Modelling of the Relaxation Least Squares-Based Neural Networks and Its Application

A relaxation least squares-based learning algorithm for neual networks is proposed. Not only does it have a fast convergence rate, but it involves less computation quantity. Therefore, it is suitable to deal with the case when a network has a large scale but the number of training data is very limited. It has been used in converting furnace process modelling, and impressive result has been obtained.

Robust On-Line Fault Diagnosis for Nonlinear Difference-Algebraic Systems Using Least Squares Estimate

A robust on-line fault diagnosis methor based on least squares estimate for nonlinear difference-algebraic systems (DAS) with uncertainties is proposed. Based on the known nominal model of the DAS, this method firstly constructs an auxiliary system consisting of a difference equation and an algebraic equation, then, based on the relationship between the state deviation and the faults in the difference equation and the relationship between the algebraic variable deviation and the faults in algebraic equation, it identifies the faults on-line through least squares estimate. This method can not only detect, isolate and identify faults for DAS, but also give the upper bound of the error of fault identification. The simulation results indicate that it can give satisfactory diagnostic results for both abrupt and incipient faults.

Neural Network inverse Adaptive Controller Based on Davidon Least Square

General neural network inverse adaptive controller has two flaws: the first is the slow convergence speed; the second is the invalidation to the non-minimum phase system. These defects limit the scope in which the neural network inverse adaptive controller is used. We employ Davidon least squares in training the multi-layer feedforward neural network used in approximating the inverse model of plant to expedite the convergence, and then through constructing the pseudo-plant, a neural network inverse adaptive controller is put forward which is still effective to the nonlinear non-minimum phase system. The simulation results show the validity of this scheme.

A 3D shell-like approach using element-free Galerkin method for analysis of thin and thick plate structures

A new efficient meshless method based on the element-free Galerkin method is proposed to analyze the static deformation of thin and thick plate structures in this paper. Using the new 3D shell-like kinematics in analogy to the solid-shell concept of the finite element method, discretization is carried out by the nodes located on the upper and lower surfaces of the structures. The approximation of all unknown field variables is carried out by using the moving least squares （MLS） approximation scheme in the in-plane directions, while the linear interpolation is applied through the thickness direction. Thus, different boundary conditions are defined only using displacements and penalty method is used to enforce the essential boundary conditions. The constrained Galerkin weak form, which incorporates only dis- placement degrees of freedom （d.o.f.s）, is derived. A modified 3D constitutive relationship is adopted in order to avoid or eliminate some self-locking effects. The numeric efficiency of the proposed meshless formulation is illustrated by the numeric examples.

ANALYSIS OF 2-D THIN STRUCTURES BY THE MESHLESS REGULAR HYBRID BOUNDARY NODE METHOD

Thin structures are generally solved by the Finite Element Method(FEM), using plate or shell finite elements which have manylimitations in applications, such as numerical locking, edge effects,length scaling and the cnvergence problem. Recently, by proposing anew approach to tranting the nearly- singular integrals, Liu et al.developed a BEM to successfully solve thin structures with thethickness-to- length ratios in the micro-or nano-scales. On the otherhand, the meshless Regular Hybrid Boundary Node Method (RHBNM), whichis proposed by the current authors and based on a modified functionaland the Moving Least-Square (MLS) approximation, has very promisingapplications for engineering problems owing To its meshless natureand dimension-reduction advantage, and not involving any singular ornearly-singular Integrals. Test examples show that the RHBNM can alsobe applied readily to thin structures with high accu- Racy withoutany modification.

Quaternion based joint DOA and polarization parameters estimation with stretched three-component electromagnetic vector sensor array

The three-component electromagnetic vector sensor (EMVS) consisting of co-centered orthogonally oriented x-dipole, z-dipole and z-loop is considered. In order to make full use of the spatial aperture of each component, the original uniform linear three-component EMVS array (ULTEA) is stretched into one half-wavelength spaced uniform linear loop subarray (ULLSA) along the z axis, and one sparse uniform linear co-centered orthogonally oriented dual-dipole (CODD) subarray (SULCSA) along the x axis. Then, a generalized rotation invariance based quaternion multiple signal classification (GRIQ-MUSIC) algorithm is presented for direction of arrival (DOA) and polarization parameters estimation. According to the proposed algorithm, the elevation angles are firstly estimated based on the half-wavelength spaced ULLSA. Then the polarization phase differences and azimuth angles are obtained based on the coupling relationship between the angle domain and polarization domain, but the azimuth angles are in coarse-resolution since the array aperture is not utilized. Next, the SULCSA is used to re-estimate the azimuth angles in fine-resolution, and the ambiguity problem can be resolved by the least square method. Finally, based on the estimated elevation angles, azimuth angles and polarization phase differences, the corresponding auxiliary polarization angles can be estimated by N times one-dimensional parameter search, where N is the sources number, and the parameters are matched automatically. Based on the GRIQ-MUSIC algorithm, the high dimensional parameters search problem of the conventional Q-MUSIC algorithm is simplified to a one-dimensional parameter search problem, thus the proposed algorithm not only reduces the computation complexity considerably, but also avoids the performance degradation caused by the failure in parameters pairing. The simulation examples demonstrate the effectiveness and feasibility of the proposed algorithm. ? 1990-2011 Beijing Institute of Aerospace Information.

Meshless analysis of an improved element-free Galerkin method for linear and nonlinear elliptic problems

We first give a stabilized improved moving least squares （IMLS） approximation, which has better computational stability and precision than the IMLS approximation. Then, analysis of the improved element-free Galerkin method is provided theoretically for both linear and nonlinear elliptic boundary value problems. Finally, numerical examples are given to verify the theoretical analysis.

Crystallite Orientation Analysis for a Multidirectionally Cold Rolled α-Ti Alloy (TA7) Thin Sheet

A microcomputer software determining the crystallite orientation distribution functions (ODFs) and inverse pole figures of hexagonal materials with or without orthorhombic physical symmetry has been worked out the first time. The texture measurements and the ODF calculations were performed for a multidirectionally cold rolled α-Ti alloy (TA7) sheet by the application of this software. It is shown that the rolling planes of most grains in the sheet tend to be parallel to (0001) with a deviation to the extent of 40° and is shown a predominance of the orientation zone containing (1016), while the rolling directions are, as a whole, uniformly distributed along all the directions over the rolling planes. Of all the texture components, (2ˉ117) [01ˉ10] is slightly stronger than the other.

Time -Sharing Power Supply Optimal Decision forElectrolytic Deposition Process of Zinc Based onSimulated Annealing Algorithm

According to time-sharing valuation principle (TSVP) of power supply, the relationships of current density and current efficiency at different acidities are obtained based on the processed data of electrolytic deposition process of zinc (EDPZ) with the least square method (LSM). Thus an optimal model of time-sharing power supply system for EDPZ is established, which has been optimized by use of an improved efficient simulated annealing algorithm (SAA). Practical results show that industrial and mining enterprises can obtain enormous economic benefits every year.

Determination of Crystal Structure of Britholite-Y

Britholite-Y is milkwhite, rosy in colour. The measured specific gravity is 4.35, with Ng′ = 1.791, Np′ = 1.784. As determined by electron microprobe, its crystal formula is (Y2.82Ca1.58Ce0.27Dy0.21Er0.11)5 [(Si2.95P0.05)3O12](OH,F), space group = C22-P21, a = (0.9504±0.0005) nm, b = (0.9414±0.0004) nm, c = (0.6922±0.0002) nm, r = (119.71±0.04)°, V = (53.79±0.04) nm3, Z = 2. Least-squares refinements with 2272 independent reflection (F0>3σ|F0|) yielded R = 0.111. The change of symmetry group P63/m of apatite to P21 of britholite-Y results from the shifts of Y, Ca, Si, O and (OH) atoms (anions) from the pseudohexagonal P63/m equivalent positions (6h), (4f), (12i) and (2a) as produced by distortion of the polyhedra with 7-, 9-, and 4-corners. The substitution of Ca in apatite for Y and the order distribution of atoms Y and Ca on the equivalent positions (6h) and (4f) have contributed to the distortion of 7- and 9- cornered polyhedra. The substitutions of Si4+ for P5+ and OH- for F- may also be effected. The crystal chemistry of apatite-group minerals is also discussed.

具有阶梯状海底的表面穿透柔性多孔屏障结构斜波捕获（英文）

The present study deals with the oblique wave trapping by a surface-piercing flexible porous barrier near a rigid wall in the presence of step-type bottoms under the assumptions of small amplitude water waves and the structural response theory in finite water depth.The modified mild-slope equation along with suitable jump conditions and the least squares approximation method are used to handle the mathematical boundary value problem.Four types of edge conditions,i.e.,clamped-moored,clamped-free,moored-free,and moored-moored,are considered to keep the barrier at a desired position of interest.The role of the flexible porous barrier is studied by analyzing the reflection coefficient,surface elevation,and wave forces on the barrier and the rigid wall.The effects of step-type bottoms,incidence angle,barrier length,structural rigidity,porosity,and mooring angle are discussed.The study reveals that in the presence of a step bottom,full reflection can be found periodically with an increase in(i)wave number and(ii)distance between the barrier and the rigid wall.Moreover,nearly zero reflection can be found with a suitable combination of wave and structural parameters,which is desirable for creating a calm region near a rigid wall in the presence of a step bottom.

STUDY OF C_D, C_M, C_L AND WAVE FORCES ON PIPE LINES NEAR THE OCEAN BOTTOM

The wave forces on pipes near the ocean bottom are studied with model test in this paper. Comparisons of four different methods show that the uncommonly used method - Least Square Mass (LSM) is the most stable one. The in-line and transverse forces on the pipe, which is placed at various distances from the bottom of the wave tank, are measured. The force transfer coefficients (CD, CM, CL) are much larger when the pipe is near the bottom than when it is free. But the coefficients do not increase unlimitedly: they reach their maxima at ζ (gap ratio = e / D) = 0.1 (gap ratio ζ = e / D). An interesting result is that the ratio of lift force frequency (f′L) to wave frequency (fw) is 2.0. In the paper, the curves of coefficients are given.

Inverse Design of Electron Lens

The inverse design of electron lens is realized by two different methods in this paper. One is damped least square method and the other is the artificial neural network method. Their merits and defects are discussed according to our calculation results in the paper. In the condition of selecting the learning samples properly, the artificial neural network has obvious advantages in the inverse design of electron lens. It is an effective method to solve the inverse design problem in the electron optic system.

The improved element-free Galerkin method forthree-dimensional wave equation

The paper presents the improved element-free Galerkin （IEFG） method for three-dimensional wave propa- gation. The improved moving least-squares （IMLS） approx- imation is employed to construct the shape function, which uses an orthogonal function system with a weight function as the basis function. Compared with the conventional moving least-squares （MLS） approximation, the algebraic equation system in the IMLS approximation is not ill-conditioned, and can be solved directly without deriving the inverse matrix. Because there are fewer coefficients in the IMLS than in the MLS approximation, fewer nodes are selected in the IEFG method than in the element-free Galerkin method. Thus, the IEFG method has a higher computing speed. In the IEFG method, the Galerkin weak form is employed to obtain a dis- cretized system equation, and the penalty method is applied to impose the essential boundary condition. The traditional difference method for two-point boundary value problems is selected for the time discretization. As the wave equations and the boundary-initial conditions depend on time, the scal- ing parameter, number of nodes and the time step length are considered for the convergence study.

Determination of human skin optical properties in vivo from reflectance spectroscopic measurements

A novel approach has been proved to quickly and non-invasively determine the optical properties of human skin in vivo. It is based on the diffuse reflectance approximation model and subjected to the well established library of absorption spectra of water and hemoglobin. Under the nonlinear least-square algorithm, fitting the measured spectra in the range of 400--1000 nm to the diffusion approximation model, the reduced scattering coefficient and absorption coefficient of skin tissue can be quickly determined in vivo. The results show that this method is convenient and suitable for the real-time clinical application.

Real-time restoration of rotational blurred image using gradient-loading

The key to the restoration of rotational motion blurred image is how to restore the image under a low cost and to correct the irreversibility of the degradation function matrix. Based on the special qualities of degradation function matrix and precise deduction in space-domain, we present a new approach using gradient-loading for restoration of rotational blurred image. By easily adding a gradient operator, the irreversibility of the original matrix is corrected and can be applied for inverse filtering then. Gradient- loading is the optimized approach which combines the advantages of both the approaches using constrained least square filtering and traditional diagonal-loading. Compared with the approach using least square filtering, its peak signal-to-noise ratio （PSNR） is improved from 3.18 to 6.46 dB, while the computing time is reduced to 1/2 - 1/3. Experimental results demonstrate the effectiveness, noise-resistibility, robustness, and low complexity of this approach, which make it more suitable for real-time environment.

Hilbert Space of Probability Density Functions Based on Aitchison Geometry

The set of probability functions is a convex subset of L1 and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise when dealing with distances between densities. The crucial point is that usual distances are not invariant under relevant transformations of densities. To overcome these limitations, Aitchison＇s ideas on compositional data analysis are used, generalizing perturbation and power transformation, as well as the Aitchison inner product, to operations on probability density functions with support on a finite interval. With these operations at hand, it is shown that the set of bounded probability density functions on finite intervals is a pre-Hilbert space. A Hilbert space of densities, whose logarithm is square-integrable, is obtained as the natural completion of the pre-Hilbert space.

Investigation of self-adaptive algebraic tomography for gas reconstruction in larger temperature range by multiple wavelengths absorption spectroscopy

We develop a self-adaptive algebraic tomography algorithm （SAATA） to investigate the simultaneons reconstruction of concentration and temperature distributions in larger temperature range from two views. The simplified optical arrangement with fewer projections is realized by extension of spectral information at multiple wavelengths, resulting in great potential in applications of practical combustion diagnosis. Tile results show SAATA can perform much better reconstructions in 300 3000 K temperature range than genetic simulated annealing algorithm and least-square orthogonal-triangular decomposition method with two- wavelength scheme. More phantoms are created to demonstrate the capability of SAATA to capture the peaks and adapt for both flat and sharp temperature distributions. Meanwhile, the advantage of high stability ensures better reconstruction performance at noise levels from 0.1% to 10% in projections.

Measurement of borneol based on infrared spectrometry

The infrared spectrometry contains multiple information of the sample, and it is easy to be applied to online measurement. To Chinese medicine, this technology can improve the standard of quality control and accelerate the modernization course. In this paper, we investigate the spectral characteristics of borneol, an effective ingredient in many Chinese medicines. The following results are achieved. In middle infrared （MIR） region, utilizing the linear relationship between absorption and concentration, the concentration of borneol with relative error within 4.30% in the strongest absorption region （2950-2970 cm^-1） is measured; in near infrared （NIR） region, the predicted concentrations of borneol are calculated by using partial least squares （PLS） regression analysis, in which the wavelengths are selected by genetic algorithm （GA） from the absorption bands of borneol in NIR region. The predicted relative error of calibration model is less than 2%. This result shows that PLS regression analysis combining genetic algorithm is a good method to improve prediction and reduce data in NIR region.

Research on error compensation method for dual-beam measurement of roll angle based on rhombic prism(Invited Paper)

The fabrication deviation of prisms and the error crosstalk are two major factors that produce serious systematic errors in dual-beam roll measurement based on a rhombic prism, and an error compensation method is put forward in this letter to reduce these systematic errors. The rotation matrix, reflection matrix, and refraction matrix are used to calculate and obtain the mathematical relationship model of the roll angle as well as the fabrication deviation of prism and error crosstalk. The fabrication deviation can be obtained through comparison experiments and using the least square method. In this way, the systematic error of the roll measurement caused by fabrication deviation of prism and error crosstalk can be eliminated theoretically. The experimental results show that the maximum error of the roll angle measurement reduces evidently to 3.5″ from the previous 347.2″ after compensation.