A Galerkin least-squares finite element method for the two-dimensional Helmholtz equation

In this paper a Galerkin least-squares (GLS) finite element method, in which residuals in least-squares form are added to the standard Galerkin variational equation, is developed to solve the Helmholtz equation in two dimensions. An important feature of GLS methods is the introduction of a local mesh parameter that may be designed to provide accurate solutions with relatively coarse meshes. Previous work has accomplished this for the one-dimensional Helmholtz equation using dispersion analysis. In this paper, the selection of the GLS mesh parameter for two dimensions is considered, and leads to elements that exhibit improved phase accuracy. For any given direction of wave propagation, an optimal GLS mesh parameter is determined using two-dimensional Fourier analysis. In general problems, the direction of wave propagation will not be known a priori. In this case, an optimal GLS parameter is found which reduces phase error for all possible wave vector orientations over elements. The optimal GLS parameters are derived for both consistent and lumped mass approximations. Several numerical examples are given and the results compared with those obtained from the Galerkin method. The extension of GLS to higher-order quadratic interpolations is also presented.     

A Novel Technique for Estimating the Numerical Error in Solving the Helmholtz Equation

In this study, we applied a defined auxiliary problem in a novel error estimation technique to estimate the numerical error in the method of fundamental solutions (MFS) for solving the Helmholtz equation. The defined auxiliary problem is substituted for the real problem, and its analytical solution is generated using the complementary solution set of the governing equation. By solving the auxiliary problem and comparing the solution with the quasianalytical solution, an error curve of the MFS versus the source location parameters can be obtained. Thus, the optimal location parameter can be identified. The convergent numerical solution can be obtained and applied to the case of an unavailable analytical solution condition in the real problem. Consequently, we developed a systematic error estimation scheme to identify an optimal parameter. Through numerical experiments, the optimal location parameter of the source points and the optimal number of source points in the MFS were studied and obtained using the error estimation technique.     

基于支持向量机的地震预警震级快速估算研究

以更准确的估算地震预警(earthquake early warning,EEW)震级为目标,利用P波触发后3 s内的日本K-net强震数据,选取幅值参数、周期参数、能量参数、衍生参数这4大类共12个P波特征参数作为输入,构建基于支持向量机震级预测模型(support vector machine for earthquake magnitude estimation,SVM-M)。结果表明,比较传统的震级估算“τc方法”与“P d方法”,建立的SVM-M模型震级预测误差明显减小且不受震中距变化的影响,小震高估问题得到明显改善。2016年日本熊本地震主震(M j7.3)与2008年中国汶川地震主震(M s8.0)的震例分析结果表明,3 s时间窗不能匹配震源破裂全过程而出现了一定程度的震级低估,但仍可在P波触发后短时间窗内明确是大地震事件。建立的SVM-M模型可应用于地震预警震级快速估算。     

“Design of Experiments” for the Identification of Linear Dynamic Systems

One of the most important problems in direct digital controller design is to determine the process model from the sampled data. Goodness of the control depends considerably on the accuracy of the identified model. This paper investigates how to generate optimal input signal series for the identification of linear discrete-time systems in order to improve the accuracy of estimates. The determinant of the covariance matrix or of the inverse of the information matrix is considered as a measure of the error in the parameter estimates. Very simple methods are presented for the minimization of these criteria in case of an amplitude constrained input signal.     

An optimal choice of window width for LOWESS normalization of microarray data

The purpose of normalization in microarray data analysis is to minimize systematic variations in the measured gene expression levels of two co-hybridized mRNA samples so that biological differences can be more easily distinguished. The most commonly and widely used normalization procedure for spotted arrays is probably the intensity dependent and print-tip LOWESS normalization. It is well known that the choices of different parameter values greatly affect the quality of the normalization results, and thus poor quality of the normalization results could be due to the arbitrary choice of the smoothing parameters for LOWESS normalization. In many normalization studies, however, LOWESS has been simply used without rigorous consideration of the parameters. In this article, we propose a bootstrap method to find the optimal window width in print-tip normalization by applying the cross validation technique. We also compare through simulation studies the normalization results by using the proposed method with those by fixing the window width.     

Age replacement policy in the case of no data: the effect of Weibull parameter estimation

Age replacement is a common maintenance policy when wear-out failures occur, and it is characterised by periodic replacement of components. Data on time to failure (TTF), often modelled with the Weibull function, are necessary for estimating optimal replacement intervals to minimise the total maintenance costs. In many cases, such as new components, new machines or new installations, no TTF data are available, so the Weibull parameters and optimal replacement interval cannot be estimated. To overcome this problem, these parameters can be assessed from the experience of the maintenance engineers and technicians. The aim of this study is investigating the relationship between the error in parameter estimation and additional maintenance costs related to this error. Analysis of variance (ANOVA) and multifactorial analysis are carried out for investigating the influence of these estimations on the final costs. Economic decision maps are introduced for supporting maintenance engineering in defining the maintenance policy with minimal additional cost in the case of no data being available. The analysis shows that, when no data are available, the application of the age replacement policy can result in a global saving of more than 50% compared with corrective maintenance.     

Automatic selection of optimal Savitzky-Golay smoothing

A method to select the optimal window size of the Savitzky-Golay (SG) algorithm is presented. The approach is based on a comparison of the fitting residuals (i.e., the differences between the input signal and the smoothed signal) with the noise of the instrument. The window size that yields an autocorrelation of the residuals closest to the autocorrelation of the noise of the instrument is considered optimal. The method is applied in two steps. In a first step, the lag-one autocorrelation value of the noise of the instrument is computed through the study of a blank signal. In a second step, the SG algorithm is applied to "smooth" the signal using different window sizes. The method was applied to data from NMR, chromatography, and mass spectrometry and was shown to be robust. It finds the optimal window size for different signal features. This allows the method to be used in an unsupervised way, embedded in a more complex algorithm in which smoothing and/or differentiation of signals is required, provided that the lag-one autocorrelation value of the instrument noise does not change.     

调频初相位补偿的广义Warblet变换时频分析

信号时频分析的长时间窗时频分析法通常可提高输出信噪比和频率分辨率,但对于调频信号,会降低线谱时频能量聚集度并影响瞬时频率估计。对于调频信号广义Warblet变换(Generalized Warblet Transform,GWT),具有较短时傅里叶变换(Short Time Fourier Transform,STFT)更优的时频分析性能,但在长时间窗分析时,调频初相位估计误差会使算法性能下降甚至失效。针对该问题,提出调频初相位补偿的GWT(Frequency Modulation Initial Phase CompensationGWT,FMIPC-GWT)时频分析方法。在调频参数估计时将一半时间窗长所经过的相位补偿到调频初相位中,提高调频参数估计的准确性以增加瞬时频率估计精度。仿真和实验数据验证了,相比STFT法和GWT法,FMIPC-GWT法对于非线性调频信号时频分析性能更优。FMIPC-GWT法在调频信号线谱检测与瞬时频率估计等方面具有应用前景。     

Random optical codes used in optical networks

An analysis of a simple way to design generalised optical orthogonal codes to be used in optical code-division multiple-access systems is presented. They are random optical codes (ROCs). This novel family is especially suitable for optical networks with a large number of channels, low bit rate requirements, energy limitations and packed data. For example, sensor networks need these requirements. An application in an intra-spacecraft telecommand and telemeasurement (TC/TM) optical wireless network is also described. ROCs are selected randomly from all possible rearrangements. However, its probability of error is adequate in many useful parameter ranges. Moreover, ROCs present features not found in other families of codes such as huge cardinality and parameter adaptation to the system necessities. Here, the main contribution is to present a method to optimise the values of the parameters. Furthermore, the optimal weight of the codes is found, given two out of the other set of parameters, that is, the length, the number of users and the probability of error. In addition, a comparison between the length and the power consumption of ROCs and prime codes is also developed.     

A Bayesian framework for uncertainty quantification of perturbed gamma process based on simulated likelihood

The perturbed gamma process (PGP) has recently been widely used in modeling the noisy degradation data collected from engineering structures and components since it can simultaneously consider the temporal variability of degradation and measurement uncertainty. As a result of the sampling and inspection uncertainty in engineering practice, it is necessary to account for the resulting parameter uncertainty. Meanwhile, the flexibility of the form of measurement error motivates a potential demand for quantifying the model uncertainty and selecting the most fitting error model for the given inspection data. The Bayesian approach is well-suited to quantity the parameter uncertainty induced by imperfect inspection and limited inspection data, but its practical implementation is extremely challenging due to the intractable likelihood function of PGP. In the paper, a novel Bayesian framework for quantifying parameter and model uncertainty of PGP is presented, where the simulated likelihood that is an unbiased estimator generated by Sequential Monte Carlo (SMC) is introduced to overcome the intractable likelihood of PGP. More specifically, an Adaptive Particle Markov chain Monte Carlo (APMCMC) is proposed to perform the Bayesian sampling from the posterior distributions of parameters, achieving the requirement for the quantification of parameter uncertainty. By utilizing the posterior samples from APMCMC, a model selection method based on the Bayes factor is employed to determine the most fitting one from some alternative error models. Finally, two simulation examples are presented to illustrate the efficiency and accuracy of the proposed framework and its applicability is confirmed by a practical case involving the corrosion modeling of a group of pipelines.     

Estimations of frequency and its drift rate

This paper presents an analysis of frequency and its drift rate estimation by the difference method, the least-squares method, and the Kalman filter. Error formulas are derived for all five noise processes: white phase, flicker phase, white frequency, flicker frequency, and random walk frequency. The error formulas show the relationship between the estimate error and the noise spectral density coefficients, the same interval τ, and the data number N. Because of the existence of some nonstationary noise processes, a large data number may not yield a good estimation. One should choose an appropriate sample interval and data number so as to control the estimate error. An optimal solution based on the Kalman filter is presented     

Isotherms and thermodynamics by linear and non-linear regression analysis for the sorption of methylene blue onto activated carbon: comparison of various error functions

A comparison of linear and non-linear regression method in selecting the optimum isotherm was made to the experimental equilibrium data of methylene blue sorption by activated carbon. The r2 was used to select the best fit linear theoretical isotherm. In the case of non-linear regression method, six error functions, namely coefficient of determination (r2), hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), average relative error (ARE), sum of the errors squared (ERRSQ) and sum of the absolute errors (EABS) were used to predict the parameters involved in the two and three parameter isotherms and also to predict the optimum isotherm. For two parameter isotherm, MPSD was found to be the best error function in minimizing the error distribution between the experimental equilibrium data and predicted isotherms. In the case of three parameter isotherm, r2 was found to be the best error function to minimize the error distribution structure between experimental equilibrium data and theoretical isotherms. The present study showed that the size of the error function alone is not a deciding factor to choose the optimum isotherm. In addition to the size of error function, the theory behind the predicted isotherm should be verified with the help of experimental data while selecting the optimum isotherm. A coefficient of non-determination, K2 was explained and was found to be very useful in identifying the best error function while selecting the optimum isotherm.     

DNA计算模型在圆柱度误差评定中的应用

提出了DNA计算模型应用于圆柱度误差评定的方法,除了常规遗传算法搜索效率高、全局优化性能好的特点外,该方法的一个突出特点是可以根据待求设计参数的取值范围,设计相应的参数遗传密码表,从而将所有的误差评定算法统一在一个算法之中。     

Estimation of piezoelastic and viscoelastic properties in laminated structures

An inverse method for material parameter estimation of elastic, piezoelectric and viscoelastic laminated plate structures is presented. The method uses a gradient based optimization technique in order to solve the inverse problem, through minimization of an error functional which expresses the difference between experimental free vibration data and corresponding numerical data produced by a finite element model. The complex modulus approach is used to model the viscoelastic material behavior, assuming hysteretic type damping. Applications that illustrate the influence of adhesive material interfaces and viscoelastic parameter identification are presented and a few simulated test cases aid the interpretation of results.     

LIDFT-the DFT linear interpolation method

The method of linear interpolation of the discrete Fourier transform (LIDFT) to estimate parameters of a signal consisting of many sinusoidal oscillations, has been presented in the paper. The LIDFT method combines beneficial properties from known procedures of nonlinear interpolation of a spectrum, obtained as a result of DFT and from parametric methods based on the Prony method. The LIDFT algorithm with beneficial numerical properties has been obtained after formulating the assumptions of the LIDFT method, providing a linear matrix equation and following symbolic transformations of this equation. The basic operations involved are the FFT algorithm and linear matrix equation solving procedure. The parametric, linearizing data window together with the method-developed to choose the window parameter allow for effective application of the LIDFT method depending on the examined signal character     

Comparison of various error functions in predicting the optimum isotherm by linear and non-linear regression analysis for the sorption of basic red 9 by activated carbon

A comparison of linear and non-linear regression method in selecting the optimum isotherm was made to the experimental equilibrium data of basic red 9 sorption by activated carbon. The r(2) was used to select the best fit linear theoretical isotherm. In the case of non-linear regression method, six error functions namely coefficient of determination (r(2)), hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), the average relative error (ARE), sum of the errors squared (ERRSQ) and sum of the absolute errors (EABS) were used to predict the parameters involved in the two and three parameter isotherms and also to predict the optimum isotherm. Non-linear regression was found to be a better way to obtain the parameters involved in the isotherms and also the optimum isotherm. For two parameter isotherm, MPSD was found to be the best error function in minimizing the error distribution between the experimental equilibrium data and predicted isotherms. In the case of three parameter isotherm, r(2) was found to be the best error function to minimize the error distribution structure between experimental equilibrium data and theoretical isotherms. The present study showed that the size of the error function alone is not a deciding factor to choose the optimum isotherm. In addition to the size of error function, the theory behind the predicted isotherm should be verified with the help of experimental data while selecting the optimum isotherm. A coefficient of non-determination, K(2) was explained and was found to be very useful in identifying the best error function while selecting the optimum isotherm.     

基于子结构分析的多重子步模型修正方法

为了解决模型修正过程中修正目标众多和测量信息有限的矛盾，提出了多重子步模型修正方法(MSMUM)，先进行误差定位，再实现参数修正，把复杂的模型修正过程分步实现。利用子结构技术，使结构模型在整体上仅包含有限数目的子结构，对各子结构所对应的超级单元的刚度参与系数进行识别来实现误差定位，通过建立测量信息与待修正参数间的代数方程来修正误差定位后子结构内部构件的参数。数值算例表明，建立的模型修正方法有效可靠。利用建立的多重子步模型修正方法对润扬大桥南汊悬索桥桥塔模型进行了修正。     

Automated spectral smoothing with spatially adaptive penalized least squares

A variety of data smoothing techniques exist to address the issue of noise in spectroscopic data. The vast majority, however, require parameter specification by a knowledgeable user, which is typically accomplished by trial and error. In most situations, optimized parameters represent a compromise between noise reduction and signal preservation. In this work, we demonstrate a nonparametric regression approach to spectral smoothing using a spatially adaptive penalized least squares (SAPLS) approach. An iterative optimization procedure is employed that permits gradual flexibility in the smooth fit when statistically significant trends based on multiscale statistics assuming white Gaussian noise are detected. With an estimate of the noise level in the spectrum the procedure is fully automatic with a specified confidence level for the statistics. Potential application to the heteroscedastic noise case is also demonstrated. Performance was assessed in simulations conducted on several synthetic spectra using traditional error measures as well as comparisons of local extrema in the resulting smoothed signals to those in the true spectra. For the simulated spectra, a best case comparison with the Savitzky-Golay smoothing via an exhaustive parameter search was performed while the SAPLS method was assessed for automated application. The application to several dissimilar experimentally obtained Raman spectra is also presented.     

Bayesian optimized collection strategies for fatigue strength testing

A statistical framework is presented enabling optimal sampling and analysis of constant life fatigue data. Protocols using Bayesian maximum entropy sampling are built based on conventional staircase and stress step methods, reducing the requirement of prior knowledge for data collection. The Bayesian Staircase method shows improved parameter estimation efficiency, and the Bayesian Stress Step method shows equal accuracy to the standard method at larger step size allowing experimentalists to lessen concerns of loading history. Statistical methods for determining model suitability are shown, highlighting the influence of protocol. Experimental validation is performed, showing the applicability of the methods in laboratory testing.     

特征系统实现算法的识别特性研究及算法的推广

特征系统实现算法是近年来出现的时域模态参数识别技术。本文首先研究了该算法对混有白噪音的加速度及位移自由响应信号的识别特性,并发现辊速度信号和位移信号分别对系统的高频模态和低频模态敏感;然后结合算法的高速识别特点及滑动时间窗技术,研究了算法对振动水平的跟踪能力,并在此基础上提出识别混叠频率的方法;最后将该算法推广至利用常力强迫响应数据进行模态参数的情况,导出了相应的算法,并进行了算例验证。