Rayleigh wave inversion using heat-bath simulated annealing algorithm

Shuffled complex evolution approach for effective and efficient surface wave analysis

An essential step in surface wave exploration is the inversion of dispersion curves. By inverting dispersion curves, we can effectively establish the shear-wave velocity model and obtain reliable subsurface stratigraphic information. The inversion of dispersion curves is an inversion problem with multiple parameters and multiple poles, and obtaining a high precision solution is difficult. Among the methods of inversion of dispersion curves, local search methods are prone to fall into local extremes, and global search methods such as particle swarm optimization (PSO) and genetic algorithm (GA) present the disadvantages of slow convergence speed and low precision. Deep learning models with strong nonlinear mapping capability can effectively solve nonlinear problems. Therefore, we propose a method called PSO-optimized long short-term memory (LSTM) network (PSO-LSTM) to invert the dispersion curves in order to improve the effect of inversion of dispersion curves. The method is based on the LSTM network, and PSO is used to optimize the LSTM network structure and other parameters that need to be given manually to improve the prediction of the network. Two theoretical geological models are used in the paper: Model A and Model B to test the PSO-LSTM. The tests include the noisy data test and noise-free data test. Model A was tested without noise, and Model B was tested with noise. In addition, PSO and LSTM were tested on model A to compare the performance of PSO-LSTM. In Model A, the maximum relative errors of PSO and LSTM are 20.76% and 5.85%, respectively, and the maximum standard deviations of PSO and LSTM are 57.37 and 1.97, respectively. For PSO-LSTM, the maximum relative errors of Model A and Model B in the inverse results are 2.05% and 2.09%, and the maximum standard deviations of Model A and Model B in the inverse results are 1.23 and 3.87, respectively. The test results of Model A show that the inversion performance of PSO-LSTM is better than those of LSTM and PSO, and the performance of the network can be improved after PSO is used to optimize the network parameters. The inverse results from Model B show that the PSO-LSTM is robust and can invert the dispersion curves well even after adding noise to the model. Finally, the PSO-LSTM is used to invert the actual data from Wyoming, USA, which demonstrates that the PSO-LSTM can be used for the quantitative interpretation of Rayleigh wave dispersion curves.

Summary The Simulated Annealing (SA) algorithm has been widely used in geophysical data processing. However, the seri al SA algorithm is limited by low computing efficiency. In this paper, the annealing schedule has been improved in the SA algorithm, and a constrained inversion of magnetotelluric (MT) data using the parallel SA algorithm has been applied. The test of synthetic data shows that the improved Very Fast Simulated Annealing (VFSA) method is significantly better than the traditional method. Additionally, the computing efficiency has been improved using the parallel SA inversion algorithm. This method has also been applied in MT data processing for geothermal exploration and good geological results have been achieved.

An implementation of differential search algorithm (DSA) for inversion of surface wave data

DYNAMIC FINITE ELEMENT MODEL UPDATING USING SIMULATED ANNEALING AND GENETIC ALGORITHMS

SUMMARY Many interesting inverse problems in geophysics are non-linear and multimodal. Parametrization of these problems leads to an objective function, or measure of agreement between data and model predictions, that has a complex topography with many local minima. Optimization algorithms that rely on local gradients in the objective function or that search the model space locally may become trapped in these local minima. By combining simulated annealing with the downhill simplex method, a hybrid global search algorithm is presented in this paper for non-linear, multimodal, inverse problems. The hybrid algorithm shares the advantages of both local search methods that perform well if the local model is suitable, and global methods that are able to explore efficiently the full model space. The hybrid algorithm also utilizes a larger and more complex memory to store information on the objective function than simulated annealing algorithms. The effectiveness of this new scheme is evaluated in three problems: minimization of the multidimensional Rosenbrock function, non-linear, 1 -D, acoustic waveform inversion, and residual statics. The performance of the hybrid algorithm is compared with simulated annealing and genetic algorithms and is shown to converge more rapidly and to have a higher success rate of locating the global minimum for the cases investigated.

This paper introduces a new class of D-dimensional density probability functions to be used in Simulated Annealing algorithms and derives an appropriate cooling schedule that is proved to be inversely proportional to a previously chosen power n of time. This generates a new algorithm, the nFast Simulated Annealing (nFSA), from which the Fast Simulated Annealing (FSA) is a particular case. As will be shown, this new algorithm achieves results with an accuracy that increases with n, at the expense of an initial convergence speed that decreases with n. This drawback is solved by the use of an adaptive algorithm, the Adaptive nFast Simulated Annealing (AnFSA), where the parameter n starts at small value, producing a fast initial convergence, and is raised as the algorithm runs, finding global minima points quickly and with great accuracy.

A combined strategy of an improved simulated annealing (SA) algorithm and genetic algorithm is presented, with the goal of reducing the computational expenses. The improvements made on the SA algorithm include two parts, i.e., the adaptive regulating for the step vector, and the dynamic testing for the equilibrium of the Metropolis process. The proposed strategy has both the advantage of SA algorithm, the ability to avoid being trapped in a local optimum, and that of genetic algorithm, the ability to use the information about the searched states for the next iteration. A practical application on geometry optimization of pole shoes in large salient pole synchronous generators is effectively implemented using the strategy. The numerical results show that the number of iterations used by executing the combined strategy are only about 75% of those by executing basic SA algorithm.

We compare inversions of Rayleigh wave dispersion curves for shear wave velocity depth profiles based on the L2‐norm (Occam's Inversion) and L1‐norm (TV Regularization). We forward model Rayleigh waves using a finite‐element method instead of the conventional technique based on a recursion formula and root‐finding. The forward modeling naturally leads to an inverse problem that is overparameterized in depth. Solving the inverse problem with Occam's Inversion gives the smoothest subsurface model that satisfies the data. However, the subsurface need not be smooth and we therefore also solve the inverse problem with TV Regularization, a procedure that does not penalize discontinuities. The use of such a regularization scheme for such an overparameterized inverse problem means blocky subsurface models can be obtained without fixing the layer boundaries in advance. This represents an entirely new philosophy for surface wave inversion.

Utilization of surface wave dispersive properties may be roughly divided into three steps: field data acquisition, dispersion-curve picking, and inversion of phase velocities (

Revisiting simulated annealing: A component-based analysis

In this paper, simulated annealing (SA) algorithm is employed to solve the flowshop scheduling problem with the objective of minimising the completion time variance (CTV) of jobs. Four variants of the two-phase SA algorithm (SA-I to SA-IV) are proposed to solve flowshop scheduling problem with the objective of minimising the CTV of jobs without considering the right shifting of completion time of jobs on the last machine. The proposed SA algorithms have been tested on 90 benchmark flowshop scheduling problems. The solutions yielded by the proposed SA variants are compared with the best CTV of jobs reported in the literature, and the proposed SA-III is found to perform well in minimising the chosen performance measure (CTV) particularly in medium and large size problems.

In this paper, we perform a comparative study of four stochastic optimization methods for calculating the phase stability of reactive and nonreactive mixtures. We have compared the algorithms: simulated annealing, very fast simulated annealing, a modified version of direct search simulated annealing, and stochastic differential equations. We test the numerical performance and reliability of these methods using several stability problems. From our results, the simulated annealing algorithm appears to be the most reliable method for minimization of the tangent plane distance function for both reactive and nonreactive mixtures.

Joint inversion of Rayleigh and Love wave dispersion curves for improving the accuracy of near-surface S-wave velocities

This paper addressed the modeling and optimization of loading path in T‐shape hydroforming of tubes using Simulated Annealing (SA) algorithm. Analysis of variance shows that some of pre‐selected parameters in loading paths have not significant effect on the deformed tube. Hence, some of optimized parameters found initially, are replaced with their own fixed optimum values in order to seek for the other parameters in more detail by the Simulated Annealing (SA) algorithm. According to the intensity of effectiveness on the deformation, six more important parameters are chosen and their minimum and maximum limitation values are determined. In this case, sixty four different tests for different loading paths are designed by Design of Experiment (DOE) and full factorial method. By using mathematical modeling all required loading parameters are obtained. Proposed models of formability embedded into Simulated Annealing algorithm and optimum value for loading parameters and optimal load paths are found. The obtained results show that more accurate loading path may be found for T‐shape of tube hydroforming.