Parameter Estimation Phase Research Articles

A remaining useful life prediction method of aluminum electrolytic capacitor with adaptive degradation model selection

The degradation process of aluminum electrolytic capacitors(AECs) usually exhibits characteristics such as non-linearity and multi-stage. These degradation features lead to the difficulty to accurately predict the remaining useful life(RUL) of the whole degradation process of AECs. To address this, by dividing the capacitor degradation process into two stages, a two-stage RUL prediction method for AECs considering multiple degradation models is proposed in this paper.In the offline parameter estimation phase, the initial degradation model parameters of two stages are estimated using two-step maximum likelihood estimation combined with particle swarm optimization(PSO) algorithm. In the dynamic parameter updating phase, a sequential Bayesian method is used to update the model parameters. To select the optimal degradation model, an evaluation method based on historical RUL similarity is proposed to calculate the fitness of each model. Finally, the effectiveness of the method is verified on NASA’s accelerated degradation data set and several widely used methods are used for comparison. The experimental results show that the proposed method has higher accuracy, which proves the superiority of the method.

Modified Maximum Entropy Method and Estimating the AIF via DCE-MRI Data Analysis.

Background: For the kinetic models used in contrast-based medical imaging, the assignment of the arterial input function named AIF is essential for the estimation of the physiological parameters of the tissue via solving an optimization problem. Objective: In the current study, we estimate the AIF relayed on the modified maximum entropy method. The effectiveness of several numerical methods to determine kinetic parameters and the AIF is evaluated—in situations where enough information about the AIF is not available. The purpose of this study is to identify an appropriate method for estimating this function. Materials and Methods: The modified algorithm is a mixture of the maximum entropy approach with an optimization method, named the teaching-learning method. In here, we applied this algorithm in a Bayesian framework to estimate the kinetic parameters when specifying the unique form of the AIF by the maximum entropy method. We assessed the proficiency of the proposed method for assigning the kinetic parameters in the dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), when determining AIF with some other parameter-estimation methods and a standard fixed AIF method. A previously analyzed dataset consisting of contrast agent concentrations in tissue and plasma was used. Results and Conclusions: We compared the accuracy of the results for the estimated parameters obtained from the MMEM with those of the empirical method, maximum likelihood method, moment matching (“method of moments”), the least-square method, the modified maximum likelihood approach, and our previous work. Since the current algorithm does not have the problem of starting point in the parameter estimation phase, it could find the best and nearest model to the empirical model of data, and therefore, the results indicated the Weibull distribution as an appropriate and robust AIF and also illustrated the power and effectiveness of the proposed method to estimate the kinetic parameters.

Multi‐phase initial ranging process for OFDMA systems: improved dynamic threshold‐based multi‐user detection approach

Initial ranging (IR) is a process of performing power adjustment, timing offset estimation, and synchronisation between the base station (BS) and all users. It plays a vital role in mobile WiMAX standard, which establishes a communication link between BS and ranging subscriber stations (RSSs). Since RSS is located far away from the BS and uplink signal is corrupted by noise, the IR process becomes inferior. Thus, the authors propose an improved dynamic threshold-based IR method comprising three phases: (i) code detection phase, (ii) filtering phase, and (iii) parameter estimation phase. In the first two phases, the received signal is pre-processed to eliminate noise and unselected codes from the codeset by employing adaptive filter and weight-based code detection method. Then, the noise-free signal is considered for the final phase, which improves accuracy. The iterative expectation maximisation algorithm is involved in the estimation of channel coefficient and timing offset. All possible active paths are detected by setting a dynamic threshold value for each channel by the enhanced dynamic threshold method. For all active channels, round trip delay, and power level are estimated by considering particular channel coefficient and timing offset. Extensive simulation of proposed work shows considerable improvements in performance.

Nonlinear system modeling using self-organizing fuzzy neural networks for industrial applications

In this paper, a novel self-organizing fuzzy neural network with an adaptive learning algorithm (SOFNN-ALA) for nonlinear system modeling and identification in industrial processes is proposed. To efficiently enhance the generalization capability, the proposed SOFNN-ALA is designed by using both structure identification and parameter estimation simultaneously in the learning process. In the structure identification phase, the rule neuron with the highest neuronal activity will be split into two new rule neurons. Meanwhile, the redundant rule neurons with small singular values will be removed to simplify the network structure. In the parameter estimation phase, an adaptive learning algorithm (ALA), which is designed based on the widely used Levenberg-Marquardt (LM) optimization algorithm, is adopted to optimize the network parameters. The ALA-based learning algorithm can not only speed up the convergence speed but also enhance the modeling performance. Moreover, we carefully analyze the convergence of the proposed SOFNN-ALA to guarantee its successful practical application. Finally, the effectiveness and efficiency of the proposed SOFNN-ALA is validated by several examples. The experimental results demonstrate that the proposed SOFNN-ALA exhibits a better comprehensive performance than some other state-of-the-art SOFNNs for nonlinear system modeling in industrial applications. The source code can be downloaded from https://github.com/hyitzhb/SOFNN-ALA.git.

Dependence of LET on material and its impact on current RBE model

Biological uncertainty remains one of the main sources of uncertainties in proton therapy, and is encapsulated in a scalar quantity known as relative biological effective (RBE). It is currently recognised that a constant RBE of 1.1 is not consistent with radiobiological experiment and may lead to sub-optimal exploitation of the benefits of proton therapy. To overcome this problem, several RBE models have been developed, and in most of these models, there is a dependence of RBE on dose-averaged linear energy transfer (LET), . In this work, we show that the estimation in these models during the data-fitting (or parameter estimation) phase could be subjected to a huge uncertainty due to not taking into account cellular materials during simulation, and this uncertainty can propagate down to the resulting RBE models. The dosimetric impact of this uncertainty is then evaluated on a simple clinical spread out Bragg peak (SOBP) and a prostate example. Our simulation shows that uncertainty due to the use of water as cellular material is non-negligible under low and low dose (2 Gy), and can be neglected otherwise. Thus, this study indicates that further dose and range margins may be required for low target under low dose. This is due to greater uncertainties in RBE model associated with incomplete knowledge of cellular composition for computation.

Regional-scale analysis of extreme precipitation from short and fragmented records

Abstract Rain gauge is the oldest and most accurate instrument for rainfall measurement, able to provide long series of reliable data. However, rain gauge records are often plagued by gaps, spatio-temporal discontinuities and inhomogeneities that could affect their suitability for a statistical assessment of the characteristics of extreme rainfall. Furthermore, the need to discard the shorter series for obtaining robust estimates leads to ignore a significant amount of information which can be essential, especially when large return periods estimates are sought. This work describes a robust statistical framework for dealing with uneven and fragmented rainfall records on a regional spatial domain. The proposed technique, named “patched kriging” allows one to exploit all the information available from the recorded series, independently of their length, to provide extreme rainfall estimates in ungauged areas. The methodology involves the sequential application of the ordinary kriging equations, producing a homogeneous dataset of synthetic series with uniform lengths. In this way, the errors inherent to any regional statistical estimation can be easily represented in the spatial domain and, possibly, corrected. Furthermore, the homogeneity of the obtained series, provides robustness toward local artefacts during the parameter-estimation phase. The application to a case study in the north-western Italy demonstrates the potential of the methodology and provides a significant base for discussing its advantages over previous techniques.

Incorporating transmission losses in flash flood routing in ephemeral streams by using the three-parameter Muskingum method

Stream flow in arid and semi-arid regions is usually in a form of flash floods that occur in dry bed ephemeral streams. In this research, the three-parameter Muskingum method has been investigated as a tool for flash flood routing in arid zones using data from Yiba catchment in the Kingdom of Saudi Arabia. The method is general; it takes into account both lateral inflows from side tributaries and also lateral outflow which can represent transmission losses. Applying the methodology for ephemeral streams requires some modifications of the assumptions. The ephemeral stream is considered as a long linear channel with a total movement time of the hydrograph that consists of two parts, the translation time and the redistribution time. The translation time is the travel time of the flood between two stations, while the redistribution time is the lag time that is estimated from the conventional Muskingum method due to the reshaping of the hydrograph. Eight runoff events have been studied for the model parameter estimation phase, while another four events are considered for the verification phase. A spreadsheet model has been developed to implement the methodology and checked with data from the published literature. The method shows very good results; the average RMSE value is 3 m3/s for the hydrographs of the reconstructed events. The correlation coefficients between observed and calculated parameters show relatively high correlation, i.e., 0.99 for the peak discharges, 0.95 for the time lags, and 0.99 for coefficient of transmission losses (the α-parameter). The maximum transmission loss is estimated to be 84 % of the inflow hydrograph form the studied events. A Monte Carlo approach is followed for the verification of the model. It has been found out that the following set of combination of the routing parameter, i.e., a lower limit of d 1, an upper limit of d 2 and a lower limit of d 3 produces satisfactorily good results for the four independent events. Results indicate that the three-parameter Muskingum method exhibits good results in simulating flash flood routing in arid environments.

Fundamental Limit of Sample Generalized Eigenvalue Based Detection of Signals in Noise Using Relatively Few Signal-Bearing and Noise-Only Samples

The detection problem in statistical signal processing can be succinctly formulated: given m (possibly) signal bearing, n -dimensional signal-plus-noise snapshot vectors (samples) and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> statistically independent n-dimensional noise-only snapshot vectors, can one reliably infer the presence of a signal? This problem arises in the context of applications as diverse as radar, sonar, wireless communications, bioinformatics, and machine learning and is the critical first step in the subsequent signal parameter estimation phase. The signal detection problem can be naturally posed in terms of the sample generalized eigenvalues. The sample generalized eigenvalues correspond to the eigenvalues of the matrix formed by ?whitening? the signal-plus-noise sample covariance matrix with the noise-only sample covariance matrix. In this paper, we prove a fundamental asymptotic limit of sample generalized eigenvalue-based detection of signals in arbitrarily colored noise when there are relatively few signal bearing and noise-only samples. Specifically, we show why when the (eigen) signal-to-noise ratio (SNR) is below a critical value, that is a simple function of n , m, and N, then reliable signal detection, in an asymptotic sense, is not possible. If, however, the eigen-SNR is above this critical value then a simple, new random matrix theory-based algorithm, which we present here, will reliably detect the signal even at SNRs close to the critical value. Numerical simulations highlight the accuracy of our analytical prediction, permit us to extend our heuristic definition of the effective number of identifiable signals in colored noise and display the dramatic improvement in performance relative to the classical estimator by Zhao We discuss implications of our result for the detection of weak and/or closely spaced signals in sensor array processing, abrupt change detection in sensor networks, and clustering methodologies in machine learning.

Modelling the heat dynamics of building integrated and ventilated photovoltaic modules

This paper deals with mathematical modelling of the heat transfer of building integrated photovoltaic (BIPV) modules. The efficiency of the photovoltaic (PV) module and its temperature are negatively correlated. It is therefore of interest to lower the temperature of the PV module by increasing the heat transfer from the PV module. The experiment and data originate from a test reference module the EC-JRC Ispra. The set-up provides the opportunity of changing physical parameters, the ventilation speed and the type of air flow, and this makes it possible to determine the preferable set-up. To identify best set-up, grey-box models consisting of stochastic differential equations are applied. The models are first order stochastic state space models. Maximum likelihood estimation and the extended Kalman filter are applied in the parameter estimation phase. To validate the estimated models, plots of the residuals and autocorrelation functions of the residuals are analyzed. The analysis has revealed that it is necessary to use non-linear state space models in order to obtain a satisfactory description of the PV module temperature, and in order to be able to distinguish the variations in the set-up. The heat transfer is increased when the forced ventilation velocity is increased, while the change in type of air flow does not have as striking influence. The residual analysis show that the best description of the PV module temperature is obtained when fins, disturbing the laminar flow and making it turbulent, are applied in the set-up combined with high level of air flow. The improved description by the model is mainly seen in periods with high solar radiation.

Optimal decomposition of covariance matrices for multivariate stochastic models in hydrology

A new method is proposed for decomposing covariance matrices that appear in the parameter estimation phase of all multivariate stochastic models in hydrology. This method applies not only to positive definite covariance matrices (as do the typical methods of the literature) but to indefinite matrices, too, that often appear in stochastic hydrology. It is also appropriate for preserving the skewness coefficients of the model variables as it accounts for the resulting coefficients of skewness of the auxiliary (noise) variables used by the stochastic model, given that the latter coefficients are controlled by the decomposed matrix. The method is formulated in an optimization framework with the objective function being composed of three components aiming at (1) complete preservation of the variances of variables, (2) optimal approximation of the covariances of variables, in the case that complete preservation is not feasible due to inconsistent (i.e., not positive definite) structure of the covariance matrix, and (3) preservation of the skewness coefficients of the model variables by keeping the skewness of the auxiliary variables as low as possible. Analytical expressions of the derivatives of this objective function are derived, which allow the development of an effective nonlinear optimization algorithm using the steepest descent or the conjugate gradient methods. The method is illustrated and explored through a real world application, which indicates a very satisfactory performance of the method.

Utilizing Weibull Failure Rates in Repair Limit Analysis for Equipment Replacement/Preventive Maintenance Decisions

Repair limit analysis was originally proposed as a methodology for determining whether to repair or to replace an operating unit. The approach structures the problem as a Markov or semi-Markov decision process in which state-dependent repair limits trigger the replacement decision. Such a basic framework can easily be applied to more general equipment repair/overhaul environments in which typical maintenance condition monitoring information can serve as the overhaul trigger. One unnecessary limitation of repair limit analysis found in the literature is the use of a constant force of mortality within each state of the model. The purpose of this paper is to extend the repair limit analysis by incorporating a changing force of mortality as the unit ages. In this way, the analysis is more flexible in the parameter estimation phase and it is argued here more appealing since a changing (and usually increasing) force of mortality is utilized in equipment maintenance environments.

Canonical correlation analysis, approximate covariance extension, and identification of stationary time series

In this paper we analyze a class of state space identification algorithms for time-series, based on canonical correlation analysis, in the light of recent results on stochastic systems theory. In principle, these so called “subspace methods” can be described as covariance estimation followed by stochastic realization. The methods offer the major advantage of converting the nonlinear parameter estimation phase in traditional ARMA models identification into the solution of a Riccati equation but introduce at the same time some nontrivial mathematical problems related to positivity. The reason for this is that an essential part of the problem is equivalent to the well-known rational covariance extension problem. Therefore, the usual deterministic arguments based on factorization of a Hankel matrix are not valid for generic data, something that is habitually overlooked in the literature. We demonstrate that there is no guarantee that several popular identification procedures based on the same principle will not fail to produce a positive extension, unless some rather stringent assumptions are made which, in general, are not explicitly reported. In this paper the statistical problem of stochastic modeling from estimated covariances is phrased in the geometric language of stochastic realization theory. We review the basic ideas of stochastic realization theory in the context of identification, discuss the concept of stochastic balancing and of stochastic model reduction by principal subsystem truncation. The model reduction method of Desai and Pal (1982) [A realization approach to stochastic model reduction. Proc. 1 st Decision and Control Conf., pp. 1105–1112.], based on truncated balanced stochastic realizations, is partially justified, showing that the reduced system structure has a positive covariance sequence but is in general not balanced. As a byproduct of this analysis we obtain a theorem prescribing conditions under which the ‘subspace identification’ methods produce bona fide stochastic systems.

On-line optimization of a high-pressure low-density polyethylene tubular reactor

Low-density polyethylene (LDPE) is a high-volume commodity polymer that is produced in high-capacity tubular and autoclave reactors. The extreme operating conditions employed in the high-pressure free-radical polymerization of ethylene, and the tight profit margins of the LDPE market provide a strong economic incentive to seek the optimal operation of a high-pressure LDPE reactor. In the present work, an on-line multi-level optimization procedure is developed for a high-pressure tubular LDPE reactor based on a comprehensive steady-state mathematical model of the process. Following the well-established separation hypothesis, the problem is hierarchically decomposed in two phases: (i) the parameter estimation phase where certain key model parameters are adjusted, based on selected process measurements, in order to eliminate any process/model mismatch; (ii) the optimization phase where the adapted model is optimized by minimizing a specified objective function defined in terms of the ethylene conversion and the “quality” of the final polymer product. The proposed optimization algorithm is successfully tested against the operation of a large-scale industrial reactor. The most prominent features of the procedure are highlighted. These include the development of a comprehensive mathematical model of the process, the disturbance oriented selection of the adjustable model parameters, the appropriate spatial decomposition of the parameter estimation problem into a number of subproblems and the conditional structuring of the optimization problem.