Earthquake motion simulation method for collaborative optimization of long-period multi-damping-ratio response spectrum and power spectrum

Abstract

The invention relates to a seismic oscillation simulation method for collaborative optimization of a long-period multi-damping-ratio response spectrum and a power spectrum, and the method comprises the following steps: determining a standard long-period response spectrum and a corresponding power spectrum density, forming a target power spectrum, carrying out the matching of seismic oscillation fitting of a long-period multi-damping-ratio target response spectrum-power spectrum, and carrying out the repeated iteration, and outputting the earthquake acceleration time history meeting the target requirement until the maximum difference value is smaller than the allowable error. According to the seismic oscillation simulation method, a reliable artificial vibration generation technology with higher applicability can be provided for seismic design of long-period structures such as super high-rise buildings and large water tanks.

Description

Technical Field

[0001] This application relates to a seismic motion simulation method that co-optimizes the response spectrum and power spectrum of long-period multi-damping ratio. Background Technology

[0002] A reasonable seismic motion time history is a prerequisite for seismic design of engineering structures. With the rapid development of long-period sensitive structures such as super high-rise buildings, long-span bridges, and nuclear power plant water tanks, the 0.15Hz-25Hz seismic motion frequency band, which is the focus of traditional seismic design, is no longer sufficient. In strong earthquakes, long-period structures such as cooling water tanks in nuclear power plants will suffer severe damage. One of the main causes of failure in such long-period structures is liquid sloshing, that is, the large-scale sloshing of liquid inside the tank under seismic action. Especially when the seismic motion contains significant long-period components, the liquid inside the tank is prone to resonance with the tank body, causing violent liquid surface fluctuations and impacts.

[0003] Furthermore, nuclear power equipment involves a wide range of damping ratios, ranging from 0.5% to 20%. Therefore, existing technologies require that the earthquake time history simultaneously match multiple damping ratio response spectra and satisfy power spectrum statistical characteristics. Long-period earthquakes are dominated by low-frequency energy, with the energy in the 0.1–1 Hz frequency band accounting for more than 40%, and the total duration and steady-state duration of the earthquakes are relatively long.

[0004] Traditional methods for seismic motion simulation have the following problems. First, existing seismic power spectrum models are mostly based on records with vibration periods no higher than 6s, and the standard power spectral density corresponding to the widely used NRC RG1.60 standard response spectrum only provides values ​​from 0.3 to 24Hz. Second, current mainstream design seismic motion time history fitting algorithms match the target response spectrum by adjusting the Fourier amplitude spectrum, but they mostly focus on matching the response spectrum with a single damping ratio (usually 5%), and adjusting in the frequency domain cannot achieve amplitude-phase decoupling.

[0005] Therefore, there is an urgent need to develop an efficient collaborative optimization algorithm that can match the response spectrum-power spectrum of long-period multi-damping ratio structures in order to meet the seismic design requirements of long-period sensitive structures. Summary of the Invention

[0006] The purpose of this application is to design a seismic motion simulation method that co-optimizes long-period multi-damping ratio response spectrum and power spectrum. This is achieved by establishing a long-period standard response spectrum with a vibration period up to 20s and a corresponding standard power spectral density model, and by presenting a long-period multi-damping ratio response spectrum-power spectrum co-optimization algorithm. This proposes a seismic motion simulation method that combines physical mechanisms with data-driven approaches. The seismic motion simulation method of this application can provide a reliable and more applicable artificial seismic motion generation technology for the seismic design of long-period structures such as large water tanks.

[0007] This application relates to a seismic motion simulation method that coordinates the optimization of long-period multi-damping ratio response spectrum and power spectrum, comprising the following steps:

[0008] (1) Based on the analysis of the non-stationary characteristics and long duration characteristics of long-period ground motion, a reliable acceleration record dataset with long-period characteristics was selected and established.

[0009] (2) Based on the statistics and analysis of seismic acceleration, the NRC RG1.60 standard response spectrum is extended to the range of vibration period of 20s, and a corresponding standard power spectral density model is established, which is selected according to the requirements of the long period component of the simulated ground motion.

[0010] (3) Based on the standard response spectrum S0(f) and the corresponding standard power spectrum P0(f), the target acceleration response spectrum S is obtained. a (target power spectral density of f;

[0011] (4) The calculation of the matching multi-damping ratio response spectrum and power spectrum is transformed into a multi-objective optimization model. Then, adaptive weights are used to coordinate the matching priority of different damping ratio targets, and the target response spectrum is discretized into N periodic control points, namely T1, T2, ... T i ,…T N The target response spectrum of multiple damping ratios forms a target matrix composed of damping ratios and discrete periodic points, i.e.

[0012]

[0013] Among them, SA T (ζ j ,T i ) represents the damping ratio ζ j Period T i Spectral acceleration values;

[0014] The target power spectral density forms a corresponding target vector according to the periodic discrete points, that is...

[0015] P T =[P T (T1) … P T (T i ... P T (T N )];

[0016] (7) Define the objective functions for optimizing the reaction spectrum and power spectral density;

[0017] (8) For a discrete periodic point T i By superimposing incremental time histories to match spectral acceleration values ​​with different damping ratios, the corrected acceleration time histories a are obtained. i (t);

[0018] (7) The obtained acceleration time history a i (t) is used as the input variable to determine the power spectral density curve, and the incremental time history is superimposed until the average power spectrum meets the requirements.

[0019] (8) a i (t) is used as the acceleration time history before the (i+1)th cycle, and the iteration is repeated until one cycle for all cycles is completed;

[0020] (9) Iterate through the above loop until the maximum difference value is less than the allowable error, and output the seismic acceleration time history that meets the target requirements.

[0021] In step (2), the established standard response spectrum model is as follows: the acceleration response spectra corresponding to a damping ratio of 5% and period values ​​of 0.03, 0.111, 0.40, and 20.0 seconds are 1g, 2.61g, 3.13g, and 0.125g, respectively.

[0022] The established standard power spectral density model is as follows:

[0023] or

[0024]

[0025] In step (6), the acceleration time history after the i-th period is fitted as follows:

[0026] a i (t=a i-1 (t+Δa i (t) (1)

[0027] Among them, a i-1 (t) represents the acceleration time history of the (i-1)th cycle; Δa i (t is the incremental acceleration in the i-th period, and its calculation formula is:

[0028] Δa i (t=r·B eq (t,ω i )h(t m -t) (2)

[0029] Where r is the scaling factor; ω i =2π / T i and B eq (t,ω i ) is used to maintain the initial motion at frequency ω i The time modulation function with time-varying characteristics; h(t) m-t) is constructed using unit incremental acceleration and is the unit impulse response function of a damped single-degree-of-freedom system, i.e.:

[0030]

[0031] In the formula, ξ is the damping ratio; It is a damped vibration frequency; It is the acceleration time history h(t) m The initial phase of -t).

[0032] In formula (2), the scaling factor r is calculated using the following formula:

[0033] ΔSA(T i ) = SA T (T i )-SA C (T i (4)

[0034] ΔSA(T i )=Cr (5)

[0035]

[0036]

[0037] In formula (4), ΔSA(T) represents i ) for calculating spectrum SA C (T i ) and target spectrum SA T (T i The difference in spectral acceleration at the i-th period is represented by ΔSA(T) in formula (7). i ) equals the incremental time history at t m The response acceleration at time t, where t m It is a i-1 The peak response time of (t). Attached Figure Description

[0038] Figure 1 This is a flowchart illustrating the seismic motion simulation method of this application.

[0039] Figure 2 This is a schematic diagram of the target response spectrum with multiple damping ratios in the embodiment.

[0040] Figure 3 This is a time-frequency characteristic diagram of the fitted acceleration time history in the embodiment.

[0041] Figure 4 This is a schematic diagram illustrating the fitting of the target reaction spectrum in the embodiment.

[0042] Figure 5 This is a schematic diagram illustrating the fitting of the power spectrum in the embodiment. Detailed Implementation

[0043] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in detail below with reference to the accompanying drawings. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of this application can be arbitrarily combined with each other; the terms "long" and "short" in this application are only for comparative purposes and do not represent a limitation on their respective numerical ranges.

[0044] According to the seismic motion simulation method of this application, which involves synergistic optimization of long-period multi-damping ratio response spectrum and power spectrum, the method includes the following steps:

[0045] (1) Based on the analysis of the non-stationary characteristics and long duration characteristics of long-period ground motion, a reliable acceleration record dataset with long-period characteristics was selected and established.

[0046] (2) Based on the statistics and analysis of seismic acceleration, the NRC RG1.60 standard response spectrum is extended to the range of vibration period of 20s, and a corresponding standard power spectral density model is established, which is selected according to the requirements of the long period component of the simulated ground motion.

[0047] (3) Based on the standard response spectrum S0(f) and the corresponding standard power spectrum P0(f), the target acceleration response spectrum S is obtained. a (target power spectral density of f;

[0048] (4) The calculation of the matching multi-damping ratio response spectrum and power spectrum is transformed into a multi-objective optimization model. Then, adaptive weights are used to coordinate the matching priority of different damping ratio targets, and the target response spectrum is discretized into N periodic control points, namely T1, T2, ... T i ,…T N The target response spectrum of multiple damping ratios forms a target matrix composed of damping ratios and discrete periodic points, i.e.

[0049]

[0050] Among them, SA T (ζ j ,T i ) represents the damping ratio ζ j Period T i Spectral acceleration values;

[0051] The target power spectral density forms a corresponding target vector according to the periodic discrete points, that is...

[0052] P T =[P T (T1) … PT (T i ... P T (T N )];

[0053] (5) Define the objective functions for optimizing the reaction spectrum and power spectral density;

[0054] (6) For a discrete periodic point T i By superimposing incremental time histories to match spectral acceleration values ​​with different damping ratios, the corrected acceleration time histories a are obtained. i (t);

[0055] (7) The adjusted acceleration time history a i (t is used as an input variable to determine the power spectral density (PSD) curve, and the incremental time history is superimposed until the average power spectrum meets the requirements.)

[0056] (8) a i (t) is used as the acceleration time history before the (i+1)th cycle, and the iteration is repeated until one cycle for all cycles is completed;

[0057] (9) Iterate through the above loop until the maximum difference value is less than the allowable error, and output the seismic acceleration time history that meets the target requirements.

[0058] According to the seismic motion simulation method based on the synergistic optimization of long-period response spectrum and power spectrum of this application, the following specific implementation steps can be adopted:

[0059] Step 1: Determine the standard long-period response spectrum and the corresponding power spectral density (PSD).

[0060] First, based on the analysis of the non-stationary and long-duration characteristics of long-period ground motions, a reliable acceleration record dataset with long-period characteristics was selected and established, resulting in acceleration records rich in long-period components. Then, based on the statistics and analysis of the acceleration of actual earthquake records, the NRC RG1.60 standard response spectrum was extended to 20s, as shown in Table 1, and two corresponding standard power spectral density models were established, as shown in formulas (1) and (2). One of them was selected according to the requirement for the long-period components of the simulated ground motion. For example, if rich low-frequency components of the ground motion are required, formula (2) is selected. Otherwise, formula (1) is selected. In formulas (1) and (2), f represents the range of ground motion frequencies, and P0(f) represents the standard power spectrum.

[0061] Table 1. Horizontal long-period standard acceleration response spectrum (5% damping ratio)

[0062]

[0063]

[0064]

[0065] or,

[0066]

[0067] Step 2: Forming the target power spectral density

[0068] Based on the standard response spectrum S0(f) and the corresponding standard power spectrum P0(f), the acceleration response spectrum S is obtained according to equation (3). a (the power spectral density of f, i.e.)

[0069]

[0070] Among them, a max The peak acceleration over time is S0(f); S0(f) is the standard response spectrum (in terms of a). max =1.0g calibration), specific values ​​can be found in Table 1; P0(f) is the standard power spectrum corresponding to the standard reaction spectrum.

[0071] Step 3: Simultaneously match the long-period multi-damping ratio response spectrum-power spectrum for seismic motion fitting.

[0072] 1. Set the target vector:

[0073] The calculation of matching response spectra and power spectra with different damping ratios is transformed into a multi-objective optimization model. Then, adaptive weights are used to coordinate the matching priorities of targets with different damping ratios. The target response spectrum is discretized into N periodic control points, namely T1, T2, ... T. i ,…T N The target response spectrum with multiple damping ratios forms a target matrix composed of damping ratios and discrete periodic points, i.e.

[0074]

[0075] Among them, SA T (ζ j ,T i ) represents the damping ratio ζ j Period T i The spectral acceleration value.

[0076] Similarly, the target power spectral density forms a corresponding target vector according to the periodic discrete points, i.e.

[0077] P T =[P T (T1) … P T (T i ... P T (T N )]

[0078] 2. Define the optimization objective function

[0079] The objective function used to adjust the matching accuracy is defined as:

[0080]

[0081] In the formula, SA T (ζ j ,T i SA represents the target value of spectral acceleration. C (ζ j ,T i () represents the simulated value.

[0082] For power spectral density, the objective function for controlling the power spectrum is defined as:

[0083] P C (T i )-P T (T i )≥0

[0084] In the formula, P C (T i Period T i The average power spectrum at that point, i.e., taking the frequency band [T] i -0.2T i ,T i +0.2T i Power spectral density P(T) within ] i Average value; P T (T i ) is the target power spectrum.

[0085] 3. Iterative optimization based on the objective function

[0086] When performing ground motion fitting, because there are multiple objectives to be met, it is necessary to perform ground motion fitting in a hierarchical manner, and the iterative process is as follows: Figure 1 As shown. More specifically, the iterative optimization method based on the objective function in this application includes the following steps:

[0087] (3.1) For a discrete periodic point T i First, follow the steps below to match the spectral acceleration values ​​for different damping ratios, thus completing the target SA. T (ζ1,T i ) to SA T (ζ M ,T i By fitting the data, the corrected acceleration time history a is obtained. i (t).

[0088] The specific matching steps are as follows: Assume that before fitting the i-th period, the acceleration time history is a. i-1 (t), current spectrum SA C (T i ) and target spectrum SA T (T i The difference in spectral acceleration at the i-th period is:

[0089] ΔSA(T i ) = SA T (T i )-SA C (T i (4)

[0090] Then, ΔSA(T) i It should be equal to the incremental time history at t m The response acceleration at time t, where t m It is a i-1 The peak response time of (t) is:

[0091]

[0092] Where, Δa i (t) represents the incremental acceleration in the i-th period, which can be obtained by multiplying the unit incremental acceleration by the scaling factor r, i.e.:

[0093] Δa i (t=r·B eq (t,ω i )h(t m -t) (6)

[0094] In the above formula, ω i =2π / T i and B eq (t,ω i ) is used to maintain the initial motion at frequency ω i The time modulation function with time-varying characteristics; h(t) m -t) is constructed using unit incremental acceleration, because it is the unit impulse response function of a damped single-degree-of-freedom system, i.e.:

[0095]

[0096] In the formula, ξ is the damping ratio; It is a damped vibration frequency; It is the acceleration time history h(t) m The initial phase of -t).

[0097] According to equations (4)-(6), we can obtain

[0098] ΔSA(T i)=C·r (8)

[0099] Wherein, C essentially represents the time history of unit increment acceleration over time t. m The response acceleration at time t, i.e.

[0100]

[0101] After calculating C, the scaling factor r can be obtained from equation (8), and then Δa can be calculated from equation (6). i (t). Subsequently, the acceleration time history after the i-th cycle is fitted as follows:

[0102] a i (t=a i-1 (t+Δa i (t) (10)

[0103] (3.2) The adjusted acceleration time history a i (t) is used as an input variable to determine the PSD curve.

[0104] For the i-th period T i Calculate the power spectrum P C (T i ) and target power spectrum P T (T i The difference is:

[0105] P(T i ) = P C (T i )-P T (T i (11)

[0106] In the formula, P C (T i Period T i The average power spectrum at the specified frequency band [T] is taken. i -0.2T i ,T i +0.2T i Power spectral density P(T) within ] i Average value; P T (T i ) is the target power spectrum.

[0107] We only consider the power spectrum during the stable phase of a strong earthquake, specifically between times t1 and t2, and therefore only consider the acceleration increment during this stable phase; the rest is assumed to be zero. If ΔSP(T i If ) < 0, then the power spectrum is adjusted as follows, with the adjustment time history... According to the time t when the response peak occurs m Defined as:

[0108] When t m ≤ t1,

[0109]

[0110] where β2 is the phase corresponding to the time (t2 + t m ) / 2.

[0111] [[ID=1s]]When t m > t2,

[0112]

[0113] where β1 is the phase corresponding to the time (t1 + t m ) / 2.

[0114] When t1 < t m < t2,

[0115]

[0116] Then the acceleration time history after the adjustment of the i-th cycle is: <000044s>

[0118] In the formula, δ is the adjustment coefficient. It can start from a small value according to the situation of meeting the target power spectrum, and gradually adjust the incremental time history until the average power spectrum meets the requirements. [[ID=ss]]

[0119] Taking a<0000s71>(t) as the acceleration time history before fitting the (i + 1)-th cycle, and repeating the steps of formulas (14) - (15), a i+1 (t) can be obtained until one cycle of all cycles is completed. Iteratively execute the above cycle until the maximum difference value is less than the allowable error.

[0120] Since the envelope function B eq (t, ω<00001s4>​​​​​​​​The long-period response spectrum (20s) with multiple damping ratios shown is used as the target for seismic acceleration time history simulation. In the ground motion fitting, it is necessary to simultaneously match the acceleration response spectra with six damping ratios of 0.005, 0.02, 0.03, 0.04, 0.05 and 0.07, with a peak ground acceleration (PGA) of 0.2g.

[0123] To ensure that the artificially fitted ground motions satisfy multiple fitting objectives while preserving the non-stationary characteristics of ground motions at a specific site, actual seismic acceleration records were selected as the initial ground motions, and ground motion fitting was performed according to the aforementioned fitting method. The control period of the response spectrum was discretized into 84 control points within the range of [0.03s-20s], uniformly distributed on a logarithmic coordinate system. In the ground motion fitting, the time step was set to 0.005 seconds, with a total duration of approximately 68.0 seconds. Following the aforementioned ground motion adjustment method, adjustments were first made to the 84 period points (504 target values) for 6 damping ratios, followed by adjustments to the 84 power spectrum target values, with the order of the target values ​​optimized during iteration.

[0124] Figure 3 The fitted acceleration time history is given, and the steady-state duration is calculated to be about 14.3 s based on 5% to 75% of the Arias intensity. It can be seen from the dominant frequency curve and time-frequency power spectrum of the fitted ground motion that the fitted ground motion has well preserved the characteristics of long-period ground motion. Figure 4 The figure shows the fitting of acceleration time history to the response spectrum of six damping ratios. For any target response with any damping ratio, the number of calculated spectral acceleration values ​​lower than the target response spectrum does not exceed five, and the maximum relative error of values ​​lower than the target response spectrum is 6.3%. Figure 5 The average power spectral density curve of the fitted seismic acceleration time history stationary segment is given as the envelope of 80% of the target power spectrum. It can be seen that the target power spectrum can be completely enveloped in the considered frequency band.

[0125] This application proposes a seismic power spectrum (PSD) model capable of accurately matching long-period multi-damped ratio response spectra up to 20 s, and develops a seismic motion simulation method for synchronously matching multi-damped ratio response spectra and PSDs. First, based on statistical analysis of seismic acceleration rich in long-period components, the NRC RG1.60 standard response spectrum is extended to 20 s, and a corresponding standard PSD model is established. Then, through a multi-objective optimization framework, the problem of matching multi-damped ratio response spectra and power spectra is transformed into a collaborative optimization model. An adaptive dynamic weighting strategy coordinates the priority of multi-damped ratio (0.5%-10%) targets, and the PSD parameters are adjusted to preserve the non-stationary characteristics of seismic motion, achieving high-precision synchronous matching of long-period multi-damped ratio response spectra. Numerical examples show that this method can simultaneously match six damping ratio target spectra, with a relative fitting error ≤10% in the control frequency band from 0.03 s to 20 s, significantly improving the collaborative matching accuracy of long-period multi-damped ratio response spectra, and effectively reproducing the time history characteristics of long-period acceleration in the generated seismic motion. This application can provide a more reliable artificial seismic input for long-period structures such as large water tanks in nuclear power plants, thereby contributing to their seismic design.

[0126] Although the embodiments disclosed in this application are as described above, the content is merely for the purpose of facilitating understanding of this application and is not intended to limit this application. Any person skilled in the art to which this application pertains may make any modifications and changes in the form and details of the implementation without departing from the spirit and scope disclosed in this application; however, the scope of patent protection of this application shall still be determined by the scope defined in the appended claims.

Claims

1. A seismic motion simulation method that co-optimizes long-period multi-damping ratio response spectrum and power spectrum, characterized in that, Includes the following steps: (1) Based on the analysis of the non-stationary characteristics and long duration characteristics of long-period ground motion, a reliable acceleration record dataset with long-period characteristics was selected and established. (2) Based on the statistics and analysis of seismic acceleration, the NRC RG1.60 standard response spectrum is extended to the range of vibration period of 20s, and a corresponding standard power spectral density model is established, which is selected according to the requirements of the long period component of the simulated ground motion. (3) Based on the standard response spectrum S0(f) and the corresponding standard power spectrum P0(f), the target acceleration response spectrum S is obtained. a (f) Target power spectral density; (4) The calculation of the matching multi-damping ratio response spectrum and power spectrum is transformed into a multi-objective optimization model. Then, adaptive weights are used to coordinate the matching priority of different damping ratio targets, and the target response spectrum is discretized into N periodic control points, namely T1, T2, ... T i ,…T N The target response spectrum of multiple damping ratios forms a target matrix composed of damping ratios and discrete periodic points, i.e. Among them, SA T (ζ j ,T i ) represents the damping ratio ζ j Period T i Spectral acceleration values; The target power spectral density forms a corresponding target vector according to the periodic discrete points, that is... P T =[P T (T1) … P T (T i ) … P T (T N )]; (5) Define the objective functions for optimizing the reaction spectrum and power spectral density; (6) For a discrete periodic point T i By superimposing incremental time histories to match spectral acceleration values ​​with different damping ratios, the corrected acceleration time histories a are obtained. i (t); (7) The obtained acceleration time history a i (t) is used as the input variable to determine the power spectral density curve, and the incremental time history is superimposed until the average power spectrum meets the requirements. (8) a i (t) is used as the acceleration time history before the (i+1)th cycle, and the iteration is repeated until one cycle for all cycles is completed; (9) Iterate through the above loop until the maximum difference value is less than the allowable error, and output the seismic acceleration time history that meets the target requirements.

2. The seismic motion simulation method according to claim 1, characterized in that, In step (2), The established standard response spectrum model is as follows: the acceleration response spectra corresponding to a damping ratio of 5% and period values ​​of 0.03, 0.111, 0.40, and 20.0 seconds are 1g, 2.61g, 3.13g, and 0.125g, respectively. The established standard power spectral density model is as follows: or 3. The seismic motion simulation method according to claim 1 or 2, characterized in that, In step (6), the acceleration time history after the i-th period is fitted as follows: a i (t)=a i-1 (t)+Δa i (t) (1) Among them, a i-1 (t) represents the acceleration time history of the (i-1)th cycle; Δa i (t) represents the incremental acceleration in the i-th period, and its calculation formula is: Δa i (t)=rB eq (t,ω i )h(t m -t) (2) Where r is the scaling factor; ω i =2π / T i and B eq (t,ω i ) is used to maintain the initial motion at frequency ω i The time modulation function with time-varying characteristics; h(t) m -t) is constructed using unit incremental acceleration and is the unit impulse response function of a damped single-degree-of-freedom system, i.e.: In the formula, ξ is the damping ratio; It is a damped vibration frequency; It is the acceleration time history h(t) m The initial phase of -t).

4. The seismic motion simulation method according to claim 3, characterized in that, In formula (2), the scaling factor r is calculated by the following formula: ΔSA(T i )=SA T (T i )-SA C (T i ) (4) ΔSA(T i )=C·r (5) In formula (4), ΔSA(T) represents i ) for calculating spectrum SA C (T i ) and target spectrum SA T (T i The difference in spectral acceleration at the i-th period is represented by ΔSA(T) in formula (7). i ) equals the incremental time history at t m The response acceleration at time t, where t m It is a i-1 The peak response time of (t).

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