whitening according to the whitening matrix W and the acceleration signal is as follows:
Z＝WA。
s4, calculating a time delay covariance matrix R of the whitened input signal Z z (τ). Further, step S4 includes:
s41, calculating
Wherein superscript T represents matrix transposition; z (: 1;
s42, calculating m according to the following formula 3 And m 4 ；
Wherein mean (Z (1, 1 n- τ)) represents the average of the 1 st;
s43, calculating
S44, calculating a symmetric time delay covariance matrix:
s5, according to the time-delay covariance matrix R z (τ) calculating an orthogonal matrix V; step S5 comprises the following steps:
s51, respectively aligning the time delay covariance matrixes R z Tau of (tau) takes a value delta t,2 delta t z (τ) value; wherein Δ t is the sampling interval of the acceleration test signal; since the signals of the modal vibration of the structure in the two yaw directions are independent, the description R z (τ) may be diagonalized. Only the first two-order side-sway mode of the structure is considered, that is, the structure is regarded as a two-degree-of-freedom system, and the mode is set to phi. For a series of τ values τ = Δ t,2 Δ t z (τ) value.
S52, setting the initial value of the orthogonal matrix V as
S53, according to R z Givens rotation is carried out on the initial value of the (tau) and the initial value of the orthogonal matrix to obtain a rotation matrix, and the rotation matrix is used as the orthogonal matrix V;
s54, updating R in sequence z And (τ) and the orthogonal matrix V, repeating step S53 until the square of the off-diagonal element of the rotation matrix is greater than a preset minimum positive value, and taking the rotation matrix as the final orthogonal matrix V. Preset minimum positive value of 10 -5 。
S6, solving the vibration mode matrix phi according to the orthogonal matrix V, wherein the formula of the vibration mode matrix phi according to the orthogonal matrix V is as follows:
Φ＝W -1 V。
and S7, solving a deflection angle between the main shaft of the modal vibration and the geometric main shaft according to the mode matrix phi. S7, solving for modal vibration according to the mode matrix phiThe deviation angle of the main shaft and the geometric main shaft comprises: the included angle alpha = arctan (phi) between the vibration main shaft of the first side pendulum and the x axis 21 /φ 11 ) An angle α = arctan (Φ) between the principal axis of vibration of the second side-sway mode and the x-axis 22 /φ 12 ) Wherein
After the deflection angle between the main shaft of the modal vibration and the geometric main shaft is obtained, the main shaft direction of the modal vibration can be obtained according to the deflection angle and the acquired acceleration signal of the geometric main shaft.
In step S1, an acceleration sensor is used to collect an acceleration signal a of a geometric principal axis of a structure, and a two-axis acceleration sensor is arranged on the geometric principal axis (x, y axis) of the structure on a device floor of a building near the top, and the two-axis acceleration sensor tests acceleration signals in two orthogonal directions. As another practical example, two single-axis sensors are orthogonally arranged on the geometrical principal axis (x, y axis) of the structure on the equipment floor near the top position of a building. As shown in fig. 2, the acceleration time-course signal a for measuring the x-axis and y-axis of the building under the environment vibration or wind-induced vibration condition x And a y Acceleration time-course signal a x And a y As shown in fig. 3 and 4, respectively.
The vibration mode matrix of the structure can be obtained by calculation according to the steps 1 to 9
The column 1 of the Φ matrix is the 1 st order mode of the structure, and the column 2 is the 2 nd order mode of the structure. From this calculation, 1 order mode direction x 0 The angle between the x-axis and the 2 nd order mode is arctan (-0.356/0.462) =52.4 °, and the angle between the x-axis and the 2 nd order mode is arctan (-0.247/0.259) = -46.36 °. Two vibration directions are respectively x 0 ，y 0 As shown. Therefore, the deflection angle between the actual vibration mode of the structure and the geometric main shaft can be accurately obtained according to the scheme.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent should be subject to the appended claims.
Claims (10)
1. A method for determining a modal vibration main shaft of a high-rise building based on biaxial measured acceleration is characterized by comprising the following steps:
s1, acquiring an acceleration signal A of a geometric main shaft of a structure;
s2, calculating to obtain a whitening matrix W according to the acceleration signal A;
s3, solving a whitened input signal Z according to the whitening matrix W and the acceleration signal A;
s4, calculating a time delay covariance matrix R of the whitened input signal Z z (τ)；
S5, according to the time-delay covariance matrix R z (τ) calculating an orthogonal matrix V;
s6, solving a vibration mode matrix phi according to the orthogonal matrix V,
and S7, solving a deflection angle between the main shaft of the modal vibration and the geometric main shaft according to the mode matrix phi.
2. The method for determining the modal vibration principal axis of the high-rise building based on the biaxial measured acceleration according to claim 1, wherein the step S2 comprises:
s21, calculating a covariance matrix R of the acceleration signal A A (0)；
S22, to covariance matrix R A (0) Performing singular value decomposition;
and S23, obtaining a whitening matrix W.
3. The method for determining the main axis of modal vibration of high-rise building based on two-axis measured acceleration as claimed in claim 2, wherein S21, a covariance matrix R of an acceleration signal A is calculated A (0) The method comprises the following steps:
s211, calculating
Wherein superscript T represents a matrix transpose; a (: 1; wherein the content of the first and second substances,
x i 、y i the test values of acceleration signals of x (t) and y (t) at the ith time point are respectively, and x (t) and y (t) are respectively acceleration signals in x and y directions of a geometric main shaft of the structure sampled at the time point t;
s212, calculating m according to the following formula 1 And m 2 ；
Wherein mean (A (1, 1 n- τ)) represents an average value of 1 st;
s213, calculating
S214, according to
Computing a symmetric delay covariance matrix R A (τ)；/>
S215, let tau =0, obtaining covariance matrix R A (0)。
4. The dual axis based measurement of claim 3The method for determining the modal vibration principal axis of high-rise building of speed is characterized in that S22, a covariance matrix R is matched A (0) The formula for singular value decomposition is:
R A (0)＝UλU T ；
where U is a unit matrix in which column vectors are orthogonal to each other, and λ is a diagonal matrix.
5. The method for determining the modal vibration principal axis of the high-rise building based on the biaxial measured acceleration as claimed in claim 4, wherein the whitening matrix W is formulated as:
6. the method for determining the modal vibration principal axis of the high-rise building based on the biaxial measured acceleration as claimed in claim 5, wherein S3, the formula for obtaining the whitened input signal Z according to the whitening matrix W and the acceleration signal A is as follows:
Z＝WA。
7. the method for determining the modal vibration principal axis of a high-rise building based on biaxial measured acceleration as claimed in claim 6, wherein S4, a time-delay covariance matrix R of the whitened input signal Z is calculated z (τ) comprises:
s41, calculating
Wherein superscript T represents a matrix transpose; z (: 1;
s42, calculating m according to the following formula 3 And m 4 ；
Wherein mean (Z (1, 1 n- τ)) represents an average value of 1 st;
s43, calculating
S44, calculating a symmetric time delay covariance matrix:
8. the method for determining the modal principal axis of vibration of a high-rise building based on biaxial measured acceleration as claimed in claim 7, wherein S5 is based on a time-delay covariance matrix R z (τ) calculating the orthogonal matrix V includes:
s51, respectively aligning the delay covariance matrixes R z Tau of (tau) takes a value delta t,2 delta t z (τ) value; wherein Δ t is the sampling interval of the acceleration test signal;
s52, setting the initial value of the orthogonal matrix V as
S53, according to R z Performing Givens rotation on the initial value of the (tau) and the initial value of the orthogonal matrix to obtain a rotation matrix, and taking the rotation matrix as the orthogonal matrix V;
s54, updating R in sequence z And (τ) and the orthogonal matrix V, repeating step S53 until the square of the off-diagonal element of the rotation matrix is greater than a preset minimum positive value, and taking the rotation matrix as the final orthogonal matrix V.
9. The method for determining the modal vibration principal axis of the high-rise building based on the biaxial measured acceleration as claimed in claim 8, wherein S6, the formula of the vibration mode matrix Φ according to the orthogonal matrix V is:
Φ＝W -1 V。
10. the method for determining the modal principal axis of high-rise building vibration based on the biaxial measured acceleration according to claim 9, wherein S7, determining the deviation angle between the principal axis of modal vibration and the geometric principal axis according to the mode matrix Φ comprises: the angle between the main vibration axis of the first side pendulum and the x axis is alpha = arctan (phi) 21 /φ 11 ) An angle α = arctan (Φ) between the principal axis of vibration of the second side-sway mode and the x-axis 22 /φ 12 ) Wherein
/>
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910776761.9A CN110457858B (en) | 2019-08-22 | 2019-08-22 | Method for determining modal vibration main shaft of high-rise building based on double-shaft actual measurement acceleration |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910776761.9A CN110457858B (en) | 2019-08-22 | 2019-08-22 | Method for determining modal vibration main shaft of high-rise building based on double-shaft actual measurement acceleration |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN110457858A CN110457858A (en) | 2019-11-15 |
| CN110457858B true CN110457858B (en) | 2023-04-07 |
Family
ID=68488519
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910776761.9A Active CN110457858B (en) | 2019-08-22 | 2019-08-22 | Method for determining modal vibration main shaft of high-rise building based on double-shaft actual measurement acceleration |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110457858B (en) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111076722B (en) * | 2019-11-18 | 2022-07-19 | 广州南方卫星导航仪器有限公司 | Attitude estimation method and device based on self-adaptive quaternion |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2017089151A (en) * | 2015-11-05 | 2017-05-25 | 清水建設株式会社 | Vibration control structure of building |
| CN107288400A (en) * | 2017-06-12 | 2017-10-24 | 浙江大学 | High-rise building wind resistant structural system optimization method based on the mutual interference principle of mode |
| CN109063310A (en) * | 2018-07-26 | 2018-12-21 | 广州大学 | A kind of skyscraper HFFB wind shake analysis method considering mode of oscillation drift angle |
-
2019
- 2019-08-22 CN CN201910776761.9A patent/CN110457858B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2017089151A (en) * | 2015-11-05 | 2017-05-25 | 清水建設株式会社 | Vibration control structure of building |
| CN107288400A (en) * | 2017-06-12 | 2017-10-24 | 浙江大学 | High-rise building wind resistant structural system optimization method based on the mutual interference principle of mode |
| CN109063310A (en) * | 2018-07-26 | 2018-12-21 | 广州大学 | A kind of skyscraper HFFB wind shake analysis method considering mode of oscillation drift angle |
Non-Patent Citations (2)
| Title |
|---|
| 建筑结构模态参数测试的若干问题;王海波等;《天津建设科技》;20130630(第03期);全文 * |
| 超高层建筑风致响应及等效静力风荷载研究;李寿英等;《建筑结构学报》;20100305(第03期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN110457858A (en) | 2019-11-15 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| US10648877B2 (en) | Mechanical strain-based weather sensor | |
| Yi et al. | Clustering number determination for sparse component analysis during output-only modal identification | |
| Ramos | Damage identification on masonry structures based on vibration signatures | |
| JP5916865B2 (en) | Method for determining the inclination of tower structures | |
| CN107356387A (en) | Multisensor additional mass removing method in a kind of modal test | |
| Hou et al. | Frequency-domain substructure isolation for local damage identification | |
| Huang et al. | Wavelet‐based approach of time series model for modal identification of a bridge with incomplete input | |
| CN109282785A (en) | A kind of deformation monitoring method of the elastically supported plate based on strain monitoring | |
| CN110457858B (en) | Method for determining modal vibration main shaft of high-rise building based on double-shaft actual measurement acceleration | |
| Zhi1a et al. | A Kalman filter based algorithm for wind load estimation on high-rise buildings | |
| Wei et al. | Boundary condition modelling and identification for cantilever-like structures using natural frequencies | |
| JPH0827192B2 (en) | How to measure angles and angle characteristic curves | |
| CN116522085A (en) | Full-automatic inhaul cable frequency extraction, fixed-order and cable force identification method and application | |
| Wang et al. | Damping identification with acceleration measurements based on sensitivity enhancement method | |
| RU2562273C2 (en) | Test bench for measurement of mass-inertia characteristics of item | |
| Nesterenko et al. | Stiffness evaluation of a metal frame by the method of dynamic tests | |
| Sun et al. | Safety and serviceability assessment for high-rise tower crane to turbulent winds | |
| JP3550296B2 (en) | Measuring method of tension and bending stiffness of structures | |
| Zhang | Controlled substructure identification for shear structures | |
| CN103472669B (en) | The method of testing of a kind of camera shutter micro-vibration physical simulation test processes system | |
| JP3696298B2 (en) | Seismic evaluation method and apparatus for buildings | |
| Sasaki et al. | Study on Performance Evaluation of MEMS Sensors and Data Integration Methods for Expected Use to Determine Damage Degrees of Existing Structures | |
| Zhan et al. | Large bridge cable tension estimation with cyber vibration sensing system | |
| Concha et al. | Identification of torsionally coupled shear buildings models using a vector parameterization | |
| JPH0682067B2 (en) | Earthquake detector |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |