Application of the Conjugate Gradient Optimization Algorithm of Neural Network on Laser Machining

在应用激光技术加工复杂曲面时,通常以采样点集为插值点来建立曲面函数,然后实现曲面上任意坐标点的精确定位。人工神经网络的BP算法能实现函数插值,但计算精度偏低,往往达不到插值精确要求,造成较大的加工误差。提出人工神经网络的共轭梯度最优化插值新算法,并通过实例仿真,证明了这种曲面精确定位方法的可行性,从而为激光加工的三维精确定位提供了一种良好解决方案。这种方法已经应用在实际中。

基于信息重建技术的地震信号处理方法研究

The dissertation addressed the problems of signals reconstruction and data restoration in seismic data processing, which takes the representation methods of signal as the main clue, and take the seismic information reconstruction (signals separation and trace interpolation) as the core. On the natural bases signal representation, I present the ICA fundamentals, algorithms and its original applications to nature earth quake signals separation and survey seismic signals separation. On determinative bases signal representation, the paper proposed seismic dada reconstruction least square inversion regularization methods, sparseness constraints, pre-conditioned conjugate gradient methods, and their applications to seismic de-convolution, Radon transformation, et. al. The core contents are about de-alias uneven seismic data reconstruction algorithm and its application to seismic interpolation. Although the dissertation discussed two cases of signal representation, they can be integrated into one frame, because they both deal with the signals or information restoration, the former reconstructing original signals from mixed signals, the later reconstructing whole data from sparse or irregular data. The goal of them is same to provide pre-processing methods and post-processing method for seismic pre-stack depth migration. ICA can separate the original signals from mixed signals by them, or abstract the basic structure from analyzed data. I surveyed the fundamental, algorithms and applications of ICA. Compared with KL transformation, I proposed the independent components transformation concept (ICT). On basis of the ne-entropy measurement of independence, I implemented the FastICA and improved it by covariance matrix. By analyzing the characteristics of the seismic signals, I introduced ICA into seismic signal processing firstly in Geophysical community, and implemented the noise separation from seismic signal. Synthetic and real data examples show the usability of ICA to seismic signal processing and initial effects are achieved. The application of ICA to separation quake conversion wave from multiple in sedimentary area is made, which demonstrates good effects, so more reasonable interpretation of underground un-continuity is got. The results show the perspective of application of ICA to Geophysical signal processing. By virtue of the relationship between ICA and Blind Deconvolution , I surveyed the seismic blind deconvolution, and discussed the perspective of applying ICA to seismic blind deconvolution with two possible solutions. The relationship of PC A, ICA and wavelet transform is claimed. It is proved that reconstruction of wavelet prototype functions is Lie group representation. By the way, over-sampled wavelet transform is proposed to enhance the seismic data resolution, which is validated by numerical examples. The key of pre-stack depth migration is the regularization of pre-stack seismic data. As a main procedure, seismic interpolation and missing data reconstruction are necessary. Firstly, I review the seismic imaging methods in order to argue the critical effect of regularization. By review of the seismic interpolation algorithms, I acclaim that de-alias uneven data reconstruction is still a challenge. The fundamental of seismic reconstruction is discussed firstly. Then sparseness constraint on least square inversion and preconditioned conjugate gradient solver are studied and implemented. Choosing constraint item with Cauchy distribution, I programmed PCG algorithm and implement sparse seismic deconvolution, high resolution Radon Transformation by PCG, which is prepared for seismic data reconstruction. About seismic interpolation, dealias even data interpolation and uneven data reconstruction are very good respectively, however they can not be combined each other. In this paper, a novel Fourier transform based method and a algorithm have been proposed, which could reconstruct both uneven and alias seismic data. I formulated band-limited data reconstruction as minimum norm least squares inversion problem where an adaptive DFT-weighted norm regularization term is used. The inverse problem is solved by pre-conditional conjugate gradient method, which makes the solutions stable and convergent quickly. Based on the assumption that seismic data are consisted of finite linear events, from sampling theorem, alias events can be attenuated via LS weight predicted linearly from low frequency. Three application issues are discussed on even gap trace interpolation, uneven gap filling, high frequency trace reconstruction from low frequency data trace constrained by few high frequency traces. Both synthetic and real data numerical examples show the proposed method is valid, efficient and applicable. The research is valuable to seismic data regularization and cross well seismic. To meet 3D shot profile depth migration request for data, schemes must be taken to make the data even and fitting the velocity dataset. The methods of this paper are used to interpolate and extrapolate the shot gathers instead of simply embedding zero traces. So, the aperture of migration is enlarged and the migration effect is improved. The results show the effectiveness and the practicability.

Splitting the fast and slow motions in molecular dynamics simulations based on the change of cold potential well bottom

Abstract. The atomic motion is coupled by the fast and slow components due to the high frequency vibration of atoms and the low frequency deformation of atomic lattice, respectively. A two-step approximate method was presented to determine the atomic slow motion. The first step is based on the change of the location of the cold potential well bottom and the second step is based on the average of the appropriate slow velocities of the surrounding atoms. The simple tensions of one-dimensional atoms and two-dimensional atoms were performed with the full molecular dynamics simulations. The conjugate gradient method was employed to determine the corresponding location of cold potential well bottom. Results show that our two-step approximate method is appropriate to determine the atomic slow motion under the low strain rate loading. This splitting method may be helpful to develop more efficient molecular modeling methods and simulations pertinent to realistic loading conditions of materials.

Molecular modeling on some human interleukins sharing gamma c of interleukin-2 receptor, and structure-function relationships

Five models for human interleukin-7 (HIL-7), HIL-9, HIL-13, HIL-15 and HIL-17 have been generated by SYBYL software package. The primary models were optimized using molecular dynamics and molecular mechanics methods. The final models were optimized using a steepest descent algorithm and a subsequent conjugate gradient method. The complexes with these interleukins and the common gamma chain of interleukin-2 receptor (IL-2R) were constructed and subjected to energy minimization. We found residues, such as Gln127 and Tyr103, of the common gamma chain of IL-2R are very important. Other residues, e.g. Lys70, Asn128 and Glu162, are also significant. Four hydrophobic grooves and two hydrophilic sites converge at the active site triad of the gamma chain. The binding sites of these interleukins interaction with the common gamma chain exist in the first helical and/or the fourth helical domains. Therefore, we conclude that these interleukins binds to the common gamma chain of IL-2R by the first and the fourth helix domain. Especially at the binding sites of some residues (lysine, arginine, asparagine, glutamic acid and aspartic acid), with a discontinuous region of the common gamma chain of IL-2R, termed the interleukins binding sites (103-210). The study of these sites can be important for the development of new drugs. (C) 2000 Elsevier Science B.V. All rights reserved.

Splitting the Fast and Slow Motions in Molecular Dynamics Simulations Based on the Change of Cold Potential Well Bottom

The atomic motion is coupled by the fast and slow components due to the high frequency vibration of atoms and the low frequency deformation of atomic lattice, respectively. A two-step approximate method was presented to determine the atomic slow motion. The first step is based on the change of the location of the cold potential well bottom and the second step is based on the average of the appropriate slow velocities of the surrounding atoms. The simple tensions of one-dimensional atoms and two-dimensional atoms were performed with the full molecular dynamics simulations. The conjugate gradient method was employed to determine the corresponding location of cold potential well bottom. Results show that our two-step approximate method is appropriate to determine the atomic slow motion under the low strain rate loading. This splitting method may be helpful to develop more efficient molecular modeling methods and simulations pertinent to realistic loading conditions of materials.

地下水流动数值模拟的并行计算方法研究

Numerical modeling of groundwater is very important for understanding groundwater flow and solving hydrogeological problem. Today, groundwater studies require massive model cells and high calculation accuracy, which are beyond single-CPU computer’s capabilities. With the development of high performance parallel computing technologies, application of parallel computing method on numerical modeling of groundwater flow becomes necessary and important. Using parallel computing can improve the ability to resolve various hydro-geological and environmental problems. In this study, parallel computing method on two main types of modern parallel computer architecture, shared memory parallel systems and distributed shared memory parallel systems, are discussed. OpenMP and MPI (PETSc) are both used to parallelize the most widely used groundwater simulator, MODFLOW. Two parallel solvers, P-PCG and P-MODFLOW, were developed for MODFLOW. The parallelized MODFLOW was used to simulate regional groundwater flow in Beishan, Gansu Province, which is a potential high-level radioactive waste geological disposal area in China. 1. The OpenMP programming paradigm was used to parallelize the PCG (preconditioned conjugate-gradient method) solver, which is one of the main solver for MODFLOW. The parallel PCG solver, P-PCG, is verified using an 8-processor computer. Both the impact of compilers and different model domain sizes were considered in the numerical experiments. The largest test model has 1000 columns, 1000 rows and 1000 layers. Based on the timing results, execution times using the P-PCG solver are typically about 1.40 to 5.31 times faster than those using the serial one. In addition, the simulation results are the exact same as the original PCG solver, because the majority of serial codes were not changed. It is worth noting that this parallelizing approach reduces cost in terms of software maintenance because only a single source PCG solver code needs to be maintained in the MODFLOW source tree. 2. P-MODFLOW, a domain decomposition–based model implemented in a parallel computing environment is developed, which allows efficient simulation of a regional-scale groundwater flow. The basic approach partitions a large model domain into any number of sub-domains. Parallel processors are used to solve the model equations within each sub-domain. The use of domain decomposition method to achieve the MODFLOW program distributed shared memory parallel computing system will process the application of MODFLOW be extended to the fleet of the most popular systems, so that a large-scale simulation could take full advantage of hundreds or even thousands parallel processors. P-MODFLOW has a good parallel performance, with the maximum speedup of 18.32 (14 processors). Super linear speedups have been achieved in the parallel tests, indicating the efficiency and scalability of the code. Parallel program design, load balancing and full use of the PETSc were considered to achieve a highly efficient parallel program. 3. The characterization of regional ground water flow system is very important for high-level radioactive waste geological disposal. The Beishan area, located in northwestern Gansu Province, China, is selected as a potential site for disposal repository. The area includes about 80000 km2 and has complicated hydrogeological conditions, which greatly increase the computational effort of regional ground water flow models. In order to reduce computing time, parallel computing scheme was applied to regional ground water flow modeling. Models with over 10 million cells were used to simulate how the faults and different recharge conditions impact regional ground water flow pattern. The results of this study provide regional ground water flow information for the site characterization of the potential high-level radioactive waste disposal.

地震波阻抗反演的迭代正则化算法

Post-stack seismic impedance inversion is the key technology of reservoir prediction and identification. Geophysicists have done a lot of research for the problem, but the developed methods still cannot satisfy practical requirements completely. The results of different inversion methods are different and the results of one method used by different people are different too. The reasons are due to the quality of seismic data, inaccurate wavelet extraction, errors between normal incidence assumption and real situation, and so on. In addition, there are two main influence factors: one is the band-limited property of seismic data; the other is the ill-posed property of impedance inversion. Thus far, the most effective way to solve the band-limited problem is the constrained inversion. And the most effective way to solve ill-posed problems is the regularization method assisted with proper optimization techniques. This thesis systematically introduces the iterative regularization methods and numerical optimization methods for impedance inversion. A regularized restarted conjugate gradient method for solving ill-posed problems in impedance inversion is proposed. Theoretic simulations are made and field data applications are performed. It reveals that the proposed algorithm possesses the superiority to conventional conjugate gradient method. Finally, non-smooth optimization is proposed as the further research direction in seismic impedance inversion according to practical situation.

南海张裂大陆边缘数值模拟研究

The South China Sea (SCS) is one of the largest marginal seas in the western Pacific, which is located at the junction of Eurasian plate, Pacific plate and Indian-Australian plate. It was formed by continent breakup and sea-floor spreading in Cenozoic. The complicated interaction among the three major plates made tectonic movement complex and geological phenomena very rich in this area. The SCS is an ideal place to study the formation and evolution of rifted continental margin and sea-floor spreading since it is old enough to have experienced the major stages of the basin evolution but still young enough to have preserved its original nature. As the demand for energy grows day by day in our country, the deep water region of the northern continental margin in the SCS has become a focus of oil and gas exploration because of its huge hydrocarbon potential. Therefore, to study the rifted continental margin of the SCS not only can improve our understanding of the formation and evolution processes of rifted continental margin, but also can provide theoretical support for hydrocarbon exploration in rifted continental margin. This dissertation mainly includes five topics as follows: (1) Various classic lithosphere stretching models are reviewed, and the continuous non-uniform stretching model is modified to make it suitable for the case where the extension of lithopheric mantle exceeds that of the crust. Then simple/pure shear flexural cantilever model is applied to model the basement geometries of SO49-18 profile in the northern continental margin of the SCS. By fitting the basements obtained by using 2DMove software with modeling results, it is found that the reasonable effective elastic thickness is less than 5km in this region. According to this result, it is assumed that there is weak lower crust in the northern continental margin in the SCS. (2) We research on the methods for stretching factor estimation based on various lithosphere stretching models, and apply the method based on multiple finite rifting model to estimate the stretching factors of several wells and profiles in the northern continental margin of the SCS. (3) We improve one-dimension strain rate inversion method with conjugate gradient method, and apply it to invert the strain rate of several wells in the northern continental margin of the SCS. Two-dimension strain rate forward modeling is carried out, and the modeling results show that effective elastic thickness is a key parameter to control basin’s geometry. (4) We simulate divergent upwelling mantle flow model using finite difference method, and apply this newly developed model to examine the formation mechanism of the northwest and central sub-basin in the SCS. (5) We inverse plate thickness and basal temperature of oceanic lithosphere using sea-floor ages and bathymetries of the North Pacific and the North Atlantic based on varied-parameters plate model, in which the heat conductivity, heat capacity and coefficient of thermal expansion depend on temperature or depth. A new empirical formula is put forward based the inversed parameters, which depicts the relation among sea-floor age, bathymetry and heat flow. Then various similar empirical formulae, including the newly developed one, are applied to examine the sea-floor spread issue in the SCS based on the heat flow and bathymetry data of the abyssal sub-basin.

三维油藏数值模拟正反演算法研究

The dynamic prediction of complex reservoir development is one of the important research contents of dynamic analysis of oil and gas development. With the increase development of time, the permeabilities and porosities of reservoirs and the permeability of block reservoir at its boundaries are dynamically changing. How to track the dynamic change of permeability and porosity and make certain the permeability of block reservoir at its boundary is an important practical problem. To study developing dynamic prediction of complex reservoir, the key problem of research of dynamic prediction of complex reservoir development is realizing inversion of permeability and porosity. To realize the inversion, first of all, the fast forward and inverse method of 3-dimension reservoir simulation must be studied. Although the inversion has been widely applied to exploration and logging, it has not been applied to3-dimension reservoir simulation. Therefore, the study of fast forward and inverse method of 3-dimension reservoir simulation is a cutting-edge problem, takes on important realistic signification and application value. In this dissertation, 2-dimension and 3-dimension fluid equations in porous media are discretized by finite difference, obtaining finite difference equations to meet the inner boundary conditions by Peaceman's equations, giving successive over relaxation iteration of 3-dimension fluid equations in porous media and the dimensional analysis. Several equation-solving methods are compared in common use, analyzing its convergence and convergence rate. The alternating direction implicit procedure of 2-dimension has been turned into successive over relaxation iteration of alternating direction implicit procedure of 3-dimension fluid equations in porous media, which possesses the virtues of fast computing speed, needing small memory of computer, good adaptability for heterogeneous media and fast convergence rate. The geological model of channel-sandy reservoir has been generated with the help of stochastic simulation technique, whose cross sections of channel-sandy reservoir are parabolic shapes. This method makes the hard data commendably meet, very suit for geological modeling of containing complex boundary surface reservoir. To verify reliability of the method, theoretical solution and numerical solution are compared by simplifying model of 3-dimension fluid equations in porous media, whose results show that the only difference of the two pressure curves is that the numerical solution is lower than theoretical at the wellbore in the same space. It proves that using finite difference to solve fluid equations in porous media is reliable. As numerical examples of 3-dimension heterogeneous reservoir of the single-well and multi-well, the pressure distributions have been computed respectively, which show the pressure distributions there are clearly difference as difference of the permeabilities is greater than one order of magnitude, otherwise there are no clearly difference. As application, the pressure distribution of the channel-sandy reservoir have been computed, which indicates that the space distribution of pressure strongly relies on the direction of permeability, and is sensitive for space distributions of permeability. In this dissertation, the Peaceman's equations have been modified into solving vertical well problem and horizontal well problem simultaneously. In porous media, a 3D layer reservoir in which contain vertical wells and horizontal wells has been calculated with iteration. For channel-sandy reservoir in which there are also vertical wells and horizontal wells, a 3D transient heterogeneous fluid equation has been discretized. As an example, the space distribution of pressure has been calculated with iteration. The results of examples are accord with the fact, which shows the modification of Peaceman's equation is correct. The problem has been solved in the space where there are vertical and horizontal wells. In the dissertation, the nonuniform grid permeability integration equation upscaling method, the nonuniform grid 2D flow rate upscaling method and the nonuniform grid 3D flow rate upscaling method have been studied respectively. In those methods, they enhance computing speed greatly, but the computing speed of 3D flow rate upscaling method is faster than that of 2D flow rate upscaling method, and the precision of 3D flow rate upscaling method is better than that of 2D flow rate upscaling method. The results also show that the solutions of upscaling method are very approximating to that of fine grid blocks. In this paper, 4 methods of fast adaptive nonuniform grid upscaling method of 3D fluid equations in porous media have been put forward, and applied to calculate 3D heterogeneous reservoir and channel-sandy reservoir, whose computing results show that the solutions of nonuniform adaptive upscaling method of 3D heterogeneous fluid equations in porous media are very approximating to that of fine grid blocks in the regions the permeability or porosity being abnormity and very approximating to that of coarsen grid blocks in the other region, however, the computing speed of adaptive upscaling method is 100 times faster than that of fine grid block method. The formula of sensitivity coefficients are derived from initial boundary value problems of fluid equations in porous media by Green's reciprocity principle. The sensitivity coefficients of wellbore pressure to permeability parameters are given by Peaceman's equation and calculated by means of numerical calculation method of 3D transient anisotropic fluid equation in porous media and verified by direct method. The computing results are in excellent agreement with those obtained by the direct method, which shows feasibility of the method. In the dissertation, the calculating examples are also given for 3D reservoir, channel-sandy reservoir and 3D multi-well reservoir, whose numerical results indicate: around the well hole, the value of the sensitivity coefficients of permeability is very large, the value of the sensitivity coefficients of porosity is very large too, but the sensitivity coefficients of porosity is much less than the sensitivity coefficients of permeability, so that the effect of the sensitivity coefficients of permeability for inversion of reservoir parameters is much greater than that of the sensitivity coefficients of porosity. Because computing the sensitivity coefficients needs to call twice the program of reservoir simulation in one iteration, realizing inversion of reservoir parameters must be sustained by the fast forward method. Using the sensitivity coefficients of permeability and porosity, conditioned on observed valley erosion thickness in wells (hard data), the inversion of the permeabilities and porosities in the homogeneous reservoir, homogeneous reservoir only along the certain direction and block reservoir are implemented by Gauss-Newton method or conjugate gradient method respectively. The results of our examples are very approximating to the real data of permeability and porosity, but the convergence rate of conjugate gradient method is much faster than that of Gauss-Newton method.

ω循环型预条件矩阵及其应用

In this paper, we apply the preconditioned conjugate gradient method to the solution of positive-definite Toeplitz systems, especially we introduce a new kind of co-circulant preconditioners Pn[ca] by the use of embedding method. We have also discussed the properties of these new preconditioners and proved that many of former preconditioners can be considered as some special cases of Pn[co\. Because of the introduction of co-circulant preconditioners pn[a>], we can greatly overcome the singularity caused by circulant preconditioners. We have discussed the oo-circulant series and functions. We compare the ordinary circularity with the co-circularity, showing that the latter one can be considered as the extended form of the former one; correspondingly, many methods and theorems of the ordinary circularity can be extended. Furthermore, we present the co-circulant decompositional method. By the use of this method, we can divide any co-circulant signal into a summation of many sub-signals; especially among those sub-signals, there are many subseries of which their period is just equal to 1, which are actually the frequency elements of the original co-circulant signal. In this way, we can establish the relationship between the signal and its frequency elements, that is, the frequency elements hi the frequency domain are actually signals with the period of 1 in the spatial domain. We have also proved that the co-circulant has already existed in the traditional Fourier theory. By the use of different criteria for constructing preconditioners, we can get many different preconditioned systems. From the preconditioned systems PN[

地震反射系数成像方法研究

Reflectivity sequences extraction is a key part of impedance inversion in seismic exploration. Although many valid inversion methods exist, with crosswell seismic data, the frequency brand of seismic data can not be broadened to satisfy the practical need. It is an urgent problem to be solved. Pre-stack depth migration which developed in these years becomes more and more robust in the exploration. It is a powerful technology of imaging to the geological object with complex structure and its final result is reflectivity imaging. Based on the reflectivity imaging of crosswell seismic data and wave equation, this paper completed such works as follows: Completes the workflow of blind deconvolution, Cauchy criteria is used to regulate the inversion(sparse inversion). Also the precondition conjugate gradient(PCG) based on Krylov subspace is combined with to decrease the computation, improves the speed, and the transition matrix is not necessary anymore be positive and symmetric. This method is used to the high frequency recovery of crosswell seismic section and the result is satisfactory. Application of rotation transform and viterbi algorithm in the preprocess of equation prestack depth migration. In equation prestack depth migration, the grid of seismic dataset is required to be regular. Due to the influence of complex terrain and fold, the acquisition geometry sometimes becomes irregular. At the same time, to avoid the aliasing produced by the sparse sample along the on-line, interpolation should be done between tracks. In this paper, I use the rotation transform to make on-line run parallel with the coordinate, and also use the viterbi algorithm to complete the automatic picking of events, the result is satisfactory. 1. Imaging is a key part of pre-stack depth migration besides extrapolation. Imaging condition can influence the final result of reflectivity sequences imaging greatly however accurate the extrapolation operator is. The author does migration of Marmousi under different imaging conditions. And analyzes these methods according to the results. The results of computation show that imaging condition which stabilize source wave field and the least-squares estimation imaging condition in this paper are better than the conventional correlation imaging condition. The traditional pattern of "distributed computing and mass decision" is wisely adopted in the field of seismic data processing and becoming an obstacle of the promoting of the enterprise management level. Thus at the end of this paper, a systemic solution scheme, which employs the mode of "distributed computing - centralized storage - instant release", is brought forward, based on the combination of C/S and B/S release models. The architecture of the solution, the corresponding web technology and the client software are introduced. The application shows that the validity of this scheme.

MILU-CG method and the numerical study on the flow around a rotating circular cylinder

A hybrid finite difference method and vortex method (HDV), which is based on domain decomposition and proposed by the authors (1992), is improved by using a modified incomplete LU decomposition conjugate gradient method (MILU-CG), and a high order implicit difference algorithm. The flow around a rotating circular cylinder at Reynolds number R-e = 1000, 200 and the angular to rectilinear speed ratio alpha is an element of (0.5, 3.25) is studied numerically. The long-time full developed features about the variations of the vortex patterns in the wake, and drag, lift forces on the cylinder are given. The calculated streamline contours agreed well with the experimental visualized flow pictures. The existence of critical states and the vortex patterns at the states are given for the first time. The maximum lift to drag force ratio can be obtained nearby the critical states.

Compact finite difference - Fourier spectral method for three-dimensional incompressible Navier-Stokes equations

A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported.