Research Article

Inversion of Rayleigh Wave Dispersion Curves via Long Short-Term Memory Combined with Particle Swarm Optimization

Table 1

Dispersion curves inversion studies carried out in recent decades (performed algorithms with their merits and demerits).

AlgorithmReference numberMeritsDemeritsCompared with

Least-squares algorithm[4](1) High calculation speed;
(2) High precision of solution
(1) The appropriate initial model needs to be given;
(2) The partial derivative needs to be calculated;
(3) Easy to fall into local minima
None

Levenberg–Marquardt algorithm combined with the singular value decomposition technique[5](1) High calculation speed;
(2) Excellent stability
(1) The appropriate initial model needs to be given;
(2) The partial derivative needs to be calculated;
(3) Easy to fall into local minima
None

Occam algorithm[6](1) High calculation speed;
(2) High precision of solution;
(3) Excellent stability
(1) The appropriate initial model needs to be given;
(2) The partial derivative needs to be calculated;
(3) Easy to fall into local minima
None

Genetic algorithm[7](1) Excellent ability to escape from local minima;
(2) Independent of selecting the initial model;
(3) Calculation of partial derivatives is avoided
(1) Huge computational time cost;
(2) Low accuracy of calculation
None

Genetic algorithm combining elite selection and dynamic mutation strategy[8](1) Excellent stability;
(2) Excellent ability to escape from local minima;
(3) Independent of selecting the initial model;
(4) Calculation of partial derivatives is avoided
(1) Huge computational time cost;
(2) Low accuracy of calculation
Marquardt algorithm

Genetic algorithms combining marginal posterior probability density estimation[9](1) Excellent ability to escape from local minima;
(2) Independent of selecting the initial model;
(3) Calculation of partial derivatives is avoided
(1) Huge computational time cost;
(2) Low accuracy of calculation
None

Heat-bath simulated annealing algorithm[10](1) Excellent ability to escape from local minima;
(2) Independent of selecting the initial model;
(3) Calculation of partial derivatives is avoided;
(4) Suitable for parallel programming
(1) Low accuracy of calculationLevenberg–Marquardt algorithm and fast simulated annealing algorithm

Artificial neural network[18](1) Excellent stability;
(2) High inversion efficiency
(1) Requires large amounts of training data;
(2) Training the network costs a lot of time
Monte Carlo approach and gray wolf optimizer

LSTM based on the first height last velocity[19](1) Excellent stability;
(2) High inversion efficiency
(1) Requires large amounts of training data;
(2) Training the network costs a lot of time
None