Modal Estimation Research Articles

Revealing the hidden signature of fault slip history in the morphology of degrading scarps

Active faults accommodate tectonic plate motion through different slip modes, some stable and aseismic, others characterized by the occurrence of large earthquakes after long periods of inactivity. Although the slip mode estimation is of primary importance to improve seismic hazard assessment, this parameter inferred today from geodetic observations needs to be better constrained over many seismic cycles. From an analytical formulation developed for analyzing fault scarp formation and degradation in loosely consolidated material, we show that the final topographic shape generated by one earthquake rupture or by creep (i.e., continuous slip) deviates by as much as 10–20%, despite a similar cumulated slip and a constant diffusion coefficient. This result opens up the theoretical possibility of inverting, not only the cumulated slip or averaged slip rate, but also the number of earthquakes and their sizes from scarp morphologies. This approach is all the more relevant as the number of rupture events is limited. Estimating the fault slip history beyond a dozen earthquakes becomes very difficult as the effect of erosion on scarp morphology prevails. Our modeling also highlights the importance of trade-offs between fault slip history and diffusive processes. An identical topographic profile can be obtained either with a stable fault creep associated with rapid erosion, or a single earthquake rupture followed by slow erosion. These inferences, derived from the simplest possible diffusion model, are likely to be even more pronounced in nature.

Robust Control of UAV with Disturbances and Uncertainty Estimation

In this work, a nonlinear estimator-based robust controller is designed for the position and yaw control of a quadrotor with uncertainty estimation. This controller ensures the tracking of desired references in the presence of parameters variation and external disturbances, making use of high-order sliding mode (HOSM) estimators to estimate these perturbations that can be canceled by the control, thus improving the dynamic behavior of the controlled system. Its performance is evaluated making use of a Simcenter Amesim quadrotor based on physical models generated from experimental data in a co-simulation framework with Matlab–Simulink used to implement the designed controller with FPGA implementation. A challenging and generic maneuver with time-varying wind disturbances and uncertainty model parameters is considered.

Profiles of Two JOMAE Associate Editors (The Fifth in a Continuing Series)

Profiles of Two JOMAE Associate Editors (The Fifth in a Continuing Series)

Biorthogonal harmonics for the decomposition of gravitational radiation. I. Angular modes, completeness, and the introduction of adjoint-spheroidal harmonics

The estimation of radiative modes is a central problem in gravitational wave theory, with essential applications in signal modeling and data analysis. This problem is complicated by most astrophysically relevant systems not having modes that are analytically tractable. A ubiquitous workaround is to use not modes, but multipole moments defined by spin-weighted spherical harmonics. However, spherical multipole moments are only related to the modes of systems without angular momentum. As a result, they can obscure the underlying physics of astrophysically relevant systems, such as binary black hole merger and ringdown. In such cases, spacetime angular momentum means that radiative modes are not spherical, but spheroidal in nature. Here, we work through various problems related to spheroidal harmonics. We show for the first time that spheroidal harmonics are not only capable of representing arbitrary gravitational wave signals, but that they also possess a kind of orthogonality not used before in general relativity theory. Along the way we present a new class of spin-weighted harmonic functions dubbed ``adjoint-spheroidal'' harmonics. These new functions may be used for the general estimation of spheroidal multipole moments via complete biorthogonal decomposition (in the angular domain). By construction, adjoint-spheroidal harmonics suppress mode-mixing effects known to plague spherical harmonic decomposition; as a result, they better approximate a system's true radiative modes. We discuss potential applications of these results. Lastly, we briefly comment on the challenges posed by the analogous problem with Teukolsky's radial functions.

Traveling Wave-Based Fault Localization in FACTS-Compensated Transmission Line via Signal Decomposition Techniques

Modern power systems are structurally complex and are vulnerable to undesirable events like faults. In the event of faults in transmission line, accurate fault location improves restoration process, thereby enhancing the reliability of the overall system. Fault location methods (FLMs) are tools which assist in identifying fault locations quickly. However, the accuracy of these FLMs gets affected in the presence of flexible alternating current transmission system (FACTS) devices. Therefore, in this work, the performance of four different signal decomposition techniques aided traveling wave aided FLMs are qualitatively compared in the context of fault localization in FACTS-compensated systems. FLMs based on intrinsic time decomposition (ITD), empirical mode decomposition (EMD), S-transform (ST), and estimation of signal parameters via rotational invariance technique (ESPRIT) are investigated. The accuracy of FLMs is tested for different cases of series, shunt, and series-shunt FACTS-compensated systems. A 500 kV system employed with 100 MVAr FACTS device is used for simulation. The instant of arrival wave at end of transmission line is from all aforementioned FLMs. The obtained ATWs are used in fault localization. Further, the associated percentage errors are calculated. The results suggest that EMD and ESPRIT-based FLMs are more accurate than others.

A distributed predefined-time attitude coordination control scheme for multiple rigid spacecraft

In this paper, the distributed predefined-time attitude coordination control problem is investigated for multiple rigid spacecraft systems when only a subset of spacecraft has access to the reference attitude and angular velocity. Two sliding mode estimators are proposed to estimate the reference attitude and angular velocity, respectively. It is proved that the states of the two proposed estimators can converge to zero in a predefined time. Then, a predefined-time control scheme is designed for the multiple rigid spacecraft systems subject to inertial uncertainty and external disturbance. The practical predefined-time stability is proved for the multiple rigid spacecraft system under the presented controller. It should be pointed out that the most important feature of the proposed estimators and controller is the tunable settling time characteristic. To be specific, based on ensuring that the settling time is less than the predefined value, the actual settling time of the system states can be further adjusted for different task requirements by a tunable parameter. Finally, some simulations are conducted to illustrate the effectiveness and advantages of the proposed tunable predefined-time control scheme.

Capacity and degradation mode estimation for lithium-ion batteries based on partial charging curves at different current rates

The open circuit voltage (OCV) curve of a lithium-ion cell can be described as the difference between the half-cell open circuit potential curves of both electrodes. Fitting a reconstructed OCV curve to the OCV curve of an aged cell allows identification of degradation modes. In this study, we show that this method can also be applied to partial charging curves of a commercial cell with silicon–graphite and NMC-811 as electrode materials. Both the degradation modes and the remaining cell capacity can be determined from the reconstructed OCV curve. For the investigated cell, accurate OCV reconstruction and degradation mode estimation can be obtained from C/30 partial charging curves if the state of charge (SOC) window between 20% and 70% is available. We show that the method is also applicable to charging curves at higher current rates if the additional overpotential is considered by subtracting a constant voltage offset. Capacity estimation with an accuracy of 2% of the nominal capacity is possible for current rates up to approximately C/4 if partial charging curves between 10% and 80% SOC are used, while a maximum current rate of C/15 should be used for accurate estimation of the degradation modes.

Improving the accuracy and the estimation time of inter-area modes in power system based on Tufts-Kumaresan algorithm

ABSTRACT In this paper, a new method based on the Tufts–Kumaresan (TK) algorithm is used to process nonstationary signals and extract system modes. This new algorithm for mode estimation is proposed to improve estimation accuracy under dynamic conditions. The key contribution in TK is the use of multiple orthogonal sliding windows rather than a single pair of sliding windows. Simulation results under various scenarios, such as different types of faults and load changes are used to evaluate the performance of the proposed method. The proposed method will accurately extract system modes. This method will also reduce the required memory and the calculation time of estimation in nonstationary signals. In complement to successful applications in studying the dynamic behavior of the power system, identifying and analyzing low-frequency electromechanical oscillations, and removing signal noise, this method can accurately estimate the modes of a power system. To validate the accuracy of the proposed method, the Wavelet and the Prony methods have been used for comparison. The proposed method is implemented using simulated ringdown data of standard two-area power system and real measurement data of the WSCC system breakup on 10 August 1996.

Fast estimation method of optimal modal gain for adaptive optical system

In an adaptive optical system, the optimal modal control method refers to applying proportional integral control of different bandwidths to the wavefront aberrations after modal decomposition to achieve better closed-loop results than the unified bandwidth modal control. The optimal modal gain usually needs to be obtained by ergodic solution based on the transfer function model of the adaptive optical system, the measured disturbance power spectral density, and the noise power spectral density, which usually takes a long time. Owing to the time-varying statistical characteristics of atmospheric turbulence, it is difficult to ensure the timeliness of the optimal modal gain. Therefore, we propose a method of fast estimating optimal modal gain based on quadratic polynomial fitting. In the method, it is only necessary to choose three reasonable gain coefficients and calculate their corresponding closed-loop residual errors respectively in order to estimate the optimal gain of single mode. The simulated slope data used in this work are cited from Lijiang 1.8 m adaptive telescope system, which consists of a 241-unit deformable secondary mirror and a Shaker-Hartmann wavefront sensor with 192 sub-apertures, with the first 135-order modes corrected by modal method. Our experiment is to test directly on-line on this system. The results show that under the same atmospheric environment, the proposed method can accurately estimate the optimal modal gain in a very short time and effectively suppress the high-order wavefront aberration. At the same time, owing to the reduced time complexity of the algorithm, the improved optimal modal gain estimation method takes only 0.33 s. Comparatively, it will take 7.08 s to obtain the optimal modal gain coefficient by using the parameter traversal method. Therefore the time spent on obtaining the optimal modal gain is shortened by about 95.3%, which is easier to meet the real-time requirements of the telescope, and beneficial to the adaptive optics system with more high-order modes. For the future adaptive optics system with more than one-thousand units, the proposed method can update the optimal gain to the second level, while the traversal method can only reach the minute level.

Evaluation of recursive Bayesian filters for modal contribution estimation in high-tech compliant mechanisms

This study evaluates three recursive Bayesian input and state estimation algorithms, as introduced in the field of Structural Health Monitoring, for estimating modal contributions for high-tech compliant mechanisms. The aim of estimating modal contributions is the use for active vibration control. High-tech compliant motion stages allow for different sensor configurations, making new and interesting performance evaluations of these filters possible. The algorithms used, namely, the Augmented Kalman Filter (AKF), Dual Kalman Filter (DKF) and Gilijns de Moor Filter (GDF) are implemented on a compliant motion stage for guidance flexure deformation estimation. Our results show the GDF performs overall best, with good estimation performance and real-world tuning capability.

Maps of dynamic invariants in the estimation of modes of motion of mechanical oscillatory systems

Maps of dynamic invariants in the estimation of modes of motion of mechanical oscillatory systems

On the central limit theorem for a conditional mode estimator in the single functional index modeling for functional time series data under random censorship

The main objective of this paper is to investigate the estimation of conditional density function based on the single-index model in the censorship model when the sample is considered as an dependent random variables. First of all, a kernel type estimator for the conditional density function (cond-df) is introduced. Afterwards, the asymptotic properties are stated when the observations are linked with a single-index structure. The pointwise almost complete convergence and the uniform almost complete convergence (with rate) of the kernel estimate of this model are established. As an application the conditional mode in functional single-index model is presented. Under general conditions, the asymptotic normality of the conditional density estimator is established. Simulation study is also presented to illustrate the validity and finite sample performance of the considered estimator. Finally, the estimation of the functional index via the pseudo-maximum likelihood method is discussed, but not tackled.

Analytical and statistical properties of local depth functions motivated by clustering applications

Local general depth (LGD) functions are used for describing the local geometric features and mode(s) in multivariate distributions. In this paper, we undertake a rigorous systematic study of LGD and establish several analytical and statistical properties. First, we show that, when the underlying probability distribution is absolutely continuous with density f(⋅), the scaled version of LGD (referred to as τ-approximation) converges, uniformly and in Ld(Rp) to f(⋅) when τ converges to zero. Second, we establish that, as the sample size diverges to infinity the centered and scaled sample LGD converge in distribution to a centered Gaussian process uniformly in the space of bounded functions on HG, a class of functions yielding LGD. Third, using the sample version of the τ-approximation (SτA) and the gradient system analysis, we develop a new clustering algorithm. The validity of this algorithm requires several results concerning the uniform finite difference approximation of the gradient system associated with SτA. For this reason, we establish Bernstein-type inequality for deviations between the centered and scaled sample LGD, which is also of independent interest. Finally, invoking the above results, we establish consistency of the clustering algorithm. Applications of the proposed methods to mode estimation and upper level set estimation are also provided. Finite sample performance of the methodology are evaluated using numerical experiments and data analysis.

Dilemmas relating to mode estimation of wages and salaries

The mode of wages and salaries is an important indicator describing their distribution; however, due to the strong asymmetry of the distribution of this feature in Poland, mode estimation is not a standard procedure in the analysis of the structure of wages and salaries. The aim of the article is to discuss selected methods of estimating the mode and to compare the mode estimation results obtained by means of various methods. The research is based on data on individual gross wages and salaries registered in October 2018 in Poland. The data came from a survey of the structure of wages and salaries conducted by Statistics Poland. In the case of the standard method based on the interpolation formula and histogram, the mode estimate is sensitive to the assumed span of intervals in the frequency table and the beginning of the first interval. Reducing the span of the intervals causes the mode to reach the value of the minimum wage. The application of advanced methods, including those using a kernel estimator, leads to significantly different estimates of the mode depending on the method used (the dispersion reaches the value of approximately PLN 800). Additionally, the analysis of the obtained results gives grounds to considering a thesis that wage and salary distribution is a mixture of the following distributions: discrete (for the minimum wage) and continuous (for wages and salaries above the minimum wage), and is characterised by cyclicality (in Poland, more contracts offer remunerations which are a multiple of PLN 50 or PLN 100 than remunerations for other amounts).

Estimation of Failure Mode of Mortar-Filled Sleeve Rebar Splices

In order to establish a more rational structural design method for mortar-filled sleeve rebar splices, it is necessary to analyze and evaluate structural factors affecting the structural performance of these rebar splices. It is very desirable to be able to quantitatively estimate the failure mode of the splices at the design stage. A method for estimating the failure mode of mortar-filled sleeve rebar splices presented from the existing research is not clear because the boundary of failure mode is not expressed in formulas. There are also limitations using the methods because the research is based on limited number of test variables, insufficient number of test specimens, and the fact that only steel pipe sleeves were used. Therefore, to establish a more general and comprehensive failure mode estimation method, it needs to be presented in a more quantitative and explicit fashion and evaluated using more diverse variables. In this study, as part of an effort to generate basic data for the establishment of a more rational and quantitative structural design method for mortar-filled sleeve rebar splices, the failure mode estimation method is presented based on the existing bond strength equations of sleeve rebar splices. In addition, to examine the suitability of this failure mode estimation method, the failure modes of 303 sleeve rebar splices were evaluated. The evaluation results indicated that the failure mode estimation method for mortar-filled sleeve rebar splices proposed by this study would yield a failure mode estimation with a sufficiently practical accuracy.

Fault-tolerant control and sinusoidal disturbance attenuation for a class of hybrid dynamic systems

The design of an accurate fault-tolerant control fault-tolerant control is still an active researches of switched hybrid system whose switching mechanism is unknown. In this paper, a new approach is proposed to deal with switching mode estimation and control problems for switched system subject to actuator faults and disturbances. First, the switching mode is estimated off-line using the Chiu clustering algorithm. Then, actuator fault estimation is proposed using data-based projection approach based on performance measures that allow fault estimation without relying on mathematical models and fault assumptions. Second, a novel switching control strategy is developed for actuator fault compensation and recovering the desired performances. These strategy integrate a set of controllers, corresponding to a set of partial modes to design a bank of switching control laws, compensating for the actuator fault effect and attenuating the sinusoidal disturbance. A new linear matrix inequality is proposed to compute control gains based on Lyapunov stability. This approach allows finding the optimal control gains matrices and ensure both actuator fault compensation and disturbance attenuation. Simulation results of two numerical examples shows the effectiveness of the proposed estimation and control strategies in spite of the presence of actuator faults and sinusoidal disturbance.

Multivariate expectile-based distribution: Properties, Bayesian inference, and applications

Expectiles form a family of risk measures that have recently gained interest over the more common value-at-risk or return levels, primarily due to their capability to be determined by the probabilities of tail values and magnitudes of realizations at once. However, a prevalent and ongoing challenge of expectile inference is the problem of uncertainty quantification, which is especially critical in sensitive applications, such as in medical, environmental, or engineering tasks. We address this issue by developing a novel distribution, termed the multivariate expectile-based distribution (MED), that possesses an expectile as a closed-form parameter. Desirable properties of the distribution, such as log-concavity, make it an excellent fitting distribution in multivariate applications. Maximum likelihood estimation and Bayesian inference algorithms are described. Simulated examples and applications to expectile and mode estimation illustrate the usefulness of the MED for uncertainty quantification.

Asymptotic properties of a kernel etimate of the conditional mode in the presence of doubly censored data

We introduce a double kernel conditional mode estimator when the response variable is doubly censored. In this situation, the variable of interest may be right censored by a variable R or left censored by a variable L and L is not greater than R almost surely. Self- consistent estimators of R and L are extensively studied in literature. As they fit in the expression of the conditional density estimator, using their known properties, among other tools, we establish the uniform almost sure convergence of the conditional density estimator and its derivatives. Then, we deduce the consistency and the asymptotic normality of our conditional mode estimator. For that, we use the theory of Vapnik- ervonenkis classes of measurable functions. We also show the quality of this estimation and the Gaussian behavior of our proposed estimator through a simulation study in which, we consider various regression models with different sample sizes and censoring rates. Finally, we illustrate the performance of our estimator on a real data set which concerns the Stanford heart transplant data.

Regularized conditional estimators of unit inefficiency in stochastic frontier analysis, with application to electricity distribution market

In stochastic frontier analysis, the conventional estimation of unit inefficiency is based on the mean/mode of the inefficiency, conditioned on the composite error. It is known that the conditional mean of inefficiency shrinks towards the mean rather than towards the unit inefficiency. In this paper, we analytically prove that the conditional mode cannot accurately estimate unit inefficiency, either. We propose regularized estimators of unit inefficiency that restrict the unit inefficiency estimators to satisfy some a priori assumptions, and derive the closed form regularized conditional mode estimators for the three most commonly used inefficiency densities. Extensive simulations show that, under common empirical situations, e.g., regarding sample size and signal-to-noise ratio, the regularized estimators outperform the conventional (unregularized) estimators when the inefficiency is greater than its mean/mode. Based on real data from the electricity distribution sector in Sweden, we demonstrate that the conventional conditional estimators and our regularized conditional estimators provide substantially different results for highly inefficient companies.

Methodology of estimation of temperature mode in the 2xBgu type railway braking system

The article presents finite element models of the 2xBgu type tread brake for the simulation of extended repeated frictional heating carried out on a full-scale inertia dynamometer. The numerical calculations were conducted for the brake blocks made of two organic composite materials newly developed specifically for this study. The transient temperature changes obtained from the 2D axisymmetric and 3D finite element analyses and experimental data agreed well during continuous process of about 1200 s. Simulation of such a long period of braking sequence required introducing simplifications in the boundary conditions in the contact area, convection cooling, arrangement of the model (2D axisymmetric, 3D). The focus was laid on representation of variation of the coefficient of friction and the temperature dependence of the properties of the friction materials during braking. The carried out research indicates limitations in the finite element analysis and directions of necessary improvements in modelling as well as measurements with the use of embedded thermocouples.