Parameters Estimation for Wear-out Failure Period of Three-Parameter Weibull Distribution

The shape parameter estimation using the minimum-variance linear estimator with hyperparameter (MVLE-H) method is believed to be effective for a wear-out failure period in a small sample. In the process of the estimation, our method uses the hyperparameter and estimate shape parameters of the MVLE-H method. To obtain the optimal hyperparameter c, it takes a long time, even in the case of the small sample. The main purpose of this paper is to remove the restriction of small samples. We observed that if we set the shape parameters, for sample size n and c, we can use the regression equation to infer the optimal c from n. So we searched in five increments and complemented the hyperparameter for the remaining sample sizes with a linear regression line. We used Monte Carlo simulations (MCSs) to determine the optimal hyperparameter for various sample sizes and shape parameters of the MVLE-H method. Intrinsically, we showed that the MVLE-H method performs well by determining the hyperparameter. Further, we showed that the location and scale parameter estimations are improved using the shape parameter estimated by the MVLE-H method. We verified the validity of the MVLE-H method using MCSs and a numerical example.

Optimal Designs for Comparing Regression Curves: Dependence Within and Between Groups

We consider the problem of designing experiments for the comparison of two regression curves describing the relation between a predictor and a response in two groups, where the data between and within the group may be dependent. In order to derive efficient designs we use results from stochastic analysis to identify the best linear unbiased estimator (BLUE) in a corresponding continuous model. It is demonstrated that in general simultaneous estimation using the data from both groups yields more precise results than estimation of the parameters separately in the two groups. Using the BLUE from simultaneous estimation, we then construct an efficient linear estimator for finite sample size by minimizing the mean squared error between the optimal solution in the continuous model and its discrete approximation with respect to the weights (of the linear estimator). Finally, the optimal design points are determined by minimizing the maximal width of a simultaneous confidence band for the difference of the two regression functions. The advantages of the new approach are illustrated by means of a simulation study, where it is shown that the use of the optimal designs yields substantially narrower confidence bands than the application of uniform designs.

Nonparametric Pointwise Estimation for a Regression Model with Multiplicative Noise

In this paper, we consider a general nonparametric regression estimation model with the feature of having multiplicative noise. We propose a linear estimator and nonlinear estimator by wavelet method. The convergence rates of those regression estimators under pointwise error over Besov spaces are proved. It turns out that the obtained convergence rates are consistent with the optimal convergence rate of pointwise nonparametric functional estimation.

Dynamic Expectation Maximization Algorithm for Estimation of Linear Systems with Colored Noise

The free energy principle from neuroscience has recently gained traction as one of the most prominent brain theories that can emulate the brain’s perception and action in a bio-inspired manner. This renders the theory with the potential to hold the key for general artificial intelligence. Leveraging this potential, this paper aims to bridge the gap between neuroscience and robotics by reformulating an FEP-based inference scheme—Dynamic Expectation Maximization—into an algorithm that can perform simultaneous state, input, parameter, and noise hyperparameter estimation of any stable linear state space system subjected to colored noises. The resulting estimator was proved to be of the form of an augmented coupled linear estimator. Using this mathematical formulation, we proved that the estimation steps have theoretical guarantees of convergence. The algorithm was rigorously tested in simulation on a wide variety of linear systems with colored noises. The paper concludes by demonstrating the superior performance of DEM for parameter estimation under colored noise in simulation, when compared to the state-of-the-art estimators like Sub Space method, Prediction Error Minimization (PEM), and Expectation Maximization (EM) algorithm. These results contribute to the applicability of DEM as a robust learning algorithm for safe robotic applications.

Rough Estimator Based Asynchronous Distributed Super Points Detection on High Speed Network Edge

Super points detection plays an important role in network research and application. With the increase of network scale, distributed super points detection has become a hot research topic. The key point of super points detection in a multi-node distributed environment is how to reduce communication overhead. Therefore, this paper proposes a three-stage communication algorithm to detect super points in a distributed environment, Rough Estimator based Asynchronous Distributed super points detection algorithm (READ). READ uses a lightweight estimator, the Rough Estimator (RE), which is fast in computation and takes less memory to generate candidate super points. Meanwhile, the famous Linear Estimator (LE) is applied to accurately estimate the cardinality of each candidate super point, so as to detect the super point correctly. In READ, each node scans IP address pairs asynchronously. When reaching the time window boundary, READ starts three-stage communication to detect the super point. This paper proves that the accuracy of READ in a distributed environment is no less than that in the single-node environment. Four groups of 10 Gb/s and 40 Gb/s real-world high-speed network traffic are used to test READ. The experimental results show that READ not only has high accuracy in a distributed environment, but also has less than 5% of communication burden compared with existing algorithms.

Sensorless Adaptive Voltage Control for Classical DC-DC Converters Feeding Unknown Loads: A Generalized PI Passivity-Based Approach

The problem of voltage regulation in unknown constant resistive loads is addressed in this paper from the nonlinear control point of view for second-order DC-DC converters. The converters’ topologies analyzed are: (i) buck converter, (ii) boost converter, (iii) buck-boost converter, and (iv) non-inverting buck-boost converter. The averaging modeling method is used to model these converters, representing all these converter topologies with a generalized port-Controlled Hamiltonian (PCH) representation. The PCH representation shows that the second-order DC-DC converters exhibit a general bilinear structure which permits to design of a passivity-based controller with PI actions that ensures the asymptotic stability in the sense of Lyapunov. A linear estimator based on an integral estimator that allows reducing the number of current sensors required in the control implementation stage is used to determine the value of the unknown resistive load. The main advantage of this load estimator is that it ensures exponential convergence to the estimated variable. Numerical simulations and experimental validations show that the PI passivity-based control allows voltage regulation with first-order behavior, while the classical PI controller produces oscillations in the controlled variable, significantly when the load varies.

Resolvent-based estimation of turbulent channel flow using wall measurements

We employ a resolvent-based methodology to estimate velocity and pressure fluctuations within turbulent channel flows at friction Reynolds numbers of approximately 180, 550 and 1000 using measurements of shear stress and pressure at the walls, taken from direct numerical simulation (DNS) databases. Martini et al. (J. Fluid Mech., vol. 900, 2021, p. A2) showed that the resolvent-based estimator is optimal when the true space–time forcing statistics are utilised, thus providing an upper bound for the accuracy of any linear estimator. We use this framework to determine the flow structures that can be linearly estimated from wall measurements, and we characterise these structures and the estimation errors in both physical and wavenumber space. We also compare these results to those obtained using approximate forcing models – an eddy-viscosity model and white-noise forcing – and demonstrate the significant benefit of using true forcing statistics. All models lead to accurate results up to the buffer layer, but only using the true forcing statistics allows accurate estimation of large-scale logarithmic-layer structures, with significant correlation between the estimates and DNS results throughout the channel. The eddy-viscosity model displays an intermediate behaviour, which may be related to its ability to partially capture the forcing colour. Our results show that structures that leave a footprint on the channel walls can be accurately estimated using the linear resolvent-based methodology, and the presence of large-scale wall-attached structures enables accurate estimations through the logarithmic layer.

Optimal Combination of Linear and Spectral Estimators for Generalized Linear Models

We study the problem of recovering an unknown signal $${\varvec{x}}$$ x given measurements obtained from a generalized linear model with a Gaussian sensing matrix. Two popular solutions are based on a linear estimator $$\hat{\varvec{x}}^\mathrm{L}$$ x ^ L and a spectral estimator $$\hat{\varvec{x}}^\mathrm{s}$$ x ^ s . The former is a data-dependent linear combination of the columns of the measurement matrix, and its analysis is quite simple. The latter is the principal eigenvector of a data-dependent matrix, and a recent line of work has studied its performance. In this paper, we show how to optimally combine $$\hat{\varvec{x}}^\mathrm{L}$$ x ^ L and $$\hat{\varvec{x}}^\mathrm{s}$$ x ^ s . At the heart of our analysis is the exact characterization of the empirical joint distribution of $$({\varvec{x}}, \hat{\varvec{x}}^\mathrm{L}, \hat{\varvec{x}}^\mathrm{s})$$ ( x , x ^ L , x ^ s ) in the high-dimensional limit. This allows us to compute the Bayes-optimal combination of $$\hat{\varvec{x}}^\mathrm{L}$$ x ^ L and $$\hat{\varvec{x}}^\mathrm{s}$$ x ^ s , given the limiting distribution of the signal $${\varvec{x}}$$ x . When the distribution of the signal is Gaussian, then the Bayes-optimal combination has the form $$\theta \hat{\varvec{x}}^\mathrm{L}+\hat{\varvec{x}}^\mathrm{s}$$ θ x ^ L + x ^ s and we derive the optimal combination coefficient. In order to establish the limiting distribution of $$({\varvec{x}}, \hat{\varvec{x}}^\mathrm{L}, \hat{\varvec{x}}^\mathrm{s})$$ ( x , x ^ L , x ^ s ) , we design and analyze an approximate message passing algorithm whose iterates give $$\hat{\varvec{x}}^\mathrm{L}$$ x ^ L and approach $$\hat{\varvec{x}}^\mathrm{s}$$ x ^ s . Numerical simulations demonstrate the improvement of the proposed combination with respect to the two methods considered separately.

Predicting robust complete and full band gaps in three-dimensional frame structures

Vibration can cause structural damage in dynamic systems when not designed properly. Recently, several approaches are emerging in structural dynamics as possible alternatives for passive vibration and noise control, such as phononic crystals and metamaterials. In this work, a three-dimensional frame that presents intersection of longitudinal, flexural and torsional band gaps is investigated. For periodic structures, the Irreducible Brillion Zone (IBZ) gives information for any possible angle of propagation of a wave. The manufacturing process induces variability along each three-dimensional frame element. The present study verifies the robustness of the band gaps of the three-dimensional structure against spatially varying geometry and mechanical properties. The spatial random fields are modeled using the expansion optimal linear estimator (EOLE). Bayesian statistics is used to infer on the stochastic response simulated using the Monte Carlo method combined with the EOLE. The three-dimensional frame is modeled via Euler-Bernoulli beam and ordinary shaft theories as well as with Timoshenko and Saint-Venant theories. It is shown that the three-dimensional frame structure exhibits a complete (for all waves) and full (throughout the IBZ) robust band gap against the proposed variability. Both models are able to predict this robust band gap.

The estimate of amplitude and phase of harmonics in power system using the extended kalman filter

Nowadays, the amplitude of the harmonics in the power grid has increased unwittingly due to the increasing use of the nonlinear elements and power electronics. It has led to a significant reduction in power quality indicators. As a first step, the estimate of the amplitude, and the phase of the harmonics in the power grid are essential to resolve this problem. We use the Kalman filter to estimate the phase, and we use the minimal squared linear estimator to assess the amplitude. To test the aforementioned method, we use terminal test signals of the industrial charge consisting of the power converters and ignition coils. The results show that this algorithm has a high accuracy and estimation speed, and they confirm the proper performance in instantaneous tracking of the parameters.