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.

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.

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.

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 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.

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.

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.

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.

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.

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.

Application of artificial bee colony algorithm in Rayleigh wave inversion

In order to solve the problems of multi-parameter,multi-extreme and multi-solution in the nonlinear iterative optimization process of Rayleigh wave inversion,the artificial bee colony(ABC)algorithm is selected for global nonlinear inversion.The global nonlinear inversion method does not rely on a strict initial model and does not need to calculate the derivative of the objective function.The ABC algorithm uses the local optimization behavior of each individual artificial bee to finally highlight the global optimal value in the colony,and the convergence speed is faster.While searching for the global optimal solution,an effective local search can also be performed to ensure the reliability of the inversion results.This paper uses the ABC algorithm to perform Rayleigh wave dispersion inversion on the actual seismic data to obtain a clear undergrounding of shear wave velocity profile and accurately identify the location of the high-velocity interlayer.It is verified that the ABC algorithm used in the inversion of the Rayleigh wave dispersion curve is stable and converges quickly.

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 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.

Research of the Conductive Structure of Crust and the Upper Mantle beneath the South-Central Tibetan Plateau

With the super-wide band magnetoteiluric sounding data of the JUong （吉隆）-Cuoqin （措勤） profile （named line 800） which was completed in 2001 and the Dingri （定日）-Cuomai （措迈） profile （named line 900） which was completed in 2004, we obtained the strike direction of each MT station by strike analysis, then traced profiles that were perpendicular to the main strike direction, and finally obtained the resistivity model of each profile by nonlinear conjugate gradients （NLCG） inversion. With these two models, we described the resistivity structure features of the crust and the upper mantle of the center-southern Tibetan plateau and its relationship with Yalung Tsangpo suture： the upper crust of the research area is a resistive layer with resistivity value range of 200-3 000 Ω.m. The depth of its bottom surface is about 15-20 km generally, but the bottom surface of resistive layer is deeper in the middle of these two profiles. At llne 900, it is about 30 km deep, and even at line 800, it is about 38 km deep. There is a gradient belt of resistivity at the depth of 15-45 km, and a conductive layer is beneath it with resistivity even less than 5 Ω.m. This conductive layer is composed of individual conductive bodies, and at the south of the Yalung Tsangpo suture, the conductive bodies are smaller with thickness about 10 km and lean to the north slightly. However, at the north of the Yalung Tsangpo suture, the conductive bodies are larger with thickness about 30 km and also lean to the north slightly. Relatively, the conductive bodies of line 900 are thinner than those of line 800, and the depth of the bottom surface of line 900 is also shallower. At last, after analyzing the effect factors to the resistivity of rocks, it was concluded that the very conductive layer was caused by partial melt or connective water in rocks. It suggests that the middle and lower crust of the center-southern Tibetan plateau is very thick, hot, flabby, and waxy.

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.

Towards a Theoretical Background for Strong-Scattering Inversion–Direct Envelope Inversion and Gel’fand-Levitan-Marchenko Theory

Strong-scattering inversion or the inverse problem for strong scattering has different physical-mathematical foundations from the weak-scattering case.Seismic inversion based on wave equation for strong scattering cannot be directly solved by Newton’s local optimization method which is based on weak-nonlinear assumption.Here I try to illustrate the connection between the Schr̈odinger inverse scattering(inverse problem for Schr̈odinger equation)by GLM(Gel’fand-Levitan-Marchenko)the-ory and the direct envelope inversion(DEI)using reflection data.The difference between wave equation and Schr̈odinger equation is that the latter has a potential independent of frequency while the former has a frequency-square dependency in the potential.I also point out that the traditional GLM equation for potential inversion can only recover the high-wavenumber components of impedance profile.I propose to use the Schr̈odinger impedance equation for direct impedance inversion and introduce a singular impedance function which also corresponds to a singular potential for the reconstruction of impedance profile,including discontinuities and long-wavelength velocity structure.I will review the GLM theory and its application to impedance inversion including some numerical examples.Then I analyze the recently developed multi-scale direct envelope inversion(MS-DEI)and its connection to the inverse Schr̈odinger scattering.It is conceivable that the combination of strong-scattering inversion(inverse Schr̈odinger scattering)and weak-scattering inversion(local optimization based inversion)may create some inversion methods working for a whole range of inversion problems in geophysical exploration.

A robust method for inverse halftoning via two-dimensional nonlinear pyramid

Based on the principle of spatial pyramid for signal, a multi-scale transform of two-dimensional （2D） interpolating pyramid is constructed by the nonlinear median operator. The transform properties of error diffuse halftoning noise on multiple scales are investigated and analyzed through experiments. According to these properties, a robust inverse halftoning method is proposed. The halftoning image is firstly preprocessed by a Gaussian low-pass filter, and decomposed by the one-scale transform. Then a Wiener filter is employed to the detailed coefficients. Finally an inverse image is reconstructed. Experimental results show that the proposed transform has the advantage of separating the halftoning noise and image detail over linear multi-resolution transform. The presented inverse halftoning method performs some excellent abilities on sharp edge, high peak signal-to-noise ratio （PSNR）, and small memory requirement.

A CFD-based numerical virtual flight simulator and its application in control law design of a maneuverable missile model

A CFD-based Numerical Virtual Flight(NVF)simulator is presented,which integrates an unsteady flow solver on moving hybrid grids,a Rigid-Body Dynamics(RBD)solver and a module of the Flight Control System(FCS).A technique of dynamic hybrid grids is developed to control the active control surfaces with body morphing,with a technique of parallel unstructured dynamic overlapping grids generating proper moving grids over the deflecting control surfaces(e.g.the afterbody rudders of a missile).For the flow/kinematic coupled problems,the 6 Degree-Of-Freedom(DOF)equations are solved by an explicit or implicit method coupled with the URANS CFD solver.The module of the control law is explicitly coupled into the NVF simulator and then improved by the simulation of the pitching maneuver process of a maneuverable missile model.A nonlinear dynamic inversion method is then implemented to design the control law for the pitching process of the maneuverable missile model.Simulations and analysis of the pitching maneuver process are carried out by the NVF simulator to improve the flight control law.Higher control response performance is obtained by adjusting the gain factors and adding an integrator into the control loop.

A STOCHASTIC ALGORITHM FOR FAULT INVERSE PROBLEMS IN ELASTIC HALF SPACE WITH PROOF OF CONVERGENCE

A general stochastic algorithm for solving mixed linear and nonlinear problems was introduced in[11].We show in this paper how it can be used to solve the fault inverse problem,where a planar fault in elastic half-space and a slip on that fault have to be reconstructed from noisy surface displacement measurements.With the parameter giving the plane containing the fault denoted by m and the regularization parameter for the linear part of the inverse problem denoted by C,both modeled as random variables,we derive a formula for the posterior marginal of m.Modeling C as a random variable allows to sweep through a wide range of possible values which was shown to be superior to selecting a fixed value[11].We prove that this posterior marginal of m is convergent as the number of measurement points and the dimension of the space for discretizing slips increase.Simply put,our proof only assumes that the regularized discrete error functional for processing measurements relates to an order 1 quadrature rule and that the union of the finite-dimensional spaces for discretizing slips is dense.Our proof relies on trace class operator theory to show that an adequate sequence of determinants is uniformly bounded.We also explain how our proof can be extended to a whole class of inverse problems,as long as some basic requirements are met.Finally,we show numerical simulations that illustrate the numerical convergence of our algorithm.