A method for evaluating building vibration using Z-level vibration

Abstract

The application relates to a method for evaluating building vibration by using a Z vibration level, which comprises the following steps: performing fast Fourier transform on an original acceleration time history signal of a complete time length of a building to obtain an original acceleration frequency spectrum; performing frequency weighting on the original acceleration frequency spectrum to obtain a weighted acceleration frequency spectrum; performing inverse fast Fourier transform on the weighted acceleration frequency spectrum to obtain a weighted acceleration time history signal of the complete time length; sliding a 1-second rectangular window function along a time axis of the weighted acceleration time history signal to extract a series of 1-second acceleration signals, and a specified overlap rate can be set between adjacent 1-second rectangular windows; calculating the root mean square of each 1-second acceleration signal and then calculating a Z vibration level; and performing comfort evaluation of the building after the Z vibration level is obtained.

Description

Technical Field

[0001] This application relates to a method for evaluating building vibration using Z-level vibration. Background Technology

[0002] Engineering vibration has become a key focus in the construction of livable cities, significantly impacting the comfort of the living environment. A scientifically sound evaluation system is fundamental to addressing building vibration comfort issues. One commonly used evaluation index for the impact of building vibration on comfort is the Z-level (VLz), which is based on calculating the vibration acceleration level (VAL) using an acceleration time-history signal corrected for frequency weighting. The Z-level is a unit used to describe vibration intensity and is closely related to the vibration intensity perceived by users; it is used in the field of vibration control for building / engineering structures. By efficiently and accurately calculating the building's Z-level and comparing it with the Z-level limits specified in relevant codes or standards, the vibration comfort of the building can be evaluated.

[0003] However, the Z-level calculation process in existing technologies is quite complex. For each building's acceleration time history signal, steps such as time-frequency conversion, frequency band division and weighting, numerical integration, and logarithmic operations are required. For large and complex structural vibration problems with multiple nodes and multiple operating conditions, the computational workload will be enormous. For example, in the vibration analysis of a large integrated transportation hub, considering various vibration sources and their combinations, such as high-speed rail, subway, urban rail, road traffic, equipment, and pedestrians, there may be tens of thousands of operating conditions. Each operating condition involves calculating the Z-level of a large number of areas and nodes of interest, and the total number of acceleration time history signals may be millions or even tens of millions. In actual vibration signal measurements, measurements may be taken at multiple measuring points for several hours or even days. The post-processing of large amounts of data to obtain the Z-level is also quite time-consuming.

[0004] On the other hand, the time integration constant in existing technologies is typically 1 second, resulting in only a 1-second fast Fourier transform (FFT) being performed on the acceleration time history signal during frequency weighting. Since the frequency resolution is the reciprocal of the FFT duration, the frequency resolution of a 1-second signal after FFT is only 1 Hz, which cannot meet the requirements for fine frequency band division during weighting operations. Furthermore, existing technologies require FFT, frequency weighting, and IFFT processes for each 1-second acceleration signal segment, failing to address the issue of high computational complexity in calculating large batches of Z-level vibrations.

[0005] Therefore, improving the Z-level calculation method and enhancing its efficiency and accuracy are crucial for comprehensive and efficient building vibration evaluation in practical engineering. Summary of the Invention

[0006] The purpose of this application is to provide a method for evaluating building vibration using Z-level, addressing the problems of low efficiency and accuracy in existing Z-level evaluation methods, which are insufficient to meet the needs of large-scale Z-level calculations. This application decomposes the Z-level calculation process of a building into multiple steps, and by adjusting the order of linear operations, significantly improves calculation efficiency, enabling efficient calculation of large batches of Z-level vibrations. The vibration evaluation method of this application has the technical advantages of high accuracy, high efficiency, and ease of operation.

[0007] This application relates to a method for evaluating building vibration using Z-level vibration, comprising the following steps:

[0008] (1) Calculate the acceleration data of the building vibration over a period of time based on the building structural model or record the acceleration data using an accelerometer, and analyze the original acceleration time history signal for the complete duration. Perform an FFT to obtain the original acceleration spectrum. ;

[0009] (2) The original acceleration spectrum Frequency weighting is performed to obtain the weighted acceleration spectrum. ;

[0010] (3) The weighted acceleration spectrum Perform IFFT to obtain the weighted acceleration time history signal of the complete duration. ;

[0011] (4) Use the 1-second rectangular window function Along the weighted acceleration time history signal Slide the time axis to extract a series of 1-second acceleration signals. , This represents the starting time of the i-th 1-second rectangular window;

[0012] (5) Calculate the series of 1-second duration acceleration signals. root mean square of acceleration The calculation formula is:

[0013]

[0014] (6) Calculate the root mean square of the acceleration. Z-level The calculation formula is:

[0015]

[0016] In the formula, The reference acceleration is 1 × 10⁻⁶. -6 m / s 2 ;

[0017] (7) Based on the calculated Z vibration level The vibration comfort of buildings is evaluated.

[0018] In step (2), for the i-th frequency band, the weighted acceleration spectrum The calculation formula is:

[0019]

[0020] In the formula, The weighting coefficients for the i-th frequency band are... and These are the lower and upper frequency bounds of the i-th frequency band, respectively.

[0021] In step (4), the 1-second rectangular window function Defined as:

[0022]

[0023] In the formula, The weighted acceleration time history signal The full duration.

[0024] This application proposes a method for evaluating building vibration using Z-level, which offers significant advantages in terms of computational accuracy and speed. First, by performing an FFT on the acquired acceleration signal for the entire duration of the building, it corrects the insufficient frequency resolution and inaccurate weighting issues caused by conventional methods performing FFT on 1-second acceleration signals. Second, the improved method only requires one FFT, frequency weighting, and IFFT process, significantly reducing the computational load and improving efficiency compared to conventional methods that perform these processes for each 1-second acceleration signal segment. Therefore, the proposed method for evaluating building vibration using Z-level can effectively improve computational accuracy and efficiency, thus meeting the needs for large-scale Z-level calculations. Attached Figure Description

[0025] Figure 1 This is a flowchart of the method for evaluating building vibration using Z-level vibration according to this application.

[0026] Figure 2 This is the finite element model of the shear wall residential building in the embodiments of this application.

[0027] Figure 3 This is a typical raw acceleration time history signal in the embodiments of this application.

[0028] Figure 4 This is a typical raw acceleration spectrum in the embodiments of this application.

[0029] Figure 5 It is the weighting coefficient used in frequency weighting in the embodiments of this application.

[0030] Figure 6 This is a typical weighted acceleration spectrum in the embodiments of this application.

[0031] Figure 7 This is a typical weighted acceleration time history signal in the embodiments of this application.

[0032] Figure 8 This is a schematic diagram of the 1-second window function in an embodiment of this application.

[0033] Figure 9 It is the 1-second duration acceleration signal in the embodiments of this application.

[0034] Figure 10 This is a comparison of the Z-level time history curves calculated by the method of this application and conventional methods.

[0035] Figure 11 This is a graph showing the relationship between the calculation time and overlap rate of a large number of Z-level vibrations. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0037] This application proposes a method for evaluating building vibration using Z-level. By decomposing the Z-level calculation process into multiple steps and adjusting the order of linear operations, the calculation efficiency is significantly improved. This method enables efficient calculation of large batches of Z-levels and has the technical advantages of high precision, high efficiency, and ease of operation.

[0038] A method for evaluating building vibration using Z-level vibration according to this application includes the following steps:

[0039] Step 1: Calculate the building's vibration acceleration data over a period of time based on the building structure model or record the acceleration data using an accelerometer. Then, analyze the original acceleration time history signal for the complete duration. Perform a Fast Fourier Transform (FFT) to obtain the original acceleration spectrum. .

[0040] Step 2, process the obtained raw acceleration spectrum Frequency weighting is performed to obtain the weighted acceleration spectrum. .

[0041] Frequency weighting refers to the process of weighting the original acceleration spectrum. The amplitude is multiplied by a specified weighting coefficient to enhance or suppress specific frequency components in the acceleration signal. In practice, the original acceleration spectrum can first be adjusted according to specifications or standards. Frequency bands are divided, and then the spectral amplitude of each band is multiplied by the corresponding weighting coefficient. For the i-th frequency band, the calculation formula is:

[0042]

[0043] In the formula, The weighting coefficients for the i-th frequency band are... and These are the lower and upper frequency bounds of the i-th frequency band, respectively.

[0044] Step 3, calculate the weighted acceleration spectrum. Perform an inverse fast Fourier transform (IFFT) to obtain the weighted acceleration time history signal of the complete duration. .

[0045] Step 4, apply the 1-second rectangular window function Along the weighted acceleration time history signal Slide the time axis to extract a series of 1-second acceleration signals. .

[0046] Among them, the 1-second rectangular window function The definition of is:

[0047]

[0048] In the formula, This represents the starting time of the i-th 1-second rectangular window. The weighted acceleration time history signal The complete duration. A series of the 1-second rectangular window functions are compared with the weighted acceleration time history signal. By multiplying them, a series of 1-second acceleration signals can be extracted.

[0049] like Figure 8-9 As shown, the essence of windowing is to retain only the 1-second segment of signal of interest, while setting the signal of the remaining time periods to zero, that is:

[0050]

[0051] In the formula: This represents the original acceleration time history signal; Indicated by The acceleration time history signal is obtained by adding a 1-second rectangular window to the starting point. By performing windowing operations, the original signal duration can be preserved when extracting the 1-second segment, so that the frequency resolution after FFT meets the requirements of fine weighting.

[0052] Preferably, an overlap rate can be specified between adjacent 1-second rectangular windows. This is to avoid missing the period with the highest vibration level, which could lead to an underestimated response. A higher overlap rate means more 1-second rectangular windows. By setting the overlap rate, the period of maximum vibration centered on the peak can be captured, without failing to capture the intervals on both sides of the peak simultaneously. The curve showing the relationship between calculation time and overlap rate is displayed. The larger the overlap rate, the steeper the curve, indicating a significantly faster increase in calculation time. This is because the overlap rate is... At that time, the computational cost is approximately 1 / 3 of the time that does not consider overlap. times, its derivative is Therefore, increasing the overlap rate will significantly increase the computational load. It is known that increasing the overlap rate has limited effect on improving the calculation accuracy of the Z-vibration level; in engineering practice, the overlap rate is generally taken as 0.7~0.9.

[0053] Step 5: Calculate the series of 1-second duration acceleration signals. root mean square of acceleration The calculation formula is:

[0054]

[0055] Step 6: Calculate the root mean square of the acceleration. Z-level The calculation formula is:

[0056]

[0057] In the formula, The reference acceleration is 1 × 10⁻⁶. -6 m / s 2 .

[0058] Step 7, obtain the Z vibration level. This allows for comparison with the Z-vibration level limit specified in relevant codes or standards, thereby evaluating the vibration comfort of the building.

[0059] Example

[0060] Taking the vehicle-induced vibration analysis of a shear wall residential building near a subway station as an example, the method of this application is described. The building has 11 floors above ground and 1 floor below ground, with a partial 3-story underground section. The analysis model is shown in the figure. Through time history analysis, the vertical vibration acceleration time history signals of the floor slab nodes of each floor of the building were obtained. A typical acceleration time history signal is shown in the figure.

[0061] The original acceleration time history signal is shown. For example, firstly, according to step 1 of this application, an FFT transformation is performed to obtain the original acceleration spectrum. As shown in the figure.

[0062] Then, according to step 2 described in this application, for Frequency weighting is performed, with the weight values ​​shown. The weighted acceleration spectrum is obtained by multiplying the spectral amplitude by the corresponding frequency and the weighting coefficients shown. As shown in the figure.

[0063] Then, according to step 3 described in this application, for Perform IFFT to obtain the weighted acceleration time history signal of the complete duration. As shown in the figure.

[0064] Then, according to step 4 of this application, a series of 1-second duration acceleration signals are extracted using a 1-second rectangular window function, and the window functions at adjacent time points maintain a 90% overlap rate. Let t i Taking a specific time interval as an example, the 1-second rectangular window function is shown in the figure. Compare it with... Figure 7 of Multiplication can extract t i 1-second duration acceleration signal at time ,like Figure 9 As shown.

[0065] Then, the Z-level vibration at each moment is calculated according to steps 5 and 6 of this application, and the results are as follows: Figure 10 As shown. Figure 10 The paper also presents the Z-level time history curves obtained by performing FFT, frequency weighting, and IFFT processes on each 1-second acceleration signal segment using conventional methods. The two methods show good agreement. It should be noted that the conventional method takes 0.027 seconds to calculate a single acceleration time history signal; however, the improved method proposed in this application only requires 0.0012 seconds, improving computational efficiency by 22 times. Based on the calculated Z-level results, the comfort level of the building can be evaluated.

[0066] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for evaluating building vibration using Z level, characterized by: The method comprises the following steps: (1) calculating or recording the acceleration data of building vibration in a period of time according to a building structure model or using an acceleration recorder, and performing FFT on the original acceleration time history signal a0(t) to obtain an original acceleration spectrum A0(ω); (2) frequency weighting the original acceleration spectrum A0(ω) to obtain a weighted acceleration spectrum A w (ω); (3) performing an IFFT on the weighted acceleration spectrum A w (ω) to obtain a full-length weighted acceleration time history signal a w (t); (4) slide a 1-second rectangular window function w(t, t i ) along the time axis of the weighted acceleration time history signal a w (t) to extract a series of 1-second duration acceleration signals a w (t, t i ), where t i denotes the starting time of the i-th 1-second rectangular window; (5) calculating the acceleration root mean square A w (t, t i ) of the series of 1-second-long acceleration signals a eff (t i ), according to the formula: (6) Calculate the acceleration root mean square A eff (t i ) of the Z vibration level VL z (t i ), the calculation formula is: In the formula, A0 is a reference acceleration, and has a value of 1 x 10 -6 m / s 2 ; (7) The Z vibration level VL is calculated z (t i ), the vibration comfort of the building is evaluated.

2. The method of claim 1, wherein: In step (2), for the i-th frequency band, the weighted acceleration spectrum A w The formula for calculating A(ω) is: |A w (ω)|=w i |A0(ω)|,ω∈[ω i ,ω i+1 ] In the formula, w i is the weight coefficient of the i-th frequency band, ω i and ω i+1 are the lower and upper bounds of the frequency of the i-th frequency band, respectively.

3. The method according to claim 1 or 2, characterized in that: In step (4), the 1 second rectangular window function w(t, t i ) is defined as: where T is the weighted acceleration time history signal a w the full duration of (t).

4. The method of claim 1 or 2, wherein: A specified overlap rate is set between adjacent 1-second rectangular windows, and the overlap rate is 0.7-0.9.

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