This study suggests the use of fuzzy-filtering algorithms to deal with the uncertainties associat... more 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 ...
This study, for any unknown physical process y=f(x1,...,xn), is concerned with the: 1) fuzzy part... more This study, for any unknown physical process y=f(x1,...,xn), is concerned with the: 1) fuzzy partition of n-dimensional input space X=X1timesmiddotmiddotmiddottimesXn into K different clusters, 2) estimating the process behavior ycirc=f(xcirc) for a given input xcirc=(xcirc1,middotmiddotmiddot,xcircn )isinX, and 3) fuzzy approximation of the process, with uncertain input-output identification data {(x(k)plusmndeltaxk ),(y(k)plusmnvk)}k=1,..., using a Sugeno type fuzzy inference system. A unified min-max approach (that attempts to minimize the worst-case effect of data uncertainties and modeling errors on estimation performance), is suggested to provide robustness against data uncertainties and modeling errors. The proposed method of min-max fuzzy parameters estimation does not make any assumption and does not require a priori knowledge of upper bounds, statistics, and distribution of data uncertainties and modeling errors. To show the feasibility of the approach, simulation studies and a real-world application of physical fitness classification based on the fuzzy interpretation of physiological parameters, have been provided
This study presents a method of adaptive identification of parameters describing Sugeno fuzzy inf... more This study presents a method of adaptive identification of parameters describing Sugeno fuzzy inference system in presence of bounded disturbances while maintaining the readability and interpretability of the fuzzy model during and after identification. This method do not require any a priori knowledge of a bound on the disturbance and noise and of a bound on the unknown parameters values. The method can be used for the robust and adaptive identification of slowly time varying nonlinear systems using fuzzy inference systems. The suggested method was used to build a fuzzy expert system that approximates the functional relationship between physical fitness and some of the measurable physiological parameters by their real measurements and opinion (human-experiences) of a medical expert.
This study presents a new approach to adaptation of Sugeno type fuzzy inference systems using reg... more This study presents a new approach to adaptation of Sugeno type fuzzy inference systems using regularization, since regularization improves the robustness of standard parameter estimation algorithms leading to stable fuzzy approximation. The proposed method can be used for modelling, identification and control of physical processes. A recursive method for on-line identification of fuzzy parameters employing Tikhonov regularization is suggested. The power of approach was shown by applying it to the modelling, identification, and adaptive control problems of dynamic processes. The proposed approach was used for modelling of human-decisions (experience) with a fuzzy inference system and for the fuzzy approximation of physical fitness with real world medical data.
This study considers the problem of Robust Fuzzy approximation of a time-varying nonlinear proces... more This study considers the problem of Robust Fuzzy approximation of a time-varying nonlinear process in the presence of uncertainties in the identification data using a Sugeno Fuzzy System while maintaining the interpretability of the fuzzy model during identification. A recursive procedure for the estimation of fuzzy parameters is proposed based on solving local optimization problem that attempt to minimize the worst-case effect of data uncertainties on approximation performance. To illustrate the approach, several simulation studies on numerical examples are provided. The developed scheme was applied to handle the vagueness, ambiguity and uncertainty inherently present in the general notion of a Medical Expert about Physical Fitness based on a set of various Physiological parameters measurements.
This study considers the robust identification of the parameters describing a Sugeno type fuzzy i... more This study considers the robust identification of the parameters describing a Sugeno type fuzzy inference system with uncertain data. The objective is to minimize the worst-case residual error using a numerically efficient algorithm. The Sugeno type fuzzy systems are linear in consequent parameters but nonlinear in antecedent parameters. The robust consequent parameters identification problem can be formulated as second-order cone programming problem. The optimal solution of this second-order cone problem can be interpreted as solution of a Tikhonov regularization problem with a special choice of regularization parameter which is optimal for robustness (Ghaoui and Lebret (1997). SAIM Journal of Matrix Analysis and Applications 18, 1035–1064). The final regularized nonlinear optimization problem allowing simultaneous identification of antecedent and consequent parameters is solved iteratively using a generalized Gauss–Newton like method. To illustrate the approach, several simulation studies on numerical examples including the modelling of a spectral data function (one-dimensional benchmark example) is provided. The proposed robust fuzzy identification scheme has been applied to approximate the physical fitness of patients with a fuzzy expert system. The identified fuzzy expert system is shown to be capable of capturing the decisions (experiences) of a medical expert.
The first aim of this study was to compare an ambulatory five-lead ECG system with the commercial... more The first aim of this study was to compare an ambulatory five-lead ECG system with the commercially available breast belt measuring devices; Polar S810i and Suunto t6, in terms of R–R interval measures and heart rate variability (HRV) indices. The second aim was to compare different HRV spectral analysis methods. Nineteen young males (aged between 22 and 31 years, median 24 years) underwent simultaneous R–R interval recordings with the three instruments during supine and sitting rest, moderate dynamic, and moderate to vigorous static exercise of the upper and lower limb. For each subject, 17 R–R interval series of 3-min length were extracted from the whole recordings and then analyzed in frequency domain using (1) a fast Fourier transform (FFT), (2) an autoregressive model (AR), (3) a Welch periodogram (WP) and (4) a continuous wavelet transform (CWT). Intra-class correlation coefficients (ICC) and Bland–Altman limits of agreement (LoA) method served as criteria for measurement agreement. Regarding the R–R interval recordings, ICC (lower ICC 95% confidence interval >0.99) as well as LoA (maximum LoA: −15.1 to 14.3 ms for ECG vs. Polar) showed an excellent agreement between all devices. Therefore, the three instruments may be used interchangeably in recording and interpolation of R–R intervals. ICCs for HRV frequency parameters were also high, but in most cases LoA analysis revealed unacceptable discrepancies between the instruments. The agreement among the different frequency transform methods can be taken for granted when analyzing the normalized power in low and high frequency ranges; however, not when analyzing the absolute values.
AbstractThis study derives a class of filtering algorithms for TakagiSugeno fuzzy models via so... more AbstractThis study derives a class of filtering algorithms for TakagiSugeno 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 exponen-tial of filtering errors ...
IEEE Transactions on Systems, Man, and Cybernetics, 2006
This study is concerned with the adaptive learning of an interpretable Sugeno-type fuzzy inferenc... more 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
This study suggests the use of fuzzy-filtering algorithms to deal with the uncertainties associat... more 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 ...
This study, for any unknown physical process y=f(x1,...,xn), is concerned with the: 1) fuzzy part... more This study, for any unknown physical process y=f(x1,...,xn), is concerned with the: 1) fuzzy partition of n-dimensional input space X=X1timesmiddotmiddotmiddottimesXn into K different clusters, 2) estimating the process behavior ycirc=f(xcirc) for a given input xcirc=(xcirc1,middotmiddotmiddot,xcircn )isinX, and 3) fuzzy approximation of the process, with uncertain input-output identification data {(x(k)plusmndeltaxk ),(y(k)plusmnvk)}k=1,..., using a Sugeno type fuzzy inference system. A unified min-max approach (that attempts to minimize the worst-case effect of data uncertainties and modeling errors on estimation performance), is suggested to provide robustness against data uncertainties and modeling errors. The proposed method of min-max fuzzy parameters estimation does not make any assumption and does not require a priori knowledge of upper bounds, statistics, and distribution of data uncertainties and modeling errors. To show the feasibility of the approach, simulation studies and a real-world application of physical fitness classification based on the fuzzy interpretation of physiological parameters, have been provided
This study presents a method of adaptive identification of parameters describing Sugeno fuzzy inf... more This study presents a method of adaptive identification of parameters describing Sugeno fuzzy inference system in presence of bounded disturbances while maintaining the readability and interpretability of the fuzzy model during and after identification. This method do not require any a priori knowledge of a bound on the disturbance and noise and of a bound on the unknown parameters values. The method can be used for the robust and adaptive identification of slowly time varying nonlinear systems using fuzzy inference systems. The suggested method was used to build a fuzzy expert system that approximates the functional relationship between physical fitness and some of the measurable physiological parameters by their real measurements and opinion (human-experiences) of a medical expert.
This study presents a new approach to adaptation of Sugeno type fuzzy inference systems using reg... more This study presents a new approach to adaptation of Sugeno type fuzzy inference systems using regularization, since regularization improves the robustness of standard parameter estimation algorithms leading to stable fuzzy approximation. The proposed method can be used for modelling, identification and control of physical processes. A recursive method for on-line identification of fuzzy parameters employing Tikhonov regularization is suggested. The power of approach was shown by applying it to the modelling, identification, and adaptive control problems of dynamic processes. The proposed approach was used for modelling of human-decisions (experience) with a fuzzy inference system and for the fuzzy approximation of physical fitness with real world medical data.
This study considers the problem of Robust Fuzzy approximation of a time-varying nonlinear proces... more This study considers the problem of Robust Fuzzy approximation of a time-varying nonlinear process in the presence of uncertainties in the identification data using a Sugeno Fuzzy System while maintaining the interpretability of the fuzzy model during identification. A recursive procedure for the estimation of fuzzy parameters is proposed based on solving local optimization problem that attempt to minimize the worst-case effect of data uncertainties on approximation performance. To illustrate the approach, several simulation studies on numerical examples are provided. The developed scheme was applied to handle the vagueness, ambiguity and uncertainty inherently present in the general notion of a Medical Expert about Physical Fitness based on a set of various Physiological parameters measurements.
This study considers the robust identification of the parameters describing a Sugeno type fuzzy i... more This study considers the robust identification of the parameters describing a Sugeno type fuzzy inference system with uncertain data. The objective is to minimize the worst-case residual error using a numerically efficient algorithm. The Sugeno type fuzzy systems are linear in consequent parameters but nonlinear in antecedent parameters. The robust consequent parameters identification problem can be formulated as second-order cone programming problem. The optimal solution of this second-order cone problem can be interpreted as solution of a Tikhonov regularization problem with a special choice of regularization parameter which is optimal for robustness (Ghaoui and Lebret (1997). SAIM Journal of Matrix Analysis and Applications 18, 1035–1064). The final regularized nonlinear optimization problem allowing simultaneous identification of antecedent and consequent parameters is solved iteratively using a generalized Gauss–Newton like method. To illustrate the approach, several simulation studies on numerical examples including the modelling of a spectral data function (one-dimensional benchmark example) is provided. The proposed robust fuzzy identification scheme has been applied to approximate the physical fitness of patients with a fuzzy expert system. The identified fuzzy expert system is shown to be capable of capturing the decisions (experiences) of a medical expert.
The first aim of this study was to compare an ambulatory five-lead ECG system with the commercial... more The first aim of this study was to compare an ambulatory five-lead ECG system with the commercially available breast belt measuring devices; Polar S810i and Suunto t6, in terms of R–R interval measures and heart rate variability (HRV) indices. The second aim was to compare different HRV spectral analysis methods. Nineteen young males (aged between 22 and 31 years, median 24 years) underwent simultaneous R–R interval recordings with the three instruments during supine and sitting rest, moderate dynamic, and moderate to vigorous static exercise of the upper and lower limb. For each subject, 17 R–R interval series of 3-min length were extracted from the whole recordings and then analyzed in frequency domain using (1) a fast Fourier transform (FFT), (2) an autoregressive model (AR), (3) a Welch periodogram (WP) and (4) a continuous wavelet transform (CWT). Intra-class correlation coefficients (ICC) and Bland–Altman limits of agreement (LoA) method served as criteria for measurement agreement. Regarding the R–R interval recordings, ICC (lower ICC 95% confidence interval >0.99) as well as LoA (maximum LoA: −15.1 to 14.3 ms for ECG vs. Polar) showed an excellent agreement between all devices. Therefore, the three instruments may be used interchangeably in recording and interpolation of R–R intervals. ICCs for HRV frequency parameters were also high, but in most cases LoA analysis revealed unacceptable discrepancies between the instruments. The agreement among the different frequency transform methods can be taken for granted when analyzing the normalized power in low and high frequency ranges; however, not when analyzing the absolute values.
AbstractThis study derives a class of filtering algorithms for TakagiSugeno fuzzy models via so... more AbstractThis study derives a class of filtering algorithms for TakagiSugeno 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 exponen-tial of filtering errors ...
IEEE Transactions on Systems, Man, and Cybernetics, 2006
This study is concerned with the adaptive learning of an interpretable Sugeno-type fuzzy inferenc... more 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
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