corso|33610

I Module Errors (2h): types of errors (sensitivity error, experimental error, propagation error, systematic error, statistical error in inference); significant figures: definition, calculation and rounding; exercises (1h) on calculation of propagation errors. Descriptive statistics (2h): histograms, sample summaries, position indices, box plots; exercises (1h) for the construction of histograms in Excel and JMP, descriptive statistics functions in Excel and JMP. Probability distributions (4h): discrete and continuous random variables, mass function and probability density function (definition, properties, expected value and variance operators), distribution function; normal probability distribution, chi-squared distribution, Student's t distribution, Fisher's F distribution (probability density function, characteristic parameters, statistical tables); exercises (2h) on direct and inverse functions in Excel for the calculation of characteristic values of distributions). Sampling distributions (4h): definition of sampling distribution, the central limit theorem, sampling distribution for sample means of small samples, sampling distribution for sample variance and ratios of sample variances; sampling distribution for differences in sample means for large and small samples; methods for verifying the normal distribution of a sample: normal control chart, quantile-quantile diagrams; exercises (2h) for building quantile-quantile diagrams in Excel and JMP. Confidence intervals (4h): definition, confidence intervals for mean with small and large samples, confidence intervals for variance and for variance ratios; confidence intervals for the difference between means for small and large samples; exercises (2h) in Excel for calculating confidence intervals. Hypothesis test (10h): test phases (definition of hypotheses, identification of descriptive statistics, identification of rejection zones for one-way and two-way tests, test results, type I and II error, operating curves and their use upstream and downstream of the experiment), hypothesis test for comparing the mean with a reference value (large samples and small samples), hypothesis test for comparing two means (large samples and small samples, homo- and heteroscedasticity), hypothesis test for comparing one variance with a reference value, hypothesis test for comparing two variances; hypothesis test for the comparison of means in the case of paired samples; exercises (6h) in Excel and JMP for performing hypothesis tests. Analysis of variance for a multilevel factor (8h): statistical model for variance decomposition; variance decomposition and hypothesis testing, least significant difference method for identifying pairs of means that differ, operating curves; verification of the hypotheses upstream of the Anova (homoskedasticity verification by means of Bartlett's test, verification of the normal distribution of errors by quantile-quantile plot); exercises (5h) in Excel and JMP. Factorial experimentation (6h): definitions and advantages of factorial experimentation; statistical model, variance decomposition, hypothesis testing; examples of experimentation with 2 and 3 factors; non-replicated two-factor factor experimentation (model, variance decomposition and Anova), derivation of an empirical multivariate model downstream of the Anova, testing of hypotheses upstream of the Anova; exercises (4h) in Excel and JMP on factorials with 2 and 3 factors with and without replication. Factorials 2^k (6h): definition, introduction of the sign code for treatments, calculation of contrasts using table of signs and Yates algorithm, calculation of effects and sums of squared deviations from contrasts, statistical model and variance decomposition, table Anova, empirical models in coded variables, verification of the adequacy of the empirical model downstream of the Anova by analyzing the normal distribution of model-data deviations; identification of significant effects by graphical method for 2^k experiments in single replication, projection of a 2^k factorial in single replication; addition of the central points in the 2^k experimentation: verification of the curvature of the effects and Anova table; exercises (4h) in Excel and JMP for 2^k factorials replicated, single replicate and with central points. Linear regression (8h): Simple linear regression: modified linear model, calculation of parameters using the least squares method, confidence intervals on the parameters, confidence interval around the regression, hypothesis testing on the model parameters, Anova (test for the significance of the regression, test for the adequacy of the linear model, the coefficient of determination R2), regression for the origin, inverse regression (confidence interval on the estimate of x); multiple linear regression: assumptions (linearity, non-collinearity), least squares parameter estimation, confidence intervals on parameters, hypothesis testing on parameters, Anova for multiple linear regression model, corrected R2 and R2, choice of explanatory variables (stepwise methods); exercises (5h) in Excel and JMP on determination of parameters, confidence intervals, test of significance of the regression and model adequacy for simple and multiple regression. Parameter regression for nonlinear models (6h): linearizable models (example Langmuir), nonlinear regression for nonlinear models: algorithms for determining parameters, confidence intervals on parameters; exercises (4h) in Excel and Matlab.

Mathematics I and Mathematics II or equivalent courses as content.

Handouts provided by the teacher

The course includes frontal lectures and classroom exercises with the computer and on the blackboard Attendance is optional

in person

The course is divided into two modules: Module I and Module II. Both Modules provide assessment methods that include written exercises in progress (optional) and/or a final oral assessment. The assessment allows to verify the achievement of the objectives in terms of knowledge acquired (descriptor 1) and skills acquired (descriptor 2). The ongoing assessments for Module I (2 in number) concern the application of statistical inference methods (confidence intervals, hypothesis tests, analysis of variance and regression analysis) including the execution of exercises and open-ended or multiple-choice questions. The ongoing tests for Module I take place approximately around the end of March and around the end of April. The first test with topics related to confidence intervals, hypothesis tests and analysis of variance for 1-factor multi-level experimentation. The second test on topics related to the analysis of variance for factorials and regression analysis. A third in-progress test is scheduled for module II at the beginning of June. The in-progress tests are evaluated in thirtieths and the final grade is the average of the three in-progress tests. The student who passes all three in-progress written tests with a grade of at least 18/30 can confirm the grade in the oral exam, or recover the insufficient part with a supplementary written or oral exam concerning the specific part. As an alternative to the in-progress written tests, the student can directly take the final oral exam in which questions are asked regarding the completion of specific exercises but also the exposition of principles underlying the knowledge acquired in relation to statistical inference, experimental design and regression of model parameters. To pass the exam, the student must demonstrate both in the in-progress tests and in the oral exam that he has acquired the specific knowledge provided in the course and that he knows how to use the skills acquired to complete the proposed exercises. The evaluation is expressed in thirtieths with a minimum grade of 18/30 and a maximum grade of 30/30 with honors.

D.C. Montgomery: Design and Analysis of Experiments (Mc Graw-Hill)

The course includes frontal lectures and classroom exercises with the computer and on the blackboard Attendance is optional

I Module Errors (2h): types of errors (sensitivity error, experimental error, propagation error, systematic error, statistical error in inference); significant figures: definition, calculation and rounding; exercises (1h) on calculation of propagation errors. Descriptive statistics (2h): histograms, sample summaries, position indices, box plots; exercises (1h) for the construction of histograms in Excel and JMP, descriptive statistics functions in Excel and JMP. Probability distributions (4h): discrete and continuous random variables, mass function and probability density function (definition, properties, expected value and variance operators), distribution function; normal probability distribution, chi-squared distribution, Student's t distribution, Fisher's F distribution (probability density function, characteristic parameters, statistical tables); exercises (2h) on direct and inverse functions in Excel for the calculation of characteristic values of distributions). Sampling distributions (4h): definition of sampling distribution, the central limit theorem, sampling distribution for sample means of small samples, sampling distribution for sample variance and ratios of sample variances; sampling distribution for differences in sample means for large and small samples; methods for verifying the normal distribution of a sample: normal control chart, quantile-quantile diagrams; exercises (2h) for building quantile-quantile diagrams in Excel and JMP. Confidence intervals (4h): definition, confidence intervals for mean with small and large samples, confidence intervals for variance and for variance ratios; confidence intervals for the difference between means for small and large samples; exercises (2h) in Excel for calculating confidence intervals. Hypothesis test (10h): test phases (definition of hypotheses, identification of descriptive statistics, identification of rejection zones for one-way and two-way tests, test results, type I and II error, operating curves and their use upstream and downstream of the experiment), hypothesis test for comparing the mean with a reference value (large samples and small samples), hypothesis test for comparing two means (large samples and small samples, homo- and heteroscedasticity), hypothesis test for comparing one variance with a reference value, hypothesis test for comparing two variances; hypothesis test for the comparison of means in the case of paired samples; exercises (6h) in Excel and JMP for performing hypothesis tests. Analysis of variance for a multilevel factor (8h): statistical model for variance decomposition; variance decomposition and hypothesis testing, least significant difference method for identifying pairs of means that differ, operating curves; verification of the hypotheses upstream of the Anova (homoskedasticity verification by means of Bartlett's test, verification of the normal distribution of errors by quantile-quantile plot); exercises (5h) in Excel and JMP. Factorial experimentation (6h): definitions and advantages of factorial experimentation; statistical model, variance decomposition, hypothesis testing; examples of experimentation with 2 and 3 factors; non-replicated two-factor factor experimentation (model, variance decomposition and Anova), derivation of an empirical multivariate model downstream of the Anova, testing of hypotheses upstream of the Anova; exercises (4h) in Excel and JMP on factorials with 2 and 3 factors with and without replication. Factorials 2^k (6h): definition, introduction of the sign code for treatments, calculation of contrasts using table of signs and Yates algorithm, calculation of effects and sums of squared deviations from contrasts, statistical model and variance decomposition, table Anova, empirical models in coded variables, verification of the adequacy of the empirical model downstream of the Anova by analyzing the normal distribution of model-data deviations; identification of significant effects by graphical method for 2^k experiments in single replication, projection of a 2^k factorial in single replication; addition of the central points in the 2^k experimentation: verification of the curvature of the effects and Anova table; exercises (4h) in Excel and JMP for 2^k factorials replicated, single replicate and with central points. Linear regression (8h): Simple linear regression: modified linear model, calculation of parameters using the least squares method, confidence intervals on the parameters, confidence interval around the regression, hypothesis testing on the model parameters, Anova (test for the significance of the regression, test for the adequacy of the linear model, the coefficient of determination R2), regression for the origin, inverse regression (confidence interval on the estimate of x); multiple linear regression: assumptions (linearity, non-collinearity), least squares parameter estimation, confidence intervals on parameters, hypothesis testing on parameters, Anova for multiple linear regression model, corrected R2 and R2, choice of explanatory variables (stepwise methods); exercises (5h) in Excel and JMP on determination of parameters, confidence intervals, test of significance of the regression and model adequacy for simple and multiple regression. Parameter regression for nonlinear models (6h): linearizable models (example Langmuir), nonlinear regression for nonlinear models: algorithms for determining parameters, confidence intervals on parameters; exercises (4h) in Excel and Matlab.

Mathematics I and Mathematics II or equivalent courses as content.

Handouts provided by the teacher

The course includes frontal lectures and classroom exercises with the computer and on the blackboard Attendance is optional

in person

The course is divided into two modules: Module I and Module II. Both Modules provide assessment methods that include written exercises in progress (optional) and/or a final oral assessment. The assessment allows to verify the achievement of the objectives in terms of knowledge acquired (descriptor 1) and skills acquired (descriptor 2). The ongoing assessments for Module I (2 in number) concern the application of statistical inference methods (confidence intervals, hypothesis tests, analysis of variance and regression analysis) including the execution of exercises and open-ended or multiple-choice questions. The ongoing tests for Module I take place approximately around the end of March and around the end of April. The first test with topics related to confidence intervals, hypothesis tests and analysis of variance for 1-factor multi-level experimentation. The second test on topics related to the analysis of variance for factorials and regression analysis. A third in-progress test is scheduled for module II at the beginning of June. The in-progress tests are evaluated in thirtieths and the final grade is the average of the three in-progress tests. The student who passes all three in-progress written tests with a grade of at least 18/30 can confirm the grade in the oral exam, or recover the insufficient part with a supplementary written or oral exam concerning the specific part. As an alternative to the in-progress written tests, the student can directly take the final oral exam in which questions are asked regarding the completion of specific exercises but also the exposition of principles underlying the knowledge acquired in relation to statistical inference, experimental design and regression of model parameters. To pass the exam, the student must demonstrate both in the in-progress tests and in the oral exam that he has acquired the specific knowledge provided in the course and that he knows how to use the skills acquired to complete the proposed exercises. The evaluation is expressed in thirtieths with a minimum grade of 18/30 and a maximum grade of 30/30 with honors.

D.C. Montgomery: Design and Analysis of Experiments (Mc Graw-Hill)

The course includes frontal lectures and classroom exercises with the computer and on the blackboard Attendance is optional

Introduction to the study of the dynamics and control of chemical processes (6h) Introduction to chemical process control; First principles mathematical models of chemical processes; Definition of dynamical system; Orbits and phase diagram; Stationary points; Stability of stationary points; Van Heerden stability criterion; Linearization of a dynamical system; Evaluation of the stability of stationary points by linearization analysis; Monod's chemostat; Substrate inhibition chemostat; CSTR with irreversible exothermic reaction; Linear systems (9h) Analysis of linear dynamical systems by applying the Laplace transform; Classification of the variables of a dynamical system (state variables, manipulable variables and disturbances); input-output structures (I/O); transfer functions for single-input/single-output (SISO); poles and zeros of transfer functions; dynamics of first order systems; dynamics of second order systems; dynamics of higher order systems; stability assessment through pole analysis; Proposed exercises: linearization, response analysis and stability study of systems of interest in industrial chemistry; Control of chemical processes (9h) Control systems: objectives, configurations in closed loop (feedback) and open loop (feedforward); Feedback control scheme for SISO systems; Proportional/integral/derivative type controllers (PID); Dynamics of closed loop controlled systems: effect of PID controller parameters; Stability of closed loop controlled systems; Criteria for designing a PID controller; Exercises proposed during the lessons: blackboard exercises to derive the dynamic response of I and II order processes in closed loop with derivative controllers and their combinations; stabilization and destabilization of systems by means of control systems.

The course is included among the basic courses. Preparatory knowledge on Chemical Processes is considered to facilitate the acquisition of the illustrated methodologies.

Reccomended textbooks: George Stephanopoulos (1984), Chemical Process Control: An Introduction to Theory and Practice. Prentice-Hall, Englewood Cliffs, New Jersey (USA)

In presence

The exam can be carried out through an in itinere written test. Alternatively, the exam can be carried out through an oral interview. During the oral exam, problems similar to those covered by in intinere test are proposed to the students. Both the written test and the oral interview aim to evaluate the student's ability to solve problems of dynamics and control of chemical processes.

The course includes frontal lectures. The lectures are given through the use of power-point slides or a dashboard.

Introduction to the study of the dynamics and control of chemical processes (6h) Introduction to chemical process control; First principles mathematical models of chemical processes; Definition of dynamical system; Orbits and phase diagram; Stationary points; Stability of stationary points; Van Heerden stability criterion; Linearization of a dynamical system; Evaluation of the stability of stationary points by linearization analysis; Monod's chemostat; Substrate inhibition chemostat; CSTR with irreversible exothermic reaction; Linear systems (9h) Analysis of linear dynamical systems by applying the Laplace transform; Classification of the variables of a dynamical system (state variables, manipulable variables and disturbances); input-output structures (I/O); transfer functions for single-input/single-output (SISO); poles and zeros of transfer functions; dynamics of first order systems; dynamics of second order systems; dynamics of higher order systems; stability assessment through pole analysis; Proposed exercises: linearization, response analysis and stability study of systems of interest in industrial chemistry; Control of chemical processes (9h) Control systems: objectives, configurations in closed loop (feedback) and open loop (feedforward); Feedback control scheme for SISO systems; Proportional/integral/derivative type controllers (PID); Dynamics of closed loop controlled systems: effect of PID controller parameters; Stability of closed loop controlled systems; Criteria for designing a PID controller; Exercises proposed during the lessons: blackboard exercises to derive the dynamic response of I and II order processes in closed loop with derivative controllers and their combinations; stabilization and destabilization of systems by means of control systems.

The course is included among the basic courses. Preparatory knowledge on Chemical Processes is considered to facilitate the acquisition of the illustrated methodologies.

Reccomended textbooks: George Stephanopoulos (1984), Chemical Process Control: An Introduction to Theory and Practice. Prentice-Hall, Englewood Cliffs, New Jersey (USA)

In presence

The exam can be carried out through an in itinere written test. Alternatively, the exam can be carried out through an oral interview. During the oral exam, problems similar to those covered by in intinere test are proposed to the students. Both the written test and the oral interview aim to evaluate the student's ability to solve problems of dynamics and control of chemical processes.

The course includes frontal lectures. The lectures are given through the use of power-point slides or a dashboard.