A modified sequential function specification finite element-based method for parabolic inverse heat conduction problems

A method for enhancing the stability of parabolic inverse heat conduction problems (IHCP) is presented. The investigation extends recent work on non-iterative finite element-based IHCP algorithms which, following Becks two-step approach, first derives a discretized standard form equation relating the instantaneous global temperature and surface heat flux vectors, and then formulates a least squares-based linear matrix normal equation in the unknown flux. In the present study, the non-iterative IHCP algorithm is stabilized using a modified form of Becks sequential function specification scheme in which: (i) inverse solution time steps, t, are set larger than the data sample rate, , and (ii) future temperatures are obtained at intervals equal to . These modifications, contrasting with the standard approach in which the computational, experimental, and future time intervals are all set equal, are designed respectively to allow for diffusive time lag (under the typical circumstance where is smaller than, or on the order of the characteristic thermal diffusion time scale), and to improve the temporal resolution and accuracy of the inverse solution. Based on validation tests using three benchmark problems, the principle findings of the study are as follows: (i) under dynamic surface heating conditions, the modified and standard methods provide comparable levels of early-time resolution; however, the modified technique is not subject to over-damped estimation (as characteristic of the standard scheme) and provides improved error suppression rates, (ii) the present method provides superior performance relative to the standard approach when subjected to data truncation and thermal measurement error, and (iii) in the nonlinear test problem considered, both approaches provide comparable levels of performance. Following validation, the technique is applied to a quenching experiment and estimated heat flux histories are compared against available analytical and experimental results.     

Stochastic finite element-based reliability analysis of space frames

In the present paper the weighted integral method in conjunction with Monte Carlo simulation is used for the stochastic finite element-based reliability analysis of space frames. The limit state analysis required at each Monte Carlo simulation is performed using a non-holonomic step-by-step elasto-plastic analysis based on the plastic node method in conjunction with efficient solution techniques. This implementation results in cost effective solutions both in terms of computing time and storage requirements. The numerical results presented demonstrate that this approach provides a realistic treatment for the stochastic finite element-based reliability analysis of large scale three-dimensional building frames.     

基于扩展有限元的钢瓶爆破数值仿真研究

金属钢瓶的爆破压力是其重要的安全技术指标,目前的数值计算方法不能有效对气瓶的爆破压力进行准确预测。提出了基于扩展有限元的数值计算方法对钢瓶的爆破进行了数值仿真,仿真结果表明该方法能准确预测钢瓶的爆破压力,可以为钢瓶工程设计和事故预防提供支撑。     

A global optimization technique for microwave nondestructive evaluation

A global optimization technique based on a genetic algorithm is proposed for microwave nondestructive evaluation. Starting from an integral formulation of the inverse scattering problem, the detection of a flaw in a known host medium is reduced to the minimization of a suitable nonlinear functional relating the measured field to the field predicted at a given iteration. The geometrical parameters of the flaw are retrieved by using a tomographic imaging approach. Numerical results are reported concerning cracks in lossless and lossy structures. The effects of the noise on measured input data are also analyzed.     

A technique for microwave ranging and remote phase synchronization

A very precise electrical-distance measurement system that is also capable of supplying a phase-synchronous signal to a remote location is required for a new type of radio telescope, the large adaptive reflector (LAR). The system is based on a round-trip phase synchronization method, and is designed to work over a free-space path of length up to 1 km, the focal distance of the telescope. The electrical length of this path is to be measured with an accuracy of 70 μm and a phase-stable signal is to be provided at the remote end as the basis for a local-oscillator signal of stability equivalent to 5° at 22 GHz. Phase synchronization and distance measurement are accomplished with the same microwave ranging circuit. The distance measurement is derived from phase comparison of high-frequency signals, including a novel use of the Chinese Remainder Theorem (CRT) to resolve the unavoidable wavelength ambiguity. The design of the system is described, and limitations imposed by phase-measurement and frequency-setting accuracy are explored. Errors due to atmospheric dispersion are negligible under most circumstances. Accurate phase synchronization has been demonstrated over a free-space path of ~300 m. The complete system has been simulated under noisy conditions, and its ability to meet the specifications demonstrated     

A general advancing front technique for filling space with arbitrary objects

An advancing front space‐filling technique for arbitrary objects has been developed. The input required consists of the specification of the desired mean point distance in space and an initial triangulation of the surface. One object at a time is removed from the active front, and, if possible, surrounded by admissible new objects. This operation is repeated until no active objects are left. Two techniques to obtain maximum packing are discussed: closest object placement (during generation) and move/enlarge (after generation). Different deposition or layering patterns can be achieved by selecting the order in which objects are eliminated from the active front. Timings show that for simple objects like spheres the scheme is considerably faster than volume mesh generators based on the advancing front technique, making it possible to generate large (> 10⁶) yet optimal clouds of points in a matter of minutes on a PC. For more general objects, the performance may degrade depending on the complexity of the penetration checks. Several examples are included that demonstrate the capabilities of the technique. Copyright © 2004 John Wiley & Sons, Ltd.     

A technique for dielectric measurement of cylindrical objects in arectangular waveguide

In this paper, the inverse scattering problem of a homogeneous dielectric post in a rectangular waveguide is considered. A novel inversion algorithm, based on the method of moments and eigen analysis, for computation of the dielectric constant of the post (ϵ) from the measured voltage reflection coefficient is introduced. In this method the integral equation for the polarization current induced in the dielectric post is cast into a matrix equation, and then the contribution of ϵ to the resulting reflection coefficient is expressed explicitly using the eigen analysis. It is shown that the dielectric constant can be obtained from the solution of a complex polynomial function which in turn can be obtained numerically using the conjugate gradient method. Practical aspects of dielectric measurement using this technique are discussed. The HP-8510 network analyzer is used to measure the reflection coefficient of dielectric posts in an X-band waveguide sample holder. Metallic and known dielectric posts are used to determine the accuracy of the dielectric measurement technique     

A three-dimensional least-squares finite element technique for deformation analysis

The development of a three-dimensional least-squares finite element technique suitable for deformation analysis was presented. By adopting a spatial viewpoint, a consistent rate formulation that treats deformation as a process was established. The technique utilized the least-squares variational principle that minimizes the squares of errors encountered in any attempt to meet the field equations exactly. Both velocity and Cauchy stress rate fields were discretized by the same linear interpolation function. The discretization always yields a sparse, symmetric, and positive-definite coefficient matrix. A conjugate gradient iterative solver with incomplete-Choleski preconditioner was used to solve the resulting linear system of equations. Issues such as finite element formulation, mesh design, code efficiency, and time integration were addressed. A set of linear elastic problems was used for patch-test; both homogeneous and non-homogeneous deformations were considered. Additionally, two finite elastic deformation problems were analysed to gauge the overall performance of the technique. The results demonstrated the computational feasibility of a three-dimensional least-squares finite element technique for deformation analysis. © 1997 John Wiley & Sons, Ltd.     

Phase shift migration for imaging layered objects and objects immersed in water

This paper proposes the use of phase shift migration for ultrasonic imaging of layered objects and objects immersed in water. The method, which was developed in reflection seismology, is a frequency domain technique that in a computationally efficient way restores images of objects that are isotropic and homogeneous in the lateral direction but inhomogeneous in depth. The performance of the proposed method was evaluated using immersion test data from a block with side-drilled holes with an additional scatterer residing in water. In this way, the method's capability of simultaneously imaging scatterers in different media and at different depths was investigated. The method was also applied to a copper block with flat bottom holes. The results verify that the proposed method is capable of producing high-resolution and low-noise images for layered or immersed objects.     

Tensor objects in finite element programming

This paper describes a novel programming tool, nDarray, which is designed using an Object Oriented Paradigm (OOP) and implemented in the C++ programming language. Finite element equations, represented in terms of multidimensional tensors are easily manipulated and programmed. The usual matrix form of the finite element equations are traditionally coded in FORTRAN, which makes it difficult to build and maintain complex program systems. Multidimensional data systems and their implementation details are seldom transparent and thus not easily dealt with and usually avoided. On the other hand, OOP together with efficient programming in C++ allows building new concrete data types, namely tensors of any order, thus hiding the lower level implementation details. These concrete data types prove to be quite useful in implementing complicated tensorial formulae associated with the numerical solution of various elastic and elastoplastic problems in solid mechanics. They permit implementing complex nonlinear continuum mechanics theories in an orderly manner. Ease of use and the immediacy of the nDarray programming tool in constitutive driver programming and in building finite element classes will be shown. © 1998 John Wiley & Sons, Ltd.     

Superhigh image resolution for microwave imaging

Algorithms for extrapolating the scattered field along the frequency direction and the azimuthal direction are developed and analyzed. Their effects on the image resolution for polar format processing and rectangular format processing are discussed. Simulation and experimental results show that extrapolation along the frequency direction does increase the range resolution. While extrapolation along the azimuthal direction improves the cross-range resolution for small angle imaging, it does not improve image resolution of complex-shaped objects for wide angle imaging. Both range and cross-range resolutions can be improved simultaneously for small angle imaging using rectangular format processing if the angular interval and the resolution cells are suitably chosen. A promising application for the algorithms developed is in microwave dynamic imaging.     

A neural network approach to microwave imaging

We present a neural network approach to microwave imaging for medical diagnosis. The problem is to reconstruct the complex permittivity of the biological tissues illuminated by the transverse magnetic (TM) incident waves. In order to avoid the inherent ill‐posedness of the inverse scattering problem, we introduce a stochastic process based on Markov random field and a priori knowledge. A coupled gradient neural network is proposed to deal with the mixed‐variable problem because the reconstructed dielectric permittivities are continuous complex variables and the line processes, which can preserve the edges of the reconstructed image, are binary variables. We report the numerical results of a simple human forearm model. We also point out the advantages and the limitations of this method. © 2001 John Wiley & Sons, Inc. Int J Imaging Syst Technol 11, 159–163, 2000     

A solution technique for indefinite systems of mixed finite elements

A solution technique for indefinite systems of symmetric linear, simultaneous equations, via the Hellinger–Reissner variational principle, is presented. The method utilizes symmetry of the global matrix and its expected real eigenvalues. Premultiplication of the global matrix with itself renders a positive definite matrix, hence enabling the use of any standard equation solver for a positive definite system and requiring only about twice the memory requirement for the original set of equations. Two subroutines, MULT and MULTIP, which are compatible with the sky-line technique, are also listed.     

A robust preconditioning technique for the extended finite element method

The extended finite element method enhances the approximation properties of the finite element space by using additional enrichment functions. But the resulting stiffness matrices can become ill‐conditioned. In that case iterative solvers need a large number of iterations to obtain an acceptable solution. In this paper a procedure is described to obtain stiffness matrices whose condition number is close to the one of the finite element matrices without any enrichments. A domain decomposition is employed and the algorithm is very well suited for parallel computations. The method was tested in numerical experiments to show its effectiveness. The experiments have been conducted for structures containing cracks and material interfaces. We show that the corresponding enrichments can result in arbitrarily ill‐conditioned matrices. The method proposed here, however, provides well‐conditioned matrices and can be applied to any sort of enrichment. The complexity of this approach and its relation to the domain decomposition is discussed. Computation times have been measured for a structure containing multiple cracks. For this structure the computation times could be decreased by a factor of 2. Copyright © 2010 John Wiley & Sons, Ltd.     

A finite plate technique for the determination of piezoelectricmaterial constants

An improved resonator method is presented for the determination of piezoelectric material constants. The improved method addresses a fundamental limitation of the measurement methods recommended in the current IEEE Standard on Piezoelectricity: the relations between vibrator response and material constants presented in this Standard are based upon the 1-D approximation of an essentially infinite flat plate with a uniform distribution of vibratory motion. The calculation or measurement of the effects due to the nonuniform vibrational amplitude distribution in a laterally bounded plate is a nontrivial task. The practical result is that the current IEEE 176-1987 resonator method recommendations are of limited usefulness in the determination of “intrinsic” piezoelectric material constants. This limitation can, however, readily be overcome using an improved measurement technique based on measurands unaffected by the vibrational amplitude distribution. In the improved technique, the measurands of choice are the zero-mass-loading, fundamental mode, thickness-field excitation (TE) antiresonance, or lateral-field excitation (LE) resonance frequencies. A recommended experimental procedure, using the preferred measurands, is presented     

Depth extraction of three-dimensional objects in space by the computational integral imaging reconstruction technique

A novel approach to extract the depth data of 3D objects in space by using the computational integral imaging reconstruction (CIIR) technique is proposed. With elemental images of 3D objects captured by the CCD camera through a pinhole array, depth-dependent object images can be reconstructed on the output plane by the CIIR technique. Only the images reconstructed on the output planes where 3D objects were located are clearly focused; so the depth data of 3D objects in space can be extracted by discriminating these focused output images from the others by using an image separation technique. A feasibility test of the proposed CIIR-based depth extraction method is carried out, and its results are discussed as well.     

有限空间内三维声成像的简易算法

文章提出了一个可用于有限空间内三维声成像的简易算法。根据回声测距原理，得到有限空间中底面上所有采样点在三维笛卡儿空间内的坐标(z，y，z)，然后将其转换为计算机屏幕上的像素点的坐标(z，y)，从而绘制出具有真实立体感的图像。实践证明，利用此算法可以很方便地在计算机屏幕上绘制任意旋转的三维图像。     

Microwave imaging of moving objects

Microwave images for objects in motion can be obtained with quality as good as those obtained in the stationary case if the signal waveforms, data acquisition systems, and image reconstruction algorithms are cleverly designed. The principle of imaging for objects in motion is to eliminate the gross Doppler effect of the echo signals and only reserve the differential Doppler information to reconstruct the image. Accordingly, requirements for parameters of the signal waveform are established. Two steps are involved in the image reconstruction algorithm: range alignment and phase compensation. Focused images of complex-shaped targets with simulated motion have been obtained experimentally.     

New calibration technique for microwave moisture sensors

A new calibration technique was developed for implementation with microwave moisture sensors. The calibration permittivity function used for this purpose allows computation of moisture content in granular materials with significant differences in shape, dimensions, and composition, independent of bulk density and with temperature compensation. A 3D representation is used to plot the calibration permittivity function as it depends on temperature and moisture content in wheat and corn. For each material, data points form a plane surface. These planes have nearly the same coefficients, which can be utilized for the development of a “universal” calibration method for moisture sensing in natural and manufactured granular materials. Foundations of the method are discussed based on results obtained for wheat and corn over a wide temperature range and at moisture contents of practical interest     

A balanced expansion technique for constructing accurate finite difference advection schemes

A new procedure, called the Balanced Expansion Technique (BET), is employed to construct accurate finite difference advection schemes that, for the model equation considered, are neutrally stable. By applying BET systematically, the phase error can be made as small as one wishes. Test calculations with one-dimensional problems have confirmed the expected accuracy of these methods.