Uncertain Variances Research Articles

Nonsingular Gradient Descent Algorithm for Interval Type-2 Fuzzy Neural Network.

Interval type-2 fuzzy neural network (IT2FNN) is widely used to model nonlinear systems. Unfortunately, the gradient descent-based IT2FNN with uncertain variances always suffers from low convergence speed due to its inherent singularity. To cope with this problem, a nonsingular gradient descent algorithm (NSGDA) is developed to update IT2FNN in this article. First, the widths of type-2 fuzzy rules are transformed into root inverse variances (RIVs) that always satisfy the sufficient condition of differentiability. Second, the singular RIVs are reformulated by the nonsingular Shapley-based matrices associated with type-2 fuzzy rules. It averts the convergence stagnation caused by zero derivatives of singular RIVs, thereby sustaining the gradient convergence. Third, an integrated-form update strategy (IUS) is designed to obtain the derivatives of parameters, including RIVs, centers, weight coefficients, deviations, and proportionality coefficient of IT2FNN. These parameters are packed into multiple subvariable matrices, which are capable to accelerate gradient convergence using parallel calculation instead of sequence iteration. Finally, the experiments showcase that the proposed NSGDA-based IT2FNN can improve the convergence speed through the improved learning algorithm.

PROGRESSIVE STEP MAXIMUM POWER TRACKER FOR CASCADED INVERTER INDUCTION MOTOR DRIVE

This paper presents the idea of an isolated photovoltaic (PV) based cascaded two-level inverter (CTLI), driving squirrel cage induction motor (SCIM). The connected non-linear load approximately represents a centrifugal pump. The control system of this drive is based on a motor control system along with a progressive step perturb and observe (PSPnO) maximum power point tracking (MPPT) technique for the PV sources towards better utilization of the source. This PSPnO MPPT system intends to operate the SCIM so that the energy developed by PV is utilized entirely through variation of the dc-link voltages of the CTLI under both uncertain variances of non-linear load torque and unpredictable solar irradiance. This PSPnO MPPT algorithm has been engaged in the control scheme for generating reference dc-link voltage. This motor control system is designed to operate in a rotor-flux-oriented rotating reference frame. As for generating CTLI’s switching pulses, the space vector pulse width modulation (SVPWM) technique has been used for its good dynamic response. The whole system is designed to be deployable on a low-computation device. The simulations conducted by Simulink and the results are furnished considering various operational conditions.

Distributed fusion robust filter for multisensor networked singular control system with uncertain variances and missing measurement

AbstractA distributed fusion time‐varying robust filtering algorithm for multisensor networked singular control system is studied in this paper, mainly aiming at the system with missing measurement and uncertain variances in practical application. First, the singular value decomposition (SVD) method and de‐randomization method are used to transform the singular control system into a standard system only with uncertain variances. Based on the new standard system, a minimax robust local Kalman filter is proposed by using the minimax robust estimation principle, which ensures that the actual filtering error variance has the corresponding minimum upper bound for all allowable uncertainties. Further, the robust local and distributed fusion filters for original singular control systems are proposed, and the actual and conservative filtering error variances are obtained. Their robustness is proved by Lyapunov equation method and nonnegative definite matrix decomposition method. A simulation example of two‐loop system verifies the effectiveness of the proposed results.

Automated sleep spindle detection with mixed EEG features

Detection of sleep spindles, a special type of burst brainwaves recordable with electroencephalography (EEG), is critical in examining sleep-related brain functions from memory consolidation to cortical development. It has long been an onerous and highly professional task to visually position individual sleep spindles and label their onset & offset. Automated spindle detection (template- and classifier-based) is experiencing performance bottleneck due to uncertain variances between spindles in both duration & formation.This study then develops a generic framework based on Deep Neural Network for accurate spindle detection by mixing the deep (micro-scale) features and the entropy (macro-scale) of sleep EEG. First, an “elastic” time window applies to adapt to the significantly varied durations of spindles in EEG, after which regulated deep features of EEG epochs with variable-lengths are obtained via a compact Convolutional Neural Network (CNN) with spatial pyramid pooling. Second, these deep features are mixed with the entropy of EEG epochs to support spindle classification. Focal loss applies to ease the severe imbalance between spindles and other epochs. Finally, elastic EEG epochs are set to capture the individual spindles.Experimental results on a public sleep EEG dataset (DREAMS) with the proposed framework against the state-of-the-art counterparts indicate that (1) it outperforms the counterparts with an F1-score of 0.66(0.11) while introducing entropy information gains 0.034(0.02) in this process; (2) it incurs less errors in identifying the onset & offset of spindles. Overall, the core design of the framework paves the way for detection of complicated EEG waveforms or time series in general.

A new mean-variance-entropy model for uncertain portfolio optimization with liquidity and diversification

Abstract This paper deals with a portfolio optimization problem with uncertain returns. Here, the returns of risky assets are regarded as uncertain variables which are estimated by experienced experts. First, a mean-variance-entropy model for uncertain portfolio optimization problem is presented by taking into account four criteria viz., return, risk, liquidity and diversification degree of portfolio. In our model, the investment return is quantified by uncertain expected value, the investment risk is characterized by uncertain variance and entropy is used to measure the diversification degree of portfolio. Moreover, different from the previous bi-objective optimization model, our model achieves both the maximum return and the minimum risk in a single objective form by introducing a risk aversion factor and the dimensional influence caused by different units is eliminated by normalization method. Then, two auxiliary portfolio selection models are transformed into different equivalent deterministic models. Finally, a numerical simulation is given to verify the effectiveness and practicality of our model.

Interval Type-2 Mutual Subsethood Fuzzy Neural Inference System (IT2MSFuNIS)

This paper presents an interval type-2 mutual subsethood fuzzy neural inference system (IT2MSFuNIS). A mutual subsethood measure between two interval type-2 fuzzy sets (IT2 FS) has been derived and has been used in determining the similarity between the IT2 FS inputs and IT2 FS antecedents. The consequent weights are taken to be interval sets. The inputs to the system are fuzzified into IT2 FSs with Gaussian primary membership function having fixed center and uncertain variance. Aggregation of type-2 mutual subsethood based activation spreads is performed using product operator. The output is obtained using simplified type-reduction followed by defuzzification. The system learns using memetic procedure involving differential evolution for global search and gradient descent for local exploitation in solution space. The mathematical modeling and empirical studies of IT2MSFuNIS bring forth its efficacy in problems pertaining to function approximation, time-series prediction, control, and classification. Comparisons with other type-1 and type-2 neuro-fuzzy systems verify that IT2MSFuNIS compares excellently with other models with a performance better than most of them both in terms of total number of trainable parameters and result accuracy. Empirical studies indicate the intelligent decision making capability of the proposed model. The main contribution of this paper lies in the identification of mutual subsethood to find out the correlation between IT2 FSs and to find out its applicability in diverse application domains. The improved performance of the proposed method can be attributed to the better contrast handling capacity of mutual subsethood method and uncertainty handling capacity of IT2 FSs. The integration of mutual subsethood with interval type-2 fuzzy logic puts forth a novel model with various merits as demonstrated amply with the help of well-known problems reported in the literature.

Robust Kalman estimators for systems with mixed uncertainties

SummaryThis paper addresses the problem of designing robust Kalman estimators for uncertain systems with mixed uncertainties including the same uncertain‐variance multiplicative noise in state and measurement matrices, missing measurements, and uncertain‐variance linearly correlated measurement and process white noise. By introducing fictitious noise to compensate for multiplicative noise, the system under consideration is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, on the basis of the worst‐case system with known conservative upper bounds of uncertain variances, the minimax robust time‐varying Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Their robustness is proved by using a Lyapunov equation approach, such that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. The corresponding robust steady‐state Kalman estimators are also presented, and 3 modes of convergence in a realization among the time‐varying and steady‐state robust Kalman estimators for the time‐varying and time‐invariant systems are presented and proved by the dynamic error system analysis method. A simulation example with application to autoregressive signal processing is also given to show the effectiveness and correctness of the proposed results.

A differential harmony search based hybrid interval type2 fuzzy EGARCH model for stock market volatility prediction

In this paper a new hybrid model integrating an interval type2 fuzzy logic system (IT2FLS) with a computationally efficient functional link artificial neural network (CEFLANN) and an Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) model has been proposed for accurate forecasting and modeling of financial data with changing variance over time. The proposed model denoted as IT2F-CE-EGARCH helps to enhance the ability of EGARCH model through a joint estimation of the important features of EGARCH like leverage effect, asymmetric shock by leverage effect with the secondary membership functions of interval type2 TSK FLS and the functional expansion and learning component of a CEFLANN. The secondary membership functions with upper and lower limits of IT2FLS provide a forecasting interval for handling more complicated uncertainties involved in volatility forecasting compared to type1 FLS. The performance of the proposed model has been observed with two membership functions i.e. Gaussian with fixed mean, uncertain variance and Gaussian with fixed variance and uncertain mean. The proposed model has also been compared with a few other fuzzy time series models and GARCH family models based on four performance metrics: MSFE, RMSFE, MAFE and Rel MAE. Again a differential harmony search (DHS) algorithm has been suggested for optimizing the parameters of all the fuzzy time series models. The results indicate that the proposed IT2F-CE-EGARCH model offers significant improvements in volatility forecasting performance in comparison with all other specified models over BSE Sensex and CNX Nifty dataset.

An artificial bee colony algorithm for uncertain portfolio selection.

Portfolio selection is an important issue for researchers and practitioners. In this paper, under the assumption that security returns are given by experts' evaluations rather than historical data, we discuss the portfolio adjusting problem which takes transaction costs and diversification degree of portfolio into consideration. Uncertain variables are employed to describe the security returns. In the proposed mean-variance-entropy model, the uncertain mean value of the return is used to measure investment return, the uncertain variance of the return is used to measure investment risk, and the entropy is used to measure diversification degree of portfolio. In order to solve the proposed model, a modified artificial bee colony (ABC) algorithm is designed. Finally, a numerical example is given to illustrate the modelling idea and the effectiveness of the proposed algorithm.

Integrated, age-structured, length-based stock assessment model with uncertain process variances, structural uncertainty, and environmental covariates: case of Central Baltic herring

We developed a generic, age-structured, state-space stock assessment model that can be used as a platform for including information elicited from stakeholders. The model tracks the mean size-at-age and then uses it to explain rates of natural and fishing mortality. The fishery selectivity is divided to two components, which makes it possible to model the active seeking of the fleet for certain sizes of fish, as well as the selectivity of the gear itself. The model can account for uncertainties that are not currently accounted for in state-of-the-art models for integrated assessments: (i) The form of the stock–recruitment function is considered uncertain and is accounted for by using Bayesian model averaging. (ii) In addition to recruitment variation, process variation in natural mortality, growth parameters, and fishing mortality can also be treated as uncertain parameters. The use of the model is exemplified in the context of participatory modelling where stakeholders have specified how environmental variables affect the stock dynamics of Central Baltic herring (Clupea harengus membras).

Ameliorated Austenite Carbon Content Control in Austempered Ductile Irons by Support Vector Regression

Austempered ductile iron has emerged as a notable material in several engineering fields, including marine applications. The initial austenite carbon content after austenization transform but before austempering process for generating bainite matrix proved critical in controlling the resulted microstructure and thus mechanical properties. In this paper, support vector regression is employed in order to establish a relationship between the initial carbon concentration in the austenite with austenization temperature and alloy contents, thereby exercising improved control in the mechanical properties of the austempered ductile irons. Particularly, the paper emphasizes a methodology tailored to deal with a limited amount of available data with intrinsically contracted and skewed distribution. The collected information from a variety of data sources presents another challenge of highly uncertain variance. The authors present a hybrid model consisting of a procedure of a histogram equalizer and a procedure of a support-vector-machine (SVM-) based regression to gain a more robust relationship to respond to the challenges. The results show greatly improved accuracy of the proposed model in comparison to two former established methodologies. The sum squared error of the present model is less than one fifth of that of the two previous models.

Probabilistic distance based abnormal pattern detection in uncertain series data

Abnormal pattern detection is an important task in series data anomaly detection. Because of the noise interference, the accuracy of abnormal detection method based on deterministic value is decreased. Whereas, most recent studies aimed at solving the anomaly detection problem in uncertain series use possible world models to describe the uncertainty in discrete data and select outliers as the anomaly detection objects. Abnormal pattern detection problems in continuous uncertain data are rarely reported.In order to improve the accuracy of abnormal pattern detection for uncertain data, we propose a Probabilistic Distance based approach for mining Abnormal Pattern Detection from uncertain series data (PD_ APD). Our considered approach re-express the Euclidean distance according to data’s probability density function (PDF), and get a probabilistic metric to compute the dissimilarity of two uncertain series. Our experiments show that, compared with Tarzan, a deterministic approach that directly processes data without considering uncertainty, PD_ APD provides a flexible trade-off between false alarms and miss ratios by controlling a probabilistic abnormality threshold. Especially, when data uncertain variance is large, PD_ APD has lower false alarms under the same specific miss ratio.

CROSS-LAYER DESIGN FOR MOBILE AD HOC NETWORKS USING INTERVAL TYPE-2 FUZZY LOGIC SYSTEMS

In this paper, we introduce a new method for packet transmission delay analysis and prediction in mobile ad hoc networks. We apply a fuzzy logic system (FLS) to coordinate physical layer and data link layer. We demonstrate that type-2 fuzzy membership function (MF), i.e., the Gaussian MFs with uncertain variance is most appropriate to model BER and MAC layer service time. Two FLSs and one neural network: a singleton type-1 FLS, an interval type-2 FLS and back-prop neural network (NN) are designed to predict the packet transmission delay based on the BER and MAC layer service time. Simulation results show that the interval type-2 FLS performs much better than the type-1 FLS in transmission delay prediction. And FLSs performs better than back-prop NN. We use the forecasted transmission delay to adjust the transmission power, and it shows that the interval type-2 FLS performs much better than a type-1 FLS, and FLSs are performs better than back-prop NN in terms of energy consumption, average delay and throughput. Besides, we obtain the performance bound based on the actual transmission delay.

A Bayesian Model for the Probability Distribution of Fatigue Damage in Tubular Joints

A Bayesian framework is used for updating the probability distributions of the parameters of a fracture mechanics model and of crack size in tubular joints using information from inspection reports of fixed offshore structures. An error model, defined as the logarithmic difference between measured crack size during inspection and crack size predicted by the fracture mechanics model, is assumed to have a normal distribution with known mean and uncertain variance. The distribution of the error variance is modeled by a conjugate distribution for samples of normal variables with known mean and uncertain variance. Based on these assumptions, an analytical model is obtained using a Bayesian approach for the updated distributions of the parameters of the fracture mechanics model and of crack size based. The capabilities of the model are illustrated by means of examples using the Paris-Erdogan formulation for crack growth. The examples illustrate the effects of inspection times, measured crack size, and the distribution of stress ranges on the updated density functions of crack size, time varying reliability and expected cost of failure.

MPEG VBR video traffic modeling and classification using fuzzy technique

We present an approach for MPEG variable bit rate (VBR) video modeling and classification using fuzzy techniques. We demonstrate that a type-2 fuzzy membership function, i.e., a Gaussian MF with uncertain variance, is most appropriate to model the log-value of I/P/B frame sizes in MPEG VBR video. The fuzzy c-means (FCM) method is used to obtain the mean and standard deviation (std) of T/P/B frame sizes when the frame category is unknown. We propose to use type-2 fuzzy logic classifiers (FLCs) to classify video traffic using compressed data. Five fuzzy classifiers and a Bayesian classifier are designed for video traffic classification, and the fuzzy classifiers are compared against the Bayesian classifier. Simulation results show that a type-2 fuzzy classifier in which the input is modeled as a type-2 fuzzy set and antecedent membership functions are modeled as type-2 fuzzy sets performs the best of the five classifiers when the testing video product is not included in the training products and a steepest descent algorithm is used to tune its parameters.

Rainfall estimation using raingages and radar ? A Bayesian approach: 2. An application

In Seo and Smith (this issue), a set of estimators was built in a Bayesian framework to estimate rainfall depth at an ungaged location using raingage measurements and radar rainfall data. The estimators are equivalent to lognormal co-kriging (simple co-kriging in the Gaussian domain) with uncertain mean and variance of gage rainfall. In this paper, the estimators are evaluated via cross-validation using hourly radar rainfall data and simulated hourly raingage data. Generation of raingage data is based on sample statistics of actual raingage measurements and radar rainfall data. The estimators are compared with lognormal co-kriging and nonparametric estimators. The Bayesian estimators are shown to provide some improvement over lognormal co-kriging under the criteria of mean error, root mean square error, and standardized mean square error. It is shown that, if the prior could be assessed more accurately, the margin of improvement in predicting estimation variance could be larger. In updating the uncertain mean and variance of gage rainfall, inclusion of radar rainfall data is seen to provide little improvement over using raingage data only.

Rainfall estimation using raingages and radar ? A Bayesian approach: 1. Derivation of estimators

Procedures for estimating rainfall from radar and raingage observations are constructed in a Bayesian framework. Given that the number of raingage measurements is typically very small, mean and variance of gage rainfall are treated as uncertain parameters. Under the assumption that log gage rainfall and log radar rainfall are jointly multivariate normal, the estimation problem is equivalent to lognormal co-kriging with uncertain mean and variance of the gage rainfall field. The posterior distribution is obtained under the assumption that the prior for the mean and inverse of the variance of log gage rainfall is normal-gamma 2. Estimate and estimation variance do not have closed-form expressions, but can be easily evaluated by numerically integrating two single integrals. To reduce computational burden associated with evaluating sufficient statistics for the likelihood function, an approximate form of parameter updating is given. Also, as a further approximation, the parameters are updated using raingage measurements only, yielding closed-form expressions for estimate and estimation variance in the Gaussian domain. With a reduction in the number of radar rainfall data in constructing covariance matrices, computational requirements for the estimation procedures are not significantly greater than those for simple co-kriging. Given their generality, the estimation procedures constructed in this work are considered to be applicable in various estimation problems involving an undersampled main variable and a densely sampled auxiliary variable.

Uncertain variance in an optimal linear system with white gain

Abstract For scalar quadratic optimal linear systems with a white gain coefficient, the influence of the uncertainty of the gain variance is analysed by means of elementary methods. First, the mean-square stability of the closed loop systems is analysed on the assumption that the controller is designed with an erroneous variance. It is shown that the use of an overestimated value of the variance less than a threshold value, which is infinite for the stable free systems, does not damage the stability of closed-loop systems. A relative underestimation error bound guaranteeing the stability of closed-loop systems is obtained. Secondly, performance of the controller designed with an erroneous variance is compared analytically with that of the certainty equivalence controller. An explicit relative overestimation error bound on the variance guaranteeing the superiority of the controller over the certainty equivalence controller is obtained.

Portfolio Analysis Under Uncertain Means, Variances, and Covariances

Portfolio Analysis Under Uncertain Means, Variances, and Covariances