Frequency- and time-limited balanced truncation for large-scale second-order systems

A new mixed method for relative error model order reduction is proposed. In the proposed method the frequency domain balanced stochastic truncation method is improved by applying the generalized singular perturbation method to the frequency domain balanced system in the reduction procedure. The frequency domain balanced stochastic truncation method, which was proposed in [15] and [17] by the author, is based on two recently developed methods, namely frequency domain balanced truncation within a desired frequency bound and inner-outer factorization techniques. The proposed method in this paper is a carry over of the frequency-domain balanced stochastic truncation and is of interest for practical model order reduction because in this context it shows to keep the accuracy of the approximation as high as possible without sacrificing the computational efficiency and important system properties. It is shown that some important properties of the frequency domain stochastic balanced reduction technique are extended to the proposed reduction method by using the concept and properties of the reciprocal systems. Numerical results show the accuracy, simplicity and flexibility enhancement of the method.

Heart period variability has been considered for clinical assessment of autonomic function, determining the presence of haemorrhage or disease states, and for predicting mortality from traumatic injury. However, for heart period variability to be clinically useful, a number of important methodological issues should be addressed, including the minimum number of R-R intervals (RRI) required for accurate derivation, and the reproducibility of these metrics. ECGs were recorded for > or =10 min in 18 resting, supine subjects (12 M/6 F; 19-55 years). Heart period variability analyses included 21 time, frequency and complexity domain metrics. For assessment of minimum RRIs required, measurements were made from ECG recordings of 5 min down to 30 s for time and frequency domain metrics, and from 800 RRIs down to 100 RRIs for complexity metrics, by methodical truncation of the data set. Inter-subject variability was assessed by calculating the range and co-efficient of variation (%CV) across all subjects. Two independent 30 s or 100 RRI ECG segments were used to assess intra-subject variability via calculation of %CV in each subject. Six time and frequency domain metrics were robust down to 30 s of data, while five complexity metrics were robust down to 100 RRIs. All time and frequency domain metrics (except for RRI) exhibited high inter-subject variability (CVs > or = 30.0%), while five of eleven complexity metrics displayed low inter-subject variability (CVs < or = 8.5%). In the assessment of intra-subject variability in metrics valid with 30 s or 100 RRIs of ECG, only one time domain and four complexity metrics had CVs < 10%. Metrics that are highly reproducible and require few RRIs are advantageous for patient monitoring as less time is required to assess physiological status and initiate early interventions. Based on our analyses from healthy, resting humans, we have identified a select cohort of heart period variability metrics that performed well in regards to these two criteria.

Third order time and frequency analysis has exhibited great potential for correlation analysis of multi-sensor datasets, but is usually presented as separate time domain and frequency domain approaches. A combined framework of both frequency domain and time domain has rarely been used. This paper proposes a non-parametric third order time and frequency domain framework which used two dimensional Fourier transforms to bridge the gap between time domain and frequency domain. A unified framework offers flexibility and efficiency to apply to data. In this paper we study neural spike train data treated as stochastic point processes. In time domain direct analysis, third order cumulant densities of spike trains are applied, which need all first-, secondand third order product densities to be calculated before constructing the third order cumulant density, which brings additional challenges. The novelty in this study is that a new framework is proposed which can offer an alternative approach without calculating lower order quantities and can reveal nonlinear relationship between neural recordings. The results show that the present framework provides a novel non-parametric method to estimate both time and frequency domain measurements which is applicable to neural spike trains.

We describe the main properties of the EQUATOR airborne geophysical system and how the system can be employed to solve some engineering and environmental problems. To date, the EQUATOR system has been used for groundwater search in 2014 and 2015 in Siberia. The name “EQUATOR” originates from the intention to EQUATE, or to balance time and frequency domain approaches in airborne electromagnetics, which is why the system was originally designed. To the best of our knowledge, EQUATOR is the only system to collect electromagnetic data both in time and in frequency domains. We further explain the difference between the two methods on some numerical and field examples. Also we describe some advantages of their coupling. In particular, by virtue of our approach, a numerically more robust solution of the one-dimensional electromagnetic inverse problem may be achieved. The recorded full-time measurements are further converted to in-phase, quadrature and off-time responses, as opposed to standard frequency or time domain solutions, which have been widely adapted within the industry. When inverting the data, our main focus is within the top 100 m of the Earth, which are the most relevant for engineering and environmental studies. We emphasize that a combined use of frequency and time domain data gives more detailed information about geological structures in the near-surface. As an example, we present some case studies obtained over a platform (Siberia) and a crystalline shield (Western Africa) setting. We further suggest using these results in such near-surface studies as sediment thickness estimation, soil state analysis, groundwater search, and geological structural analysis.

This paper presents a framework for model order reduction based on Balanced Truncation (BT) method and Artificial Neural Networks (ANN). As social, architectural and technical models are witnessing rapid complexity increase, it has become essential to find solutions to obtain a lower complex version of models while still preserving the model integrity. The main idea of the proposed framework is to reduce uncertainty by cascading two different Model Order Reduction (MOR) approaches, the BT technique and the Jordan Recurrent Neural Network (JRNN). The reduced model obtained by the JRNN network is estimated using the Instrument Variable (IV) estimation approach. Finally, the BT reduced model and the estimated JRNN reduced model are cascaded to obtain the final reduced order version of the original plant. The cascading procedure takes the powerfulness of both techniques and present them in a single system capable to compensate for possible errors and uncertainties. Simulation results prove the efficiency of the proposed framework in terms of the deduction strength and the integrity level.

BackgroundIn investigations of the human motor system, two approaches are generally employed toward the identification of common modulating drives from motor unit recordings. One is a frequency domain method and uses the coherence function to determine the degree of linear correlation between each frequency component of the signals. The other is a time domain method that has been developed to determine the strength of low frequency common modulations between motor unit spike trains, often referred to in the literature as 'common drive'.MethodsThe relationships between these methods are systematically explored using both mathematical and experimental procedures. A mathematical derivation is presented that shows the theoretical relationship between both time and frequency domain techniques. Multiple recordings from concurrent activities of pairs of motor units are studied and linear regressions are performed between time and frequency domain estimates (for different time domain window sizes) to assess their equivalence.ResultsAnalytically, it may be demonstrated that under the theoretical condition of a narrowband point frequency, the two relations are equivalent. However practical situations deviate from this ideal condition. The correlation between the two techniques varies with time domain moving average window length and for window lengths of 200 ms, 400 ms and 800 ms, the r2 regression statistics (p < 0.05) are 0.56, 0.81 and 0.80 respectively.ConclusionsAlthough theoretically equivalent and experimentally well correlated there are a number of minor discrepancies between the two techniques that are explored. The time domain technique is preferred for short data segments and is better able to quantify the strength of a broad band drive into a single index. The frequency domain measures are more encompassing, providing a complete description of all oscillatory inputs and are better suited to quantifying narrow ranges of descending input into a single index. In general the physiological question at hand should dictate which technique is best suited.

&lt;div class="section abstract"&gt;&lt;div class="htmlview paragraph"&gt;Simulation based design optimization has become the common practice in automotive product development. Increasing computer models are developed to simulate various dynamic systems. Before applying these models for product development, model validation needs to be conducted to assess their validity. In model validation, for the purpose of obtaining results successfully, it is vital to select or develop appropriate metrics for specific applications. For dynamic systems, one of the key obstacles of model validation is that most of the responses are functional, such as time history curves. This calls for the development of a metric that can evaluate the differences in terms of phase shift, magnitude and shape, which requires information from both time and frequency domain. And by representing time histories in frequency domain, more intuitive information can be obtained, such as magnitude-frequency and phase-frequency characteristics. However, Most of the existing metrics only focus on time domain. In this paper, a validation method combining analysis in time and frequency domain is proposed. Two analytical cases are then utilized for the illustration of the proposed method and process. A real-world children restraint system design case is then conducted. The evaluation results are consistent with Subjective Matter Experts' judgments.&lt;/div&gt;&lt;/div&gt;

Influence of water activity on acoustic emission of flat extruded bread

In this article, theoretical modeling and simulations are introduced to explore the contact failure characteristics for connectors both in time and frequency domains. The equivalent models are developed to describe the impedance performances of un‐degraded and degraded connectors with the time domain and frequency domain, respectively. The experiments using a Network Analyzer for time and frequency domains analyses are conducted to verify the proposed models. The measured results agree well with the simulation results in the time and frequency domains.

We study here three topics in Ultra-Wideband Antennas. First, we consider a standard for characterizing antenna performance in the time domain, We develop a single time domain function, called antenna impulse response, which fully describes antenna performance with equations that are as simple as possible in both the frequency and time domains. Next, we survey the available large UWB antennas, primarily consisting of variations of Impulse Radiating Antennas. These consist of a reflector and a wideband feed, and are capable of nearly two decades of bandwidth; or a 100:1 band ratio. Finally, we review the status of time domain UWB antenna ranges, which can be used to characterize both wideband and narrowband antennas in both the time and frequency domains. Such systems also measure the impulse response of an antenna.

The relevance of research is due to the need to establish the true causes and patterns of changes in the hydrometric characteristics of the global water balance as a whole and its components, natural environments on Earth.&#x0D; Purpose of research: to establish patterns and causes of changes in the components of the global water balance on Earth: trends in the increase in water mass reserves, dynamics of the water balance of the South Seas of Europe, the Black Sea, dynamics of levels of the Indian Ocean, Western and Central Pacific Ocean, Eastern Pacific and Atlantic Oceans, level fluctuations of the World Ocean, changes in sea ice cover, river resources, reservoirs, variability of sea levels in the Arctic Ocean according to observations at coastal stations, changes in the balance of ice masses in glacial areas, changes in interseasonal thawing in the permafrost zones of the continent.&#x0D; Objects of research: time series of heliocosmic, climatic variables, hydrometric characteristics of the components of the global water balance.&#x0D; Methods of research: developed by the author, a method for interaction of observations of a variable or variables with groups of specified heliocosmic and climatic factors in the frequency and time domains, obtained using wavelet transformations of observations with the calculation of phase-frequency and phase-time characteristics in equal time intervals; comparative analysis of changes in the obtained phase characteristics of groups of variables with the calculation of their consistency matrices and the construction of graphs in the frequency and time domains.&#x0D; Main results of research: in the observed time intervals, in the trend of periodic changes in the reserves of water masses (glaciers, groundwater, lakes, reservoirs) in the frequency domain, significant negative unidirectional influences of changes in heliocosmic and multidirectional influences of climatic variables are observed; changes in the reserves of the World Ocean are more influenced by multidirectional changes in climatic factors compared to the unidirectional influences of heliocosmic factors; the frequency bands of changes in water mass reserves are less than the frequency bands of heliocosmic factors, due to the influence of climatic factors; The variability of water mass reserves on Earth is significantly and unidirectionally consistent with changes in evaporation, evaporation and precipitation on land, and in different directions with changes in cloudiness on the continents. Similar patterns are observed in changes in the water balance of the South Seas in Europe, the Black Sea, sea ice cover, river resources, reservoirs on land, ice mass balances in glacial areas, and interseasonal thawing in the permafrost zones of the continent. In the dynamics of the levels of the Indian, Western and Central Pacific, Eastern Pacific and Atlantic, fluctuations in the level of the World Ocean, significant multidirectional changes in levels in the frequency domain are observed on the effects of heliocosmic variables with the greatest influences of solar activity and long-term solar insolation, the Ap-index of geomagnetic activity, the parameter the ratio of plasma pressure to magnetic solar wind, changes in the ozone layer in the ionosphere, changes in the speed of rotation of the Earth, the influence of climate variables in the frequency domain with the greatest influences of solar radiation, precipitation, atmospheric processes, PTV is significant. The variability of sea levels in the Arctic Ocean, as observed at coastal stations, is characterized by significant multidirectional changes in the frequency domain due to the influence of heliocosmic and climatic factors, multidirectional mutual consistency of the component levels of the ocean seas, caused by anomalous changes in the Earths magnetic field in areas of the Northern Hemisphere. In changes in the phase-time characteristics of groups of factors, lattice structures of differently and unidirectional changes in variables are observed, characterizing the cyclical nature of climate change on Earth.

In this paper, a least-mean-square (LMS) based adaptive channel tracking scheme for space-time block coded orthogonal frequency division multiplexing (STBC-OFDM) systems is proposed. Based on the recursion of channel impulse response, the proposed channel tracking is essentially carried out in the time domain, which is referred as the time domain LMS scheme (TD-LMS). Since the number of channel taps in the time domain is much smaller than that of the frequency domain in a practical OFDM system, the time domain channel tracking may attain more accurate channel state information than the frequency domain. Moreover, the proposed TD-LMS scheme fully utilizes both the time and frequency domain correlation of the time-variant and frequency-selective channels. Simulation results show that the proposed scheme performs much better than the frequency domain adaptive tracking schemes, which only exploits the time domain correlation. Henceforth, the proposed scheme will approach the performance of the system with perfect channel state information at moderate Doppler frequencies

Duality between time and frequency domains for vibration serviceability analysis of floor structures

Time domain simulations of an offshore floating wind turbine have been performed. Hydrodynamic impulse responses of the floating platform are calculated with linear hydrodynamic simulation tool ACHIL3D. A user defined module for the wind turbine design code FAST has been developed to calculate hydrodynamic and mooring loads on the structure. Resolution of the movements of the system is done with FAST. Simulation results in time domain are compared with frequency domain results. In the frequency domain model, the whole system is linearized. In the time domain model, the wind turbine model is not linearized. A good agreement between time and frequency domain calculations is observed, even for the pitch motion. Furthermore we observe a non linearity in the response of sway, roll and yaw degrees of freedom around 0.3 rad.s-1. The effect of viscous damping on the movements of the floating wind turbine system has been studied with the time domain model, and a non linear hydrostatic and Froude-Krylov load model has been developed. Effects of these non linear terms are shown.

Frequency and time domain analyses of sensor signals in drilling—I. Correlation with drill wear