A method for fitting ground motion response spectra without baseline drift

Abstract

The present invention discloses a method for fitting ground motion response spectra that can operate continuously and stably without baseline drift, belonging to the technical field of seismic safety assessment services. The present invention includes the following three parts: First, the triangular series superposition method is combined with the single-degree-of-freedom system recursion method to generate the initial time history; Second, the wavelet function superposition is combined with the step-by-step adjustment scheme to adjust the response spectrum error to the specified range; Third, the item-by-item analysis method is used to eliminate the time histories with correlation coefficients not meeting the requirements. The present invention uses the triangular series superposition method combined with the single-degree-of-freedom system recursion method to generate the initial time history, solving the problem of non-existent baseline drift in the initial time history. The present invention uses the wavelet function superposition combined with the step-by-step adjustment scheme to adjust the response spectrum error to the specified range, greatly improving the efficiency of time history fitting. The present invention uses the item-by-item analysis method to eliminate the time histories with correlation coefficients not meeting the requirements, without the need for manual elimination of time histories. The present invention is applicable to seismic safety assessment work, and can achieve ground motion time histories without baseline drift and operate continuously and stably.

Description

Technical Field

[0001] The present invention belongs to the technical field of seismic safety evaluation services, and particularly relates to a method for fitting ground motion response spectra without baseline drift. Background Art

[0002] Existing seismic design of building structures generally adopts the form of design response spectra. Ground motion response spectrum fitting means that, given a known response spectrum, a ground motion time history is synthesized such that the response spectrum of this time history is basically the same as the known response spectrum, with the difference in the response spectra controlled within a certain error range. Ground motion response spectrum fitting includes two parts. The first part is the determination of the initial ground motion time history, which generally uses two methods: the trigonometric series superposition method or actual natural ground motions. In seismic safety evaluation work, the trigonometric series superposition method is mainly used. The second part is the adjustment of the time history response spectrum, which usually uses the time domain superposition method and the overall approximation method of the response spectrum, with the time domain superposition method being the main one.

[0003] Currently, in seismic safety evaluation work, the ground motion response spectrum fitting software mainly consists of the ground motion synthesis modules in ESE, XQH, and SEC software. Among the current ground motion response spectrum fitting software, the ground motion synthesis module of ESE software uses the trigonometric series superposition method and the time domain superposition method. The ground motion synthesis module of XQH software uses the trigonometric series superposition method, the overall approximation of the response spectrum, and the time domain superposition method. The problem with these two systems is that the fitted time histories generally have varying degrees of baseline drift. The ground motion synthesis module in SEC software has improved the problem of baseline drift. It uses the method of baseline correction for the initial time history to remove baseline drift and superimposes zero-drift displacement wavelet functions, so that the fitted time history has no baseline drift problem.

[0004] However, the above three mainstream ground motion synthesis modules all have the problem of "stubborn points", that is, at a certain period point, after multiple iterations, the error of the response spectrum value no longer converges, or there is mutual interference with adjacent period points, resulting in the situation where the error of the response spectrum "fluctuates" repeatedly. This leads to the situation that for a certain time history, the response spectrum error cannot meet the specified requirements within the specified number of iterations, or the program loops iteratively for a long time and cannot reach the error limit requirement. At the same time, all three ground motion synthesis modules have the problem that the correlation coefficients between the fitted time histories are relatively large. In current seismic safety evaluation work, it is still necessary to manually eliminate the time histories whose correlation does not meet the requirements. Summary of the Invention

[0005] In view of the many problems existing in the above background art, the present invention aims to provide a method for fitting ground motion response spectra that can operate continuously and stably without baseline drift.

[0006] To this end, the present invention adopts the following technical solutions: A method for fitting ground motion response spectra that can operate continuously and stably without baseline drift, including the following three main parts:

[0007] In the first step, the trigonometric series superposition method is combined with the single-degree-of-freedom system recursion method to generate the initial time history.

[0008] In the second step, the wavelet function superposition is combined with the step-by-step adjustment scheme to adjust the response spectrum error to the specified range.

[0009] In the third step, the time histories with correlation coefficients not meeting the requirements are eliminated by the item-by-item analysis method.

[0010] The present invention can achieve the following beneficial effects: 1. The present invention combines the trigonometric series superposition method with the single-degree-of-freedom system recursion method to generate the initial time history, and there is no baseline drift problem in the initial time history. The present invention combines the wavelet function superposition with the step-by-step adjustment scheme to adjust the response spectrum error to the specified range, greatly improving the efficiency of time history fitting. The present invention eliminates the time histories with correlation coefficients not meeting the requirements by the item-by-item analysis method, without the need for manual elimination of time histories. 2. The present invention is applicable to seismic safety evaluation work, and can achieve that the fitted ground motion time history has no baseline drift, can operate continuously and stably. The present invention will not have the phenomenon of "infinite loop" during operation, does not limit the target response spectrum and the number of time history samples of the fitted ground motion, and the multiple time histories obtained by fitting meet the correlation requirements. At the same time, the efficiency of time history fitting of the present invention is greatly improved compared with existing products. Description of the Drawings

[0011] Figure 1 It is a schematic diagram of generating the initial time history in the first step of the present invention.

[0012] Figure 2 It is a schematic diagram of removing the baseline drift of the initial time history by using the single-degree-of-freedom system recursion method in the first step of the present invention.

[0013] Figure 3 It is a schematic diagram of the iterative adjustment process in the second step of the present invention.

[0014] Figure 4 It is a schematic diagram of the step-by-step adjustment scheme of the response spectrum deviation in the second step of the present invention.

[0015] Figure 5 It is a schematic diagram of the adjacent period linkage adjustment method.

[0016] Figure 6 It is a schematic diagram of eliminating the time histories with correlation coefficients not meeting the requirements by the item-by-item analysis method.

[0017] Figure 7 It is the implementation step flow of the method system of the present invention. Detailed Description of the Invention

[0018] The following describes in detail the specific implementation manners of the present invention with reference to the drawings. The described embodiments are only illustrative and explanatory of the present invention, and do not constitute the sole limitation of the present invention.

[0019] A method for fitting the seismic ground motion response spectrum that can operate continuously and stably without baseline drift, including the following three major parts

[0020] In the first step, the triangular series superposition method is combined with the single-degree-of-freedom system recursion method to generate the initial time history.

[0021] The initial time history a(t) generally adopts the following form:

[0022]

[0023] Among them, f(t) is the intensity envelope function:

[0024]

[0025] Ψ i is a random phase in the range of 0 to 2π;

[0026] n is the total number of angular frequency discrete points, ω i is the i-th angular frequency;

[0027] A i is the harmonic amplitude corresponding to the i-th angular frequency.

[0028] 1. Adjust the duration of the rising section of the low-frequency harmonics so that it is not less than one period. The end time of the steady section is determined according to the amplitude ratio and the envelope curve, and the duration of the steady section is increased. This method has a certain impact on the intensity envelope of the seismic ground motion time history, but generally the amplitude of the low-frequency harmonics is relatively small, and only adjusting the low-frequency part has a small impact on the overall situation.

[0029] 2. Use the single-degree-of-freedom system recursion method to process the harmonics of each angular frequency that have been processed for amplitude intensity envelope, and remove the baseline drift generated by the single harmonic due to the intensity envelope processing. Each angular frequency harmonic after processing is multiplied by the amplitude and then superimposed to generate the initial time history, and the initial time history then has no baseline drift problem.

[0030] Such as Figure 1As shown in the figure, the present invention adopts an innovative intensity envelope optimization method. By adjusting the duration of the rising segment of the low-frequency harmonic to be not less than one cycle, the end time of the stable segment is determined according to the amplitude ratio and the envelope curve, and the duration of the stable segment is increased. This method has a certain impact on the intensity envelope of the ground motion time history. The amplitude ratio of the low-frequency harmonic is relatively small, and the intensity envelope curve of the overall time history is mainly dominated by the high-frequency part. Only adjusting the intensity envelope curve of the low-frequency part has a small impact on the overall. In the adjustment of the time history envelope, the amplitude of the low-frequency harmonic is much smaller than that of the high-frequency, and the adjustment of the amplitude of the low-frequency harmonic has a small impact on the overall envelope. The present invention adopts the recursive method of a single-degree-of-freedom system to process each angular frequency harmonic after the amplitude intensity envelope processing, and removes the baseline drift generated by the single harmonic due to the intensity envelope processing. Each angular frequency harmonic after processing is multiplied by the amplitude and then superimposed to generate the initial time history, as Figure 2 shown, there is no baseline drift problem in the initial time history

[0031] In the second step, the wavelet function superposition joint step-by-step adjustment scheme is adopted to adjust the response spectrum error to the specified range.

[0032] For the initial random time history generated in the first step, there is a certain difference between its response spectrum value and the target value. The adjustment method is mainly the time domain superposition method. For the difference in the response spectrum at different periods, the time history sequence of the reverse difference amount is superimposed to make the response spectrum value approach the target value. In the prior art, the superimposed time history given the intensity envelope will inevitably generate baseline drift, and the response spectrum values at different period points are affected by other period points within a certain adjacent range. When the response spectrum errors at adjacent period points are opposite, "stubborn period points" that do not meet the requirements are likely to appear in the iterative adjustment process, causing the iterative process to fall into an infinite loop, as Figure 3 shown.

[0033] For the baseline drift in the present invention, the recursive method of a single-degree-of-freedom system in the initial time history can be used to remove it. Since the initial ground motion time history is formed by superimposing a large number of trigonometric function time series with random phases, the combination scheme of random phases determines the subsequent iterative rate, and the appearance of iterative "stubborn period points" becomes a random event, and its cause is difficult to accurately analyze with theoretical formulas. Through a large number of analyses, tests and studies, a step-by-step adjustment scheme can be adopted to classify and process different degrees of "stubborn period points", as Figure 4 shown, the specific methods and ideas are as follows:

[0034] 1. For the response spectrum error at each period point, generate a wavelet function time series corresponding to the period. The duration of the series is related to the period value, and the series is translated and reversed according to the response maximum moment corresponding to the response spectrum at this period. At the same time, the recursive method of a single-degree-of-freedom system is used to remove the drift of the series;

[0035] 2. First-level processing: Use wavelet function time series to perform time domain superposition processing on each periodic point that does not meet the error requirements, and perform iterative cycles. Within a certain number of cycles, when the errors of all periodic points meet the requirements, the program ends;

[0036] 3. Second level processing: When a certain level of processing still fails to meet the requirements after a certain number of cycles, it may be that the response spectrum error of the period point is adjusted too slowly, or the response spectrum errors of adjacent period points are "one after another". The adjacent period linkage adjustment method can be used to reduce the response spectrum error limit of other period points that may have an impact within a certain range near the period point, such as Figure 5 As shown, the purpose of reducing the response spectrum error of the periodic point is achieved;

[0037] 4. Third-level processing: When the secondary processing still fails to meet the requirements after a certain number of cycles, the adjacent cycle may have a major impact on the cycle point. The method of fine-tuning the superimposed wavelet function time series cycle can be used to perform dislocation adjustment;

[0038] 5. Fourth-level processing: When the third-level processing still fails to meet the requirements after a certain number of cycles, it means that there are stubborn points in the time-course phase combination scheme of the period point and a certain period range nearby. The phase random number of the initial time-course sequence within the local period range can be adjusted, and then the processing can be carried out step by step;

[0039] 6. Final processing: When the four-level processing still fails to meet the requirements after a certain number of cycles, it means that the overall random phase scheme of the initial time series does not meet the requirements. The initial random time series is regenerated and then processed step by step.

[0040] The third step is to use the item-by-item analysis method to eliminate the time series whose correlation coefficients do not meet the requirements.

[0041] In the second step, when there are multiple earthquake time histories that meet the response spectrum error, there may be a large correlation between them because the time histories are fitted using the random phase method. In order to ensure that there is a reasonable lack of correlation between the time histories, the correlation coefficient of the time histories is calculated using the line-by-line analysis method, that is, the current synthesized time histories and the completed time histories are analyzed and calculated line by line, such as Figure 6 As shown, the calculation formula is as follows:

[0042]

[0043] Among them, x 1 For time sequence 1, x 2 For time sequence 2, A 1 is the average value of sequence 1, A 2 is the average value of time series 2, σ 1 is the standard deviation of the time series, σ 2Standard deviation of the time history for two periods

[0044] When the correlation coefficients between the time history being synthesized and all completed time histories meet the requirements, the time history fitting ends; if not, a new initial time history phase randomization scheme is generated and the process continues with the second step.

[0045] The implementation system of the method of the present invention, as Figure 7 shown, inputs parameters such as the target response spectrum values, intensity envelope parameters, number of time history fittings, correlation coefficient limit values, etc. into the "parameter input module". The "initial time history generation module" and the "baseline drift removal module" generate an initial random ground motion time history using the input parameters. The "superposed time history module" analyzes the difference between the initial time history response spectrum and the target response spectrum and generates a wavelet function superposed time history sequence. The "step-by-step adjustment module" processes the time history in different levels according to different response spectrum differences and iteration times. The "time history correlation analysis module" calculates the correlation coefficients between the newly generated time history and the existing time histories, eliminates those that do not meet the standards, and finally outputs a time history file that meets the requirements and enters the next time history fitting process. When the number of fitted time histories reaches the requirement, the program stops.

[0046] The implementation steps of the time history fitting system are as follows:

[0047] 1) Enter the "parameter input module" and input the target time history parameters to be fitted, including the target response spectrum, error limit, time history envelope parameters, number of time history fittings, etc.;

[0048] 2) Enter the "initial time history generation module", use the random function and the intensity envelope function to generate non-repeating random phase angular frequency harmonics, use the "baseline drift removal module" to remove the baseline drift of the harmonics, and superimpose the harmonics after intensity amplitude to generate an initial time history;

[0049] 3) Enter the "superposed time history module", analyze the difference between the initial time history response spectrum and the target response spectrum, generate the corresponding wavelet function time history sequence, and perform superposition processing;

[0050] 4) Enter the "step-by-step adjustment module", analyze the change trend of the response spectrum difference through continuous iterative time history superposition processing, and perform time history adjustment at different levels;

[0051] 5) Enter the "time history correlation analysis module", perform pairwise correlation analysis between the newly generated time history and the existing time histories. When all meet the correlation requirements, output this time history; when not meeting the correlation requirements, eliminate this time history and enter the next time history fitting.

[0052] When the effective number of time history fittings reaches the requirement, the program stops.

[0053] The foregoing has shown and described the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments, and what is described in the above embodiments and the specification is only to illustrate the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements fall within the scope of the present invention claimed. The scope of the present invention claimed is defined by the appended claims and their equivalents.

Claims

1. A seismic response spectrum fitting method that can operate continuously and stably without baseline drift, characterized in that: The seismic response spectrum fitting method capable of continuous and stable operation without baseline drift includes the following three parts: In the first step, the trigonometric series superposition method combined with the single-degree-of-freedom system recursive method is used to generate the initial time history; The specific steps include: 1) By adjusting the duration of the rising phase of the low-frequency harmonic to be no less than one cycle, the end time of the stable phase is determined according to the amplitude ratio and the envelope curve, and the duration of the stable phase is increased; 2) Using the single degree of freedom system recursive method, the angular frequency harmonics that have been processed by the amplitude intensity envelope are processed to remove the baseline drift of the single harmonic caused by the intensity envelope processing; Each angular frequency harmonic after processing is multiplied by the amplitude and superimposed to generate the initial time course, and there is no baseline drift problem in the initial time course; In the second step, the response spectrum error is adjusted to a limited range by using the wavelet function superposition combined with step-by-step adjustment scheme; The specific steps include: 1) For the response spectrum error of each periodic point, a wavelet function time series of the corresponding period is generated. The duration of the series is related to the periodic value, and the series is translated and reversed according to the maximum response moment corresponding to the response spectrum of the periodic point. At the same time, the series is de-drifted using a single-degree-of-freedom system recursive method; 2) First-level processing: Use wavelet function time series to perform time domain superposition processing on each periodic point that does not meet the error requirements, and perform iterative cycles. Within a certain number of cycles, when the errors of all periodic points meet the requirements, the program ends; 3) Second level processing: When a certain number of cycles is reached and a certain level of processing still fails to meet the requirements, there is a slow adjustment of the response spectrum error at this period point. The adjacent period linkage adjustment method is used to achieve the purpose of reducing the response spectrum error at this period point; 4) Third-level processing: When the secondary processing still fails to meet the requirements after a certain number of cycles, the method of fine-tuning the superimposed wavelet function time series period is used to perform dislocation adjustment; 5) Fourth level processing: When the third level processing still fails to meet the requirements after a certain number of cycles, the phase random number of the initial program sequence within the local cycle range is adjusted, and then the processing is carried out step by step; 6) Final treatment: When the four-level treatment still fails to meet the requirements after a certain number of cycles, the initial random time schedule is regenerated and then the treatment is carried out step by step; The third step is to use the item-by-item analysis method to eliminate the time series whose correlation coefficients do not meet the requirements.

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