System Impulse Response Function Research Articles

Wavelet Characterizations for Investigating Nonlinear Oscillators

This study investigates the wavelet-based system identification capabilities on determining the system nonlinearity based on the system impulse response function. Wavelet estimates of the instantaneous envelopes and instantaneous frequency are used to plot the system backbone curve. This wavelet estimate is then used to estimate the values of the parameter for the system. Two weakly nonlinear oscillators, which are the Duffing and the Van der Pol oscillators, have been analyzed using this wavelet approach. A case study based on a model of an oscillating flap wave energy converter (OFWEC) was also discussed in this study. Based on the results, it was shown that this technique is recommended for nonlinear system identification provided the impulse response of the system can be captured. This technique is also suitable when the system's form is unknown and for estimating the instantaneous frequency even when the impulse responses were polluted with noise.

Diffuse Attenuation Coefficient (Kd) from ICESat-2 ATLAS Spaceborne Lidar Using Random-Forest Regression

This study investigates a new method for measuring water turbidity—specifically, the diffuse attenuation coefficient of downwelling irradiance Kd —using data from a spaceborne, green-wavelength lidar aboard the National Aeronautics and Space Administration's ICESat-2 satellite. The method enables us to fill nearshore data voids in existing Kd data sets and provides a more direct measurement approach than methods based on passive multispectral satellite imagery. Furthermore, in contrast to other lidar-based methods, it does not rely on extensive signal processing or the availability of the system impulse response function, and it is designed to be applied globally rather than at a specific geographic location. The model was tested using Kd measurements from the National Oceanic and Atmospheric Administration's Visible Infrared Imaging Radiometer Suite sensor at 94 coastal sites spanning the globe, with Kd values ranging from 0.05 to 3.6 m –1 . The results demonstrate the efficacy of the approach and serve as a benchmark for future machine-learning regression studies of turbidity using ICESat-2.

Damage detection through nonparametric models using Kautz filters

The goal of this paper is to present an approach to detect structural changes by using nonparametric models. The impulse response functions (IRFs) of mechanical systems in healthy conditions are identified through the sum of convolution expanded on an orthonormal basis. The Kautz filters with multiple poles optimized are implemented as an efficient orthonormal basis to identify nonparametric reference models. Identifying the IRFs of a smart beam with PZTs actuators/sensors coupled is used to illustrate the necessary procedures. The damages are simulated as a loss of bolts, nuts, and washers attached near a PZT sensor. A statistical procedure of a hypothesis test is also used to confirm the smart beam’s structural state. The experimental results achieved show that it is possible to detect the structural changes with statistical confidence.

Monte-Carlo Integration Models for Multiple Scattering Based Optical Wireless Communication

Monte-Carlo models are analyzed for multiple scattering channels in optical wireless communications. It is demonstrated that the system impulse response function can be obtained by Monte-Carlo integration model. The convergence performance for the Monte-Carlo integration model is analyzed and improved by introducing different sampling methods. The simulation results show that the gamma function model for channel impulse response function can only be applied to the cases where the common volume between the transmitted light beam and the receiving field-of-view is open. Numerical simulation suggests that for a three-order scattering case, the computation efficiency of the Monte-Carlo integration model based on partial importance sampling is about 12 times of the original Monte-Carlo integration model based on uniform sampling, and 5.6 times of the widely used Monte-Carlo simulation model. The numerical results also show that the Monte-Carlo integration model based on partial importance sampling has higher computation efficiency than the Monte-Carlo simulation model in a higher-order scattering communication scenario.

Characterizing the System Impulse Response Function From Photon-Counting LiDAR Data

NASA’s Multiple Altimeter Beam Experimental LiDAR (MABEL) is an aircraft-based photon-counting laser altimeter designed as a simulator to test measurement techniques and algorithms for Advanced Topographic Laser Altimeter System (ATLAS), the sole instrument on NASA’s Ice, Cloud, and land Elevation Satellite-2 (ICESat-2) mission. By measuring the time of flight, pointing angle, and absolute position for individual photons, ICESat-2 provides detailed elevation measurements of earth’s surface. Calculating accurate and precise elevations requires an understanding of how photons interact with surfaces, and characterization of the photon distribution after returning from surfaces. Neither MABEL nor ATLAS records the transmitted laser pulse shape, relying instead on aggregating several pulses worth of photons, often using histograms, to characterize the pulse shape. In this paper, we assess the limitations of using histograms and propose a more robust method to describe MABEL’s system impulse-response function using an exponentially modified Gaussian distribution. We also provide standard error estimates for the arithmetic mean and standard deviation calculations, and for exponentially modified Gaussian parameters using a Monte Carlo sensitivity analysis. We apply this method to photon returns from a sea ice lead and from a dry salt lake bed as case studies for estimating the standard error associated with sample size for the arithmetic mean and standard deviation, and for the exponentially modified Gaussian parameters. We use these standard errors to calculate the minimum number of photons required to find both Gaussian and exponentially modified Gaussian distribution parameters within 3 cm of their parent population values.

Planar Vibrations of Massive Vibro-Insulated Bodies Upon Arbitrary Displacement of the Base

The solutions of the equations of planar vibrations of massive bodies upon arbitrary timevarying horizontal displacement of the base are constructed using transfer functions (TF) and impulse response functions (ITF) of linear dynamic systems. This approach makes it possible to obtain the closed-form solutions with harmonic and free vibrations and to construct stable algorithms for calculating systems arbitrary displacement of the base. The solutions are written in the form of an expansion in 'normal forms' directly in generalized coordinates. An example of a calculation is presented for the response and operating regimes of the vibrations due to an instantaneously applied harmonic perturbation.

Removal of Differential Capacitive Interferences in Fast-Scan Cyclic Voltammetry.

Due to its high spatiotemporal resolution, fast-scan cyclic voltammetry (FSCV) at carbon-fiber microelectrodes enables the localized in vivo monitoring of subsecond fluctuations in electroactive neurotransmitter concentrations. In practice, resolution of the analytical signal relies on digital background subtraction for removal of the large current due to charging of the electrical double layer as well as surface faradaic reactions. However, fluctuations in this background current often occur with changes in the electrode state or ionic environment, leading to nonspecific contributions to the FSCV data that confound data analysis. Here, we both explore the origin of such shifts seen with local changes in cations and develop a model to account for their shape. Further, we describe a convolution-based method for removal of the differential capacitive contributions to the FSCV current. The method relies on the use of a small-amplitude pulse made prior to the FSCV sweep that probes the impedance of the system. To predict the nonfaradaic current response to the voltammetric sweep, the step current response is differentiated to provide an estimate of the system’s impulse response function and is used to convolute the applied waveform. The generated prediction is then subtracted from the observed current to the voltammetric sweep, removing artifacts associated with electrode impedance changes. The technique is demonstrated to remove select contributions from capacitive characteristics changes of the electrode both in vitro (i.e., in flow-injection analysis) and in vivo (i.e., during a spreading depression event in an anesthetized rat).

Joint reconstruction of dynamic PET activity and kinetic parametric images using total variation constrained dictionary sparse coding

Dynamic positron emission tomography (PET) is capable of providing both spatial and temporal information of radio tracers in vivo. In this paper, we present a novel joint estimation framework to reconstruct temporal sequences of dynamic PET images and the coefficients characterizing the system impulse response function, from which the associated parametric images of the system macro parameters for tracer kinetics can be estimated. The proposed algorithm, which combines statistical data measurement and tracer kinetic models, integrates a dictionary sparse coding (DSC) into a total variational minimization based algorithm for simultaneous reconstruction of the activity distribution and parametric map from measured emission sinograms. DSC, based on the compartmental theory, provides biologically meaningful regularization, and total variation regularization is incorporated to provide edge-preserving guidance. We rely on techniques from minimization algorithms (the alternating direction method of multipliers) to first generate the estimated activity distributions with sub-optimal kinetic parameter estimates, and then recover the parametric maps given these activity estimates. These coupled iterative steps are repeated as necessary until convergence. Experiments with synthetic, Monte Carlo generated data, and real patient data have been conducted, and the results are very promising.

Vibration isolation systems, considered as systems with single degree of freedom

The research considers and analyzes vibration isolation systems, whose design schemes are single degree of freedom systems, including nonlinear elements - displacement limiter and viscous damper. Presented are calculation formulas in closed form for linear systems in operational modes (for harmonic and impulse loads), algorithms and examples of calculation of linear and nonlinear systems in operational and transient modes. The calculation method and the above dependences are written using the transfer (TF) and impulse response functions (IRF) of linear dynamical systems and dependencies that determine the relationship between these functions. The effectiveness of 2 options of vibration isolation systems in transient modes is analyzed. There is significant reduction of load from the equipment to the supporting structures in the starting-stopping modes by the use of displacement limiter.

SAR Doppler Ambiguity Resolver Based on Entropy Minimization

The determination of Doppler ambiguity number (DAN) is indispensable for the generation of high-quality synthetic aperture radar (SAR) images. An incorrect DAN leads to lower image signal-to-noise ratio and degradation in the system impulse response function. Based on the relationship between DAN errors and the image quality, a novel DAN estimation algorithm named image-quality-based Doppler ambiguity resolver is presented. In the proposed algorithm, the DAN-dependent linear range cell migration correction and DAN-dependent azimuth compression are carried out in subscenes to obtain 2-D compressed SAR images, which are further employed to estimate DAN via minimizing the entropy. The presented algorithm is more robust than conventional methods to cope with demands of both low- and high-contrast scene applications. In addition, the approach is computationally efficient because it can be properly applied to segments of range-compressed data in small size and only a few sets of short fast Fourier transforms are required. Finally, experiments over real data of airborne X-band and spaceborne C-band are carried out to demonstrate the performance of the proposed approach.

Overlap time-gating approach for improving time-domain diffuse fluorescence tomography based on the IRF-calibrated Born normalization

Diffuse fluorescence tomography (DFT) methods using the full time-resolved (TR) data have been demonstrated to substantially improve the spatial resolution and quantitative accuracy of reconstructed images. However, these methods usually suffer from low practical feasibility because of the influence of the system impulse response function (IRF) and the trade-off between the used data time-resolution and the required signal-to-noise ratio (SNR). We present a full TR approach that combines an IRF-calibrated full TR Born normalization and an overlap-delaying time-gate scheme for attaining high SNR without sacrificing the TR information content. The approach is validated with full TR data from phantom experiments for its better performances in the spatial resolution and reconstruction fidelity compared to the traditional DFT methods.

An efficient numerical method for estimating reliabilities of linear structures under fully nonstationary earthquake

Abstract The Conte–Peng’s equations for a fully nonstationary model of an earthquake are reformulated as modulated filtered white-noise processes so that the reliabilities of a linear structure under the fully nonstationary earthquake model can be estimated through calculating the first passage time probabilities of several time-varying linear systems subjected to independent white-noise processes. Each time-varying linear system consists of a second-order single-degree-of-freedom (SDOF) linear oscillator, a deterministic time-modulating function applied at the stationary oscillator’s responses and the linear structure considered. The unit impulse response functions of these time-varying linear systems are derived, from which the useful spectral characteristics of system responses in estimating the crossing rates and limiting decay rates can be numerically calculated. To save computation time, efficient matrix procedures in the time domain are proposed. The reliability analysis of a moment-resisting steel frame subjected to El-Centro-like earthquake demonstrates the effectiveness, accuracy and application of the numerical method.

Changes in the response of the AL Index with solar cycle and epoch within a corotating interaction region

Abstract. We use observations in the solar wind and on the ground to study the interaction of the solar wind and interplanetary magnetic field with Earth's magnetosphere. We find that the type of response depends on the state of the solar wind. Coupling functions change as the properties of the solar wind change. We examine this behavior quantitatively with time dependent linear prediction filters. These filters are determined from ensemble arrays of representative events organized by some characteristic time in the event time series. In our study we have chosen the stream interface at the center of a corotating interaction region as the reference time. To carry out our analysis we have identified 394 stream interfaces in the years 1995–2007. For each interface we have selected ten-day intervals centered on the interface and placed data for the interval in rows of an ensemble array. In this study we use Es the rectified dawn-dusk electric field in gsm coordinates as input and the AL index as output. A selection window of width one day is stepped across the ensemble and for each of the nine available windows all events in a given year (~30) are used to calculate a system impulse response function. A change in the properties of the system as a consequence of changes in the solar wind relative to the reference time will appear as a change in the shape and/or the area of the response function. The analysis shows that typically only 45% of the AL variance is predictable in this manner when filters are constructed from a full year of data. We find that the weakest coupling occurs around the stream interface and the strongest well away from the interface. The interface is the time of peak dynamic pressure and strength of the electric field. We also find that coupling appears to be stronger during recurrent high-speed streams in the declining phase of the solar cycle than it is around solar maximum. These results are consistent with the previous report that both strong driving (Es) and high dynamic pressure (Pdyn) reduce the coupling efficiency. Although the changes appear to be statistically significant their physical cause cannot be uniquely identified because various properties of the solar wind vary systematically through a corotating interaction region. It is also possible that the quality of the propagated solar wind data depends on the state of the solar wind. Finally it is likely that the quality of the AL index during the last solar cycle may affect the results. Despite these limitations our results indicate that the Es-AL coupling function is 50% stronger outside a corotating interaction region than inside.

Complete monotonicity of flow and cross-sectional impulse response functions for rigid right circular tubes

Indicator dilution theory is the conceptual base for many flow measurement methods within living organisms; a whole animal, an organ, or an individual vessel. In this manuscript, we provide a characterization of the system impulse response function for flow- and cross-sectionally sampled indicator curves within a rigid right circular tube. The curves are measured downstream from the position of an injector, which labels uniformly the streamlines of a steady, laminar power law fluid flow. The system impulse response function is shown to be the weighted sum of a Dirac delta function and a completely monotonic function. A numerical example employing data from a physical experiment involving a vertically orientated, perfused glass tube is presented, illustrating the characterization of the impulse response function between cross-sectionally sampled upstream and downstream measurement sites.

Estimation of Parameters in Shot-Noise- Driven Doubly Stochastic Poisson Processes Using the EM Algorithm

To estimate the parameters, the impulse response (IR) functions of some linear time-invariant systems generating intensity processes, in Shot-Noise-Driven Doubly Stochastic Poisson Process (SND-DSPP) in which multivariate presynaptic spike trains and postsynaptic spike trains can be assumed to be modeled by the SND-DSPPs. An explicit formula for estimating the IR functions from observations of multivariate input processes of the linear systems and the corresponding counting process (output process) is derived utilizing the expectation maximization (EM) algorithm. The validity of the estimation formula was verified through Monte Carlo simulations in which two presynaptic spike trains and one postsynaptic spike train were assumed to be observable. The IR functions estimated on the basis of the proposed identification method were close to the true IR functions. The proposed method will play an important role in identifying the input-output relationship of pre- and postsynaptic neural spike trains in practical situations.

A weighted-principal component regression method for the identification of physiologic systems

We introduce a system identification method based on weighted-principal component regression (WPCR). This approach aims to identify the dynamics in a linear time-invariant (LTI) model which may represent a resting physiologic system. It tackles the time-domain system identification problem by considering, asymptotically, frequency information inherent in the given data. By including in the model only dominant frequency components of the input signal(s), this method enables construction of candidate models that are specific to the data and facilitates a reduction in parameter estimation error when the signals are colored (as are most physiologic signals). Additionally, this method allows incorporation of preknowledge about the system through a weighting scheme. We present the method in the context of single-input and multi-input single-output systems operating in open-loop and closed-loop. In each scenario, we compare the WPCR method with conventional approaches and approaches that also build data-specific candidate models. Through both simulated and experimental data, we show that the WPCR method enables more accurate identification of the system impulse response function than the other methods when the input signal(s) is colored.

B-Spline impulse response functions (BIRF) for transient SSI analysis of rigid foundations

This work presents a simplified, yet accurate model of rigid foundation-soil systems for the dynamic analysis of structures including SSI effects. The simplified model is based on closed form solutions that reproduce the characteristic B-spline impulse response functions (BIRF) of 3D continuous soil-foundation systems, as obtained from rigorous boundary element method (BEM) analysis. The proposed simplified model is used within the framework of B-spline impulse response techniques and can be coupled directly to other solution techniques, such as the finite element method (FEM). Validation and application studies demonstrate the accuracy and versatility of the simplified model for the direct time domain solution of dynamic SSI problems involving rigid square surface foundations of any size. The proposed model, although simplified, demonstrates similar high accuracy to that of more rigorous solutions based on domain discretizations.

DEVELOPMENT OF ENHANCED WIGNER–VILLE DISTRIBUTION FUNCTION

Development of an enhanced version of the Wigner–Ville distribution function (WDF) is reported in this paper. As a preliminary study, the original WDF is compared to two other time–frequency representation techniques: the short-time Fourier transform (STFT) and the wavelet transform. Comparison of the time–frequency representations of a highly transient signal obtained by the three techniques shows that the primary advantage of WDF over the other techniques is its superior time and frequency resolutions. This advantage is diminished in the smoothed WDF, which is used to reduce the oscillating and zero-crossing phenomena of the original WDF representation. The new version of WDF developed in this work actually improves the resolutions while minimising the oscillating and zero-crossing phenomena. This enhanced WDF is defined by the convolution integral of the original WDFs of the input to the system and the system impulse response function. Theoretical and practical aspects of the proposed enhanced WDF are discussed in comparison to those of the original and the smoothed WDFs. Advantages of the enhanced WDF are demonstrated by three distinct numerical examples.

A novel across-track SAR interferometry simulator

A novel across-track interferometric synthetic aperture radar (SAR) raw signal simulator is presented. It is based on an electromagnetic backscattering model of the scene and an accurate description of the SAR system impulse response function. A set of meaningful examples are also presented. They show that the proposed simulator is structurally consistent and correctly simulates the decorrelation effect, both in the mean and in the distribution sense.

SYSTEM IDENTIFICATION FROM AMBIENT VIBRATION MEASUREMENTS ON A BRIDGE

The cross-correlation function between two response measurements made on an ambiently excited structure is shown to have the same form as the system's impulse response function. Therefore, standard time domain curve-fitting procedures, which are typically applied to impulse response functions, can now be applied to the cross-correlation functions to estimate the resonant frequencies and modal damping of the structure. This derivation is based on the assumption that the ambient vibration source is a white noise random process. Curve-fitting cross-correlation functions to obtain modal properties offers advantages over standard procedures that identify resonant frequencies from peaks in the power spectrum and damping from the width of the power spectrum. The primary advantage is the ability to identify closely spaced modes and their associated damping. The resonant frequencies of a highway bridge that were identified by curve-fitting the cross-correlation functions, using traffic excitation as the ambient vibration source, are compared to modal properties identified by standard forced vibration testing methods. Results of this comparison showed a maximum discrepancy of 3·63 percent. Similar comparisons for the average modal damping values identified by the two methods showed a 9·82 percent difference. This experimental verification implies that the proposed method of analyzing ambient vibration data can be used to accurately assess the dynamic properties of structures in a non-intrusive manner.