Andrei V. Gribok

Regularization of Ill-Posed Surveillance and Diagnostic Measurements

Most data-based predictive modeling techniques have an inherent weakness in that they may give unstable or inconsistent results when the predictor data is highly correlated. Predictive modeling problems of this design are usually under constrained and are termed ill-posed. This paper presents several examples of ill-posed diagnostic problems and regularization methods necessary for getting accurate and consistent prediction results. The examples include plant-wide sensor calibration monitoring and the inferential sensing of nuclear power plant feedwater flow using neural networks, and non-linear partial least squares techniques, and linear regularization techniques implementing ridge regression and informational complexity measures.

Selection of Multiple Regularization Parameters in Local Ridge Regression Using Evolutionary Algorithms and Prediction Risk Optimization

This paper presents a new methodology for regularizing data-based predictive models. Traditional modeling using regression can produce unrepeatable, unstable, or noisy predictions when the inputs are highly correlated. Ridge regression is a regularization technique used to deal with those problems. A drawback of ridge regression is that it optimizes a single regularization parameter while the methodology presented in this paper optimizes several local regularization parameters that operate independently on each component. This method allows components with significant predictive power to be passed while components with low predictive power are damped. The optimal combination of regularization parameters are computed using an Evolutionary Strategy search technique with the objective function being a predictive error estimate. Examples are presented to demonstrate the advantages of this technique.

APPLICATION OF LOCALIZED REGULARIZATION METHODS FOR NUCLEAR POWER PLANT SENSOR CALIBRATION MONITORING

Several U.S. Nuclear Power Plants are attempting to move from a periodic sensor calibration schedule to a condition-based schedule using on-line calibration monitoring systems. This move requires a license amendment that must address the requirements set forth in a recently released Nuclear Regulatory Commission Safety Evaluation Report (SER). The major issue addressed in the SER is that of a complete uncertainty analysis of the empirical models. It has been shown that empirical modeling techniques are inherently unstable and inconsistent when the inputs are highly correlated. Regularization methods such as ridge regression or truncated singular value decomposition produce consistent results but may be overly simplified and not produce optimal results. This paper describes a new local regularization method, generalized ridge regression (GRR), and its potential value for sensor calibration monitoring at nuclear power plants. A case study is used to quantitatively compare different modeling methods.

Kinetics of Post-Exercise Excess CO2 Production and Substrate Oxidation in Two Dysglycemic and Euglycemic Older Women A Case Study.

We examine the case of post-exercise excess CO2 production and instantaneous substrate oxidation in two older women, one with impaired glucose tolerance and the other one is euglycemic. Both subjects stayed in the room-size calorimeter for 48 hours and performed three bouts of postprandial exercise on the second day. The instantaneous gas exchange rates have been estimated along with the instantaneous respiratory exchange ratio (RER) for the whole 48- hour experiment. The relative dynamics of O2 consumption and RER showed a greater reliance on the carbohydrate as energy source in dysglycemic woman than in euglycemic woman. Also, the rate of post-exercise excessive CO2 output, quantified as the time lag between peaks in O2 consumption and peaks in RER was found to be higher in dysglycemic woman suggesting heavier reliance on anaerobic metabolism during exercise. For the first time, results relating the excess post-exercise CO2 production and impaired glucose tolerance are presented.

Subcutaneous Glucose Concentration as a Predictor Variable for Energy Expenditure during Resistance Exercise in Humans

The paper describes concurrent, minute-by-minute dynamics of subcutaneous glucose concentration and energy expenditure in young male subjects performing 40-min resistance exercise in a whole room calorimeter. The observed negative correlation between subcutaneous glucose concentration, as measured by continuous glucose monitoring (CGM) sensor and energy expenditure is exploited to propose and validate a simple linear model, which is used to estimate minute-by-minute energy expenditure from CGM sensor readings. The data were collected from seven young adult male subjects during their 48-hour stay in calorimeter room. Each subject had two 48-hour calorimeter sessions, except one subject who only performed one session. The minute-by-minute CGM data were regressed on energy expenditure (EE) data thus obtaining a linear model connecting these two quantities. This model was subsequently used to estimate EE from CGM readings for the data that were not used in the training dataset. The performance of the linear regression models was analyzed using Bland-Altman plots and it is demonstrated that the CGM sensor can provide a valid predictor variable which can be combined with other physiological parameters to estimate energy expenditure in field conditions.