Collision off-axis position dependence of relativistic nonlinear Thomson inverse scattering of an excited electron in a tightly focused circular polarized laser pulse

This paper presents a novel view of the impact of electron collision off-axis positions on the dynamic properties and relativistic nonlinear Thomson inverse scattering of excited electrons within tightly focused, circularly polarized laser pulses of varying intensities. We examine the effects of the transverse ponderomotive force, specifically how the deviation angle and speed of electron motion are affected by the initial off-axis position of the electron and the peak amplitude of the laser pulse. When the laser pulse intensity is low, an increase in the electron's initial off-axis distance results in reduced spatial radiation power, improved collimation, super-continuum phenomena generation, red-shifting of the spectrum's harmonic peak, and significant symmetry in the radiation radial direction. However, in contradiction to conventional understandings,when the laser pulse intensity is relatively high, the properties of the relativistic nonlinear Thomson inverse scattering of the electron deviate from the central axis, changing direction in opposition to the aforementioned effects. After reaching a peak, these properties then shift again, aligning with the previous direction. The complex interplay of these effects suggests a greater nuance and intricacy in the relationship between laser pulse intensity, electron position, and scattering properties than previously thought.

NONLINEAR DYNAMIC INVERSION CONTROL WITH ADAPTIVE COMPENSATION FOR FLIGHT CONTROL SYSTEM

A type of nonlinear dynamic inversion control with adaptive compensation is proposed in order to overcome its over sensitivity to parameter uncertainty and disturbance for flight control system using nonlinear dynamic inversion. This control strategy is different from the general strategy of a nonlinear adaptive control by taking into consideration both parameter uncertainty and external disturbance, the two major uncertain forms in flight control. Finally, an analysis of the stabilily of this control structure is given.

Nonlinear inversion of electrical resistivity imaging using pruning Bayesian neural networks

Conventional artificial neural networks used to solve electrical resistivity imaging （ERI） inversion problem suffer from overfitting and local minima. To solve these problems, we propose to use a pruning Bayesian neural network （PBNN） nonlinear inversion method and a sample design method based on the K-medoids clustering algorithm. In the sample design method, the training samples of the neural network are designed according to the prior information provided by the K-medoids clustering results; thus, the training process of the neural network is well guided. The proposed PBNN, based on Bayesian regularization, is used to select the hidden layer structure by assessing the effect of each hidden neuron to the inversion results. Then, the hyperparameter αk, which is based on the generalized mean, is chosen to guide the pruning process according to the prior distribution of the training samples under the small-sample condition. The proposed algorithm is more efficient than other common adaptive regularization methods in geophysics. The inversion of synthetic data and field data suggests that the proposed method suppresses the noise in the neural network training stage and enhances the generalization. The inversion results with the proposed method are better than those of the BPNN, RBFNN, and RRBFNN inversion methods as well as the conventional least squares inversion.

Nonlinear inversion for magnetotelluric sounding based on deep belief network

To improve magnetotelluric(MT)nonlinear inversion accuracy and stability,this work introduces the deep belief network(DBN)algorithm.Firstly,a network frame is set up for training in different 2D MT models.The network inputs are the apparent resistivities of known models,and the outputs are the model parameters.The optimal network structure is achieved by determining the numbers of hidden layers and network nodes.Secondly,the learning process of the DBN is implemented to obtain the optimal solution of network connection weights for known geoelectric models.Finally,the trained DBN is verified through inversion tests,in which the network inputs are the apparent resistivities of unknown models,and the outputs are the corresponding model parameters.The experiment results show that the DBN can make full use of the global searching capability of the restricted Boltzmann machine(RBM)unsupervised learning and the local optimization of the back propagation(BP)neural network supervised learning.Comparing to the traditional neural network inversion,the calculation accuracy and stability of the DBN for MT data inversion are improved significantly.And the tests on synthetic data reveal that this method can be applied to MT data inversion and achieve good results compared with the least-square regularization inversion.

Nonlinear inversion for electrical resistivity tomography based on chaotic DE-BP algorithm

Nonlinear resistivity inversion requires efficient artificial neural network(ANN)model for better inversion results.An evolutionary BP neural network(BPNN)approach based on differential evolution(DE)algorithm was presented,which was able to improve global search ability for resistivity tomography 2-D nonlinear inversion.In the proposed method,Tent equation was applied to obtain automatic parameter settings in DE and the restricted parameter Fcrit was used to enhance the ability of converging to global optimum.An implementation of proposed DE-BPNN was given,the network had one hidden layer with 52 nodes and it was trained on 36 datasets and tested on another 4 synthetic datasets.Two abnormity models were used to verify the feasibility and effectiveness of the proposed method,the results show that the proposed DE-BP algorithm has better performance than BP,conventional DE-BP and other chaotic DE-BP methods in stability and accuracy,and higher imaging quality than least square inversion.

An ICPSO-RBFNN nonlinear inversion for electrical resistivity imaging

To improve the global search ability and imaging quality of electrical resistivity imaging(ERI) inversion, a two-stage learning ICPSO algorithm of radial basis function neural network(RBFNN) based on information criterion(IC) and particle swarm optimization(PSO) is presented. In the proposed method, IC is applied to obtain the hidden layer structure by calculating the optimal IC value automatically and PSO algorithm is used to optimize the centers and widths of the radial basis functions in the hidden layer. Meanwhile, impacts of different information criteria to the inversion results are compared, and an implementation of the proposed ICPSO algorithm is given. The optimized neural network has one hidden layer with 261 nodes selected by AKAIKE's information criterion(AIC) and it is trained on 32 data sets and tested on another 8 synthetic data sets. Two complex synthetic examples are used to verify the feasibility and effectiveness of the proposed method with two learning stages. The results show that the proposed method has better performance and higher imaging quality than three-layer and four-layer back propagation neural networks(BPNNs) and traditional least square(LS) inversion.

Nonlinear amplitude inversion using a hybrid quantum genetic algorithm and the exact zoeppritz equation

The amplitude versus offset/angle(AVO/AVA)inversion which recovers elastic properties of subsurface media is an essential tool in oil and gas exploration.In general,the exact Zoeppritz equation has a relatively high accuracy in modelling the reflection coefficients.However,amplitude inversion based on it is highly nonlinear,thus,requires nonlinear inversion techniques like the genetic algorithm(GA)which has been widely applied in seismology.The quantum genetic algorithm(QGA)is a variant of the GA that enjoys the advantages of quantum computing,such as qubits and superposition of states.It,however,suffers from limitations in the areas of convergence rate and escaping local minima.To address these shortcomings,in this study,we propose a hybrid quantum genetic algorithm(HQGA)that combines a self-adaptive rotating strategy,and operations of quantum mutation and catastrophe.While the selfadaptive rotating strategy improves the flexibility and efficiency of a quantum rotating gate,the operations of quantum mutation and catastrophe enhance the local and global search abilities,respectively.Using the exact Zoeppritz equation,the HQGA was applied to both synthetic and field seismic data inversion and the results were compared to those of the GA and QGA.A number of the synthetic tests show that the HQGA requires fewer searches to converge to the global solution and the inversion results have generally higher accuracy.The application to field data reveals a good agreement between the inverted parameters and real logs.

Survey on nonlinear reconfigurable flight control

An overview on nonlinear reconfigurable flight control approaches that have been demonstrated in flight-test or highfidelity simulation is presented. Various approaches for reconfigurable flight control systems are considered, including nonlinear dynamic inversion, parameter identification and neural network technologies, backstepping and model predictive control approaches. The recent research work, flight tests, and potential strength and weakness of each approach are discussed objectively in order to give readers and researchers some reference. Finally, possible future directions and open problems in this area are addressed.

Nonlinear inversion-based output tracking control of a boiler-turbine unit

The capability to perform fast load-following has been an important issue in the power industry. An output tracking control system of a boiler-turbine unit is developed. The system is composed of stable inversion and feedback controller. The stable inversion is implemented as a feedforward controller to improve the load-following capability, and the feedback controller is utilized to guarantee the stability and robustness of the whole system. Loop-shaping H∞ method is used to design the feedback controller and the final controller is reduced to a multivariable PI form. The output tracking control system takes account of the multivariable, nonlinear and coupling behavior of boiler-turbine system, and the simulation tests show that the control system works well and can be widely applied.

An Improved Nonlinear Dynamic Inversion Method for Altitude and Attitude Control of Nano Quad-Rotors under Persistent Uncertainties

Nonlinear dynamic inversion(NDI)has been applied to the control law design of quad-rotors mainly thanks to its good robustness and simplicity of parameter tuning.However,the weakness of relying on accurate model greatly restrains its application on quad-rotors,especially nano quad-rotors(NQRs).NQRs are easy to be influenced by uncertainties such as model uncertainties(mainly from complicated aerodynamic interferences,strong coupling in roll-pitch-yaw channels and inaccurate aerodynamic prediction of rotors)and external uncertainties(mainly from winds or gusts),particularly persistent ones.Therefore,developing accurate model for altitude and attitude control of NQRs is difficult.To solve this problem,in this paper,an improved nonlinear dynamic inversion(INDI)method is developed,which can reject the above-mentioned uncertainties by estimating them and then counteracting in real time using linear extended state observer(LESO).Comparison with the traditional NDI(TNDI)method was carried out numerically,and the results show that,in coping with persistent uncertainties,the INDI-based method presents significant superiority.

Seismic fluid identification using a nonlinear elastic impedance inversion method based on a fast Markov chain Monte Carlo method

Elastic impedance inversion with high efficiency and high stability has become one of the main directions of seismic pre-stack inversion. The nonlinear elastic impedance inversion method based on a fast Markov chain Monte Carlo （MCMC） method is proposed in this paper, combining conventional MCMC method based on global optimization with a preconditioned conjugate gradient （PCG） algorithm based on local optimization, so this method does not depend strongly on the initial model. It converges to the global optimum quickly and efficiently on the condition that effi- ciency and stability of inversion are both taken into consid- eration at the same time. The test data verify the feasibility and robustness of the method, and based on this method, we extract the effective pore-fluid bulk modulus, which is applied to reservoir fluid identification and detection, and consequently, a better result has been achieved.

Nonlinear Inversion for Complex Resistivity Method Based on QPSO-BP Algorithm

The significant advantage of the complex resistivity method is to reflect the abnormal body through multi-parameters, but its inversion parameters are more than the resistivity tomography method. Therefore, how to effectively invert these spectral parameters has become the focused area of the complex resistivity inversion. An optimized BP neural network (BPNN) approach based on Quantum Particle Swarm Optimization (QPSO) algorithm was presented, which was able to improve global search ability for complex resistivity multi-parameter nonlinear inversion. In the proposed method, the nonlinear weight adjustment strategy and mutation operator were used to enhance the optimization ability of QPSO algorithm. Implementation of proposed QPSO-BPNN was given, the network had 56 hidden neurons in two hidden layers (the first hidden layer has 46 neurons and the second hidden layer has 10 neurons) and it was trained on 48 datasets and tested on another 5 synthetic datasets. The training and test results show that BP neural network optimized by the QPSO algorithm performs better than the BP neural network without initial optimization on the inversion training and test models, and the mean square error distribution is better. At the same time, a double polarized anomalous bodies model was also used to verify the feasibility and effectiveness of the proposed method, the inversion results show that the QPSO-BP algorithm inversion clearly characterizes the anomalous boundaries and is closer to the values of the parameters.

A Quadratic precision generalized nonlinear global optimization migration velocity inversion method

An important research topic for prospecting seismology is to provide a fast accurate velocity model from pre-stack depth migration. Aiming at such a problem, we propose a quadratic precision generalized nonlinear global optimization migration velocity inversion. First we discard the assumption that there is a linear relationship between residual depth and residual velocity and propose a velocity model correction equation with quadratic precision which enables the velocity model from each iteration to approach the real model as quickly as possible. Second, we use a generalized nonlinear inversion to get the global optimal velocity perturbation model to all traces. This method can expedite the convergence speed and also can decrease the probability of falling into a local minimum during inversion. The synthetic data and Mamlousi data examples show that our method has a higher precision and needs only a few iterations and consequently enhances the practicability and accuracy of migration velocity analysis （MVA） in complex areas.

Newton-type methods and their modifications for inverse heat conduction problems

This paper studies to numerical solutions of an inverse heat conduction problem.The effect of algorithms based on the Newton-Tikhonov method and the Newton-implicit iterative method is investigated,and then several modifications are presented.Numerical examples show the modified algorithms always work and can greatly reduce the computational costs.

An improved differential evolution algorithm for nonlinear inversion of earthquake dislocation

Geophysical inversion for earthquake dislocation source model from the observed crustal deformation field is a nonlinear multimodal problem. Although a lot of nonlinear algorithms have been developed, scientists are pursuing a rapid and accurate method to achieve more stable inversion solutions. Differential evolution, an improved Genetic Evolution algorithm, is implemented to solve the problem. The algorithm is fulfilled by Python 2.7 and tested for the 2004 Mw6.0 Parkfield earthquake, the 2009 Mw6.3 L＇ aquila earthquake, and a virtual MwT.3 earthquake. The inversion results demonstrate that the differential evolution algorithm is not only simple and straightforward to implement, but also robust with impressive precision even if all the 9 model parameters are loosely constrained.

Civil aircraft fault tolerant attitude tracking based on extended state observers and nonlinear dynamic inversion

For the problem of sensor faults and actuator faults in aircraft attitude control,this paper proposes a fault tolerant control(FTC)scheme based on extended state observer(ESO)and nonlinear dynamic inversion(NDI).First,two ESOs are designed to estimate sensor faults and actuator faults respectively.Second,the angular rate signal is reconstructed according to the estimation of sensor faults.Third,in angular rate loop,NDI is designed based on reconstruction of angular rate signals and estimation of actuator faults.The FTC scheme proposed in this paper is testified through numerical simulations.The results show that it is feasible and has good fault tolerant ability.

Nonlinear Inverse Relations of the Bell Polynomials via the Lagrange Inversion Formula (Ⅱ)

In this paper,by means of the classical Lagrange inversion formula,the authors establish a general nonlinear inverse relation as the solution to the problem proposed in the paper[J.Wang,Nonlinear inverse relations for the Bell polynomials via the Lagrange inversion formula,J.Integer Seq.,Vol.22(2019),Article 19.3.8].As applications of this inverse relation,the authors not only find a short proof of another nonlinear inverse relation due to Birmajer,et al.(2012),but also set up a few convolution identities concerning the Mina polynomials.

A high resolution inversion method for fluid factor with dynamic dryrock V_(P)/V_(S) ratio squared

As an important indicator parameter of fluid identification,fluid factor has always been a concern for scholars.However,when predicting Russell fluid factor or effective pore-fluid bulk modulus,it is necessary to introduce a new rock skeleton parameter which is the dry-rock VP/VS ratio squared(DVRS).In the process of fluid factor calculation or inversion,the existing methods take this parameter as a static constant,which has been estimated in advance,and then apply it to the fluid factor calculation and inversion.The fluid identification analysis based on a portion of the Marmousi 2 model and numerical forward modeling test show that,taking the DVRS as a static constant will limit the identification ability of fluid factor and reduce the inversion accuracy.To solve the above problems,we proposed a new method to regard the DVRS as a dynamic variable varying with depth and lithology for the first time,then apply it to fluid factor calculation and inversion.Firstly,the exact Zoeppritz equations are rewritten into a new form containing the fluid factor and DVRS of upper and lower layers.Next,the new equations are applied to the four parameters simultaneous inversion based on the generalized nonlinear inversion(GNI)method.The testing results on a portion of the Marmousi 2 model and field data show that dynamic DVRS can significantly improve the fluid factor identification ability,effectively suppress illusion.Both synthetic and filed data tests also demonstrate that the GNI method based on Bayesian deterministic inversion(BDI)theory can successfully solve the above four parameter simultaneous inversion problem,and taking the dynamic DVRS as a target inversion parameter can effectively improve the inversion accuracy of fluid factor.All these results completely verified the feasibility and effectiveness of the proposed method.

Zoeppritz-based AVO inversion using an improved Markov chain Monte Carlo method

The conventional Markov chain Monte Carlo （MCMC） method is limited to the selected shape and size of proposal distribution and is not easy to start when the initial proposal distribution is far away from the target distribution. To overcome these drawbacks of the conventional MCMC method, two useful improvements in MCMC method, adaptive Metropolis （AM） algorithm and delayed rejection （DR） algorithm, are attempted to be combined. The AM algorithm aims at adapting the proposal distribution by using the generated estimators, and the DR algorithm aims at enhancing the efficiency of the improved MCMC method. Based on the improved MCMC method, a Bayesian amplitude versus offset （AVO） inversion method on the basis of the exact Zoeppritz equation has been developed, with which the P- and S-wave velocities and the density can be obtained directly, and the uncertainty of AVO inversion results has been estimated as well. The study based on the logging data and the seismic data demonstrates the feasibility and robustness of the method and shows that all three parameters are well retrieved. So the exact Zoeppritz-based nonlinear inversion method by using the improved MCMC is not only suitable for reservoirs with strong-contrast interfaces and longoffset ranges but also it is more stable, accurate and antinoise.

A two-stage CO-PSO minimum structure inversion using CUDA for extracting IP information from MT data

The study of induced polarization （IP） information extraction from magnetotelluric （MT） sounding data is of great and practical significance to the exploitation of deep mineral, oil and gas resources. The linear inversion method, which has been given priority in previous research on the IP information extraction method, has three main problems as follows： 1） dependency on the initial model, 2） easily falling into the local minimum, and 3） serious non-uniqueness of solutions. Taking the nonlinearity and nonconvexity of IP information extraction into consideration, a two-stage CO-PSO minimum structure inversion method using compute unified distributed architecture （CUDA） is proposed. On one hand, a novel Cauchy oscillation particle swarm optimization （CO-PSO） algorithm is applied to extract nonlinear IP information from MT sounding data, which is implemented as a parallel algorithm within CUDA computing architecture; on the other hand, the impact of the polarizability on the observation data is strengthened by introducing a second stage inversion process, and the regularization parameter is applied in the fitness function of PSO algorithm to solve the problem of multi-solution in inversion. The inversion simulation results of polarization layers in different strata of various geoelectric models show that the smooth models of resistivity and IP parameters can be obtained by the proposed algorithm, the results of which are relatively stable and accurate. The experiment results added with noise indicate that this method is robust to Gaussian white noise. Compared with the traditional PSO and GA algorithm, the proposed algorithm has more efficiency and better inversion results.