Fractional order model identification using the sinusoidal input

An output error optimization approach for identification of parsimonious fractional order models using multi-frequency sinusoids as input is proposed. The algorithm simultaneously estimates orders, parameters and the delay of simple models with fractional orders using the Gauss–Newton optimization approach. Optimization-based methods for fractional order model identification require evaluation of the sensitivity functions which include the logarithmic derivatives of the input signal. In the existing literature, central difference or similar methods are used to numerically calculate the Jacobian matrix due to difficulties with numerical simulation of the logarithmic derivatives. We assume deterministic input signals and provide analytical expressions for the logarithmic derivatives of single and multiple frequency sinusoids. Relevant mathematical derivations are presented and the analytical expressions are used to evaluate the Jacobian. Effects of noise to signal ratio, input frequency and sampling intervals are studied in simulation to demonstrate the efficacy of the method. Convergence and robustness of the method is also studied. In theory, the approach is applicable for models with large set of parameters; however, convergence of the optimization scheme needs to be addressed.     

A STUDY OF ACTIVE NOISE CANCELLATION IN DUCTS

An infinite impulse response (IIR) filter based on RLMS algorithm is used to control the sound propagated in a duct. The offline error path modification is also included in the algorithm in order to obtain a better result. Three different types of noise source, i.e. pure tone, dual sine and narrowband-limited noise, are considered. This controller not only has a strong effect on the noise reduction for pure tone and dual sine sound sources, but also reduces the narrowband-limited noise markedly. Further study on the reduction of the broad noise source is required however.     

A new theoretical basis for the bandwidth method and optimal power ratios for the damping estimation

Using the well-known bandwidth formula and the half power bandwidth formula [R.E.D. Bishop, G.M.L. Gladwell, An investigation into the theory of resonance testing, Philosophical Transactions of the Royal Society of London A 255 (1963) 241–280], in particular, is the simplest way to estimate modal damping for engineers. By using the half power bandwidth formula, the damping factor is estimated to be approximately the half bandwidth at the half power points. One of the major limitations that restrict the use of this method is the coupling effect between closely spaced modes. In this paper, the dependence of the damping estimation accuracy on the selected power ratios is studied with both analytical and experimental data of frequency response functions. The results show that by selecting adequate power ratio values, the coupling effect can be minimized and the estimation accuracy can be significantly improved for closely spaced modes. A further improvement of accuracy can be obtained by applying the algorithm of mode isolation [H.P. Yin, D. Duhamel, Substraction technique and finite difference formulas for modal parameter estimation, Mechanical Systems and Signal Processing 18 (2004) 1497–1503; M.S. Allen, J.H. Ginsberg, A global, single-input-multi-output (SIMO) implementation of the algorithm of mode isolation and application to analytical and experimental data, Mechanical Systems and Signal Processing 20 (2006) 1090–1111]. Also an exact bandwidth formula in case of a single degree of freedom system is presented and the link between the exact formula and the classical approximated formula is indicated. The exact bandwidth formula provides a new theoretical basis of the bandwidth method for the damping estimation from frequency response functions.     

Tuning Proportional-Integral controllers to approximate simplified predictive control performance

An exact equivalence between PI (Proportional-Integral) and two-parameter SPC (Simplified Predictive Control) is developed to provide identical control of first order linear plants. A relationship between the PI control parameters and the SPC control parameters is described. This relationship that allows the same control in the case of first order linear plants is also found to provide tuning formulas that yield PI control which approximates SPC performance in the case of second order linear plants with widely separated Eigenvalues. Finally, an extension of the PI control algorithm to include future errors provides another exact PI–SPC equivalence for networked control of first order plants.     

QIM digital watermarking based on LDPC code and message passing under scaling attacks

基于量化索引调制(QIM)的数字水印系统,被越来越广泛地应用于数字水印信号的嵌入和提取,但是它对于幅度缩放攻击有明显的脆弱性。本文结合LDPC编码辅助和消息传递算法进行水印信号的提取和参数估计,改善了QIM数字水印系统的性能。对于固定幅度缩放攻击,本文提出的算法比利用重复码编码辅助的消息传递算法,更接近于脏纸码代码香农限。     

正弦信号发生器波形抖动的一种精确测量方法

介绍了一种用三参数正弦波拟合算法实现的、绝对收敛的四参数最小二乘正弦波拟合算法 ,给出了收敛区间、绝对收敛判据以及实现过程。在此基础上讨论实现了正弦信号发生器波形抖动的评价问题。使用一个周期的正弦波曲线模型的滑动拟合法 ,评价了幅度、频率、直流偏移的抖动 ,以及相位与理论值之偏差的抖动情况。在幅度、频率、相位和直流偏移分别存在固定抖动的情况下 ,仿真评价了四个正弦参数各自的抖动情况 ,同时 ,在一个实测正弦波形曲线上进行的抖动分析 ,获得了非常明确的抖动测量结果。本方法评价正弦波信号抖动时 ,准确度高、分辨力好 ,且指标全面。     

Evaluation of a four-point sine wave frequency estimator for portable DSP based instrumentation

A recent frequency estimation method was proposed in a Measurement paper for use in portable DSP based instrumentation. This method is especially important due to its low computational effort making it suitable for fast and low cost instrumentation. It has been found that many parameters can affect the frequency estimation using the proposed method. In this paper, the performance of the method in the presence of additive noise is evaluated, and the influence of signal frequency, initial phase, additive noise and number of analog-to-digital converter bits on the estimator is studied. Some caveats of the practical use of the method are addressed. Detailed numerical simulations based on a Monte Carlo procedure are presented in order to highlight the range of applicability of the method and determine the estimation bias.     

Quantitative diagnosis for bearing faults by improving ensemble empirical mode decomposition

In the bearing health assessment issues, using the adaptive nonstationary vibration signal processing methods in the time-frequency domain, lead to improving of early fault detection. On the other hand, the noise and random impulses which contaminates the input data, are a major challenge in extracting fault-related features. The main goal of this paper is to improve the Ensemble Empirical mode decomposition (EEMD) algorithm and combine it with a new proposed denoising process and the higher order spectra to increase the accuracy and speed of the fault severity and type detection. The main approach is to use statistical features without using any dimension reduction and data training. To eliminate unrelated components from faulty condition, the best combination of denoising parameters based on the wavelet transform, is determined by a proposed performance index. In order to enhance the efficiency of the EEMD algorithm, a systematic method is presented to determine the proper amplitude of the additive noise and the Intrinsic Mode Functions (IMFs) selection scheme. The fault occurrence detection and the fault severity level identification are performed by the Fault Severity Index (FSI) definition based on the energy level of the Combined Fault-Sensitive IMF (CFSIMF) envelope using the central limit theorem. Also, taking the advantages of a bispectrum analysis of CFSIMF envelope, fault type recognition can be achieved by Fault Type Index (FTI) quantification. Finally, the proposed method is validated using experimental data set from two different test rigs. Also, the role of the optimum denoising process and the algorithm of systematic selection of the EEMD parameters are described regardless of its type and estimating the consistent degradation pattern.     

四参数正弦曲线拟合的一种收敛算法

对几种典型的4参数正弦波拟合算法进行了回顾，介绍了一种用三参数正弦波拟合算法实现4参数最小二乘正弦波拟合的收敛算法，特点是将幅度、频率、相位、直流偏移的4参数四维空间的最优化问题，转变成了频率的一维空间搜索和优化问题，讨论了频率参量在此一维空间上的收敛特性与规律，给出了该算法明确的收敛区间、收敛判据及实现过程。仿真及实验均证明了该方法的有效性和可行性，可用于4参数正弦波曲线拟合及调制信号的数字化解调。     

Instantaneous frequency of an arbitrary signal

This paper defines the non-negative pointwise instantaneous frequency (pIF) and pointwise instantaneous amplitude (pIA) of an arbitrary time signal to be the circular frequency and radius of curvature of the signal’s instantaneous trajectory on the complex plane consisting of the signal and its conjugate part from the Hilbert transform. One analytical and three computational methods are derived to prove and validate this concept. The analytical method is derived based on the definition of pIF and circle fitting. A five-point frequency tracking method is developed to eliminate the incapability of the original four-point Teager–Kaiser algorithm (TKA) for obtaining pIF of signals with moving averages. A three-point conjugate-pair decomposition (CPD) method is derived based on circle fitting using a pair of conjugate harmonic functions for frequency tracking. Moreover, the Hilbert–Huang transform (HHT) uses the empirical mode decomposition (EMD) to sift a signal’s instantaneous dynamic component from its sectional moving average (sMA) as the first intrinsic mode function, and then Hilbert transform is used to compute the first IMF’s frequency and amplitude as the sectional instantaneous frequency (sIF) and sectional instantaneous amplitude (sIA). Because finite difference is used in the five-point TKA, its accuracy is easily destroyed by noise. On the other hand, because CPD uses a constant and a pair of windowed regular harmonics to fit data points and estimate pIF and pIA, noise filtering is an implicit capability of CPD and its accuracy increases with the number of processed data points. Numerical simulations confirm that pIF and pIA are non-negative and physically meaningful and can be used for frequency tracking and accurate characterization of complex signals. However, sIF and sIA from HHT are more useful for system identification because the IMFs sifted by EMD often correspond to actual vibration modes.     

一种垂直驱动型超声波送料器的研究

基于压电驱动的原理,研制了一种用于新型垂直驱动型超声波送料器,对结构进行了设计计算;同时设计了送料器的驱动装置-超声波换能器,对超声波换能器的振动模式和性能参数进行了分析,并建立了相关的方程。对本送料器的基本性能及行了测试。实验表明, 该送料器能够实现对微小物体的输送。     

The effect of sinusoidal roughness profile upon rolling plane layered contact

A numerical solution to the free rolling layered contact problem of a regular wavy surface is presented. Both bonded and unbonded layers are investigated. The governing dual elasticity equations are reduced to a system of linear equations where the solution provides a set of results for the unknown parameters. Sliding and complete adhesion cases are treated. The influence of roughness, coefficient of friction, layer thickness and layer compressibility on the results are examined. It is found that the stability of the present method is strongly dependent on the ratio of the amplitude of the wave to its wavelength. In the case of adhesive rolling, the shear traction becomes smooth for an incompressible layer. An asymptotic solution for the surface tractions is obtained when an unbonded layer in full sliding becomes thin. The numerical data showed good agreement with the existing analytical solutions for smooth surfaces and with the derived formula.     

Cultural evolutionary design of adaptive wavelet filters based on lifting scheme for micro-instruments

An evolutionary procedure based on cultural algorithms for the optimal design of adaptive wavelet filters based on lifting scheme is proposed. Numerical results of characterization, based on statistical experiment design, as well as validation, based on the comparison with a genetic optimization algorithm, are presented. Experimental results of the validation on two case studies for reducing uncertainty arising from noise in on-field corrosion rate measurements are highlighted.     

Automatic estimation and removal of noise on digital image

An spatially adaptive noise detection and removal algorithm is proposed.Under the assumption that an observed image and its additive noise have Gaussian distribution,the noise parameters are estimated with local statistics from an observed degraded image,and the parameters are used to define the constraints on the noise detection process.In addition,an adaptive low-pass filter having a variable filter window defined by the constraints on noise detection is used to control the degree of smoothness of the reconstructed image.Experimental results demonstrate the capability of the proposed algorithm.     

转子运动激励下叶片的振动特性分析

研究了航空发动机叶片在转子运动激励下的非线性动力学特性,利用一阶活塞理论来计算气动力,考虑大变形所带来的几何非线性的影响,利用Hamilton原理建立了叶片的连续体模型,采用伽辽金法将叶片简化为单自由度模型,通过多尺度法导出了叶片在参数激励与强迫激励作用下联合共振幅频响应的一阶近似方程;分析了转子扭转角度的幅值、稳定转速、气体的来流速度以及叶片的形状参数对于叶片幅频响应特性的影响。通过解析和数值分析,表明以上的参数是促使叶片动力学行为发生变化的敏感参数。同时应用奇异性理论得到系统主参数共振-主共振稳态响应的转迁集和分岔图,并对低风速情况下的叶片进行了试验分析。     

A novel design strategy for iterative learning and repetitive controllers of systems with a high modal density: Application to active noise control

This paper describes the application of a novel design strategy for iterative learning and repetitive controllers for systems with a high modal density, presented in the companion paper, on two experimental case studies. Both case studies are examples of active structural acoustic control, where the goal is to reduce the radiated noise using structural actuators. In the first case study, ILC is used to control punching noise. An electrodynamic actuator on the frame of the punching machine is driven by the ILC algorithm which takes advantage of the repetitiveness of the consecutive impacts to reduce noise radiation. In the second case study, an RC algorithm is used to control the noise radiated by rotating machinery, which is often mainly periodic. A piezoelectric actuator incorporated in the bearing is driven by the RC algorithm which is capable of reducing harmonics of the rotational frequency of the shaft. Both applications show the practical usefulness of the novel design strategy.     

An inverse shock response spectrum

The shock response spectrum (SRS) is a tool commonly used by application engineers that characterizes the severity of a transient acceleration. Due to the definition of the SRS, neither an analytical nor a unique inverse exists for an arbitrary function. An SRS presented without any temporal information makes creating a corresponding acceleration time history for an experimental or numerical study prohibitively difficult without a rigorous method to determine an inverse of the SRS (a corresponding time history). The present work develops a method to calculate an inverse of an arbitrary SRS using three sets of well characterized basis functions: an impulse function, a sine function/damped sine function, and a modified Morlet wavelet. These three basis functions are specifically chosen for the properties of their transformations: the impulse introduces a constant increase to the SRS above a given frequency, the sine wave introduces a narrow peak at a given frequency, and the Morlet wavelet introduces a plateau with an adjustable width and relative height. Using the definition of the SRS, the transformations of the basis functions are calculated and these expressions are used to derive a methodology for calculating an inverse SRS. The effectiveness of the method is demonstrated by several examples. The quality of an inverse SRS is evaluated by comparing the SRS of the inverse to the target SRS. This method is developed in order to provide a quick estimate of a corresponding time history; in applications where a higher fidelity representation of the SRS is needed than can be provided by the method developed, a genetic algorithm is used to optimize the coefficients of the basis functions. Given a sufficient number of basis functions for the optimization, the resulting SRS can almost exactly match a randomly generated target SRS that is nonzero over the frequency range considered. For applications in which the permissable basis functions are limited (such as for an experimental test apparatus), an extension of the genetic algorithm method is discussed.     

基于Duffing振子和ML的微弱信号幅值估计新方法

基于Du ffing振子和最大似然参量估计方法,提出一种微弱正弦信号幅值估计的新方法。介绍了新方法的原理和具体实现过程。将混有噪声的待测信号送入Du ffing系统,依据大周期工作状态下Du ffing系统具有优良的信噪比改善特性,采用最大似然法估计Du ffing系统的输出信号幅值,进一步由系统输入输出之间的关系确定输入的微弱正弦信号的幅值。通过仿真实验,对该方法和最大似然法直接用于微弱正弦信号幅值估计的结果进行了对比。实验结果表明:该方法明显提高了估计精度。     

On-line block pulse implementation of a sine wave using microprocessor

The present work uses a microprocessor and relevant hardware to express an integrable time-varying function, e.g., a sine wave, received as an on-line signal, in terms of equivalent block pulse functions (BPFs). The BPF coefficients, determined via experiments are employed for reconstruction of the original time signal. Two alternative methods have been adopted for practical implementation: (i) method of integration and (ii) method of sampling. BPF coefficients, determined experimentally, are compared with those obtained via exact computation. From the computed BPF coefficients, Haar spectral coefficients are determined using similarity transformation. Again, the average values, RMS values and form factors are calculated for exact and BPF approximated sine waves for comparison and relative accuracy. Relevant tables are presented to assess comparative usefulness of the work.     

Stable, inexpensive, low-frequency sine wave generator using digital techniques

Presented is a circuit for the generation of low-frequency (0.001 Hz to 63 kHz) sine waves possessing stable amplitude and frequency characteristics using digital techniques. The circuit produces a 32-step approximation to a sine wave at a frequency 1/32nd of the selected digital time-base frequency. Also presented are a crystal-controlled time base to drive the generator, and an active filter for removing the high-order harmonics produced by the generator. Advantages of the digital sine wave generator over analog oscillator techniques are described.