Method for carrying out building vibration evaluation by adopting Z vibration level

Abstract

The invention relates to a method for carrying out building vibration evaluation by adopting a Z vibration level, and the method comprises the steps: carrying out the fast Fourier transform of an obtained original acceleration time-history signal of a complete duration of a building, and obtaining an original acceleration frequency spectrum; performing frequency weighting on the original acceleration frequency spectrum to obtain a weighted acceleration frequency spectrum; inverse fast Fourier transform is carried out on the weighted acceleration frequency spectrum to obtain a weighted acceleration time history signal with complete duration; the 1-second rectangular window function slides along the time axis of the weighted acceleration time history signal, a series of 1-second acceleration signals are extracted, and the overlapping rate between adjacent 1-second rectangular windows can be specified; calculating the root mean square of the acceleration signal in each 1-second time length, and then calculating the Z vibration level; after the Z vibration level is obtained, comfort evaluation of the building can be carried out.

Description

Technical Field

[0001] The present application relates to a method for evaluating building vibration using Z vibration level. Background Art

[0002] Engineering vibration has become a focal point in the development of livable cities, significantly impacting the comfort of the human living environment. Addressing building vibration comfort requires a scientific and rational evaluation system. One commonly used evaluation metric for the impact of building vibration on comfort is the Z vibration level (VLz). Its core approach is to calculate the vibration acceleration level (VAL) using an acceleration time-history signal corrected by a frequency weighting factor. The Z vibration level is a unit used to describe vibration intensity, closely related to the vibration intensity perceived by users, and is applicable to the field of vibration control for buildings and engineering structures. By efficiently and accurately calculating a building's Z vibration level and comparing it with the Z vibration level limits specified in relevant codes or standards, the vibration comfort of a building can be evaluated.

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

[0004] On the other hand, the time integration constant in existing technologies is typically 1 second. Consequently, when frequency weighting is performed, only the 1-second acceleration time-history signal is subjected to the Fast Fourier Transform (FFT). Since the frequency resolution is the inverse of the FFT duration, the frequency resolution of a 1-second signal after the FFT is 1 Hz, which cannot meet the precise frequency band division requirements required for weighting calculations. Furthermore, existing technologies require the FFT, frequency weighting, and IFFT processes for each 1-second acceleration signal, and this does not address the computational complexity associated with large-scale Z-level calculations.

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

[0006] The purpose of this application is to provide a method for evaluating building vibration using Z vibration levels, in order to address the problem that existing Z vibration level evaluation methods are inefficient and inaccurate, making it difficult to meet the needs of large-scale Z vibration level calculations. This application decomposes the Z vibration level calculation process of a building into multiple steps. By adjusting the order of linear operations, the calculation efficiency is significantly improved, and efficient calculation of large-scale Z vibration levels can be achieved. The vibration evaluation method of this application has the technical advantages of high precision, high efficiency, and ease of operation.

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

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

[0009] (2) The original acceleration spectrum Perform frequency weighting to obtain weighted acceleration spectrum ;

[0010] (3) The weighted acceleration spectrum Perform IFFT to obtain the weighted acceleration time 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 , Indicates the starting time of the i-th 1-second rectangular window;

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

[0013]

[0014] (6) Calculate the acceleration root mean square Z vibration level , the calculation formula is:

[0015]

[0016] Where, is the reference acceleration, which is 1×10 -6 m / s 2 ;

[0017] (7) According to the calculated Z vibration level , to evaluate the vibration comfort of buildings.

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

[0019]

[0020] Where, is the weight coefficient of the i-th frequency band, and are the lower and upper frequency bounds of the i-th frequency band respectively.

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

[0022]

[0023] Where, is the weighted acceleration time history signal The full duration of .

[0024] The method proposed in this application for evaluating building vibrations using Z vibration levels has obvious advantages in terms of calculation accuracy and speed. First, by performing FFT on the acquired acceleration signal of the complete duration of the building, the problems of insufficient frequency resolution and inaccurate weighting caused by the conventional method of performing FFT on the acceleration signal of 1 second in duration are corrected. Secondly, the improved method of this application only needs to perform the processes involving FFT, frequency weighting, IFFT, etc. once. Compared with the conventional method in which FFT, frequency weighting, IFFT, etc. are required for each 1-second acceleration signal, the amount of calculation is greatly reduced and the calculation efficiency is improved. Therefore, the method proposed in this application for evaluating building vibrations using Z vibration levels can effectively improve the calculation accuracy and efficiency, thereby meeting the calculation requirements of large quantities of Z vibration levels. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 This is a flow chart of the method for using Z vibration level to evaluate building vibration in this application.

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

[0027] Figure 3 It is a typical original acceleration time history signal in the embodiment of the present application.

[0028] Figure 4 This is a typical original acceleration spectrum in the embodiment of the present application.

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

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

[0031] Figure 7 It is a typical weighted acceleration time history signal in the embodiment of the present application.

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

[0033] Figure 9 It is an acceleration signal of 1 second in the embodiment of the present application.

[0034] Figure 10 This is a comparison chart of the Z vibration level time history curves calculated by the method of the present application and the conventional method.

[0035] Figure 11 This is a graph showing the relationship between the batch Z-level calculation time and the overlap rate. DETAILED DESCRIPTION

[0036] To make the objectives, technical solutions, and advantages of this application more clear, the technical solutions in this application will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only part of the embodiments of this application, not all of them. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0037] This application proposes a method for evaluating building vibration using Z vibration level. By decomposing the Z vibration level calculation process into multiple steps and adjusting the order of linear operations, the calculation efficiency is significantly improved. Efficient calculation of large quantities of Z vibration levels can be achieved, and the method has the technical advantages of high precision, high efficiency and easy operation.

[0038] A method for evaluating building vibration using the Z vibration level according to the present application comprises the following steps:

[0039] Step 1: Calculate the acceleration data of the building vibration over a period of time according to the building structure model or use an accelerometer to record the acceleration data of the building vibration over a period of time, and calculate the original acceleration time history signal of the complete time. Perform fast Fourier transform (FFT) to obtain the original acceleration spectrum .

[0040] Step 2: Get the original acceleration spectrum Perform frequency weighting to obtain weighted acceleration spectrum .

[0041] Among them, frequency weighting refers to the original acceleration spectrum The amplitude of the acceleration signal is multiplied by the specified weight coefficient to enhance or suppress the specific frequency components in the acceleration signal. In specific implementation, the original acceleration spectrum can be first Divide the frequency bands and then multiply the spectrum amplitude of each band by the corresponding weight coefficient. For the i-th frequency band, the calculation formula is:

[0042]

[0043] Where, is the weight coefficient of the i-th frequency band, and are the lower and upper frequency bounds of the i-th frequency band respectively.

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

[0045] Step 4: Set 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 is defined as:

[0047]

[0048] Where, represents the starting time of the i-th 1-second rectangular window, is the weighted acceleration time history signal Combine a series of 1-second rectangular window functions with the weighted acceleration time history signal By multiplying them together, a series of 1-second acceleration signals can be extracted.

[0049] like Figure 8-9 As shown in Figure 2, the essence of the windowing operation is to retain only the 1s segmented signal of interest and set the signals of the remaining time periods to zero, that is:

[0050]

[0051] Where: Represents the original acceleration time history signal; Indicates This is the acceleration time-history signal after adding a 1s rectangular window to the starting point. By adding a window, the original signal duration can be maintained when extracting 1s segments, ensuring that the frequency resolution after FFT meets the requirements for precise weighting.

[0052] Preferably, the overlap rate can be specified between adjacent 1-second rectangular windows. The purpose is to avoid missing the period with the highest vibration level and thus underestimating the response. The higher the overlap rate, the more 1-second rectangular windows there are. By setting the overlap rate, the maximum vibration period centered on the peak can be captured without being unable to capture the intervals on both sides of the peak at the same time. The relationship curve between the calculation time and the overlap rate is shown. The larger the overlap rate, the steeper the curve, indicating that the calculation time growth rate is also significantly faster. This is because the overlap rate is When the calculation amount is about , the overlap is not considered. times, its derivative is Therefore, increasing the overlap ratio will significantly increase the amount of calculation. It can be seen that increasing the overlap ratio has limited effect on improving the calculation accuracy of the Z vibration level. In engineering practice, the overlap ratio can generally be taken as 0.7~0.9.

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

[0054]

[0055] Step 6: Calculate the acceleration root mean square Z vibration level , the calculation formula is:

[0056]

[0057] Where, is the reference acceleration, which is 1×10 -6 m / s 2 .

[0058] Step 7, obtain the Z vibration level , it can be compared with the Z vibration level limit specified in relevant specifications or standards, so as to evaluate the vibration comfort of the building.

[0059] Example

[0060] The method described in this application is illustrated using the vehicle-induced vibration analysis of a shear-wall residential building near a subway station as an example. The building has 11 floors above ground, one floor underground, and three floors in a section. The analysis model is shown below. Through time-history analysis, vertical vibration acceleration time-history signals at the floor slab nodes on each floor of the building are obtained. A typical acceleration time-history signal is shown below.

[0061] The original acceleration time history signal shown For example, first, according to step 1 of this application, perform FFT transformation to obtain the original acceleration spectrum , as shown.

[0062] Then according to step 2 described in this application, Perform frequency weighting, and the weight values ​​are shown below. Multiply the spectrum amplitude by the weight coefficient shown according to the corresponding frequency to obtain the weighted acceleration spectrum. , as shown.

[0063] Then, according to step 3 of this application, Perform IFFT to obtain the weighted acceleration time signal of the complete duration , as shown.

[0064] Then, according to step 4 of the present application, a series of 1-second acceleration signals are extracted using a 1-second rectangular window function, and the window functions at adjacent moments maintain a 90% overlap rate. i As an example, the 1-second rectangular window function is shown as follows. Figure 7 of Multiplying, we can extract t i 1 second acceleration signal at the moment ,like Figure 9 shown.

[0065] Then, calculate the Z vibration level at each moment according to steps 5 and 6 described in this application, and the result is as follows: Figure 10 shown. Figure 10 The Z-level time history curves obtained by performing FFT, frequency weighting, and IFFT on each 1-second acceleration signal using conventional methods are also presented. The two methods agree well. 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 takes 0.0012 seconds, a 22-fold increase in computational efficiency. The calculated Z-level results can be used to evaluate building comfort.

[0066] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present application.

Claims

1. A method for evaluating building vibration using Z vibration level, characterized by: The following steps are involved: (1) Calculate the acceleration data of the building vibration over a period of time based on the building structure model or use an accelerometer to record the acceleration data of the building vibration over a period of time, and calculate the original acceleration time history signal of the complete time. Perform FFT to obtain the original acceleration spectrum ; (2) The original acceleration spectrum Perform frequency weighting to obtain weighted acceleration spectrum ; (3) The weighted acceleration spectrum Perform IFFT to obtain the weighted acceleration time signal of the complete duration ; (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 , Indicates the starting time of the i-th 1-second rectangular window; (5) Calculate the series of 1-second acceleration signals The root mean square acceleration , the calculation formula is: (6) Calculate the acceleration root mean square Z vibration level , the calculation formula is: Where, is the reference acceleration, which is 1×10 -6 m / s 2 ; (7) According to the calculated Z vibration level , to evaluate the vibration comfort of buildings.

2. The method according to claim 1, wherein: In step (2), for the i-th frequency band, the weighted acceleration spectrum The calculation formula is: Where, is the weight coefficient of the i-th frequency band, and are the lower and upper frequency bounds 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 Defined as: Where, is the weighted acceleration time history signal The full duration of .

4. The method according to claim 1 or 2, characterized in that: The overlap ratio between adjacent 1-second rectangular windows is specified, and the folding ratio is taken as 0.7~0.9.

Images