Abstract:Particle swarm optimization is a heuristic global optimization method and also an optimization algorithm, which is based on swarm intelligence. It comes from the research on the bird and fish flock movement behavior. In this paper we introduce and use this method in gravity inverse problem. We discuss the solution for the inverse problem of determining the shape of a fault whose gravity anomaly is known. Application of the proposed algorithm to this problem has proven its capability to deal with difficult opti… Show more
“…Particularly, Fernández-Martínez et al presented in [ 18 ] the application of GPSO, CC-PSO and CP-PSO to the solution and appraisal of a 1D-DC (Vertical Electric Sounding, VES) resistivity inverse problem, successfully comparing the results with Metropolis–Hastings. In gravity inversion, PSO has been used in synthetic examples to compare with other global and local search methods without performing an uncertainty assessment (see [ 31 , 32 , 33 ]). This way of proceeding is not correct, as we have already conveniently explained.…”
Section: Sampling Uncertainty Via the Particle Swarm Optimization mentioning
Most inverse problems in the industry (and particularly in geophysical exploration) are highly underdetermined because the number of model parameters too high to achieve accurate data predictions and because the sampling of the data space is scarce and incomplete; it is always affected by different kinds of noise. Additionally, the physics of the forward problem is a simplification of the reality. All these facts result in that the inverse problem solution is not unique; that is, there are different inverse solutions (called equivalent), compatible with the prior information that fits the observed data within similar error bounds. In the case of nonlinear inverse problems, these equivalent models are located in disconnected flat curvilinear valleys of the cost-function topography. The uncertainty analysis consists of obtaining a representation of this complex topography via different sampling methodologies. In this paper, we focus on the use of a particle swarm optimization (PSO) algorithm to sample the region of equivalence in nonlinear inverse problems. Although this methodology has a general purpose, we show its application for the uncertainty assessment of the solution of a geophysical problem concerning gravity inversion in sedimentary basins, showing that it is possible to efficiently perform this task in a sampling-while-optimizing mode. Particularly, we explain how to use and analyze the geophysical models sampled by exploratory PSO family members to infer different descriptors of nonlinear uncertainty.
“…Particularly, Fernández-Martínez et al presented in [ 18 ] the application of GPSO, CC-PSO and CP-PSO to the solution and appraisal of a 1D-DC (Vertical Electric Sounding, VES) resistivity inverse problem, successfully comparing the results with Metropolis–Hastings. In gravity inversion, PSO has been used in synthetic examples to compare with other global and local search methods without performing an uncertainty assessment (see [ 31 , 32 , 33 ]). This way of proceeding is not correct, as we have already conveniently explained.…”
Section: Sampling Uncertainty Via the Particle Swarm Optimization mentioning
Most inverse problems in the industry (and particularly in geophysical exploration) are highly underdetermined because the number of model parameters too high to achieve accurate data predictions and because the sampling of the data space is scarce and incomplete; it is always affected by different kinds of noise. Additionally, the physics of the forward problem is a simplification of the reality. All these facts result in that the inverse problem solution is not unique; that is, there are different inverse solutions (called equivalent), compatible with the prior information that fits the observed data within similar error bounds. In the case of nonlinear inverse problems, these equivalent models are located in disconnected flat curvilinear valleys of the cost-function topography. The uncertainty analysis consists of obtaining a representation of this complex topography via different sampling methodologies. In this paper, we focus on the use of a particle swarm optimization (PSO) algorithm to sample the region of equivalence in nonlinear inverse problems. Although this methodology has a general purpose, we show its application for the uncertainty assessment of the solution of a geophysical problem concerning gravity inversion in sedimentary basins, showing that it is possible to efficiently perform this task in a sampling-while-optimizing mode. Particularly, we explain how to use and analyze the geophysical models sampled by exploratory PSO family members to infer different descriptors of nonlinear uncertainty.
“…б: =density contrast; t: =thickness of sheet; h 1,2 =depth of each side to the middle of the sheet; a: =fault angle (Thanassoulas et al 1987; Telford et al 1976; Toushmalani 2010a; Toushmalani 2013). Figure 1 Fault model illustrating various parameters used in work, and shape of expected gravity anomaly.…”
Section: Introductionmentioning
confidence: 99%
“…Repeat Step 2–7 until a stop criterion is satisfied or a predefined number of iterations are completed (Khan and Sahai 2012; Toushmalani 2013). …”
Section: Introductionmentioning
confidence: 99%
“…Depth to top of the fault (h2): 2001.6431 m; (Toushmalani 2013). Table 2 shows Parameters of obtained solution.…”
The purpose of this study was to compare the performance of two methods for gravity inversion of a fault. First method [Particle swarm optimization (PSO)] is a heuristic global optimization method and also an optimization algorithm, which is based on swarm intelligence. It comes from the research on the bird and fish flock movement behavior. Second method [The Levenberg-Marquardt algorithm (LM)] is an approximation to the Newton method used also for training ANNs. In this paper first we discussed the gravity field of a fault, then describes the algorithms of PSO and LM And presents application of Levenberg-Marquardt algorithm, and a particle swarm algorithm in solving inverse problem of a fault. Most importantly the parameters for the algorithms are given for the individual tests. Inverse solution reveals that fault model parameters are agree quite well with the known results. A more agreement has been found between the predicted model anomaly and the observed gravity anomaly in PSO method rather than LM method.
“…In [20] proposed the Particle Swarm Optimization (PSO) algorithm to solve problem of reverse gravity, the presented solution to the inverse problem is determining the form of error which gravity anomaly is known.…”
Optimization becomes a very important methodology appear in scientific life. It can be applied in many different application fields, like telecommunications, data mining, design, combinatorial optimization, power systems and Electronic circuits. Development of electronic circuit is a complex process that needs some simplification that may be difficult to be done using traditional way. In This paper a hybrid rough particle swarm optimization (HRSO) algorithm is proposed for electronic circuit simplification. The (HRSO) is applied to simplify circuit by reducing the components of circuit to try to find optimal value of circuit components.
General TermsSoft computing, data mining.
KeywordsRough set, particle swarm optimization and electronic circuits.
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