Modal identification based on Gaussian continuous time autoregressive moving average model

A new time-domain modal identification method of the linear time-invariant system driven by the non-stationary Gaussian random force is presented in this paper. The proposed technique is based on the multivariate continuous time autoregressive moving average (CARMA) model. This method can identify physical parameters of a system from the response-only data. To do this, we first transform the structural dynamic equation into the CARMA model, and subsequently rewrite it in the state-space form. Second, we present the exact maximum likelihood estimators of parameters of the continuous time autoregressive (CAR) model by virtue of the Girsanov theorem, under the assumption that the uniformly modulated function is approximately equal to a constant matrix over a very short period of time. Then, based on the relation between the CAR model and the CARMA model, we present the exact maximum likelihood estimators of parameters of the CARMA model. Finally, the modal parameters are identified by the eigenvalue analysis method. Numerical results show that the method we introduced here not only has high precision and robustness, but also has very high computing efficiency. Therefore, it is suitable for real-time modal identification.     

TIME-FREQUENCY ANALYSIS OF A SUSPENSION BRIDGE BASED ON GPS

This paper describes the results obtained from full-scale measurements of Humen bridge, which is the second longest suspension bridge in China. A real-time kinematic (RTK) global positioning system (GPS) has been developed and installed on the Humen bridge for on-line monitoring of bridge deck movements. The field wind-induced vibration data were measured by this monitoring system. Three system identification techniques are then adopted in the modal analysis of the wind-induced vibration response: the time-frequency Wigner distribution (WD) technique, the frequency-domain fast Fourier transform (FFT) technique and the time-domain auto-regressive moving average vector (ARMAV) technique. The WD technique can recognize close modal coupling and non-stationary response. The FFT technique can on site verify the quality of the measurements, but its frequency resolution is low and damping estimates are unreliable. The ARMAV method allows for gaining high-frequency resolution. However, it is strictly related to the stationary hypothesis. It is a general conclusion that we can improve the quality of the analysis and get more precise characteristics of the signal by these three methods. In addition, the WD combined with ARMAV seems to be the best case in quantitative analysis of fast-changing vibration signals.     

Estimation of generalized frequency response functions for quadratically and cubically nonlinear systems

A new method of estimating the Volterra kernels in the frequency-domain is introduced based on a non-parametric algorithm. Unlike the traditional non-parametric methods using the frequency-domain formulations based on discrete Fourier transform (DFT) data, this new approach uses the time-domain measurements directly to estimate the frequency-domain response functions.     

Maximum likelihood estimator of operational modal analysis for linear time-varying structures in time–frequency domain

This paper investigates the problem of modal parameter estimation of time-varying structures under unknown excitation. A time–frequency-domain maximum likelihood estimator of modal parameters for linear time-varying structures is presented by adapting the frequency-domain maximum likelihood estimator to the time–frequency domain. The proposed estimator is parametric, that is, the linear time-varying structures are represented by a time-dependent common-denominator model. To adapt the existing frequency-domain estimator for time-invariant structures to the time–frequency methods for time-varying cases, an orthogonal polynomial and z-domain mapping hybrid basis function is presented, which has the advantageous numerical condition and with which it is convenient to calculate the modal parameters. A series of numerical examples have evaluated and illustrated the performance of the proposed maximum likelihood estimator, and a group of laboratory experiments has further validated the proposed estimator.     

Two-dimensional optical coherence tomography for real-time structural dynamical characterization

We present a two-dimensional optical coherence vibration tomography (2DOCVT) system with an ultra-precision displacement resolution of ~0.1 nm that is capable of in site real-time absolute displacement measurement of structural line vibrations. Experimental results of sinusoidal, sweep and impulse vibrations were reported. The key figures of merit such as the 2DOCVT system could obtain fast line vibration measurement without scanning and it also could be used to capture structural modal parameters in one single impulse excitation measurement without any vibration excitation input information, making it attractive for the application in low-frequency vibration measurement and response-only modal analysis.     

Identification of modal parameters including unmeasured forces and transient effects

In this paper, a frequency-domain method to estimate modal parameters from short data records with known input (measured) forces and unknown input forces is presented. The method can be used for an experimental modal analysis, an operational modal analysis (output-only data) and the combination of both. A traditional experimental and operational modal analysis in the frequency domain starts respectively, from frequency response functions and spectral density functions. To estimate these functions accurately sufficient data have to be available. The technique developed in this paper estimates the modal parameters directly from the Fourier spectra of the outputs and the known input. Instead of using Hanning windows on these short data records the transient effects are estimated simultaneously with the modal parameters. The method is illustrated, tested and validated by Monte Carlo simulations and experiments. The presented method to process short data sequences leads to unbiased estimates with a small variance in comparison to the more traditional approaches.     

Picosescond fluorescence lifetime standards for frequency- and time-domain fluorescence

We characterized a series of dimethylamino-stilbene derivatives as standards for time-domain and frequency-domain lifetime measurements. The substances have reasonable quantum yields, are soluble in solvents available with a high purity, and do not show significant sensitivity to oxygen quenching. All the fluorophores displayed single exponential intensity decays, as characterized by frequency-domain measurements to 10 GHz. The decay times vary from 880 to 57 ps, depending on structure, solvent, and temperature, which is a useful range for modern picosecond time-domain or gigahertz frequency-domain instruments. These fluorophores may be used either to test an instrument or as reference compounds to eliminate color effects. We also characterized two-fluorophore mixtures, with the decay times spaced twofold (150 and 300 ps), with varying proportions. These mixtures are useful for testing the resolution of other time- and frequency-domain instrumentation. The excitation wavelength ranges from 260 to 430 nm, and the emission from 350 to 550 nm. The decay times are independent of the excitation and emission wavelengths.     

White noise nonlinear system analysis in nuclear magnetic resonance spectroscopy

Nonlinear noise excitation in nuclear magnetic resonance is a form of nonlinear spectroscopy which exploits the nonlinear susceptibilities in a very direct way. The nonlinear susceptibilities are defined by perturbation theory in the frequency domain. In nonlinear system analysis, on the other hand, the system response is described by a Volterra series in the time domain. The kernels of the Volterra functionals carry the information about the system and are to be determined by experiment.The series expansion of a molecular, atomic or nuclear system response is derived in quantum mechanics by time dependent perturbation theory, leading to a Volterra series with time ordered, triangular kernels. The kernels are multi-dimensional products of decaying exponentials, which describe coherence decays of particular density matrix elements. The Fourier transforms of the triangular Volterra kernels are the susceptibilies, which are formally identical in NMR spectroscopy and nonlinear optical spectroscopy. The nonlinear susceptibilities are multi-dimensional spectra, which in NMR spectroscopy reveal the spin communication pathways. These are established by various forms of single quantum coherence connectivities, such as indirect coupling, chemical exchange, cross-relaxation, dipolar and quadrupolar coupling.If the functionals of the Volterra series are orthogonalized with respect to Gaussian white noise excitation, the Wiener series results. The Wiener kernels can be derived by multi-dimensional cross-correlation of the system response with different powers of the Gaussian white noise excitation.Cross-correlation of the transverse magnetization response to noise excitation in NMR leads to multi-dimensional time functions, the Fourier transforms of which closely resemble the nonlinear susceptibilities. The cross-correlation spectra differ from the susceptibilities in the governing Liouvillean and the dynamic density matrix, which are affected by saturation for continuous excitation. Cross-correlation spectra and susceptibilities converge for vanishing excitation power. Therefore the cross-correlation spectra are referred to as stochastic susceptibilities.In stochastic NMR spectroscopy only odd order susceptibilities exist for transverse magnetization. The first nonlinear order is the third, and the nonlinear spectral information is derived from the third order susceptibility. Higher order susceptibilities are not feasible to derive from experimental data. An important share of the nonlinear information is found on the six subdiagonal 2D cross-sections through the third order susceptibility. These cross-sections arise in three pairs, which carry distinct information, separated according to longitudinal magnetization and population effects, zero quantum coherences, and double quantum coherences.In practice a nonlinear 3D spectrum is computed from experimental data by an algorithm in the frequency domain, which yields access to selected regions in the 3D spectrum. This spectrum is the symmetrized stochastic third order susceptibility. All its sub-diagonal 2D cross-sections are equivalent. They are the average of the six different sub-diagonal 2D cross-sections through the asymmetric third order susceptibility.The stochastic excitation technique in NMR is characterized by several unique attributes. (1) There is no minimum time for a data acquisition cycle, so that, at the expense of signal-to-noise ratio, strong samples can be investigated faster with stochastic NMR than with pulsed FT NMR. (2) Stochastic excitation tests the sample extensively, and measures a maximum amount of information in a single experiment. This feature is of particular interest for investigation of short-lived samples and of samples with little a priori information. (3) An experiment with stochastic excitation is simple to perform, but the data processing is more complex than in FT spectroscopy. (4) The nonlinear information about spin communication pathways is derived for individual frequency regions only, which are identified in the stochastic ID spectrum. This information is located primarily on the sub-diagonal 2D cross-sections through the third order susceptibility. (5) Stochastic NMR spectra derived from random noise excitation are contaminated by systematic noise. In the sub-diagonal 2D cross-sections the noise is reduced by filtering and symmetrization during data processing. (6) Sub-diagonal 2D cross-sections are sensitive to experimental phase distortions in one direction only. They are readily adjusted in phase with the same parameters as the ID spectrum. (7) Stochastic multi-dimensional spectra can be computed at variable resolution from one and the same set of raw data.So far stochastic NMR spectroscopy is not applied routinely in analytical spectroscopy. More practical experience is needed to evaluate its merits in comparison with Fourier transform NMR.Stochastic excitation is distinguished from continuous wave and sparsely pulsed excitation by low input power in connection with large bandwidth. This important property cannot be exploited in high resolution NMR in liquids, because excitation power is not a restricting factor in this case. The situation is different in NMR imaging, where large field gradients require large bandwidths and the excitation power becomes a point of concern. For this reason stochastic RF excitation is being investigated in NMR imaging.The multi-dimensional cross-correlation functions obtained from random noise excitation generally are contaminated by systematic noise. The occurrence of systematic noise can be avoided if pseudo-random excitation is used in combination with a transformation of the system response to obtain the kernels. This technique is used successfully in Hadamard spectroscopy, where the linear Volterra kernel is the Hadamard transform of the linear response functional. Nonlinear transformations^(220,221) for retrieval of nonlinear kernels have not yet been realized in NMR spectroscopy.The cross-correlation technique underlying the data evaluation in stochastic nonlinear system analysis is equivalent to interferometry in optical spectroscopy. The Michelson interferometer is the most prominent optical correlator. The time resolution of the kernels derived by cross-correlation is determined by the inverse bandwidth of the excitation. With the Michelson interferometer a time resolution of 10⁻¹⁴ s is achieved in IR spectroscopy. Since the IR correlogramm is Fourier transformed for spectral analysis, the time resolution cannot be exploited otherwise. For analysis of fast time dependent processes a two-dimensional interferometer should be constructed, which performs a 2D cross-correlation of the system response to two in general different noise inputs. One input pumps the time dependent process, the other is used to investigate the time dependence spectroscopically. This technique is introduced by the name of ‘two-dimensional interferometry’. It uses low excitation power, but provides high time resolution at large response energy. Related work is pursued in nonlinear optical spectroscopy with incoherent excitation. In this area the use of broad band lasers is investigated for generation of echoes and for correlation based measurements of relaxation times.     

Time-dependent variance and covariance of responses of structures to non-stationary random excitations

In this paper techniques for the analysis of non-stationary random responses of linear structures, discretized by the finite element method so that they can be analyzed as multi-degree of freedom systems, subjected to non-stationary random excitation are developed. The non-stationary random excitation is represented as a product of (a) an exponentially decaying function and a white noise process, and (b) a modulating function in the form of an exponential envelope and a white noise process. Closed form expressions for the time-dependent variance and covariance of response of structures are presented. Application of these expressions is made for the analysis of non-stationary random responses of a physical model of a class of mast antenna structures subjected to base excitation. It is concluded that (a) the coupling terms do have a definite influence on the response; the magnitude of the influence is proportional to the amount of damping in the structure and proximity of the modes excited; (b) the non-stationary random excitations considered are general in that the modulating functions are not necessarily identical, and therefore the influence of various modulating functions of the excitations applied to different locations of the structure on responses can be examined quantivatively; and (c) for a given damping parameter the magnitudes of the modulating function parameters cannot be chosen arbitrarily though the shapes of normalized modulating functions can be selected to best fit the excitation realizations.     

Frequency-domain modal delay measurement for higher-order mode fiber based on stretched pulse interference

We propose and demonstrate a novel modal delay measurement technique for a higher-order mode fiber (HOF) based on optical frequency-domain reflectometry (OFDR) using an extremely simple, entirely passive, and ultrafast wavelength sweeping mechanism, namely, dispersion-induced optical pulse stretching. We obtained a high temporal resolution of approximately 1.12 ps, which was sufficient for discerning the four excited modes in an HOF with a length of only approximately 5 m. The results from our measurements were very consistent with those obtained by using a traditional time-domain measurement method and a conventional OFDR measurement based on a tunable CW laser. Our proposed technique can be also easily adapted to perform conventional time-domain modal delay measurements for very long HOFs.     

Lattice plasmon mode excitation via near-field coupling

The optical response of metal nanoparticles can be modified through near-field or far-field interaction,yet the lattice plasmon modes(LPMs)considered can only be excited from the latter.Here instead,we present a theoretical evaluation for LPM excitation via the near-field coupling process.The sample is an arrayed structure with specific units composed of upper metal disks,a lower metal hole and a sandwiched dielectric post.The excitation process and underlying mechanism of the LPM and the influence of the structure parameters on the optical properties have been investigated in detail by using a finite-difference time-domain(FDTD)numerical method.Our investigation presented here should advance the understanding of near-field interaction of plasmon modes for LPM excitation,and LPMs could find some potential applications,such as in near-field optical microscopes,biosensors,optical filters and plasmonic lasers.     

太赫兹无损检测的多特征参数神经网络分析技术

提出一种基于太赫兹无损检测的多特征参数神经网络分析技术,用于分析耐高温复合材料的粘贴质量无损检测.采用抽片式方法设计了一种耐高温复合材料的脱粘缺陷样品,抽片厚度为0.1mm.采用太赫兹时域光谱无损检测技术对耐高温复合材料的多层脱粘缺陷进行了检测试验研究,对比了上下脱粘缺陷所对应的太赫兹时域波形及频谱信息的异同,针对性地建立了耐高温复合材料粘贴质量的上层脱粘参数、下层脱粘参数、频域吸收质心参数等多特征参数,将特征参数进行优化作为反向传播神经网络的输入并对其进行上下脱粘分类识别.通过对反向传播神经网络的训练测试,实现了耐高温复合材料上层脱粘0.1mm、下层脱粘0.1mm的脱粘缺陷的识别.     

Modal parameter identification using the log decrement method and band-pass filters

This paper presents a time-domain technique for identifying modal parameters of test specimens based on the log-decrement method. For lightly damped multidegree-of-freedom or continuous systems, the conventional method is usually restricted to identification of fundamental-mode parameters only. Implementation of band-pass filters makes it possible for the proposed technique to extract modal information of higher modes. The method has been applied to a polymethyl methacrylate (PMMA) beam for complex modulus identification in the frequency range 10-1100 Hz. Results compare well with those obtained using the Least Squares method, and with those previously published in literature. Then the accuracy of the proposed method has been further verified by experiments performed on a QuietSteel specimen with very low damping. The method is simple and fast. It can be used for a quick estimation of the modal parameters, or as a complementary approach for validation purposes.     

Performance of time- and frequency-domain binaural beamformers based on recorded signals from real rooms

Extraction of a target sound source amidst multiple interfering sound sources is difficult when there are fewer sensors than sources, as is the case for human listeners in the classic cocktail-party situation. This study compares the signal extraction performance of five algorithms using recordings of speech sources made with three different two-microphone arrays in three rooms of varying reverberation time. Test signals, consisting of two to five speech sources, were constructed for each room and array. The signals were processed with each algorithm, and the signal extraction performance was quantified by calculating the signal-to-noise ratio of the output. A frequency-domain minimum-variance distortionless-response beamformer outperformed the time-domain based Frost beamformer and generalized sidelobe canceler for all tests with two or more interfering sound sources, and performed comparably or better than the time-domain algorithms for tests with one interfering sound source. The frequency-domain minimum-variance algorithm offered performance comparable to that of the Peissig-Kollmeier binaural frequency-domain algorithm, but with much less distortion of the target signal. Comparisons were also made to a simple beamformer. In addition, computer simulations illustrate that, when processing speech signals, the chosen implementation of the frequency-domain minimum-variance technique adapts more quickly and accurately than time-domain techniques.     

Optical correlation techniques in fluid dynamics

Three flow measurement techniques make use of fast digital correlators. The most widely spread is photon correlation velocimetry using crossed laser beams, and detecting Doppler shifted light scattered by small particles in the flow. Depending on the processing of the photon correlation output, this technique yields mean velocity, turbulence level, and even the detailed probability distribution of one velocity component. An improved data processing scheme is demonstrated on laminar vortex flow in a curved channel. In the second method, rate correlation based upon threshold crossings of a high pass filtered laser Doppler signal can be used to obtain velocity correlation functions. The most powerful set-up developed in our laboratory uses a phase locked loop type tracker and a multibit correlator to analyze time-dependent Taylor vortex flow. With two optical systems and trackers, cross-correlation functions reveal phase relations between different vortices. The last method makes use of refractive index fluctuations (eg in two phase flows) instead of scattering particles. Interferometry with bidirectional counting, and digital correlation and probability analysis, constitutes a new quantitative technique related to classical Schlieren methods. Measurements on a mixing flow of heated and cold air contribute new ideas to the theory of turbulent random phase screens.     

Method to measure acoustic impedance and reflection coefficient.

A frequency-domain based system for measuring acoustic impedance and reflection coefficient is described. The calibration procedure uses a least-mean-squares approximation to the Thevenin parameters describing the source and receiver characteristics in which the data measured on closed, cylindrical tubes are matched to a viscothermal tube model. The system is intended for use in acoustical measurement in human ear canals, in which the cross-sectional area of the ear canal at the point of insertion is imprecisely known. This area is acoustically estimated from the impedance data, and the reflection coefficient is calculated in terms of this area and the impedance data. Measurements on a variety of closed tubes show the method is accurate over the frequency range investigated (less than 10.7 kHz). The time-domain reflection function is evaluated by transforming the reflection coefficient from the frequency domain, but the finite bandwidth of the measured data limits the accuracy of time-domain response measurements. The method is well suited for frequency-domain measurements in human ear canals.     

Time domain identification of standing wave parameters in gas piping systems

A method for experimentally determining the natural frequencies and modal pressures of an air or gas piping system is presented. Such information is of interest in installations where pressure pulsations caused by pumps or compressors are of importance. In the method a time domain based technique is used which was originally developed as an alternative to frequency response methods for determining the vibration parameters (natural frequencies, modes, damping factors) of structures, to avoid difficulties often encountered in interpreting complex and non-conclusive frequency response data such as arises from systems having numerous modes, some of which may be highly damped or closely spaced in frequency. In this application, a straight steel pipe with a sound source at one end and closed at the other end was used. Two microphones were used to measure the pressure at two locations in the pipe. The free pressure response following a rapidly swept sinewave input was recorded, digitized and then used in a computational procedure based on a lumped parameter representation of the system. The natural frequencies and the corresponding modal pressure ratios at the two stations, thus obtained, are compared with mention here that although in the experiment reported here an external frequency sweep excitation was used, the technique works as well with free decay response after a system shut-off, impulse response or random responses from normal system operation.     

Response of plates with unconstrained layer damping treatment to random acoustic excitation,part II: Response evaluation

Theoretical and experimental investigations on the response of a plate with unconstrained layer damping treatment to random acoustic excitation have been carried out. The theoretical response evaluation consisted of determining the power spectral density of the acceleration response of the layered plate by the use of generalized harmonic analysis under a specific random acoustic excitation, with use being made of modal frequencies and associated loss factors estimated as described in Part I. A study was made on the contribution of cross coupling terms of the acceleration response for the two boundary conditions investigated: namely, all edges simply supported and all edges clamped. In the experimental investigation, plates with different damping layer thicknesses were subjected to high intensity random acoustic excitation generated by an exponential horn driven by an electropneumatic transducer. The acceleration responses were recorded and later analyzed to yield the power spectral densities. Experimental and theoretical results are compared.     

Adaptive time-domain filtering for real-time spectral discrimination in a Michelson interferometer

We present a method of spectral discrimination that employs time-domain processing instead of the typical frequency-domain analysis and implement the method in a Michelson interferometer with a nonlinear mirror scan. The technique yields one analog output value per scan instead of a complete interferogram by directly filtering a measured scan with a reference function in the time domain. Such a procedure drastically reduces data-processing requirements downstream. Additionally, using prerecorded interferograms as references eliminates the need to compensate for scan nonlinearities, which broadens the field of usable components for implementation in miniaturized sensing systems. With our efficient use of known spectral signatures, we demonstrate real-time discrimination of 633- and 663-nm laser sources with a mirror scan length of 1 microm , compared with the Rayleigh criterion of 7 microm.     

Green׳s function method for piezoelectric energy harvesting beams

The development of validated mathematical models for piezoelectric harvesters is important as it provides predictive capabilities of their performance and insight to their coupled electromechanical behavior. Advanced solutions to these models allows for more realistic parameters to be considered. In this paper, we present a Fourier Transform–Green?s Function (FTGF) solution approach to the distributed parameter coupled electromechanical equations for a piezoelectric beam excited by an arbitrary external transverse force. This method, as opposed to modal analysis, allows for frequency-dependent material properties and damping coefficients to be considered. The special case of a harmonic base excitation is considered and closed-form expressions for the frequency response functions of the voltage generated by piezoelectric layer, relative tip displacement and local bending strain are obtained. Finally, the FTGF solution to these frequency response functions is compared with the modal analysis solution along with experimental data for validation.