Statistical Sensitivity Measure Research Articles

Sensitivity analysis of Takagi–Sugeno fuzzy neural network

In this paper, we first define a measure of statistical sensitivity of a zero-order Takagi–Sugeno (TS) fuzzy neural network (FNN) with respect to perturbation of weights and parameters of the system. Then we derive measures of sensitivity of the system with respect to additive and multiplicative noises to the consequent parameters. For this we consider a multiple-input multiple-output (MIMO) FNN. The derivation can be easily extended to sensitivity with respect to other parameters as well. These measures of sensitivity are then used as regularizers to the loss function while training the system. Finally, to validate the sensitivity-based learning method, another definition of statistical sensitivity measure, based on absolute output error, is proposed, and its corresponding expression for additive/multiplicative perturbations of the consequent parameters is derived as well. Using simulation results on one classification problem and two regression problems, the effectiveness of the sensitivity measures is demonstrated.

Stochastic sensitivity analysis for timing and amplitude of pressure waves in the arterial system.

In the field of computational hemodynamics, sensitivity quantification of pressure and flow wave dynamics has received little attention. This work presents a novel study of the sensitivity of pressure-wave timing and amplitude in the arterial system with respect to arterial stiffness. Arterial pressure and flow waves were simulated with a one-dimensional distributed wave propagation model for compliant arterial networks. Sensitivity analysis of this model was based on a generalized polynomial chaos expansion evaluated by a stochastic collocation method. First-order statistical sensitivity indices were formulated to assess the effect of arterial stiffening on timing and amplitude of the pressure wave and backward-propagating pressure wave in the ascending aorta, at the maximum pressure and inflection point in the systolic phase. Only the stiffness of aortic arteries was found to significantly influence timing and amplitude of the backward-propagating pressure wave, whereas other large arteries in the systemic tree showed marginal impact. Furthermore, the ascending aorta, aortic arch, thoracic aorta, and infrarenal abdominal aorta had the largest influence on amplitude, whereas only the thoracic aorta influenced timing. Our results showed that the non-intrusive polynomial chaos expansion is an efficient method to compute statistical sensitivity measures for wave propagation models. These sensitivities provide new knowledge in the relative importance of arterial stiffness at various locations in the arterial network. Moreover, they will significantly influence clinical data collection and effective composition of the arterial tree for in-silico clinical studies.

Using statistical sensitivities for adaptation of a best-estimate thermo-hydraulic simulation model

On-line adaptation of best-estimate simulations of NPP behaviour to time-dependent measurement data can be used to insure that simulations performed in parallel to plant operation develop synchronously with the real plant behaviour even over extended periods of time. This opens a range of applications including operator support in non-standard-situations, improving diagnostics and validation of measurements in real plants or experimental facilities. A number of adaptation methods have been proposed and successfully applied to control problems. However, these methods are difficult to be applied to best-estimate thermal-hydraulic codes, such as TRACE and ATHLET, with their large nonlinear differential equation systems and sophisticated time integration techniques. This paper presents techniques to use statistical sensitivity measures to overcome those problems by reducing the number of parameters subject to adaptation. It describes how to identify the most significant parameters for adaptation and how this information can be used by combining: - decomposition techniques splitting the system into a small set of component parts with clearly defined interfaces where boundary conditions can be derived from the measurement data, - filtering techniques to insure that the time frame for adaptation is meaningful, - numerical sensitivities to find minimal error conditions. The suitability of combining those techniques is shown by application to an adaptive simulation of the PKL experiment.

A comparative study of multiple amplifier active RC biquadratic sections

AbstractBiquadratic sections play an important role in the design of high order active filters. This paper compares a number of popular multiple amplifier active RC biquads on the basis of their sensitivities as well as ω0 and Q enhancement effects due to finite amplifier gain–bandwidth products (GB). For sensitivity comparison, statistical sensitivity measures, which take into account the tolerances of various passive and active elements, are used. Simple expressions for gain, phase and transfer function sensitivities are derived for the case of uncorrelated element variations. Graphic illustrations of the effects of increasing ω0 and Q on the sensitivity measures are presented. In addition, root‐loci, which show the effects of GB on the network poles are included. To further facilitate the comparison, graphs demonstrating changes in ω0 and Q due to GB are also presented.

Multiple-loop feedback topologies for the design of low-sensitivity active filters(Invited Paper)

Improved sensitivity performance of active filters in multiloop feedback (coupled) topologies is well known. Of the numerous design procedures available in the literature, in this paper those methods are reviewed which are based on first- or second-order building blocks in a feedback configuration. A statistical sensitivity measure is given which results in a realistic performance measure for the filters and which can be used to compare circuits and to optimize their design to achieve minimum sensitivity. Design procedures are provided for each topology, which result in realizations having minimum sensitivity and maximum dynamic range. Also, design tables for several examples are given, and the performance of some filters is demonstrated experimentally.

Statistical multiparameter sensitivity measures in high Q networks

Statistical sensitivity measures for gain and phase functions of high Q active networks are studied. Explicit formulas for the sensitivity measures of second-order active RC networks are presented. The formulas obtained are shown to be simple and can be readily calculated for various high Q active RC filters. General formulation of the sensitivity measure for multiple-loop feedback active networks, which use high Q biquadratic active RC networks, is also given.

Large change sensitivity—a dual pair of approximate statistical sensitivity measures

In this paper a statistical multiparameter sensitivity measure, similar in spirit to that of Rosenblum and Ghausi, is presented. The measure, utilizing a second-order series approximation for the ΔH/H( x+Δx) function, is shown to converge for pass band network functions, independent of the network Q. In addition this independece is shown to extend considerably the region of convergence (especially for narrowband bandpass network functions). In the stopband, especially when the network function is of the narrowband (finite attenuation) band reject type, equivalent results are obtained for the ΔH/H function. Finally, the ΔH/H( x+Δx) and ΔH/H sensitivity measures are shown to form a dual pair whose second-order and asymptotic behaviors conform to sound physical arguments in their respective regions of applicability (convergence).