Journal of Engineering Geology, Vol.6, No.2, Autumn 2012 & Winter 2013

Effect of Matching Period-Interval Variation on Strong Ground Motion Scaling

*M. Shahrouzi, P. Derakhshani: Department of Engineering, Kharazmi University

Received: 8 May 2012 Revised 23 Jan 2013

Abstract

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Downloaded from jeg.khu.ac.ir at 11:37 IRST on Saturday October 28th 2017

Time history analyses as crucial means in many earthquake engineering applications are highly dependent to characteristics of the seismic excitation record so that the resulting responses may vary from case to case. Strong ground motion scaling is a known codified solution to reduce such a dependency and increase reliability of time history analyses. The well-known code practice may result in highly non-economic designs due to considerable error in the spectra scaled to match the target code spectrum. This problem is formulated here in an optimization framework with the scaling coefficients as the design variables. Harmony search as a recent meta-heuristic algorithm is utilized to solve the problem and is applied to the treated examples. Using a variety of target period ranges the scaling error is evaluated and studied after more unified via optimization. The effect of base structural period and interval variation on the scaling error is then studied in addition to considerable error decrease with respect to traditional code-based procedure. The results also show dependency of spectral matching error to the period-interval elongation/variation, the base-structural period and more error sensitivity for narrow-band resonance with the filtered records on softer soil types.

KeyWords: Strong Ground Motion, Optimal Spectral Scaling, Matching Period

Interval, Harmony Search

*Corresponding author [email protected]

Introduction

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Downloaded from jeg.khu.ac.ir at 11:37 IRST on Saturday October 28th 2017

Seismic excitation for structural and geotechnical applications can be expressed in the form of recorded earthquake accelerograms. In this regard some sources for providing time-history records can be distinguished: recorded experienced earthquakes, statistically simulated accelerograms or model-based artificial records [1-3]. The first group is preferred in many practical cases because it conserves the frequency content and other characteristics of the real-world records in spite of artificial records. However, for a specific site the forthcoming earthquake cannot be deterministically predicted yet, even from the previous earthquakes.

Therefore, statistical analyses are performed to derive mean plus one standard deviation spectra. They are further smoothed and classified considering simplified interaction effects of various soil types in the design codes and amended as the mere legal source of seismic loading in terms of design spectra [3, 4]. Such design spectra are only sufficient for modal analyses of linear systems [5]. However, many practical applications needs time history analyses of soil or structural system as numerical source of seismic excitation [6-8]. Thus, a procedure to make a recorded time history accelerogram compatible with the code-based design spectrum for the site of construction with specific soil type is needed [9-11]. It is called the scaling procedure already offered by many codes of practice which is being reviewed in detail in the next section.

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According to such a procedure, the averaged spectrum extracted from a number of time-history records is scaled to match the design spectrum with in a prescribed period range. The present study first formulates it as an optimization problem to minimize such a spectral compatibility error and then concerns effect of the target period range on it. The recently developed Harmony Search algorithm is thus specialized for this optimization problem [12, 13]. A variety of period range classes are then considered for further parametric study in order to derive the error curve for each distinct class and soil-type. Final concluding remarks are then driven discussing and comparing the achieved results.

The Scaling Procedure

According to the current design codes [4-5], seismic excitation is legally introduced in terms of a few design spectra rather than timehistory records. It is due to the fact that no special time-history can be exactly predicted for all sites of construction, but design spectra are more reliable when generated based on extensive statistical operations on several previous earthquakes over the world or country. Such wellknown seismic design codes have thus offered a procedure to modify available set of accelerograms for a specific site of construction so that their corresponding spectra are compatible with the legal design code spectra.

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Downloaded from jeg.khu.ac.ir at 11:37 IRST on Saturday October 28th 2017

The procedure is called ground motion scaling and is given via following steps according to the Iranian standard 2800-84 [4]. According to it, N pairs of horizontal earthquake components are normalized to their Peak Ground Acceleration, PGA. Then response spectra of each pair is calculated and combined to generate a Square Root of Sum of Square, SRSS spectrum. Average of these N SRSS spectra are then compared with 1.4 times the standard spectrum within a, Matching Period Interval, MPI and scaled so that not fall below such target in the employed MPI. The resulting scale factors are then used to amplify the records before being employed as time history analysis input.

The aforementioned single-value scaling procedure is preferred to other simulation methods because it only amplifies the accelerogram magnitude preserving its frequency content and non-stationary characteristics of the initial time history. As can be realized in such scaling procedure, the resulted scale is dependent to the employed MPI; given [0.2TStr ,1.5TStr ]due to Iran seismic design standard-2800. The base period TStr denotes natural period of the structure and is determined computationally considering empirical design code relations [4]. In addition, the design code allows taking simple average as mean spectrum that usually results in non-economic overconservative values for the scaled spectrum far larger than the target. Much better weighted mean coefficients can be search to reduce such a compatibility error via optimization as dealt in the next section of the present article.

Optimized Scaling Using Harmony Search

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As mentioned above, the compatibility of average scaled spectrum with the design target can be maximized by optimization. In this regard, the problem is formulated as below when the coefficients to compute such an optimal weighted average, are denoted by X; i.e., vector of optimal design variables:

T2 .SA (T)SAT arg et (T)

2750304-167124

MinimizeMatchingError(x1,…, xN ) 100T1SAT arg et (T) (1)

S.t.0 xi 1

N

xiSAi (T)

SA(T)

i1 (2)

N

.SAT arg et (T)

max{

} (3)

TSA(T)

Whereas SAT arg et (T) is spectrum given by the design code at any period; T. The spectral valueSAi (T) stands for the spectral SRSS

acceleration for each earthquake and SA(T) denotes the corresponding weighted average spectrum using scale factors: xi . The coefficient β is

used to insure SA(T)does not fall below SAT arg et (T) among periods in the interval T1toT2 .

Once the optimization problem is defined, an algorithm should be employed to search for its optimal vector of continuous scaling design variables xi in range (0, 1].

Harmony Search, HS, as a recent optimization algorithm is inspired by the method a musician makes new notes considering its Harmony Memory, HM [12]. As this algorithm is best suited for continuous search spaces, it is utilized to optimize the design variables of the scaling problem in the present work. The algorithm is implemented via the following steps:

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Initialize the harmony memory: pick k random vectors; X1, X2,

X3, … , Xk

Make a new vector X’. For each component x’i: Xi’=Xi rand() with probability phmcr pick the component from memory, with probability 1 − phmcr pick a new random value in the allowed

range.

Pitch adjustment: For each component x’i:

with probability ppar change x’i by a small amount, ± bw.rand. with probability 1 − ppar do nothing.

If X ‘ is better than the worst Xi in the memory, then replace Xi by X ‘.

Repeat from step 2 until a maximum number of iterations has been reached.

According to the above algorithm, required control parameters are distinguished as:

k, the size of the memory.

phmcr, the rate of choosing from memory, HM. ppar, the ‘pitch adjustment rate’.

bw, the ‘bandwidth’ or the amount of change for pitch

adjustments.

It is possible to vary the parameters as the search progresses; this gives an effect similar to simulated annealing. In the improved harmony search, ppar is increased linearly, while bw is decreased exponentially.

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The parameter values used in this study are listed in table 1 and fitness function of each coefficient group X is identified based on the resulting spectral matching error. The fitness function is taken Fitness(X)MatchingError(X) and is to be maximized to minimize the spectral matching error.

In order to make a comparison scaling result, a sample set of records are shown in Figures 1 and 2. As can be realized from Figure 1 the manual practice as code using similar weighting factors has led to the maximum compatibility error, while it is decreased by Genetic Algorithm, GA and more decreased by HS. GA parameters in this sample run are taken 90% for crossover and 5% for mutation probability thresholds where others are taken similar to HS parameters in Table 1.

As maximizing the fitness corresponds to minimizing the spectral matching error, its trace vs. iterations of the search is demonstrated in Figure 2. It is worth mentioning that the fittest design vector in each iteration is saved and replaced with the least fit one in the next iteration. According to Figure 2 HS fitness history stands higher than sample GA continuing its progress. This shows comparable and even better performance for HS with respect to well-known GA for such parameters in the treated scaling problem.

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Table1. Control parameters of the employed HS algorithm

Population Size (k) Phmcr Ppar Bandwidth, bw Number of

Iterations

10 0.90 0.30 2 1000

0

0.5

1

1.5

1.5

2

2.5

3

3.5

4

4.5

Period (sec)

Normalized Spa

Target

Manual

GA

HS

0

0.5

قیمت: تومان