时域CFD/CSD耦合方法能量精度分析及应用

研究两类时域计算流体力学/计算结构力学（CFD/CSD）耦合方法：串行分区方法和并行分区方法。从耦合界面能量守恒的角度分析不同耦合方法对能量守恒误差的影响。在非同位方法和并行分区方法的基础上提出非同位并行分区方法。使用不同的耦合方法,对二维气动弹性算例Isogai Wing进行计算,结果表明减小耦合界面上的能量守恒误差可以有效的提高计算精度,效率高于紧耦合方法;非同位分区方法的能量守恒误差小于同位分区方法,并且可以使控制方程满足界面连续条件;非同位并行分区方法继承非同位分区方法和并行分区方法的全部优点,采用该方法计算颤振边界,和文献结果吻合。     

Two-step camera calibration method based on the SPGD algorithm

Given the rapid convergence characteristic of the stochastic parallel gradient descent (SPGD) algorithm, this study proposes a method that applies the algorithm to a two-step camera calibration method to resolve the frequent iteration and long calibration time deficiencies that exist under the traditional two-step camera calibration method, thereby achieving rapid calibration. The method first uses image coordinates obtained with subpixel positioning technology as initial values of control variables, in addition to positive disturbances produced on a two-dimensional plane, then uses two-step theory to calculate the average value of aberrations. Based on the same rationale, negative disturbances are then produced and the average value of the aberrations is calculated. Finally if, after assessing whether to continue with further iterations based on the difference in these values, continued iterations confirm new control variables based on the SPGD algorithm iteration formula, a new cycle is started until the results satisfy requirements. Theoretical analysis and experimental results show that the proposed rapid calibration method using the SPGD algorithm in the two-step camera calibration method is 3-4 times faster than the traditional two-step calibration method, and that it has significant potential value for use in certain time-constrained projects.     

Complex amplitude modulation by use of liquid-crystal spatial light modulators

We propose to study the conditions for implementation of complex amplitude modulation on standard liquid-crystal spatial light modulators when illuminated by polarized light. The spatial light modulators are used in a conventional configuration, i.e., the voltage is applied parallel to the wave-front propagation direction. The most commonly used liquid-crystal materials are compared and their usefulness in some general applications discussed. Their specificities with respect to different modulation types and application requirements are briefly described. Typical characteristics such as response time, modulation range, and wavelength insensitivity are also discussed. Finally, as an illustration, a first attempt at nomenclature is proposed for the case of a linearly polarized light.     

Applying gray-scaled detour phase hologram on liquid crystal on silicon spatial light modulator (LCoS-SLM)

In order to solve the representation problem of computer-generated holograms, multiple algorithms have been devised. One of which is the well-known detour phase method. This method has recently been modified to be optimized to display the generated hologram on twisted nematic spatial light modulators. In this paper, we apply the modified gray-scaled detour phase holograms on another type of spatial light modulators, which is of utmost importance in the field, namely the reflective liquid crystal on silicon spatial light modulator.     

A transient FETI methodology for large-scale parallel implicit computations in structural mechanics

We present a domain decomposition method for implicit schemes that requires significantly less storage than factorization algorithms, that is several times faster than other popular direct and iterative methods, that can be easily implemented on both shared and local memory parallel processors, and that is both computationally and communication-wise efficient. The proposed transient domain decomposition method is an extension of the method of Finite Element Tearing and Interconnecting (FETI) developed by Farhat and Roux for the solution of static problems. Serial and parallel performance results on the CRAY Y-MP/8 and the iPSC-860/128 systems are reported and analyzed for realistic structural dynamics problems. These results establish the superiority of the FETI method over both the serial/parallel conjugate gradient algorithm with diagonal scaling and the serial/parallel direct method, and contrast the computational power of the iPSC-860/128 parallel processor with that of the CRAY Y-MP/8 system.     

All-optical implementation of a self-organizing map: Learning and taxonomy capability assessment

We present some experimental results obtained with an all-optical implementation of a self-organizing map. The system is based on two ferroelectric liquid-crystal, bistable optically addressed spatial light modulators (BOASLM's) used as parallel read/write optical memories and as thresholding devices. Modifications made to adapt the basic algorithm to the BOASLM's are studied in computer simulations that predict training-class loss due to the simplified decision stage as the principal drawback. Experimental results show good system behavior in recognition mode, demonstrating generalization properties and confirming the choice of a BOASLM memory. All-optical learning is shown in simple cases, and the elementary BOASLM decision function is confirmed as the major limiting factor. The ultimate possible system performance is discussed, and ways of overcoming present limits are suggested.     

利用二阶循环平稳性的信道自适应盲辨识

提出了利用二阶循环平稳性信道盲辨识的自适应求解方法。通过递推更新循环相关函数,从而完成了循环相关矩阵的自适应估计。利用共轭梯度搜索的方法实现信道的自适应盲辨识,并讨论了梯度算法中步长选取的问题,提出了可变步长选取的方法。由于采用二阶循环统计量,因此算法既简单又可以很好的抑制平稳加性有色噪声。计算机仿真表明,在低信噪比情况下,自适应算法能很好的工作。     

On the real-time reconstruction of digital holograms displayed on photosensitive liquid crystal systems

Dynamic optical reconstruction of digital binary holograms projected on optically addressed liquid crystal spatial light modulators with the use of a computer driven multimedia projector is described. A high spatial resolution, sensitivity and full reversibility of the manufactured spatial light modulators are achieved by the use of a photoconducting PVK:TNF polymer layer serving as a transducer of incoming light intensity pattern into modulation of refractive index inside the adjacent LC layer. Linearly polarized laser light reconstructs the phase holograms at the video rate. The advantages and drawbacks of the presented system are discussed.     

A Modified Three-Term Conjugate Gradient Algorithm for Large-Scale Nonsmooth Convex Optimization

It is well known that Newton and quasi-Newton algorithms are effective to small and medium scale smooth problems because they take full use of corresponding gradient function’s information but fail to solve nonsmooth problems. The perfect algorithm stems from concept of ‘bundle’ successfully addresses both smooth and nonsmooth complex problems, but it is regrettable that it is merely effective to small and medium optimization models since it needs to store and update relevant information of parameter’s bundle. The conjugate gradient algorithm is effective both large-scale smooth and nonsmooth optimization model since its simplicity that utilizes objective function’s information and the technique of Moreau-Yosida regularization. Thus, a modified three-term conjugate gradient algorithm was proposed, and it has a sufficiently descent property and a trust region character. At the same time, it possesses the global convergence under mild assumptions and numerical test proves it is efficient than similar optimization algorithms.     

Correcting the aero-optical aberration of the supersonic mixing layer with adaptive optics: concept validation

We describe an adaptive optics (AO) system for correcting the aero-optical aberration of the supersonic mixing layer and test its performance with numerical simulations. The AO system is based on the measurement of distributed Strehl ratios and the stochastic parallel gradient descent (SPGD) algorithm. The aero-optical aberration is computed by the direct numerical simulation of a two-dimensional supersonic mixing layer. When the SPGD algorithm is applied directly, the AO cannot give effective corrections. This paper suggests two strategies to improve the performance of the SPGD algorithm for use in aero-optics. The first one is using an iteration process keeping finite memory, and the second is based on the frozen hypothesis. With these modifications, the performance of AO is improved and the aero-optical aberration can be corrected to some noticeable extent. The possibility of experimental implementation is also discussed.     

基于GMM-ICSA的光谱重叠峰分解研究

针对X射线荧光光谱法(XRF)中Pb元素和As元素的重叠峰导致的元素浓度建模困难、乌鸦搜索算法(CSA)鲁棒性较弱等问题,将高斯混合模型(GMM)与改进型乌鸦算法(ICSA)相结合来实现重叠峰的分解。ICSA相比于CSA的改进主要有:引入了“乌鸦反哺”的特性,将GMM与ICSA更好的衔接在一起;将固定的意识概率更改为梯度型,使种群迭代更有多样性;适当调整了全局的优化策略,使算法更稳定收敛更快。将GMM模型与GMM-ICSA模型作对比实验,可得优化后的模型分解精度提升了4.93%;同时以均方误差和迭代时间为衡量搜索算法的标准,将ICSA与同类型的4种算法做了对比实验得出:CSA的均方误差和迭代时间均优于其他算法,从而表明改进后的算法能处理重叠峰问题的可行性。     

Fast and highly parallel content addressing of a large amount of information recorded in a holographic memory

It has recently become possible to fabricate spatial light modulators for holographic information retrieval. We analyze the signal-to-noise ratios in two typical holographic information retrieval systems, serial and inverted, and we discuss the possibilities of implementing holographic information retrieval with a newly proposed spatial light modulator that uses a Fabry-Perot étalon with a piezoelectrically driven mirror.     

MR imaging reconstruction using a modified descent‐type alternating direction method

In the magnetic resonance imaging (MRI) field, total variation (TV) which is the ‐norm of the gradient‐magnitude images (GMI) is widely used as the regularization in the compressive sensing (CS) based reconstruction algorithm. Based on the classic augmented Lagrangian multiplier method, we propose a modified descent‐type alternating direction method (ADM) for solving the TV regularized reconstruction problems in the following sense: an iteration result generated by the ADM is utilized to generate a descent direction; an appropriate step size along this descent direction is identified; and the penalty parameters are updated. The proposed algorithm effectively combines alternating direction technique with the descent‐type method. Extensive results demonstrate that the proposed algorithm, is competitive with, and often outperforms, other state‐of‐the‐art solvers in the field.     

Digital optical computing with magneto-optic spatial light modulators: a new and efficient multiplication algorithm

Digital optical computing executed on arrays of binary data can offer parallel processing and multivalued output, which permits more flexibility in algorithm development. The hardware used consists of two computer-controlled magneto-optic spatial-light-modulator arrays in conjunction with a CCD detector array as the computational hardware. Algorithms for binary-processing tasks are presented. We used magneto-optic spatial light modulators for parallel processing in a way that exploits multivalued output. Also, in carrying this evaluation out, we developed a new and efficient multiplication algorithm. Multiplication is an important operation in many digital systems, and the design of fast multipliers is of great interest to computer scientists and engineers. The speed of this computing system is evaluated.     

Graphics processing unit parallel accelerated solution of the discrete ordinates for photon transport in biological tissues

As a widely used numerical solution for the radiation transport equation (RTE), the discrete ordinates can predict the propagation of photons through biological tissues more accurately relative to the diffusion equation. The discrete ordinates reduce the RTE to a serial of differential equations that can be solved by source iteration (SI). However, the tremendous time consumption of SI, which is partly caused by the expensive computation of each SI step, limits its applications. In this paper, we present a graphics processing unit (GPU) parallel accelerated SI method for discrete ordinates. Utilizing the calculation independence on the levels of the discrete ordinate equation and spatial element, the proposed method reduces the time cost of each SI step by parallel calculation. The photon reflection at the boundary was calculated based on the results of the last SI step to ensure the calculation independence on the level of the discrete ordinate equation. An element sweeping strategy was proposed to detect the calculation independence on the level of the spatial element. A GPU parallel frame called the compute unified device architecture was employed to carry out the parallel computation. The simulation experiments, which were carried out with a cylindrical phantom and numerical mouse, indicated that the time cost of each SI step can be reduced up to a factor of 228 by the proposed method with a GTX 260 graphics card.     

一种基于梯度下降的次级通道在线建模有源噪声控制算法

针对前馈式有源噪声控制系统中次级通道在线建模精度低及建模信号与控制信号相互影响的问题,提出一种基于梯度下降的次级通道在线建模有源噪声控制算法。根据主动控制环节与建模环节的误差能量比,分别调节两个环节的收敛因子,利用主动控制收敛因子和建模收敛因子的调节方式减小二者的相互干扰。在建模收敛因子调整过程中引入梯度下降方法,对步长设置检测阈值,当步长达到阈值,对收敛因子采取梯度变化。仿真结果表明,针对混频信号的有源噪声控制,这种算法对比已有算法能获得较快的建模收敛速度和较低的稳态误差,且可以获得较高的降噪量。     

Particle image velocimetry analysis using an optically addressed spatial light modulator: effects of nonlinear transfer function

Optical processors for generating a two-dimensional squared autocorrelation function have been presented for postprocessing particle image velocimetry photographs of fluid flows. The incoherent-tocoherent conversion can be performed by an optically addressed spatial light modulator. The transfer function of these devices is far from linear and will influence the performance of the optical processor.

Two different transfer functions, characterizing the two main types of commercial optically addressed spatial light modulators as an analog and a binary transfer function, have been simulated digitally.

Results of numerical simulations on the influence of introducing these nonlinear transfer functions to the correlation function for particle image velocimetry analysis are presented.

     

一个充分下降的修正 PRP 型谱共轭梯度法

谱共轭梯度法是共轭梯度法的一种重要延拓,可以通过共轭参数和谱参数二维度调整,使得所设计算法的搜索方向满足某一预设条件,比如充分下降条件或共轭条件等。谱参数和共轭参数的设计是谱共轭梯度法的两大核心工作,决定方法的收敛性和数值效果。基于 PRP 方法,构造了一个修正的 PRP 型共轭参数,该共轭参数不仅保持了 PRP 公式的结构和性能,而且具有 FR 方法的收敛性质。利用充分下降条件取定一个谱参数,与修正的 PRP 型共轭参数结合,建立一个新的谱共轭梯度算法。该算法不依赖于任何线搜索就可以满足充分下降条件。常规假设条件下,采用强 Wolfe 线搜索准则产生步长,证明了新算法的全局敛性。通过 100 个算例对该算法进行数值测试并与其他五个算法进行比较,同时采用性能图对数值结果进行直观展示,结果表明该算法是有效的。     

Approximate Fourier phase information in the phase retrieval problem: what it gives and how to use it

This work evaluates the importance of approximate Fourier phase information in the phase retrieval problem. The main discovery is that a rough phase estimate (up to π/2 rad) allows development of very efficient algorithms whose reconstruction time is an order of magnitude faster than that of the current method of choice--the hybrid input-output (HIO) algorithm. Moreover, a heuristic explanation is provided of why continuous optimization methods like gradient descent or Newton-type algorithms fail when applied to the phase retrieval problem and how the approximate phase information can remedy this situation. Numerical simulations are presented to demonstrate the validity of our analysis and success of our reconstruction method even in cases where the HIO algorithm fails, namely, complex-valued signals without tight support information.     

Experimental exploration on loss surface of deep neural network

The loss function of the deep neural network is high dimensional, nonconvex and complex. So far, the geometric properties of the loss surface of the neural network have not been well understood. Different from most theoretical studies on the loss surface, this article makes the experimental exploration on the loss surface of the deep neural network, including trajectories of various adaptive optimization algorithms, the Hessian matrix of the loss function of the deep neural network, the curvature of the loss surface along the trajectories of the various adaptive optimization algorithms. It is found that the gradient direction of the adaptive optimization algorithms is almost perpendicular to the direction of the maximum curvature of the loss surface, while the gradient directions of the stochastic gradient descent (SGD) algorithm do not have such a rule. The Hessian matrix of the loss surface along the trajectory of the optimization algorithm is degraded, which is inconsistent with the hypothetical that nonsingular of the Hessian matrix in many theoretical studies of deep learning. Besides, this article proposes a new ensemble learning method of the neural network based on the scaling invariance of the ReLu neural network and mode connectivity.