gjmas-2016-1-8 - Global journal of multidisciplinary and applied

Global journal of multidisciplinary and applied sciences
Available online at www.gjmas.com
©2016 GJMAS Journal-2016-4-1/1-8
ISSN 2313-6685 ©2016 GJMAS
A genetic based algorithm model to optimize the
nonlinear seismic site response for structural design
subjected earthquake provokes- A case study
Naser Azizi* and Abbas Abbaszadeh Shahri
Department of Civil Engineering, College of Civil Engineering, Islamic Azad University, Roudehen branch, Tehran,
Iran
Corresponding author: Naser Azizi
ABSTRACT: The genetic algorithm (GA) is a heuristic search that is routinely used to generate useful solutions to
optimization and search problems. It generates solutions to optimization problems using techniques inspired by
natural evolution, such as inheritance, mutation, selection, and crossover. GAs are one of the best ways to solve a
problem for which little is known. Therefore, considering to complexity of seismic response and related costs,
application of the GA can be an efficient tool. In the present study, an optimized developed artificial neural network
model using 59 datasets of geotechnical, dynamic soil properties and Ardabil earthquake data (1997, Iran) were
proposed and evaluated by statistical, mathematical and graph analysis criteria. Then, the model is optimized by GA
using a generated developed computer code in Matlab programming environment. The extracted results of seismic
response from GA were compared with conventional dynamic analysis and suitable accuracy as well as compatibility
has been observed. The proposed method showed and proved an alternative method that can solve the related problem
to data types, analysis time, mathematical simplifications as well as supporting the efficiency.
Keywords: genetic algorithm, optimization, analysis criteria, site response.
INTRODUCTION
In engineering practices, requirement of maximum benefit find a minimum cost design is highly considered and the trialand-error methods based have traditionally used. However, these approaches have not guaranteed optimal or near-optimal
designs, which is why researchers have been interested in optimization methods. Based on mathematical point of view,
optimization refers to finding the best vector from a set of feasible alternative vectors.
Selecting an optimized method for dynamic analysis of earthquake time history and scaling factor for the purpose of
nonlinear analysis has turned out to be one of the most important branches of the earthquake geotechnical and structural analysis
in civil engineering which derives great benefit from the optimization because these techniques can save a lot of costs in public
infrastructure construction and management that require enormous budget.
The traditional methods of search and optimization are too slow in finding a solution in a very complex search space, even
implemented in supercomputers (e.g. Bolt and Gregor, 1993; Berkeley et al., 2000). Therefore, in the recent years, various
methods have been suggested to estimate ground shaking and earthquake related parameters to solve optimization problems. To
overcome to this problem, the artificial intelligence (AI) as a result of artificial evolution became a widely recognized
optimization method. The artificial neural networks (ANNs) and genetic algorithm (GA) as sub categories of AI are search
methods that mimic the process of natural selection. The GA as a heuristic search method is a class of stochastic search strategies
models after evolutionary mechanisms and works based on a popular strategy routinely used to generate useful solutions to
optimize non-linear systems with a large number of variables (Mitchell, 1996; Whitley, 1994; Ting, 2005; Taherdangkoo et al.,
2012).
Glob. J. Mul. App. Sci., 4 (1): 1-8, 2016
The GA due to more robust is better than conventional AI. Unlike older AI systems, GA does not break easily even if the
inputs changed slightly, or in the presence of reasonable noise. Also, in searching a large state-space, multi-modal state-space,
or n-dimensional surface, a genetic algorithm may offer significant benefits over more typical search of optimization techniques.
The GA can be applied to solve problems that are not well suited for standard optimization algorithms (problems in which
the objective function is discontinuous, non differentiable, stochastic, or highly nonlinear) (Kim and Ellis 2009; Spears and
DeJong, 1991; Srinivas M and Patnaik, 1994). Therefore, prediction of an optimized site response due to soil nonlinearity, the
unavoidable uncertainties as well as assumed simplifications is may be well adopted for GA as one of the main accepted proposed
optimization method in wide range of civil and construction engineering (Alimoradi et al., 2004; Baker and Cornell, 2006;
Hancock et al., 2008; Jin et al., 2000, Ichinose et al., 1997; Prejean and Ellsworth, 2001; Camp et al., 1998).
Motivated of the success of GA in many complex nonlocal nonlinear applications with no a priori knowledge of the behavior
of the function, this study aims to use the GA approach to predict the site response in a specified area in northwest of Iran. The
studied area which is suited in a high seismic risk zone has been subjected to seismic site response analysis (Abbaszadeh Shahri
et al., 2010).
In the present study using the spectral based methods a theoretical spectrum by fitting the model to the data is proposed and
compare to response spectrum from nonlinear dynamic analysis as well as the constructed artificial neural network based model.
The importance of the adequate soil behavior using the in-situ and laboratory tests as well as geophysical surveying is used to
simulate site response spectrum. The fitting algorithm based on GA is tuned by using the obtained spectra. The results after these
tests are used to consider the utilization of the obtained spectral model for prediction of site response spectra, because of the
inherent uncertainty when working with a high level of nonlinearities. The performed analysis in this paper based on 1D site
response evaluated using various statistical and analytical criteria. The results highlighted an attractive alternative method that
can cover some limitations of the conventional method.
Basic concepts of GA
The basic principles of GA based on evolution theory of Darwin were established by Holland (1975), and are well described,
for example, by Goldberg (1989), Davis (1991), Michalewicz (1992) and Reeves (1993). In this idea a population of individuals
that each one representing a possible solution to a problem, is initially randomly created using iterative process, with the
population in each iteration called a generation. In each generation, the fitness of every individual in the population is evaluated.
The fitness is usually the value of the objective function in the optimization problem being solved. Then, couples of individuals
(solutions) are mated to produce other individuals (offspring) of the next generation.
A process of mutation, also randomly generated, modifies the genetic structure of some members in each new generation.
In each cycle, individual fitness is evaluated with respect to the objective, and the system is executed again for many hundreds
of generations. The new generation of candidate solutions is then used in the next iteration of the algorithm. Depending on the
type of algorithm, the fitness of each individual will have an influence on its mating probability, or on the probability of its
staying within the population, so that the quality of the solution becomes better as the generation number becomes higher. Hence,
the GA is a robust search method requiring little information to search effectively in a large or poorly-understood search space.
In particular, a genetic search progress through a population of points in contrast to the single point of focus of most searches
algorithms. Moreover, intrinsic parallelism (in evaluation functions, selections and so on) allows the uses of distributed
processing machines.
Commonly, the algorithm terminates when either a maximum number of generations has been produced, or a satisfactory
fitness level has been reached for the population. A typical genetic algorithm requires genetic representation of the solution
domain and fitness function to evaluate the solution domain in which a standard representation of each candidate solution is as
an array of bits (Whitley, 1994).
Basically, the GA requires two elements for a given problem including encoding of candidate structures (solutions) and
method of evaluating the relative performance of candidate structure, for identifying the better solutions.
Studied area
As presented in Figure1, The selected study in this paper (Miyaneh region with 47˚30' to 48˚ E and 37˚ to 37˚30' N) is
situated on southern part of Azarbayjan-Sharghi province in northwest of Iran. The geomorphology of this area can be divided
into two portions including eroded low height elevations with low deep and smoothed valleys in southern part as well as less
eroded with rough topography and high deep and V shape valleys (Abbaszadeh Shahri et al., 2010). This seismic active area is
located in Alborz-Azarbayjan seismotectonic province. The analysis was performed using the recorded data of Ardabil
earthquake (Mw 6.1, 1997, Iran) that lasted for 15 seconds and recorded by all available seismic stations in Iran.
To use the GA approach for modeling, data collection play important and significant role. The used data in this paper include
the mechanical and geotechnical data as well as geophysical investigation of several drilled boreholes related to Miyaneh Bridge
(a rail way bridge) which have been updated form field investigations and other relevant sources (Azizi, 2015). The used data in
this paper are categorized in borelog data (e.g. soil layer, types and thickness, depth to bedrock level) and field and laboratory
2
Glob. J. Mul. App. Sci., 4 (1): 1-8, 2016
test data (e.g. SPT, sieve analysis, unit weight, Atturberg limits, ground water table). The provided GA model to predict the
nonlinear site response is based on 1D nonlinear analysis and thus the proposed idealized soil profile by Abbaszadeh Shahri et
al., (2010) for the selected area was used.
The GA model
In the current paper, at the first an artificial neural network (ANN) based model is constructed. Considering the predominant
effect of soil deposits due to their complex structure and the highly nonlinear constitutive behavior in site response spectrum the
contribution of quantitative physical parameters should be taken into account (De Martin, 2010; Johnson et al., 2009).
Using the trial and error method, the optimized ANN model to predict the nonlinear seismic site response was found through a
developed Matlab code with the ability of testing several training algorithms as well as various activation transfer functions. By
checking more than 500 topologies using various training algorithms as well as different activation transfer functions, the 6-53-4-1 topology with logistic activation transfer function under training of Levenberg-Marquardt algorithm showed the minimum
root mean square error (RMSE) and selected as optimized model (Figure2).
Figure 1. (A) Location of Azarbayjan Sharghi province in Iran, (B) situation of the studied area in this paper and (C) the recorded earthquake
from last three years (Azizi, 2015)
The obtained data from standard penetration test (SPT), soil type, thickness, depth to bedrock and Atturberg limits were the
used ANN inputs and the pseudo spectral acceleration (PSA) as output respectively. The SPT provides an indication of the
relative density of the subsurface soil and is used in empirical geotechnical correlation to estimate the approximate shear strength
properties of the soils. The observed soil types in the studied site are classified based on Unified Soil Classification System
(USCS) and coded to be applicable in ANN. The obtained mean square error (MSE) for 1000 epochs in run and the statistical
analysis are given in Figure3 and Table (1) respectively.
3
Glob. J. Mul. App. Sci., 4 (1): 1-8, 2016
Figure 2. The optimized ANN structure model in this study (Azizi, 2015)
Figure 3. Training MSE for 3 runs using the optimized ANN based model (Azizi, 2015)
Table 1. Statistical analyses of optimized model based on number of runs in training and validation steps
All Runs
Average of Minimum MSEs
Average of Final MSEs
Training Minimum
0.02934
0.03056
Training Standard Deviation
0.0029
0.0039
Best Networks
Run #
Epoch #
Minimum MSE
Final MSE
Training
1
999
0.02602
0.02616
Validation Minimum
0.01812
0.02473
Validation Standard Deviation
0.0017
0.0074
Validation
1
1000
0.01618
0.01618
The GA is a method for solving both constrained and unconstrained optimization problems. The aim of GA in this paper is
to minimization of the error function (Z), between the averaged scaled spectra and the target spectrum in a range of T 0toTn. The
Eq.1 indicates the minimized deviation of the square root of the sum of the squares (SRSS) of the records’ spectra from a given
(target) design spectrum.
2
𝑇
2
∑𝑛
𝑖=1(𝑆𝑖 .𝑆𝐴𝑖 (𝑇))
𝑛
𝑍 = 𝑚𝑖𝑛 {∑𝑇=𝑇
(√
0
2
∑𝑛
𝑖=1 𝑆𝑖
− 𝐹𝑇 (𝑇)) }
(1)
4
Glob. J. Mul. App. Sci., 4 (1): 1-8, 2016
Where; T is the fundamental vibration period of the site; S i: the scaling factor corresponding to record number (i); SA i(T)
is value of the spectral acceleration of record number i at period T; F T(T) is value of the target design spectrum at period T, To:
initial period to consider; T n: final period to consider.
Therefore, the best combination of strong ground motion records and the corresponding scaling factors from a large database
of earthquake records are required.
The GA is not considered a mathematically guided algorithm. The optima obtained are evolved from generation to
generation without stringent mathematical formulation such as the traditional gradient-type of optimizing procedure. The
deviation from the target is measured by the mean square of error (MSE) between the SRSS of the average scaled spectrum and
the target. The Eq.1, attempt to minimize the deviation of the solution from the target and thus does not guarantee that the final
solution (Alimoradi et al, 2004), thus a second constraint as indicated in Eq.2 is required to add for optimization.
(√
∑𝑛
𝑖=1(𝑆𝑖 .𝑆𝐴𝑖 (𝑇))
2
∑𝑛
𝑖=1 𝑆𝑖
2
− 𝐹𝑇 (𝑇)) ≥ 0 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑝𝑒𝑟𝑖𝑜𝑑𝑠 𝑇0 ≤ 𝑇 ≤ 𝑇𝑛
(2)
Considering the Figure4, random initial population is begun to create by the GA and thus a sequence of new populations
will created using the algorithm. At each step, the individuals of current generation are used to create the next population. To
create the new population, the algorithm scores each member of the current population by computing its fitness value and then
scales the raw fitness scores to convert them into a more usable range of values. In the next step, the algorithm selects members,
called parents, based on their fitness. Some of the individuals in the current population that have lower fitness are chosen as elite.
These elite individuals are passed to the next population. The next step belongs to produce children from the parents. Children
are produced either by making random changes to a single parent—mutation—or by combining the vector entries of a pair of
parents—crossover and in final step, the algorithm will replace the current population with the children to form the next
generation.
Figure 4. Execute procedure in this study to optimize the site response spectrum (Azizi, 2015)
5
Glob. J. Mul. App. Sci., 4 (1): 1-8, 2016
The results of executed procedure for various generations are indicated in Figure5 and performed statistical analyses of the
generation are presented in Table (2). The comparison of the obtained results using the GA respected to target response spectrum
as well as ANN based model are presented in Figure6 respectively.
Figure 5. The results of three runs of random generations (Azizi, 2015)
Table 2. Statistical analyses of performed procedure using the GA in this paper
Performance
PSA
PSA
PSA
MSE
0.00138212
0.002209075
0.003479901
NMSE
0.118022669
0.198859182
0.290697899
MAE
0.023436864
0.03167117
0.037705689
Min Abs Error
0.000366785
0.001295355
0.000800792
Max Abs Error
0.094017851
0.133867469
0.123819716
r
0.948014043
0.916408792
0.908562234
MSE: mean absolute error; NMSE: normal MSE; MAE: mean absolute error; r: coefficient of
determination
6
Glob. J. Mul. App. Sci., 4 (1): 1-8, 2016
Figure 6. Comparison of obtained results from GA and ANN based models regarding the target spectrum (Azizi, 2015)
CONCULSION
A new method for generating the site response spectrum subjected to earthquake ground motions is presented to show the
applicability of GA in finding match at a given site-specific design spectrum.
To prove the results a comparison between the target response and those obtained by GA and ANN based models was
conducted and statistical analyses were performed. The intensive statistical analysis is necessary to prove that the GA approach
can definitely make a more realistic. The algorithm repeatedly modifies a population of individual solutions. At each step, the
GA randomly selects individuals from the current population and uses them as parents to produce the children for the next
generation. Over successive generations, the population "evolves" toward an optimal solution. The first generation of individuals
is modified through the processes that mimic mating, natural selection and mutation and continued until an optimum individual
is obtained. Then by applying the pattern recognition to the database, the data with significant similar characteristics were
localized and clustered.
The obtained results in this study highlighted and utilized the applicability of GA as a method for analyzing non-linear
dynamic site response for structure design.
REFERENCES
Abbaszadeh Shahri A, Behzadafshar K, Esfandiari B and Rajablou R 2010. Nonlinear site response evaluation procedure under the strong
motion (case study: Miyaneh- Azarbayjan sharghi province-Iran), Scientific Research and Essay, 5(16): 2257–2274.
Alimoradi A, Naeim F, Pezeshk Sh. 2004. GA-based selection and scaling of strong ground motion records for structural design, 13 th World
Conference on Earthquake Engineering, Vancouver, BC, Canada, August 1-6, Paper No. 246.
Azizi N. 2015. Simulation of seismic site response subjected to earthquake provokes using genetic algorithm- A case study (Rail road bridge
Miyaneh-Tabriz, East Azerbayjan), M.Sc thesis, Faculty of Civil Engineering, College of Civil Engineering, Islamic Azad University,
Roudehen branch, Tehran, Iran.
Baker J, Cornell CA. 2006. Spectral shape, epsilon and record selection, Earthquake Eng Struct Dynam, 35(9): 1077-95.
Bolt BA and Gregor NJ. 1993. Synthesized strong ground motions for the seismic condition assessment of the eastern portion of the San
Francisco Bay Bridge. Report UCB/EERC-93/12, University of California, Earthquake Engineering Research Center, Berkeley,CA.
Camp CV, Pezeshk S and Cao G. 1998. Optimized design of two-dimensional structures using a genetic algorithm. ASCE Journal of Structural
Engineering, 124 (5):551-559.
Carballo JE and Cornell CA. 2000. Probabilistic seismic demand analysis: spectrum matching and design, Department of Civil and
Environmental Engineering, Stanford University, Report NO. RMS-41.
Davis L. 1991. Handbook of Genetic Algorithms, Van Nostrand Reinhold, New York.
De Martin F. 2010. Influence of the nonlinear behaviour of soft soils on strong ground motions. Ph.D dissertation, Engineering Sciences. Ecole
Centrale, Paris, France.
Goldberg DE and Richardson J. 1987. Genetic algorithms with sharing for multimodal function optimization, in Genetic Algorithms and their
Applications (ICGA’87). J. J. Grefenstette (Editor), Lawrence Erlbaum Associates, Mahwah, New Jersey, 41–49.
Hancock J, Bommer J, Stafford PJ. 2008. Numbers of scaled and matched accelerograms required for inelastic dynamic analyses, Earthquake
Engng Struct, 37: 1585-607.
Holland J. 1975. Adaptation in Natural and Artificial Systems, Ph.D. Thesis, University of Michigan Press, Ann Arbor.
Ichinose GA, Smith KD and Anderson GJ. 1997. Source parameters of the 15 November 1995 Border Town, Nevada, earthquake sequence,
BBSSA, 87, 652–667.
7
Glob. J. Mul. App. Sci., 4 (1): 1-8, 2016
Jin A, Moya CA and Ando M. 2000. Simultaneous determination of site responses and source parameters of small earthquakes along the
Atotsugawa fault zone, central Japan, BSSA, 90, 1430– 1445.
Johnson PA, Bodin P, Gomberg J, Pearce F, Lawrence Z, Menq FR. 2009. Inducing in situ, nonlinear soil response applying an active source.
J Geophy Res, 114, B05304, doi: 10.1029/2008JB005832.
Kim JL and Ellis RD. 2009. Robust global and local search approach to resource-constrained project scheduling. Canadian Journal of Civil
Engineering. 36(3): 375-388.
Michalewicz Z. 1992. Genetic Algorithms + Data Structures= Evolution Programs, Springer-Verlag, Berlin Heidelberg.
Mitchell M. 1996. An introduction to Genetic Algorithms. Cambridge, MA: MIT Press. ISBN 9780585030944.
Prejean SG and Ellsworth WL. 2001. Observations of earthquake source parameters at 2 km depth in the Long Valley Caldera, Eastern
California, BSSA, 91,165–177.
Reeves C. 1993. Modern Heuristic Techniques for Combinatorial Problems, Blackwell Scientific Publications, Oxford, U.K.
Srinivas M and Patnaik LM. 1994. Genetic algorithms: A survey. Computer, 17-26.
Spears WM and DeJong K. 1991. An analysis of multi-point crossover. in Foundations of Genetic Algorithms, G. J. E. Rawlins, Ed.
Taherdangkoo M, Paziresh M, Yazdi M, Bagheri MH. 2012. An efficient algorithm for function optimization: modified stem cells
algorithm. Central European Journal of Engineering, 3 (1): 36–50.
Ting CK. 2005. On the mean convergence time of multi-parent genetic algorithms without selection. Advances in Artificial Life, ISBN 9783-540-28848-0.
Whitley D. 1994. A genetic algorithm tutorial. Statistics and Computing, 4 (2): 65–85.
8