Method for evaluating vibration comfort of building under multiple load cases based on probability

Abstract

The application relates to a probability-based building vibration comfort evaluation method under a multi-load working condition, which comprises the following steps: performing FFT on original acceleration time history signals of a building under each single load working condition to obtain original acceleration frequency spectra; performing frequency weighting on the original acceleration frequency spectra to obtain weighted acceleration frequency spectra; performing IFFT on the weighted acceleration frequency spectra to obtain weighted acceleration time history signals of the building with a complete time length; dividing the weighted acceleration time history signals into 1-second time length segmented signals; setting a total sampling number and a probability distribution model of the 1-second time length segmented signals under each single load working condition; randomly sampling the 1-second time length segmented signals under each single load working condition and combining the signals into 1-second time length segmented signals under a multi-load working condition; calculating the root mean square of the 1-second time length segmented signals under the multi-load working condition, and then calculating a Z vibration level, which is used for vibration comfort evaluation of the building under the multi-load working condition.

Description

Technical Field

[0001] This application relates to a probability-based method for evaluating the vibration comfort of buildings under multiple load conditions, which can be used to evaluate the vibration comfort of buildings. Background Technology

[0002] With the increasing diversification of building structures' functions, they may be affected by multiple vibration sources during their service life. Engineering vibration has become a key concern in the construction of livable cities. The prerequisite for assessing and mitigating engineering vibration is a scientifically sound evaluation index. Among these, Z-level is a commonly used index for vibration comfort evaluation. It can reflect the physiological sensitivity of the human body to different frequency components of vibration through frequency weighting, thereby scientifically quantifying the impact of vibration on human comfort. The calculation of Z-level involves steps such as signal time-frequency conversion, frequency weighting, numerical integration, and logarithmic operations, making the process relatively complex. Especially when large building structures are in complex environments with multiple vibration sources, a significant amount of computational resources is often required for a large-scale Z-level analysis to achieve a comprehensive and accurate vibration evaluation.

[0003] The complex environment of multiple vibration sources faced by buildings is mainly reflected in four aspects: 1) Multiple types of vibration sources. During long-term service, various types of vibration sources, such as traffic engineering, environmental excitation, personnel activities, and mechanical equipment, overlap and jointly affect the building structure. 2) Multiple spatial distributions. Vibration excitation may act on multiple locations of the structure. For example, there are multiple train lines such as subway, urban rail, and high-speed rail in integrated transportation hubs, and multiple large pieces of equipment are arranged in office and residential buildings. 3) Multiple operating states. Due to the diversity of vibration sources, there may be a large number of operating states. For example, in the vehicle-induced vibration analysis of large integrated transportation hubs, it is necessary to consider multiple trains such as high-speed rail, urban rail, and subway, as well as multiple states such as starting, braking, meeting, and passing through stations on the main line. 4) Spatiotemporal randomness. There is spatiotemporal uncertainty when multiple load conditions are combined. For example, the phase difference between multiple pieces of equipment is a random variable, and when considering the convergence of multiple trains, the meeting position of the trains is randomly distributed within the section of interest.

[0004] Under the influence of the above factors, the potential number of load case combinations for vibration assessment in complex environments with multiple vibration sources often exceeds one million, and theoretically, there are even countless combinations. When using the Z-level index for multi-load vibration evaluation, two main difficulties arise. First, neither experimental methods nor numerical simulation methods based on finite element models can obtain a sufficiently large number of statistically significant multi-load vibration responses. Second, calculating the Z-level for an extremely large number of vibration response time histories is difficult to achieve using existing instruments and software.

[0005] Therefore, improving the efficiency of large-scale Z-level analysis under multiple load combinations is crucial for achieving comprehensive and efficient vibration comfort evaluation of building structures in complex environments with multiple vibration sources. Summary of the Invention

[0006] The purpose of this application is to provide a probabilistic method for evaluating building vibration comfort under multiple load conditions, addressing the challenge of existing evaluation methods in achieving comprehensive and efficient Z-level calculations under complex multi-source environments. Common vibration sources experienced by buildings during their service life, such as traffic, equipment, pedestrian, and environmental excitations, generally do not cause significant structural damage or induce obvious plasticity; the structure is typically considered to be in an elastic phase. In this case, the building structure can be treated as a linear time-invariant system, and probabilistic sampling can efficiently synthesize single-load responses into multi-load combined responses. Simultaneously, the Z-level calculation process is decomposed into multiple steps, and efficiency is significantly improved by adjusting the order of linear operations, enabling efficient calculation of ultra-large batches of Z-levels under complex multi-source environments. Finally, vibration comfort can be evaluated based on a reasonable guarantee rate level. 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 probability-based method for evaluating building vibration comfort under multiple load conditions, including the following steps:

[0008] (1) Calculate the building's vibration acceleration data over a period of time under each single load condition based on the building's structural model or by recording the acceleration data using an accelerometer, and obtain the original acceleration time history signal for each single load condition. , , This indicates the total number of load cases;

[0009] (2) The obtained original acceleration time history signal Perform a fast Fourier transform to obtain the original acceleration spectrum. ;

[0010] (3) The obtained original acceleration spectrum Frequency weighting is performed to obtain the weighted acceleration spectrum. ;

[0011] (4) The obtained weighted acceleration spectrum Perform an inverse fast Fourier transform to obtain the weighted acceleration time history signal of the complete duration. ;

[0012] (5) Obtain the weighted acceleration time history signal of the complete duration. The signal is segmented into 1-second duration segments. , Adjacent 1-second segments of signal differ by one time step. This represents the total number of segments in the 1-second segmented signal for the k-th single load condition;

[0013] (6) Set the total number of samplings And set the probability distribution model of the 1-second segmented signal;

[0014] (7) Based on the probability distribution model in step (6), randomly select a sample from the 1-second segmented signal and synthesize it into a 1-second segmented signal under multiple load conditions. The calculation formula is:

[0015]

[0016] In the formula, Indicates the kth single working condition A sample randomly selected from a 1-second segment of signal. That is, the sequence number of the 1-second duration segment that was randomly selected;

[0017] (8) Calculate the 1-second segmented signal under the multi-load condition. root mean square acceleration The calculation formula is:

[0018]

[0019] (9) Calculate the root mean square of the acceleration. Z-level The calculation formula is:

[0020]

[0021] In the formula, The reference acceleration is 1×10⁻⁶. -6 m / s 2 ;

[0022] (10) Repeat the calculation process of steps (6) to (9). Next, that is, to proceed Second sampling and The Z-level vibration was calculated and obtained. indivual ;

[0023] (11) Set the guarantee rate The result obtained in step (10) indivual Sort by size from smallest to largest and take the first... One sample is used as a representative value of the Z vibration level for the evaluation of vibration comfort of the building.

[0024] In step (3), for the i-th frequency band, the weighted acceleration spectrum The calculation formula is:

[0025]

[0026] 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.

[0027] In step (6), the total number of samplings Take as ~ , This represents the total number of load cases; the probability distribution model adopts a uniform distribution; in step (10), The sampling and calculation processes are independent of each other and are completed in parallel, either all at once or in batches; in step (11), the guarantee rate is... The value ranges from 0.6 to 0.99.

[0028] This application proposes a probability-based method for evaluating building vibration comfort under multiple load conditions. This method simulates the probability distribution of the Z-level vibration under complex multi-source environments by using limited random sampling based on the building structure response under a single load condition. For building structures that remain elastic under vibration source action, this avoids the need for response simulation analysis or measurement work involving millions, or even theoretically countless, combinations of multiple load conditions. Furthermore, in step (5), adjacent 1-second segmented signals differ by only one time step, meaning the sample space achieves maximum numerical accuracy. Therefore, this evaluation method can balance computational accuracy and speed, achieving efficient evaluation of building vibration comfort under complex multi-source environments. Attached Figure Description

[0029] Figure 1 This is a flowchart of the probability-based multi-load condition building vibration comfort evaluation method proposed in this application.

[0030] Figure 2 This is a vehicle-induced vibration analysis model of a building surrounding a comprehensive transportation hub in this application embodiment.

[0031] Figure 3 This is a representative node Z-level histogram of five load case combinations in the embodiments of this application.

[0032] Figure 4 It is the cumulative distribution function of the Z-level vibration of the representative node for the five load case combinations in the embodiments of this application.

[0033] Figure 5 This is a cloud map of the dB value of the Z-vibration level on the first floor of the podium building with a guarantee rate of 95% in the embodiments of this application.

[0034] Figure 6 This is a cloud map of the dB value of the Z-vibration level on the first floor of the podium building with a guarantee rate of 99% in the embodiments of this application. Detailed Implementation

[0035] 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.

[0036] This application proposes a probabilistic method for evaluating building vibration comfort under multiple load conditions. Utilizing the characteristics of linear time-invariant systems, it efficiently synthesizes single-load condition responses into multi-load condition combined responses through probability-based sampling. Simultaneously, by adjusting the order of linear operations, computational efficiency is significantly improved, enabling efficient analysis of ultra-large batches of Z-level vibrations in complex environments with multiple vibration sources. The proposed method allows for setting reasonable guarantee rates based on specific engineering conditions for vibration comfort evaluation, achieving a good balance between economy and comfort. Furthermore, it possesses technical advantages such as high precision, high efficiency, and ease of operation.

[0037] According to the probability-based multi-load condition building vibration comfort evaluation method of this application, the method includes the following steps:

[0038] Step (1): Calculate the acceleration data of the building vibration over a period of time under each single load condition based on the building structural model or by recording the acceleration data using an accelerometer, to obtain the original acceleration time history signal for each single load condition. , , This indicates the total number of load conditions.

[0039] Step (2) involves processing the original acceleration time history signals for the complete duration of each individual load condition. Perform an FFT (Fast Fourier Transform) to obtain the original acceleration spectrum. .

[0040] Step (3) Analyze the original acceleration spectrum of each individual load condition. 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 (4): Weighted acceleration spectrum for each individual load condition Perform IFFT (Inverse Fast Fourier Transform) to obtain the weighted acceleration time history signal of the complete duration. .

[0045] Step (5) involves generating the weighted acceleration time history signals for the complete duration of each individual load condition. The signal is segmented into 1-second duration segments. , Adjacent 1-second segments of signal differ by one time step. This represents the total number of segments in the 1-second segmented signal for the k-th single load condition.

[0046] The sequence of the 1-second segmented signal for the k-th single load condition is as follows: .

[0047] Step (6): Set the total number of samples. And set the probability distribution model of the 1-second segmented signal for each single load condition.

[0048] Wherein, the total number of sampling times The probability distribution model can be set according to the specific engineering situation. For example, It can be set according to the accuracy requirements, for example, it can be set to . ~ , This indicates the total number of load cases. For higher accuracy requirements, Larger values ​​can also be taken. When multiple load conditions are independent of each other, a uniform distribution is preferred for the probability distribution model, i.e. In each segment, the probability of each segment being selected is the same.

[0049] Step (7): Based on the probability distribution model in step (6), randomly select a sample from the 1-second segmented signal of each single load condition and synthesize it into a 1-second segmented signal under multiple load conditions. The calculation formula is:

[0050]

[0051] In the formula, Indicates the kth single working condition A sample randomly selected from a 1-second segment of signal. That is, from the sequence The serial number is randomly selected from the list.

[0052] Step (8): Calculate the 1-second segmented signal under the multi-load condition. root mean square acceleration The calculation formula is:

[0053]

[0054] Step (9): Calculate the root mean square of the acceleration. Z-level The calculation formula is:

[0055]

[0056] In the formula, The reference acceleration can be 1×10⁻⁶. -6 m / s 2 .

[0057] Step (10): Repeat the calculation process described in steps (6) to (9). Next, that is, to proceed Second sampling and The Z-level vibration was calculated and obtained. indivual .

[0058] Among them, the The sampling and calculation processes are independent of each other and can be completed in parallel, either all at once or in batches.

[0059] Step (11), set the guarantee rate The result obtained in step (10) indivual Sort by size from smallest to largest and take the first... A sample is used as a representative value of the Z vibration level for vibration comfort evaluation.

[0060] Wherein, the guarantee rate The value should be set according to the specific project conditions, and it is recommended to take a value of 0.6 to 0.99. If the vibration control requirements are strict, a larger value should be taken. When evaluating vibration comfort, the representative value of Z vibration level obtained in step (11) can be compared with the Z vibration level limit specified in relevant specifications or standards to determine whether the requirements are met.

[0061] It should be noted that the calculation process in steps (1)-(11) is an evaluation process for one measuring point. When evaluating multiple measuring points, the evaluation process for each point is independent of each other and can be carried out in parallel. Depending on the computer performance, the evaluation can be completed at once or in batches to achieve efficient evaluation.

[0062] Example

[0063] Taking the vehicle-induced vibration analysis of buildings surrounding a comprehensive transportation hub as an example, the method of this application is illustrated. The finite element model is shown in the figure. The site includes two high-rise office buildings, A1 and A2, and a multi-story podium. The rail transit lines include high-speed rail, intercity express rail, and subway lines 2, 6, and 17.

[0064] Considering the combination of five single load conditions, the Z-level of a total of 4738 nodes on the first floor of the podium building under the five load conditions was calculated, and vibration comfort was evaluated. According to step (1) of this application, linear dynamic time history analysis was performed using the direct integration method to calculate the response time history of the first floor of the podium building under the five single load conditions. The sampling frequency was 200Hz, and the number of discrete points of the obtained response time history is shown in the figure.

[0065] List of multi-vehicle operating conditions

[0066] Train operating conditions Model Number of discrete points in response time history 350km / h mainline station Fuxing bullet train 1563 Intercity railway station entry CRH6 type 6387 Metro Line 2 entering the station Type B 5158 Metro Line 6 entering the station Type B 5158 Metro Line 17 entering the station CRH6 type 5241

[0067] For each node, extract its response time history under five single load conditions and calculate it according to steps (2)-(11) of this application. Among them: total number of sampling times The threshold value is 500,000; a uniform distribution is used in the probability model; two guarantee rates, 0.95 and 0.99, are used to evaluate vibration comfort. The calculation is performed in parallel mode, analyzing all nodes simultaneously, with the sampling and Z-level calculation for each node completed in one operation.

[0068] Taking a representative node with a high vibration level as an example, the frequency distribution and cumulative distribution function of the Z-level of 500,000 random samples are shown as follows. Figure 3 The horizontal axis represents the Z-level vibration, measured in dB; the vertical axis represents the frequency. Figure 4The horizontal axis represents the Z-level vibration, in dB; the vertical axis represents the cumulative distribution function. It can be seen that the Z-level vibration at this node has a wide distribution, ranging from 45 to 70 dB. If the traditional finite element analysis method is used, applying five different load conditions to the model and performing time history calculations, the result obtained is only... Figure 3 A few samples in the study are not statistically representative and therefore cannot truly reflect the spatiotemporal randomness of multiple vibration sources.

[0069] When the guarantee rate is 95% and 99%, the Z-vibration magnitude cloud diagrams of the first floor of the podium are as follows: Figure 5 and Figure 6 As shown, the spatial distribution of Z-level vibrations at different guarantee rates exhibits similarities, with higher vibration levels observed in floor slabs closer to the train tracks, particularly on the high-speed rail side. Furthermore, the Z-level vibration at a 99% guarantee rate is approximately 3 dB higher than that at a 95% guarantee rate, making it easier to approach the limit during vibration evaluation and representing a more stringent level of vibration control. On the other hand, a 99% guarantee rate implies an exceedance probability of only 1%, making the occurrence of vibrations highly unlikely. Therefore, it is recommended that when conducting vibration comfort evaluations in practical engineering projects, a balance between economy and comfort should be struck, and an appropriate guarantee rate level should be selected.

[0070] 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 probabilistic method for evaluating building vibration comfort under multiple load conditions, characterized in that: Includes the following steps: (1) Calculate the building's vibration acceleration data over a period of time under each single load condition based on the building's structural model or by recording the acceleration data using an accelerometer, and obtain the original acceleration time history signal for each single load condition. , , This indicates the total number of load cases; (2) The obtained original acceleration time history signal Perform a fast Fourier transform to obtain the original acceleration spectrum. ; (3) The obtained original acceleration spectrum Frequency weighting is performed to obtain the weighted acceleration spectrum. ; (4) The obtained weighted acceleration spectrum Perform an inverse fast Fourier transform to obtain the weighted acceleration time history signal of the complete duration. ; (5) Obtain the weighted acceleration time history signal of the complete duration. The signal is segmented into 1-second duration segments. , Adjacent 1-second segments of signal differ by one time step. This represents the total number of segments in the 1-second segmented signal for the k-th single load condition; (6) Set the total number of samplings And set the probability distribution model of the 1-second segmented signal; (7) Based on the probability distribution model in step (6), randomly select a sample from the 1-second segmented signal and synthesize it into a 1-second segmented signal under multiple load conditions. The calculation formula is: In the formula, Indicates the kth single working condition A sample randomly selected from a 1-second segment of signal. That is, the sequence number of the 1-second duration segment that was randomly selected; (8) Calculate the 1-second segmented signal under the multi-load condition. root mean square acceleration The calculation formula is: (9) Calculate the root mean square of the acceleration. Z-level The calculation formula is: In the formula, The reference acceleration is 1×10⁻⁶. -6 m / s 2 ; (10) Repeat the calculation process of steps (6) to (9). Next, that is, to proceed Second sampling and The Z-level vibration was calculated and obtained. indivual ; (11) Set the guarantee rate The result obtained in step (10) indivual Sort by size from smallest to largest and take the first... One sample is used as a representative value of the Z vibration level for the evaluation of vibration comfort of the building.

2. The method according to claim 1, characterized in that: In step (3), for the i-th frequency band, the weighted acceleration spectrum The calculation formula is: 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.

3. The method according to claim 1 or 2, characterized in that: In step (6), the total number of samplings Take as ~ , This represents the total number of load cases; the probability distribution model uses a uniform distribution.

4. The method according to claim 1 or 2, characterized in that: In step (10), The sampling and calculation processes are independent of each other and are carried out in parallel, either all at once or in batches.

5. The method according to claim 1 or 2, characterized in that: In step (11), the guarantee rate The value ranges from 0.6 to 0.99.

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