Spectral acceleration prediction using genetic programming based approaches
Introduction
Nowadays, with the advancement of facilities, a massive amount of data has been recorded consistently for every phenomenon. However, the more critical concern is analyzing those data and catching their underlying contents. Dealing with a large number of decision variables to predict one or more occurrences could be an impossible mathematical task. Behavioral models have been found to be an efficient solution by approximating a relationship that correlates a set of decision variables with outputs through experimental data without considering underlying physical theories [1]. This concept eliminates many setbacks behind developing a phenomenological model that requires prior knowledge about its underlying philosophy. Regression analysis, either linear or nonlinear, proved to be a broadly applicable methodology to develop a behavioral model. However, regression analysis is “low competent” in dealing with highly complex case scenarios that analyzes high-dimensional data with several outliers [2], [3]. In contrast, the artificial intelligence (AI)-based machine learning tools have been considered a perfect alternative for proposing meta-models for a given problem. Those soft-computing-based models extract a specific pattern by learning adaptively from tackled data. Their efficiency in handling complicated events is comparable to classic techniques like regression analysis.
Genetic programming (GP) [4] is a relatively new AI-based machine learning approach that introduces entirely new features and traits. GP is an evolutionary learning algorithm that mimics the genetic algorithm’s (GA) fundamental rules [2], [3]. GP is a domain-independent method that reproduces offspring through progressively refining an initial population by employing evolutionary operators (i.e., crossover, mutation, reproduction, gene duplication, and gene deletion). It is worth noting that GP represents each potential solution in terms of parse trees. The quality of the population in each generation is measured by a fitness function to guarantee the survival of the fittest solutions. Gene expression programming (GEP) is a successful GP variation that handles complex problems efficiently [5]. The main difference between GP and GEP lies in individuals’ characteristics. Parse trees in GP are nonlinear with different sizes and shapes, while the potential chromosomes are defined in terms of a fixed-length vector in GEP. Thanks to their notably successful records in handling a wide range of complex engineering problems, it is necessary to examine their potential for dealing with different problems.
Seismic hazard analysis (SHA) is a methodology that examines the stability of a structure under earthquake stimulation. Ground-motion prediction equations (GMPEs) estimates ground-motion amplitude as a necessary factor for SHA. The essential an earthquake’s characteristics from a seismological viewpoint are earthquake magnitude, source-to-site distance, fault type, and soil effects. Peak-based and spectrum-based are also the two crucial ground-motion intensity measures for the risk estimation of structures. Peak-based parameters, like peak ground acceleration (PGA), peak ground velocity (PGV), and peak ground displacement (PGD), are not dependent on the structures’ attributes. However, spectrum-based parameters like Spectral acceleration () are directly linked to the structures’ responses. is used frequently in seismic hazard studies as it is more efficient than peak-based parameters [6], [7]. Developing a direct correlation between and other variables is a difficult task because of severe nonlinearity in GMPEs. Statistical regression [8] is the most common approach for obtaining GMPEs in the active seismic zones with plenty of ground-motion recordings (e.g., western North America).
As mentioned previously, using AI-based approaches has proved to be an efficient alternative for handling this sort of problem. In this study, we concentrated on developing more sophisticated schemes for estimating GMPEs using AI techniques due to the high importance of SHA as a subcategory of earthquake engineering. Therefore, the main effort here was to develop explicit models for describing spectral acceleration () based on the following input variables: period of vibration (T), Moment magnitude (M), closest distance to fault rupture (), Joyner Boore distance (), flag for reverse faulting earthquakes (FRV), normal faulting flag (FNM), depth to top of the rupture (), dip angle (), shear wave velocity averaged over top 30 meters (), and depth to shear wave velocity equal to 2.5 km/s ().
Due to a lack of attention to the outstanding ability of GP-based approaches to develop behavioral model, we utilized two hybrid GP-based methods for developing GMPEs: (1) multi-objective GP with linear regression and (2) GEP with mesh adaptive direct search (MADS). The former is a variation of the multi-gene GP algorithm with regression analysis. This algorithm takes two following objectives into account: maximizing the goodness of a fitting solution, and minimizing the model complexity. In the latter, MADS optimization algorithms are incorporated into GEP to adjust GEP coefficients and enhance its performance as much as possible. We trained our models using the database gathered by the Pacific Earthquake Engineering Research Centre (PEER) [7]. Our generated models effectively satisfied the conditions of assessed components in prediction models. Those proposed approaches are applicable for estimating the spectral acceleration in every period of vibration. Our model produces appropriate outcomes without the need to investigate prior forms of models. The statistical analyses were conducted for the spectral periods of 0.2 s, 1 s, and 3 s. The obtained results demonstrated that our employed methodologies – multi-objective genetic programming (MOGP-R) and Gene Expression Programming with Mesh Adaptive Direct Search (GEP-MADS) – generated sufficiently fitted spectral acceleration values to the observations. Moreover, the model proposed by MOGP-R was competent to the other common approaches. Based on the results, MOGP-R was ranked as either the best or the second-best model in different spectral periods.
The rest of this paper is organized as follows. In Section 2, we present an overview of different AI-based algorithms (i.e., optimization algorithms and predicting approaches), and we review some applications of those methods to the civil engineering problems. In Section 3, we describe the details and mechanisms of our proposed algorithms. A description of the tackled problem and the utilized data is presented in Section 4. Section 5 provides a short description of the used measures to evaluate our models’ efficiencies. The developed models are assessed and analyzed in Section 6. Finally, Section 7 concludes the work and suggests future research directions.
Section snippets
Background and literature review
Nature-inspired algorithms as a subcategory of AI-based methods proved to be a very efficient alternative for highly complex problems. Those algorithms have successfully handled two significant tasks: 1- optimization, 2- prediction.
During the past few decades, many researchers attempted to introduce various nature-inspired optimization algorithms. For example, Mirjalili [9], [10], [11] developed dragonfly, moth-flame, and sine–cosine algorithms inspiring from static and dynamic swarming
Overview of the algorithms
This study utilized two different approaches to generate uniform equations for predicting spectral acceleration. The first approach tackled multi-objective genetic programming (MOGP-R) as an efficient GP variation to handle the proposed problem. Moreover, an algorithm based on hybridizing GEP and MADS (GEP-MADS) was utilized to predict spectral acceleration. This approach utilized the MADS algorithm to enhance the performance GEP through a local search. The involved parameters values were
Strong ground-motion models
Seismic hazard analysis plays a crucial role in the earthquake-resisting design of structures located in seismic prone zones. The major characteristics for describing an earthquake are magnitude, source-to-site distance, faulting type, and soil effects. Earthquake parameters can be categorized into two major groups from an engineering viewpoint: (1) peak-based parameters (e.g., PGA, PGV, and PGD) and (2) spectrum-based parameters (pseudo-spectral acceleration (PSA)) [55]. It should be
Model assessment methodology
This section explains the utilized measures to assess the validity and usability of the proposed methodology. To that end, we used three classes of metrics: (i) statistical errors, (ii) residual analysis, and (iii) goodness-of-fit measures. In the following, more details on the utilized criteria are provided.
Results and discussion
This section compares the proposed models with the ones established as part of the National Geospatial-Intelligence Agency (NGA) project. Abrahamson and Silva [77] (hereafter AS08), Boore and Atkinson [78] (hereafter BA08), Campbell and Bozorgnia [74] (hereafter CB08), and Chiou and Youngs [79] (hereafter CY08) are the four NGA models that were considered for comparisons. We benchmarked our developed models with the NGA models as the competing reference.
The applicability of here proposed
Conclusions
This study utilized two efficient hybrid variations of genetic programming (GP) – called multi-objective GP with multi-variable linear regression (MOGP-R) and hybrid gene expression programming with mesh adaptive direct search algorithm (MADS-GEP) – to generate precise formulae for predicting spectral acceleration. We used a Pacific Earthquake Engineering research center (PEER) database to develop the models. This study’s main effort was correlating spectral accelerations with critical
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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