Estimation Of Response Function Research Articles

Pinpointing the base of the AGN jets through general relativistic X-ray reverberation studies

AbstractMany theoretical models of Active Galactic Nuclei (AGN) predict that the X-ray corona, lying above the black hole, constitutes the base of the X-ray jet. Thus, by studying the exact geometry of the close black hole environment, we can pinpoint the launching site of the jet. Detection of negative X-ray reverberation time delays (i.e. soft band X-ray variations lagging behind the corresponding hard band X-ray variations) can yield significant information about the geometrical properties of the AGN, such as the location of the X-ray source, as well as the physical properties of the the black hole, such as its mass and spin. In the frame-work of the lamp-post geometry, I present the first systematic X-ray time-lag modelling results of an ensemble of 12 AGN, using a fully general relativistic (GR) ray tracing approach for the estimation of the systems' response functions. By combing these state-of-the art GR response models with statistically innovative fitting routines, I derive the geometrical layout of the close BH environment for each source, unveiling the position of the AGN jet-base.

Experimental determination of frequency response function estimates for flexible joint industrial manipulators with serial kinematics

Two different approaches for the determination of frequency response functions (FRFs) are used for the non-parametric closed loop identification of a flexible joint industrial manipulator with serial kinematics. The two applied experiment designs are based on low power multisine and high power chirp excitations. The main challenge is to eliminate disturbances of the FRF estimates caused by the numerous nonlinearities of the robot. For the experiment design based on chirp excitations, a simple iterative procedure is proposed which allows exploiting the good crest factor of chirp signals in a closed loop setup. An interesting synergy of the two approaches, beyond validation purposes, is pointed out.

Competitive devaluations and the trade balance in less developed countries: An empirical study of Latin American countries

Policymakers in less developed countries (LDCs) usually support competitive devaluations to improve the trade balance (TB). In this paper, we estimate the effects of appreciated and depreciated real exchange rates (RER) in the TB of Argentina and Brazil during the period, 1990–2010 using co-integration tests for non-stationary data and vector error correction models (VECM). The estimations confirmed the existence of a long-term relationship among the TB and the RER and foreign and domestic incomes for the countries during opposite RER policies. Based on our estimations, the Marshall–Lerner condition held during periods of more flexible and depreciated RER, and the estimation of the general impulse response functions demonstrated that devaluations in both countries did not follow a J-curve pattern in the short-term.

A global error estimator for the uncertainty of a multi-channel spectral analysis

A global estimator of the uncertainty of the average frequency response function in multi-channel spectral analysis measurements is proposed. The proposed global estimator is a generalization of the random error estimator of the frequency response function magnitude of a single-input–single-output system. In principle, the signal-to-noise ratio (and thus the quality of the frequency response function estimation) is increasing with increasing number of averages M, according to M. However, in the situation that, for practical reasons, there is a maximum imposed upon the total measurement time Tmax, it is clear that there is a trade-off between the number of averages M and the record length T (s) that is used to obtain an estimate of a single-average-frequency-response-function. There is a choice between a few long records or many short records, with the requirement that, assuming zero overlap, the number of averages M times the record length T may not exceed the total available measurement time, i.e. M×T⩽Tmax. In addition to the existence of such an optimum, a minimum record length is required as well which is related to the reverberation time of the system. The newly proposed global estimator is used to determine the optimal record length of a multi-channel system, such that a minimum error of the average frequency response function is obtained. It is also shown by experimental results that indeed the minimum allowable record length is related to the reverberation time of the system being measured.

Power Spectra Density Replication Control Strategy for 2-Axis Hydraulic Shaker Based on HV Estimator

Hydraulic shaker, equipment of simulating laboratory vibration environment, can accurately replicate the given power spectral density (PSD) and time history with an appropriate control algorithm. By studying method Hv estimator of frequency response function (FRF) estimation, a FRF identification strategy based on the Hv estimator is designed to increase the convergence rapidity and improve the system response function specialty. The system amplitude-frequency characteristics in some frequency points or frequency bands have large fluctuation. To solve this issue, a step-varying and frequency-sectioning iterative correction control algorithm is proposed for the control of 2-axial exciter PSD replication tests and the results show that the algorithm has a good effect on the control of hydraulic shaker, and can achieve reliable and high-precision PSD replication.

An integrated framework for joint HRF and drift estimation and HbO/HbR signal improvement in fNIRS data.

Nonparametric hemodynamic response function (HRF) estimation in functional near-infrared spectroscopy (fNIRS) data plays an important role when investigating the temporal dynamics of a brain region response during activations. Assuming the drift arising from both physical and physiological effects in fNIRS data is Lipschitz continuous; a novel algorithm for joint HRF and drift estimation is derived in this paper. The proposed algorithm estimates the HRF by applying a first-order differencing to the fNIRS time series samples in order to remove the drift effect. An estimate of the drift is then obtained using a wavelet thresholding technique applied to the residuals generated by removing the estimated induced activation response from the fNIRS time-series. It is shown that the proposed HRF estimator is √N consistent whereas the estimator of the drift is asymptotically optimal. The de-drifted fNIRS oxygenated (HbO) and deoxygenated (HbR) hemoglobin responses are then obtained by removing the corresponding estimated drifts from the fNIRS time-series. Its performance is assessed using both simulated and real fNIRS data sets. The application results reveal that the proposed joint HRF and drift estimation method is efficient both computationally and in terms of accuracy. In comparison to traditional model based methods used for HRF estimation, the proposed novel method avoids the selection of a model to remove the drift component. As a result, the proposed method finds an optimal estimate of the fNIRS drift and offers a model-free approach to de-drift the HbO/HbR responses.

Joint maximum likelihood estimation of activation and Hemodynamic Response Function for fMRI.

Blood Oxygen Level Dependent (BOLD) functional magnetic resonance imaging (fMRI) maps the brain activity by measuring blood oxygenation level, which is related to brain activity via a temporal impulse response function known as the Hemodynamic Response Function (HRF). The HRF varies from subject to subject and within areas of the brain, therefore a knowledge of HRF is necessary for accurately computing voxel activations. Conversely a knowledge of active voxels is highly beneficial for estimating the HRF. This work presents a joint maximum likelihood estimation of HRF and activation based on low-rank matrix approximations operating on regions of interest (ROI). Since each ROI has limited data, a smoothing constraint on the HRF is employed via Tikhonov regularization. The method is analyzed under both white noise and colored noise. Experiments with synthetic data show that accurate estimation of the HRF is possible with this method without prior assumptions on the exact shape of the HRF. Further experiments involving real fMRI experiments with auditory stimuli are used to validate the proposed method.

Correction to “Estimation of the OSCAT Spatial Response Function Using Island Targets” [Apr 14 1924-1934

In the above-named article [ibid., vol. 51, no. 5, pp 1924-1934, April 2014] there are errors in Table I. The corrected table is published here.

Biomechanical Analysis of Human Balance Control

A single-inverted-pendulum model is presented to simulate and predict the passive response of human balance control. This simplified biomechanical model was comprised of a torsional spring and damper, and a lump mass. An estimation of frequency response function was conducted to parameterize the complexity. The frequency domain identification method is used to identify the parameters of the model. The equivalent viscoelastic parameters of standing body were obtained and there was good conformity between the simulation and experimental result.

Mixed Frequency Structural VARs

A mismatch between the time scale of a structural VAR (SVAR) model and that of the time series data used for its estimation can have serious consequences for identification, estimation and interpretation of the impulse response functions. However, the use of mixed frequency data, combined with a proper estimation approach, can alleviate the temporal aggregation bias, mitigate the identification issues, and yield more reliable responses to shocks. The problems and possible remedy are illustrated analytically and with both simulated and actual data.

Improved measurement of camera response function and its performance evaluation

Estimation of camera response function (CRF) has become important in the field of computer graphics and radiance measurement to achieve accurate modeling and high dynamic range imaging. A method is proposed to provide accurate radiance for direct measurement of the CRF in this paper by using a polariscope. The experimental results indicate that the accuracy of the estimated CRF obtained by the new approach is about 5% better than that of the previous method.

Inference on impulse response functions in structural VAR models

Skepticism toward traditional identifying assumptions based on exclusion restrictions has led to a surge in the use of structural VAR models in which structural shocks are identified by restricting the sign of the responses of selected macroeconomic aggregates to these shocks. Researchers commonly report the vector of pointwise posterior medians of the impulse responses as a measure of central tendency of the estimated response functions, along with pointwise 68% posterior error bands. It can be shown that this approach cannot be used to characterize the central tendency of the structural impulse response functions. We propose an alternative method of summarizing the evidence from sign-identified VAR models designed to enhance their practical usefulness. Our objective is to characterize the most likely admissible model(s) within the set of structural VAR models that satisfy the sign restrictions. We show how the set of most likely structural response functions can be computed from the posterior mode of the joint distribution of admissible models both in the fully identified and in the partially identified case, and we propose a highest-posterior density credible set that characterizes the joint uncertainty about this set. Our approach can also be used to resolve the long-standing problem of how to conduct joint inference on sets of structural impulse response functions in exactly identified VAR models. We illustrate the differences between our approach and the traditional approach for the analysis of the effects of monetary policy shocks and of the effects of oil demand and oil supply shocks.

신경망 기법을 이용한 새로운 반응함수 추정 방법에 관한 연구

Purpose: The main objective of this paper is to propose an RD method by developing a neural network (NN)-based estimation approach in order to provide an alternative aspect of response surface methodology (RSM). Methods: A specific modeling procedure for integrating NN principles into response function estimations is identified in order to estimate functional relationships between input factors and output responses. Finally, a comparative study based on simulation is performed as verification purposes. Results: This simulation study demonstrates that the proposed NN-based RD method provides better optimal solutions than RSM. Conclusion: The proposed NN-based RD approach can be a potential alternative method to utilize many RD problems in competitive manufacturing nowadays.

Lexicographical dynamic goal programming approach to a robust design optimization within the pharmaceutical environment

The primary objective of this paper is to develop a new robust design (RD) optimization procedure based on a lexicographical dynamic goal programming (LDGP) approach for implementing time-series based multi-responses, while the conventional experimental design formats and frameworks may implement static responses. First, a parameter estimation method for time-dependent pharmaceutical responses (i.e., drug release and gelation kinetics) is proposed using the dual response estimation concept that separately estimates the response functions of the mean and variance, as a part of response surface method. Second, a multi-objective RD optimization model using the estimated response functions of both the process mean and variance is proposed by incorporating a time-series components within a dynamic modeling environment. Finally, a pharmaceutical case study associated with a generic drug development process is conducted for verification purposes. Based on the case study results, we conclude that the proposed LDGP approach effectively provides the optimal drug formulations with significantly small biases and MSE values, compared to other models.

The Optimal Economic Uncertainty Index: A Grid Search Application

A noteworthy characteristic of empirical studies on the economic uncertainty index is that very few published papers depend on normative analysis. Therefore, normative analysis cannot be used to refute the precision of the economic uncertainty index; the lack of precision is simply the outcome of a misspecification of a commonly used model and a complex data collection process. To overcome this shortcoming, this paper uses the optimal form of the economic uncertainty index and determines its empirical validity based on a sample of 7 countries, including 3 developed and 4 developing countries. Using a grid search optimization procedure, the findings provide some policy implications; the optimal economic uncertainty index can characterize the uncertainty level of macroeconomic conditions and serve as a guiding policy tool for improving uncertainty levels in macroeconomic conditions. The estimated response function of the optimal economic uncertainty index suggests that the exchange rate, inflation, interest rate and output are useful indicators for central banks' decision-making and that the optimal index supports the prediction of economic uncertainty.

Statistical modeling of frequency response function estimation for uncertainty quantification

Frequency response function (FRF) estimation is widely used for system identification and related applications, such as model updating and structural health monitoring. Whether estimated from data or from a finite element (FE) model, there is uncertainty involved that introduces variability in the FRF evaluation, which leads to misinterpretation of system identification results or false alarms (Type-I error) if used in hypothesis testing for damage detection. This paper aims to quantify the uncertainty of FRF estimated with randomly-excited experimental data using the H1 estimator, for both its magnitude and phase. A Gaussian bivariate statistical model is implemented, and probability density functions (PDF) of the magnitude and phase estimations are derived. The proposed statistical model is validated for both an ideal simulation test-bed and an experimental lab-scale structure. To further validate the model's robustness, artificial noise is added to contaminate the original data. The predicted PDFs show a very good match with histogram observations, where outlier percentage is selected as the comparison metric in this paper. For different significance levels, the outlier percentages all consistently agree with the pre-described uncertainty thresholds, indicating that the proposed statistical model suitably quantifies the uncertainty of FRF estimations using H1.

Linear mixed-effects modeling approach to FMRI group analysis

Conventional group analysis is usually performed with Student-type t-test, regression, or standard AN(C)OVA in which the variance-covariance matrix is presumed to have a simple structure. Some correction approaches are adopted when assumptions about the covariance structure is violated. However, as experiments are designed with different degrees of sophistication, these traditional methods can become cumbersome, or even be unable to handle the situation at hand. For example, most current FMRI software packages have difficulty analyzing the following scenarios at group level: (1) taking within-subject variability into account when there are effect estimates from multiple runs or sessions; (2) continuous explanatory variables (covariates) modeling in the presence of a within-subject (repeated measures) factor, multiple subject-grouping (between-subjects) factors, or the mixture of both; (3) subject-specific adjustments in covariate modeling; (4) group analysis with estimation of hemodynamic response (HDR) function by multiple basis functions; (5) various cases of missing data in longitudinal studies; and (6) group studies involving family members or twins. Here we present a linear mixed-effects modeling (LME) methodology that extends the conventional group analysis approach to analyze many complicated cases, including the six prototypes delineated above, whose analyses would be otherwise either difficult or unfeasible under traditional frameworks such as AN(C)OVA and general linear model (GLM). In addition, the strength of the LME framework lies in its flexibility to model and estimate the variance-covariance structures for both random effects and residuals. The intraclass correlation (ICC) values can be easily obtained with an LME model with crossed random effects, even at the presence of confounding fixed effects. The simulations of one prototypical scenario indicate that the LME modeling keeps a balance between the control for false positives and the sensitivity for activation detection. The importance of hypothesis formulation is also illustrated in the simulations. Comparisons with alternative group analysis approaches and the limitations of LME are discussed in details.

인공신경망을 이용한 로버스트설계에 관한 연구

Since introduced by Vining and Myers in 1990, the concept of dual response approach based on response surface methodology has widely been investigated and adopted for the purpose of robust design. Separately estimating mean and variance responses, dual response approach may take advantages of optimization modeling for finding optimum settings of input factors. Explicitly assuming functional relationship between responses and input factors, however, it may not work well enough especially when the behavior of responses are poorly represented. A sufficient number of experimentations are required to improve the precision of estimations. This study proposes an alternative to dual response approach in which additional experiments are not required. An artificial neural network has been applied to model relationships between responses and input factors. Mean and variance responses correspond to output nodes while input factors are used for input nodes. Training, validating, and testing a neural network with empirical process data, an artificial data based on the neural network may be generated and used to estimate response functions without performing real experimentations. A drug formulation example from pharmaceutical industry has been investigated to demonstrate the procedures and applicability of the proposed approach.

Novel structural flexibility identification in narrow frequency bands

A ‘Sub-PolyMAX’ method is proposed in this paper not only for estimating modal parameters, but also for identifying structural flexibility by processing the impact test data in narrow frequency bands. The traditional PolyMAX method obtains denominator polynomial coefficients by minimizing the least square (LS) errors of frequency response function (FRF) estimates over the whole frequency range, but FRF peaks in different structural modes may have different levels of magnitude, which leads to the modal parameters identified for the modes with small FRF peaks being inaccurate. In contrast, the proposed Sub-PolyMAX method implements the LS solver in each subspace of the whole frequency range separately; thus the results identified from a narrow frequency band are not affected by FRF data in other frequency bands. In performing structural identification in narrow frequency bands, not in the whole frequency space, the proposed method has the following merits: (1) it produces accurate modal parameters, even for the modes with very small FRF peaks; (2) it significantly reduces computation cost by reducing the number of frequency lines and the model order in each LS implementation; (3) it accurately identifies structural flexibility from impact test data, from which structural deflection under any static load can be predicted. Numerical and laboratory examples are investigated to verify the effectiveness of the proposed method.

Structural VAR models for Malaysian monetary policy analysis during the pre- and post-1997 Asian crisis periods

This article conducts an in-depth investigation into building a Structural Vector Autoregression (SVAR) model and analysing the Malaysian monetary policy. Considerable attention is paid to: (i) the selection of foreign, policy and target variables; (ii) establish identifying restrictions and improve the estimates of impulse response functions; (iii) assess the importance of intermediate channels in transmitting monetary policy mechanism; and (iv) the way in which the 1997 Asian financial crisis affected the working of monetary policy. Malaysia is an interesting small open economy to study because, following this crisis, the government imposed capital and exchange rate control measures. The overall results suggest that the crisis and the subsequent major shift in the exchange rate regime have significantly affected the Malaysian ‘Black Box’. In the pre-crisis period, domestic variables appear to be more vulnerable to foreign monetary shocks. Further, the exchange rate played a significant role in transmitting the interest rate shocks, whereas credit and asset prices helped to propagate the money shock. In the post-crisis period however, asset prices play a more domineering role in intensifying the effects of both interest rate and money shocks on output, and the economy was insulated from foreign shocks.