Incremental Nonlinear Dynamic Inversion(INDI)is a control approach that has gained popularity in flight control over the past decade.Besides the INDI law,several common additional components complement an INDI-based c...Incremental Nonlinear Dynamic Inversion(INDI)is a control approach that has gained popularity in flight control over the past decade.Besides the INDI law,several common additional components complement an INDI-based controller.This paper,the second part of a two-part series of surveys on INDI,aims to summarize the modern trends in INDI and its related components.Besides a comprehensive components specification,it addresses their most common challenges,compares different variants,and discusses proposed advances.Further important aspects of INDI are gain design,stability,and robustness.This paper also provides an overview of research conducted concerning these aspects.This paper is written in a tutorial style to familiarize researchers with the essential specifics and pitfalls of INDI and its components.At the same time,it can also serve as a reference for readers already familiar with INDI.展开更多
Due to the heterogeneity of rock masses and the variability of in situ stress,the traditional linear inversion method is insufficiently accurate to achieve high accuracy of the in situ stress field.To address this cha...Due to the heterogeneity of rock masses and the variability of in situ stress,the traditional linear inversion method is insufficiently accurate to achieve high accuracy of the in situ stress field.To address this challenge,nonlinear stress boundaries for a numerical model are determined through regression analysis of a series of nonlinear coefficient matrices,which are derived from the bubbling method.Considering the randomness and flexibility of the bubbling method,a parametric study is conducted to determine recommended ranges for these parameters,including the standard deviation(σb)of bubble radii,the non-uniform coefficient matrix number(λ)for nonlinear stress boundaries,and the number(m)and positions of in situ stress measurement points.A model case study provides a reference for the selection of these parameters.Additionally,when the nonlinear in situ stress inversion method is employed,stress distortion inevitably occurs near model boundaries,aligning with the Saint Venant's principle.Two strategies are proposed accordingly:employing a systematic reduction of nonlinear coefficients to achieve high inversion accuracy while minimizing significant stress distortion,and excluding regions with severe stress distortion near the model edges while utilizing the central part of the model for subsequent simulations.These two strategies have been successfully implemented in the nonlinear in situ stress inversion of the Xincheng Gold Mine and have achieved higher inversion accuracy than the linear method.Specifically,the linear and nonlinear inversion methods yield root mean square errors(RMSE)of 4.15 and 3.2,and inversion relative errors(δAve)of 22.08%and 17.55%,respectively.Therefore,the nonlinear inversion method outperforms the traditional multiple linear regression method,even in the presence of a systematic reduction in the nonlinear stress boundaries.展开更多
This paper,the first-part of a two part series of surveys on Incremental Nonlinear Dynamic Inversion(INDI),provides an overview of the evolution and developments in INDI.Written in a tutorial style,it presents differe...This paper,the first-part of a two part series of surveys on Incremental Nonlinear Dynamic Inversion(INDI),provides an overview of the evolution and developments in INDI.Written in a tutorial style,it presents different basic INDI variants and their specifics,such as modelbased INDI,sensor-based INDI,and hybrid INDI.Furthermore,it sets these different approaches in context with each other.Later developments of INDI explicitly consider actuator dynamics.Those concepts are summarized and discussed in detail.Subsequently,studies that relate INDI to other control methods are summarized.Finally,an overview of various applications of INDI is given,covering different types of control loops and various types of vehicles and plants.This paper seeks to set these developments into context with each other.The purpose of this paper is twofold.INDI is already well-known in the domain of flight control but less so in other fields.Therefore,the paper is written in a comprehensive tutorial style to provide easy access to readers unfamiliar with the topic.On the other hand,the paper can serve as a reference for readers familiar with the topic.展开更多
Fluid and effective fracture identification in reservoirs is a crucial part of reservoir prediction.The frequency-dependent AVO inversion algorithms have proven to be effective for identifying fluid through its disper...Fluid and effective fracture identification in reservoirs is a crucial part of reservoir prediction.The frequency-dependent AVO inversion algorithms have proven to be effective for identifying fluid through its dispersion property.However,the conventional frequency-dependent AVO inversion algorithms based on Smith&Gidlow and Aki&Richards approximations do not consider the acquisition azimuth of seismic data and neglect the effect of seismic anisotropic dispersion in the actual medium.The aligned fractures in the subsurface medium induce anisotropy.The seismic anisotropy should be considered while accounting for the seismic dispersion properties through fluid-saturated fractured reservoirs.Anisotropy in such reservoirs is frequency-related due to wave-induced fluid-flow(WIFF)between interconnected fractures and pores.It can be used to identify fluid and effective fractures(fluid-saturated)by using azimuthal seismic data via anisotropic dispersion properties.In this paper,based on Rüger’s equation,we derived an analytical expression in the frequency domain for the frequencydependent AVOAz inversion in terms of fracture orientation,dispersion gradient of isotropic background rock,anisotropic dispersion gradient,and the dispersion at a normal incident angle.The frequency-dependent AVOAz equation utilizes azimuthal seismic data and considers the effect of both isotropic and anisotropic dispersion.Reassigned Gabor Transform(RGT)is used to achieve highresolution frequency division data.We then propose the frequency-dependent AVOAz inversion method to identify fluid and characterize effective fractures in fractured porous reservoirs.Through application to high-qualified seismic data of dolomite and carbonate reservoirs,the results show that the method is useful for identifying fluid and effective fractures in fluid-saturated fractured rocks.展开更多
Frequency-dependent amplitude versus offset(FAVO)inversion is a popular method to estimate the frequency-dependent elastic parameters by using amplitude and frequency information of pre-stack seismic data to guide flu...Frequency-dependent amplitude versus offset(FAVO)inversion is a popular method to estimate the frequency-dependent elastic parameters by using amplitude and frequency information of pre-stack seismic data to guide fluid identification.Current frequency-dependent AVO inversion methods are mainly based on elastic theory without the consideration of the viscoelasticity of oil/gas.A fluid discrimination approach is proposed in this study by incorporating the viscoelasticity and relevant FAVO inversion.Based on viscoelastic and rock physics theories,a frequency-dependent viscoelastic solid-liquid decoupling fluid factor is initially constructed,and its sensitivity in fluid discrimination is compared with other conventional fluid factors.Furthermore,a novel reflectivity equation is derived in terms of the viscoelastic solid-liquid decoupling fluid factor.Due to the introduction of viscoelastic theory,the proposed reflectivity is related to frequency,which is more widely applicable than the traditional elastic reflectivity equation directly derived from the elastic reflectivity equation on frequency.Finally,a pragmatic frequency-dependent inversion method is introduced to verify the feasibility of the equation for frequency-dependent viscoelastic solid-liquid decoupling fluid factor prediction.Synthetic and field data examples demonstrate the feasibility and stability of the proposed approach in fluid discrimination.展开更多
The identification of hydrocarbons using seismic methods is critical in the prediction of shale oil res-ervoirs.However,delineating shales of high oil saturation is challenging owing to the similarity in the elastic p...The identification of hydrocarbons using seismic methods is critical in the prediction of shale oil res-ervoirs.However,delineating shales of high oil saturation is challenging owing to the similarity in the elastic properties of oil-and water-bearing shales.The complexity of the organic matter properties associated with kerogen and hydrocarbon further complicates the characterization of shale oil reservoirs using seismic methods.Nevertheless,the inelastic shale properties associated with oil saturation can enable the utilization of velocity dispersion for hydrocarbon identification in shales.In this study,a seismic inversion scheme based on the fluid dispersion attribute was proposed for the estimation of hydrocarbon enrichment.In the proposed approach,the conventional frequency-dependent inversion scheme was extended by incorporating the PP-wave reflection coefficient presented in terms of the effective fluid bulk modulus.A rock physics model for shale oil reservoirs was constructed to describe the relationship between hydrocarbon saturation and shale inelasticity.According to the modeling results,the hydrocarbon sensitivity of the frequency-dependent effective fluid bulk modulus is superior to the traditional compressional wave velocity dispersion of shales.Quantitative analysis of the inversion re-sults based on synthetics also reveals that the proposed approach identifies the oil saturation and related hydrocarbon enrichment better than the above-mentioned conventional approach.Meanwhile,in real data applications,actual drilling results validate the superiority of the proposed fluid dispersion attribute as a useful hydrocarbon indicator in shale oil reservoirs.展开更多
Recently,the great potential of seismic dispersion attributes in oil and gas exploration has attracted extensive attention.The frequency-dependent amplitude versus offset(FAVO)technology,with dispersion gradient as a ...Recently,the great potential of seismic dispersion attributes in oil and gas exploration has attracted extensive attention.The frequency-dependent amplitude versus offset(FAVO)technology,with dispersion gradient as a hydrocarbon indicator,has developed rapidly.Based on the classical AVO theory,the technology works on the assumption that elastic parameters are frequency-dependent,and implements FAVO inversion using spectral decomposition methods,so that it can take dispersive effects into account and effectively overcome the limitations of the classical AVO.However,the factors that affect FAVO are complicated.To this end,we construct a unified equation for FAVO inversion by combining several Zoeppritz approximations.We study and compare two strategies respectively with(strategy 1)and without(strategy 2)velocity as inversion input data.Using theoretical models,we investigate the influence of various factors,such as the Zoeppritz approximation used,P-and S-wave velocity dispersion,inversion input data,the strong reflection caused by non-reservoir interfaces,and the noise level of the seismic data.Our results show that FAVO inversion based on different Zoeppritz approximations gives similar results.In addition,the inversion results of strategy 2 are generally equivalent to that of strategy 1,which means that strategy 2 can be used to obtain dispersion attributes even if the velocity is not available.We also found that the existence of non-reservoir strong reflection interface may cause significant false dispersion.Therefore,logging,geological,and other relevant data should be fully used to prevent this undesirable consequence.Both the P-and S-wave related dispersion obtained from FAVO can be used as good indicators of a hydrocarbon reservoir,but the P-wave dispersion is more reliable.In fact,due to the mutual coupling of P-and S-wave dispersion terms,the P-wave dispersion gradient inverted from PP reflection seismic data has a stronger hydrocarbon detection ability than the S-wave dispersion gradient.Moreover,there is little difference in using post-stack data or pre-stack angle gathers as inversion input when only the P-wave dispersion is desired.The real application examples further demonstrate that dispersion attributes can not only indicate the location of a hydrocarbon reservoir,but also,to a certain extent,reveal the physical properties of reservoirs.展开更多
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 ne...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.展开更多
Cauchy priori distribution-based Bayesian AVO reflectivity inversion may lead to sparse estimates that are sensitive to large reflectivities. For the inversion, the computation of the covariance matrix and regularized...Cauchy priori distribution-based Bayesian AVO reflectivity inversion may lead to sparse estimates that are sensitive to large reflectivities. For the inversion, the computation of the covariance matrix and regularized terms requires prior estimation of model parameters, which makes the iterative inversion weakly nonlinear. At the same time, the relations among the model parameters are assumed linear. Furthermore, the reflectivities, the results of the inversion, or the elastic parameters with cumulative error recovered by integrating reflectivities are not well suited for detecting hydrocarbons and fuids. In contrast, in Bayesian linear AVO inversion, the elastic parameters can be directly extracted from prestack seismic data without linear assumptions for the model parameters. Considering the advantages of the abovementioned methods, the Bayesian AVO reflectivity inversion process is modified and Cauchy distribution is explored as a prior probability distribution and the time-variant covariance is also considered. Finally, we propose a new method for the weakly nonlinear AVO waveform inversion. Furthermore, the linear assumptions are abandoned and elastic parameters, such as P-wave velocity, S-wave velocity, and density, can be directly recovered from seismic data especially for interfaces with large reflectivities. Numerical analysis demonstrates that all the elastic parameters can be estimated from prestack seismic data even when the signal-to-noise ratio of the seismic data is low.展开更多
Multiwave seismic technology promotes the application of joint PP–PS amplitude versus offset (AVO) inversion;however conventional joint PP–PS AVO inversioan is linear based on approximations of the Zoeppritz equatio...Multiwave seismic technology promotes the application of joint PP–PS amplitude versus offset (AVO) inversion;however conventional joint PP–PS AVO inversioan is linear based on approximations of the Zoeppritz equations for multiple iterations. Therefore the inversion results of P-wave, S-wave velocity and density exhibit low precision in the faroffset;thus, the joint PP–PS AVO inversion is nonlinear. Herein, we propose a nonlinear joint inversion method based on exact Zoeppritz equations that combines improved Bayesian inference and a least squares support vector machine (LSSVM) to solve the nonlinear inversion problem. The initial parameters of Bayesian inference are optimized via particle swarm optimization (PSO). In improved Bayesian inference, the optimal parameter of the LSSVM is obtained by maximizing the posterior probability of the hyperparameters, thus improving the learning and generalization abilities of LSSVM. Then, an optimal nonlinear LSSVM model that defi nes the relationship between seismic refl ection amplitude and elastic parameters is established to improve the precision of the joint PP–PS AVO inversion. Further, the nonlinear problem of joint inversion can be solved through a single training of the nonlinear inversion model. The results of the synthetic data suggest that the precision of the estimated parameters is higher than that obtained via Bayesian linear inversion with PP-wave data and via approximations of the Zoeppritz equations. In addition, results using synthetic data with added noise show that the proposed method has superior anti-noising properties. Real-world application shows the feasibility and superiority of the proposed method, as compared with Bayesian linear inversion.展开更多
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 ...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.展开更多
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 a...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.展开更多
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 pres...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.展开更多
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 ...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.展开更多
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 M...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.展开更多
A one-dimensional equivalent linear method （EQL） is widely used in estimating seismic ground response. For this method, the shear modulus and damping ratio of inelastic soil are supposed to be frequency independent....A one-dimensional equivalent linear method （EQL） is widely used in estimating seismic ground response. For this method, the shear modulus and damping ratio of inelastic soil are supposed to be frequency independent. However, historical earthquake records and laboratory test results indicate that nonlinear soil behavior is frequency- dependent. Several frequency-dependent equivalent linear methods （FDEQL） related to the Fourier amplitude of shear strain time history have been developed to take into account the frequency-dependent soil behavior. Furthermore, the shear strain threshold plays an important role in soil behavior. For shear strains below the elastic shear strain threshold, soil behaves essentially as a linear elastic mate- rial. To consider the effect of elastic-shear-strain-threshold- and frequency-dependent soil behavior on wave propaga- tion, the shear-strain-threshold- and frequency-dependent equivalent linear method （TFDEQL） is proposed. A series of analyses is implemented for EQL, FDEQL, and TFDEQL methods. Results show that elastic-shear-strain-threshold- and frequency-dependent soil behavior plays a great influence on the computed site response, especially for the high- frequency band. Also, the effect of elastic-strain-threshold- and frequency-dependent soil behavior on the site response is analyzed from relatively weak to strong input motion, and results show that the effect is more pronounced as input motion goes from weak to strong.展开更多
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 crite...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.展开更多
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 great...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.展开更多
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...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.展开更多
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 eff...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.展开更多
文摘Incremental Nonlinear Dynamic Inversion(INDI)is a control approach that has gained popularity in flight control over the past decade.Besides the INDI law,several common additional components complement an INDI-based controller.This paper,the second part of a two-part series of surveys on INDI,aims to summarize the modern trends in INDI and its related components.Besides a comprehensive components specification,it addresses their most common challenges,compares different variants,and discusses proposed advances.Further important aspects of INDI are gain design,stability,and robustness.This paper also provides an overview of research conducted concerning these aspects.This paper is written in a tutorial style to familiarize researchers with the essential specifics and pitfalls of INDI and its components.At the same time,it can also serve as a reference for readers already familiar with INDI.
基金funded by the National Key R&D Program of China(Grant No.2022YFC2903904)the National Natural Science Foundation of China(Grant Nos.51904057 and U1906208).
文摘Due to the heterogeneity of rock masses and the variability of in situ stress,the traditional linear inversion method is insufficiently accurate to achieve high accuracy of the in situ stress field.To address this challenge,nonlinear stress boundaries for a numerical model are determined through regression analysis of a series of nonlinear coefficient matrices,which are derived from the bubbling method.Considering the randomness and flexibility of the bubbling method,a parametric study is conducted to determine recommended ranges for these parameters,including the standard deviation(σb)of bubble radii,the non-uniform coefficient matrix number(λ)for nonlinear stress boundaries,and the number(m)and positions of in situ stress measurement points.A model case study provides a reference for the selection of these parameters.Additionally,when the nonlinear in situ stress inversion method is employed,stress distortion inevitably occurs near model boundaries,aligning with the Saint Venant's principle.Two strategies are proposed accordingly:employing a systematic reduction of nonlinear coefficients to achieve high inversion accuracy while minimizing significant stress distortion,and excluding regions with severe stress distortion near the model edges while utilizing the central part of the model for subsequent simulations.These two strategies have been successfully implemented in the nonlinear in situ stress inversion of the Xincheng Gold Mine and have achieved higher inversion accuracy than the linear method.Specifically,the linear and nonlinear inversion methods yield root mean square errors(RMSE)of 4.15 and 3.2,and inversion relative errors(δAve)of 22.08%and 17.55%,respectively.Therefore,the nonlinear inversion method outperforms the traditional multiple linear regression method,even in the presence of a systematic reduction in the nonlinear stress boundaries.
文摘This paper,the first-part of a two part series of surveys on Incremental Nonlinear Dynamic Inversion(INDI),provides an overview of the evolution and developments in INDI.Written in a tutorial style,it presents different basic INDI variants and their specifics,such as modelbased INDI,sensor-based INDI,and hybrid INDI.Furthermore,it sets these different approaches in context with each other.Later developments of INDI explicitly consider actuator dynamics.Those concepts are summarized and discussed in detail.Subsequently,studies that relate INDI to other control methods are summarized.Finally,an overview of various applications of INDI is given,covering different types of control loops and various types of vehicles and plants.This paper seeks to set these developments into context with each other.The purpose of this paper is twofold.INDI is already well-known in the domain of flight control but less so in other fields.Therefore,the paper is written in a comprehensive tutorial style to provide easy access to readers unfamiliar with the topic.On the other hand,the paper can serve as a reference for readers familiar with the topic.
基金supported by the National Major Science and Technology Project of China(2016ZX05004003)the National Natural Science Foundation of China(41574103,41974120,U20B2015)Open Fund of State Key Laboratory of Coal Resources and Safe Mining(Grant No.SKLCRSM19KFA08)。
文摘Fluid and effective fracture identification in reservoirs is a crucial part of reservoir prediction.The frequency-dependent AVO inversion algorithms have proven to be effective for identifying fluid through its dispersion property.However,the conventional frequency-dependent AVO inversion algorithms based on Smith&Gidlow and Aki&Richards approximations do not consider the acquisition azimuth of seismic data and neglect the effect of seismic anisotropic dispersion in the actual medium.The aligned fractures in the subsurface medium induce anisotropy.The seismic anisotropy should be considered while accounting for the seismic dispersion properties through fluid-saturated fractured reservoirs.Anisotropy in such reservoirs is frequency-related due to wave-induced fluid-flow(WIFF)between interconnected fractures and pores.It can be used to identify fluid and effective fractures(fluid-saturated)by using azimuthal seismic data via anisotropic dispersion properties.In this paper,based on Rüger’s equation,we derived an analytical expression in the frequency domain for the frequencydependent AVOAz inversion in terms of fracture orientation,dispersion gradient of isotropic background rock,anisotropic dispersion gradient,and the dispersion at a normal incident angle.The frequency-dependent AVOAz equation utilizes azimuthal seismic data and considers the effect of both isotropic and anisotropic dispersion.Reassigned Gabor Transform(RGT)is used to achieve highresolution frequency division data.We then propose the frequency-dependent AVOAz inversion method to identify fluid and characterize effective fractures in fractured porous reservoirs.Through application to high-qualified seismic data of dolomite and carbonate reservoirs,the results show that the method is useful for identifying fluid and effective fractures in fluid-saturated fractured rocks.
基金the sponsorship of National Natural Science Foundation of China(41974119,U1762103)Science Foundation from Innovation and Technology Support Program for Young Scientists in Colleges of Shandong province and Ministry of Science and Technology of China(2020RA2C620131)。
文摘Frequency-dependent amplitude versus offset(FAVO)inversion is a popular method to estimate the frequency-dependent elastic parameters by using amplitude and frequency information of pre-stack seismic data to guide fluid identification.Current frequency-dependent AVO inversion methods are mainly based on elastic theory without the consideration of the viscoelasticity of oil/gas.A fluid discrimination approach is proposed in this study by incorporating the viscoelasticity and relevant FAVO inversion.Based on viscoelastic and rock physics theories,a frequency-dependent viscoelastic solid-liquid decoupling fluid factor is initially constructed,and its sensitivity in fluid discrimination is compared with other conventional fluid factors.Furthermore,a novel reflectivity equation is derived in terms of the viscoelastic solid-liquid decoupling fluid factor.Due to the introduction of viscoelastic theory,the proposed reflectivity is related to frequency,which is more widely applicable than the traditional elastic reflectivity equation directly derived from the elastic reflectivity equation on frequency.Finally,a pragmatic frequency-dependent inversion method is introduced to verify the feasibility of the equation for frequency-dependent viscoelastic solid-liquid decoupling fluid factor prediction.Synthetic and field data examples demonstrate the feasibility and stability of the proposed approach in fluid discrimination.
基金supported by the National Natural Science Foundation of China(Grant numbers 42074153 and 42274160)the Open Research Fund of SINOPEC Key Laboratory of Geophysics(Grant number 33550006-20-ZC0699-0006).
文摘The identification of hydrocarbons using seismic methods is critical in the prediction of shale oil res-ervoirs.However,delineating shales of high oil saturation is challenging owing to the similarity in the elastic properties of oil-and water-bearing shales.The complexity of the organic matter properties associated with kerogen and hydrocarbon further complicates the characterization of shale oil reservoirs using seismic methods.Nevertheless,the inelastic shale properties associated with oil saturation can enable the utilization of velocity dispersion for hydrocarbon identification in shales.In this study,a seismic inversion scheme based on the fluid dispersion attribute was proposed for the estimation of hydrocarbon enrichment.In the proposed approach,the conventional frequency-dependent inversion scheme was extended by incorporating the PP-wave reflection coefficient presented in terms of the effective fluid bulk modulus.A rock physics model for shale oil reservoirs was constructed to describe the relationship between hydrocarbon saturation and shale inelasticity.According to the modeling results,the hydrocarbon sensitivity of the frequency-dependent effective fluid bulk modulus is superior to the traditional compressional wave velocity dispersion of shales.Quantitative analysis of the inversion re-sults based on synthetics also reveals that the proposed approach identifies the oil saturation and related hydrocarbon enrichment better than the above-mentioned conventional approach.Meanwhile,in real data applications,actual drilling results validate the superiority of the proposed fluid dispersion attribute as a useful hydrocarbon indicator in shale oil reservoirs.
基金This work is supported by the National Natural Science Foundation of China(42304141,41574103 and 41974120)the Joint Funds of the National Natural Science Foundation of China(U20B2015).
文摘Recently,the great potential of seismic dispersion attributes in oil and gas exploration has attracted extensive attention.The frequency-dependent amplitude versus offset(FAVO)technology,with dispersion gradient as a hydrocarbon indicator,has developed rapidly.Based on the classical AVO theory,the technology works on the assumption that elastic parameters are frequency-dependent,and implements FAVO inversion using spectral decomposition methods,so that it can take dispersive effects into account and effectively overcome the limitations of the classical AVO.However,the factors that affect FAVO are complicated.To this end,we construct a unified equation for FAVO inversion by combining several Zoeppritz approximations.We study and compare two strategies respectively with(strategy 1)and without(strategy 2)velocity as inversion input data.Using theoretical models,we investigate the influence of various factors,such as the Zoeppritz approximation used,P-and S-wave velocity dispersion,inversion input data,the strong reflection caused by non-reservoir interfaces,and the noise level of the seismic data.Our results show that FAVO inversion based on different Zoeppritz approximations gives similar results.In addition,the inversion results of strategy 2 are generally equivalent to that of strategy 1,which means that strategy 2 can be used to obtain dispersion attributes even if the velocity is not available.We also found that the existence of non-reservoir strong reflection interface may cause significant false dispersion.Therefore,logging,geological,and other relevant data should be fully used to prevent this undesirable consequence.Both the P-and S-wave related dispersion obtained from FAVO can be used as good indicators of a hydrocarbon reservoir,but the P-wave dispersion is more reliable.In fact,due to the mutual coupling of P-and S-wave dispersion terms,the P-wave dispersion gradient inverted from PP reflection seismic data has a stronger hydrocarbon detection ability than the S-wave dispersion gradient.Moreover,there is little difference in using post-stack data or pre-stack angle gathers as inversion input when only the P-wave dispersion is desired.The real application examples further demonstrate that dispersion attributes can not only indicate the location of a hydrocarbon reservoir,but also,to a certain extent,reveal the physical properties of reservoirs.
基金supported by the National Natural Science Foundation of China(Grant No.41374118)the Research Fund for the Higher Education Doctoral Program of China(Grant No.20120162110015)+3 种基金the China Postdoctoral Science Foundation(Grant No.2015M580700)the Hunan Provincial Natural Science Foundation,the China(Grant No.2016JJ3086)the Hunan Provincial Science and Technology Program,China(Grant No.2015JC3067)the Scientific Research Fund of Hunan Provincial Education Department,China(Grant No.15B138)
文摘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.
基金supported by the National High-Tech Research and Development Program of China(863 Program)(No.2008AA093001)
文摘Cauchy priori distribution-based Bayesian AVO reflectivity inversion may lead to sparse estimates that are sensitive to large reflectivities. For the inversion, the computation of the covariance matrix and regularized terms requires prior estimation of model parameters, which makes the iterative inversion weakly nonlinear. At the same time, the relations among the model parameters are assumed linear. Furthermore, the reflectivities, the results of the inversion, or the elastic parameters with cumulative error recovered by integrating reflectivities are not well suited for detecting hydrocarbons and fuids. In contrast, in Bayesian linear AVO inversion, the elastic parameters can be directly extracted from prestack seismic data without linear assumptions for the model parameters. Considering the advantages of the abovementioned methods, the Bayesian AVO reflectivity inversion process is modified and Cauchy distribution is explored as a prior probability distribution and the time-variant covariance is also considered. Finally, we propose a new method for the weakly nonlinear AVO waveform inversion. Furthermore, the linear assumptions are abandoned and elastic parameters, such as P-wave velocity, S-wave velocity, and density, can be directly recovered from seismic data especially for interfaces with large reflectivities. Numerical analysis demonstrates that all the elastic parameters can be estimated from prestack seismic data even when the signal-to-noise ratio of the seismic data is low.
基金supported by the Fundamental Research Funds for the Central Universities of China(No.2652017438)the National Science and Technology Major Project of China(No.2016ZX05003-003)
文摘Multiwave seismic technology promotes the application of joint PP–PS amplitude versus offset (AVO) inversion;however conventional joint PP–PS AVO inversioan is linear based on approximations of the Zoeppritz equations for multiple iterations. Therefore the inversion results of P-wave, S-wave velocity and density exhibit low precision in the faroffset;thus, the joint PP–PS AVO inversion is nonlinear. Herein, we propose a nonlinear joint inversion method based on exact Zoeppritz equations that combines improved Bayesian inference and a least squares support vector machine (LSSVM) to solve the nonlinear inversion problem. The initial parameters of Bayesian inference are optimized via particle swarm optimization (PSO). In improved Bayesian inference, the optimal parameter of the LSSVM is obtained by maximizing the posterior probability of the hyperparameters, thus improving the learning and generalization abilities of LSSVM. Then, an optimal nonlinear LSSVM model that defi nes the relationship between seismic refl ection amplitude and elastic parameters is established to improve the precision of the joint PP–PS AVO inversion. Further, the nonlinear problem of joint inversion can be solved through a single training of the nonlinear inversion model. The results of the synthetic data suggest that the precision of the estimated parameters is higher than that obtained via Bayesian linear inversion with PP-wave data and via approximations of the Zoeppritz equations. In addition, results using synthetic data with added noise show that the proposed method has superior anti-noising properties. Real-world application shows the feasibility and superiority of the proposed method, as compared with Bayesian linear inversion.
基金Project(41304090)supported by the National Natural Science Foundation of ChinaProject(2016YFC0303104)supported by the National Key Research and Development Project of ChinaProject(DY135-S1-1-07)supported by Ocean 13th Five-Year International Marine Resources Survey and Development of China
文摘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.
基金supported by the National Natural Science Foundation of China(U19B6003,42122029)the Strategic Cooperation Technology Projects of CNPC and CUPB(ZLZX 202003)partially supported by SEG/WesternGeco Scholarship,SEG Foundation/Chevron Scholarship,and SEG/Norman and Shirley Domenico Scholarship
文摘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.
基金Project(20120162110015)supported by the Research Fund for the Doctoral Program of Higher Education,ChinaProject(41004053)supported by the National Natural Science Foundation of ChinaProject(12c0241)supported by Scientific Research Fund of Hunan Provincial Education Department,China
文摘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.
文摘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.
基金the sponsorship of the National Basic Research Program of China (973 Program,2013CB228604,2014CB239201)the National Oil and Gas Major Projects of China (2011ZX05014-001-010HZ,2011ZX05014-001-006-XY570) for their funding of this research
文摘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.
基金supported by the Science for Earthquake Resilience of China Earthquake Administration(Grant No.XH14060)the National Natural Science Foundation of China(Grant No.51478135)
文摘A one-dimensional equivalent linear method （EQL） is widely used in estimating seismic ground response. For this method, the shear modulus and damping ratio of inelastic soil are supposed to be frequency independent. However, historical earthquake records and laboratory test results indicate that nonlinear soil behavior is frequency- dependent. Several frequency-dependent equivalent linear methods （FDEQL） related to the Fourier amplitude of shear strain time history have been developed to take into account the frequency-dependent soil behavior. Furthermore, the shear strain threshold plays an important role in soil behavior. For shear strains below the elastic shear strain threshold, soil behaves essentially as a linear elastic mate- rial. To consider the effect of elastic-shear-strain-threshold- and frequency-dependent soil behavior on wave propaga- tion, the shear-strain-threshold- and frequency-dependent equivalent linear method （TFDEQL） is proposed. A series of analyses is implemented for EQL, FDEQL, and TFDEQL methods. Results show that elastic-shear-strain-threshold- and frequency-dependent soil behavior plays a great influence on the computed site response, especially for the high- frequency band. Also, the effect of elastic-strain-threshold- and frequency-dependent soil behavior on the site response is analyzed from relatively weak to strong input motion, and results show that the effect is more pronounced as input motion goes from weak to strong.
基金Project(41374118)supported by the National Natural Science Foundation,ChinaProject(20120162110015)supported by Research Fund for the Doctoral Program of Higher Education,China+3 种基金Project(2015M580700)supported by the China Postdoctoral Science Foundation,ChinaProject(2016JJ3086)supported by the Hunan Provincial Natural Science Foundation,ChinaProject(2015JC3067)supported by the Hunan Provincial Science and Technology Program,ChinaProject(15B138)supported by the Scientific Research Fund of Hunan Provincial Education Department,China
文摘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.
基金supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)the Advanced Research Project of Army Equipment Development(No.301020803)
文摘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.
基金supported by the Chinese Aviation Science Fund(20160757001)the National Natural Science Foundation of China(10577012)。
文摘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.
文摘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.
