Credits: 3 (3-0-0)
Description
Revisit of probability and random variables (rv), expectation operator, moments of distributions; Discrete rv and probability distributions: Bernoulli, Poisson, Geometric and Multinomial distributions; Continuous rv and distributions: Gaussian, Student’s- t, Chi Squared, F; Central limit theorem, Estimation: Unbiased estimator, Variance, standard error and mean square error of the estimator; Method of point estimation: Method of moments, maximum likelihood and Bayesian estimation; Interval estimation: Chebyshev’s inequality; Multivariate Gaussian distribution; Multivariate hypothesis testing: testing of mean with variance known and unknownone and two sample cases and their confidence intervals, Tests on population proportion, paired t- tests, type II error; Simple and multiple linear regression, significance of regression, confidence interval for parameters, confidence interval for mean response and prediction interval for future observation, properties of least square estimators-Gauss- Markov theorem, Model adequacy test-residual analysis, normality test and correlation coefficient, influential observations, Other regression models: polynomial regression, weighted least squares regression, total least squares regression, stepwise Regression, robust regression, ridge, quantile regression, least angle regression, lasso regression, elastic net regression, concept of regularization, multicollinearity; Application of process examples- Tennessee-Eastman process case study; Gross errors and random errors, Statistical basis of data reconciliation, data reconciliation of linear systems with all variables measured, with measured and unmeasured variables, Concept of redundancy and observability of process variables using graphs, estimation of measurement covariance, bilinear data reconciliation problems-Crowe’s method, Simpson’s method, process examples- binary distillation column, splitter, mixer, separator; Linear dynamic data reconciliation: Optimal state estimation using Kalman filter; Glimpse of nonlinear data reconciliation process; Introduction to gross error detection; Statistical tests for gross error detection: global test, measurement test, nodal test, generalized likelihood ratio test, principal component tests, type I and type II errors; detectability and identifiability of gross errors; Application of process examples- mass flow networks; Introduction to software packages: MATLAB and R; Process applications and case studies: Continuous Stirred Tank Reactor example, process flow networks and Tennessee-Eastman process case study.