Norbert Stoll

A robust design criterion for interpretable fuzzy models with uncertain data

We believe that nonlinear fuzzy filtering techniques may be turned out to give better robustness performance than the existing linear methods of estimation (H/sup 2/ and H/sup /spl infin// filtering techniques), because of the fact that not only linear parameters (consequents), but also the nonlinear parameters (membership functions) attempt to identify the uncertain behavior of the unknown system. However, the fuzzy identification methods must be robust to data uncertainties and modeling errors to ensure that the fuzzy approximation of unknown systems behavior is optimal in some sense. This study presents a deterministic approach to the robust design of fuzzy models in the presence of unknown but finite uncertainties in the identification data. We consider online identification of an interpretable fuzzy model, based on the robust solution of a regularized least-squares fuzzy parameters estimation problem. The aim is to resolve the difficulties associated with the robust fuzzy identification method due to lack of a priori knowledge about upper bounds on the data uncertainties. The study derives an optimal level of regularization that should be provided to ensure the robustness of fuzzy identification strategy by achieving an upper bound on the value of energy gain from data uncertainties and modeling errors to the estimation errors. A time-domain feedback analysis of the proposed identification approach is carried out with emphasis on stability, robustness, and steady-state issues. The simulation studies are provided to show the superiority of the proposed fuzzy estimation over the classical estimation methods.

An energy-gain bounding approach to robust fuzzy identification

A novel method for the robust identification of interpretable fuzzy models, based on the criterion that identification errors are least sensitive to data uncertainties and modelling errors, is suggested. The robustness of identification errors towards unknown disturbances (data uncertainties, modelling errors, etc.) is achieved by bounding (i.e. minimizing) the maximum possible value of energy-gain from disturbances to the identification errors. The solution of energy-gain bounding problem, being robust, shows an improved performance of the identification method. The flexibility of the proposed framework is shown by designing the variable learning rate identification algorithms in both deterministic and stochastic frameworks.

Fuzzy Techniques for Subjective Workload-Score Modeling Under Uncertainties

This paper deals with the development of a computer model to estimate the subjective workload score of individuals by evaluating their heart-rate (HR) signals. The identification of a model to estimate the subjective workload score of individuals under different workload situations is too ambitious a task because different individuals (due to different body conditions, emotional states, age, gender, etc.) show different physiological responses (assessed by evaluating the HR signal) under different workload situations. This is equivalent to saying that the mathematical mappings between physiological parameters and the workload score are uncertain. Our approach to deal with the uncertainties in a workload-modeling problem consists of the following steps: 1) The uncertainties arising due the individual variations in identifying a common model valid for all the individuals are filtered out using a fuzzy filter; 2) stochastic modeling of the uncertainties (provided by the fuzzy filter) use finite-mixture models and utilize this information regarding uncertainties for identifying the structure and initial parameters of a workload model; and 3) finally, the workload model parameters for an individual are identified in an online scenario using machine learning algorithms. The contribution of this paper is to propose, with a mathematical analysis, a fuzzy-based modeling technique that first filters out the uncertainties from the modeling problem, analyzes the uncertainties statistically using finite-mixture modeling, and, finally, utilizes the information about uncertainties for adapting the workload model to an individuals physiological conditions. The approach of this paper, demonstrated with the real-world medical data of 11 subjects, provides a fuzzy-based tool useful for modeling in the presence of uncertainties.

Deterministic approach to robust adaptive learning of fuzzy models

This study is concerned with the adaptive learning of an interpretable Sugeno-type fuzzy inference system, in a deterministic framework, in the presence of data uncertainties and modeling errors. The authors explore the use of Hinfin estimation theory and least squares estimation for online learning of membership functions and consequent parameters without making any assumption and requiring a priori knowledge of upper bounds, statistics, and distribution of data uncertainties and modeling errors. The issues of data uncertainties, modeling errors, and time variations have been considered mathematically in a sensible way. The proposed robust approach to the adaptive learning of fuzzy models has been illustrated through the examples of adaptive system identification, time-series prediction, and estimation of an uncertain process

Fuzzy Filtering for Physiological Signal Analysis

This study suggests the use of fuzzy-filtering algorithms to deal with the uncertainties associated to the analysis of physiological signals. The signal characteristics, for a given situation or physiological state, vary for an individual over time and also vary among the individuals with the same state. These random variations are due to the several factors related to the physiological behavior of individuals, which cannot be taken into account in the interpretation of signal characteristics. Our approach is to reduce the effect of random variations on the analysis of signal characteristics via filtering out randomness or uncertainty from the signal using a nonlinear fuzzy filter. A fuzzy-filtering algorithm, which is based on a modification of filtering algorithm of Kumar et al. [M. Kumar, N. Stoll, and R. Stoll, IEEE Trans. Fuzzy Syst., vol. 17, no. 1, pp. 150-166, Feb. 2009], is proposed for an improved performance. The method is illustrated by studying the effect of head-up tilting on the heart-rate signal of 40 healthy subjects.

A common wireless remote control system for mobile robots in laboratory

A common wireless remote control system based on standard APIs of robots is presented to enable a stable multi-robot transportation in distributed life science laboratories. This system consists of multi-robot board control centers (PCs), a remote server control center (PC), a wireless communication network and an infrared radio navigation module with ceiling passive landmarks. To let this system expand conveniently, the two-level Client/Server architecture is adopted, and a standard IEEE 802.11g wireless communication with TCP/IP protocol is utilized. An inside architecture is employed for signal sampling and controlling between robot board PCs and the robots hardware modules. An additional outside architecture is designed for higher remote commands between robot board PCs and remote server control PC. Two experiments in this study show that the simple ceiling landmark method is suitable for the robot indoor navigation with low costs, and this kind of remote control system can work effectively in large and distributed laboratory.

Stress Monitoring Based on Stochastic Fuzzy Analysis of Heartbeat Intervals

Quantifying stress levels of an individual based on a mathematical analysis of real-time physiological data measurements is challenging. This study suggests a stochastic fuzzy analysis method to evaluate the short time series of R-R intervals (time intervals between consecutive heart beats) for a quantification of the stress level. The 5-min-long series of R-R intervals recorded under a given stress level are modeled by a stochastic fuzzy system. The stochastic model of heartbeat intervals is individual specific and corresponds to a particular stress level. Once the different heartbeat interval models are available for an individual, an analysis of the given R-R interval series generated under an unknown stress level is performed by a stochastic interpolation of the models. The stress estimation method has been implemented in a mobile telemedical application employing an e-health system for an efficient and cost-effective monitoring of patients while at home or at work. The experiments involve 50 individuals whose stress scores were assessed at different times of the day. The subjective rating scores showed a high correlation with the values predicted by the proposed analysis method.

On the Estimation of Parameters of Takagi–Sugeno Fuzzy Filters

This study derives a class of filtering algorithms for Takagi-Sugeno fuzzy models via solving a nonlinear parameters estimation problem. The considered estimation problem is related to the problem of minimizing the expected value of the exponential of filtering errors energy. Under some stochastic assumptions, the filtering criteria (which involve an expectation operator) are replaced by the deterministic quadratic optimization problems whose solutions provide a class of fuzzy filtering algorithms. From a viewpoint of errors in the estimation of linear parameters of the fuzzy filter, the derived filtering algorithms were analyzed with emphasis on stability, robustness, and steady-state error issues. The stability and robustness analyses have been made deterministically without making any assumption.

A mixture of fuzzy filters applied to the analysis of heartbeat intervals

This study provides a stochastic modeling of the heartbeat intervals using a mixture of Takagi–Sugeno type fuzzy filters. The model parameters are inferred under variational Bayes (VB) framework. The model of the heartbeat intervals is in the form of a history-dependent probability density. The parameters, characterizing the heartbeat intervals probability density, include the estimated parameters of different fuzzy filters and may serve as the features of the heartbeat interval series. The features of the heartbeat intervals provide a description of the physiological state of an individual. A novelty of our analysis method is that the physiological state is predicted as a part of the features extraction procedure. This is done via deriving, using VB paradigm, an analytical expression for the posterior distribution that the observed heartbeat intervals have been generated by the stochastic model of the physiological state. The method is illustrated with the data of 40 healthy subjects studied in a tilt-table experiment.

Fuzzy Filtering for an Intelligent Interpretation of Medical Data

This study is concerned with an intelligent interpretation of medical data in the sense that involved complexities and uncertainties (arising in understanding the data behavior) are properly (i.e. mathematically) handled. The uncertainties in data interpretation may arise due to e.g. different behavior of individuals due to the different body conditions. We use a fuzzy model to filter out the uncertainties. The fuzzy model provides an interpretation of the data without the interpretation results being affected by the uncertainties. Such a fuzzy model (that could filter out the uncertainties) is identified using a robust identification algorithm. It was demonstrated through a real-world case study that the proposed approach of fuzzy filtering is suitable for dealing with the uncertainties involved in data interpretation. Fuzzy models, due to their capability of approximating nonlinear input-output mappings, could be exploited for the filtering of uncertainties. The efficient design of the fuzzy filter is the bottleneck of the approach.