MATHEMATICAL MODELING OF PROCESSES IN FOOD INDUSTRIES

Ingegneria Alimentare - Food Engineering MATHEMATICAL MODELING OF PROCESSES IN FOOD INDUSTRIES

0622800009
DIPARTIMENTO DI INGEGNERIA INDUSTRIALE
EQF7
FOOD ENGINEERING
2022/2023



OBBLIGATORIO
YEAR OF COURSE 2
YEAR OF DIDACTIC SYSTEM 2019
AUTUMN SEMESTER
CFUHOURSACTIVITY
660LESSONS
Objectives
KNOWLEDGE AND UNDERSTANDING
THE COURSE AIMS TO PROVIDE STUDENTS WITH BASIC KNOWLEDGE, METHODOLOGIES AND SOME SOFTWARE TOOLS TO DEAL WITH THE ABSTRACT REPRESENTATION OF SYSTEMS IN PROCESS ENGINEERING, IN PARTICULAR FOR CASES OF INTEREST IN INDUSTRIAL FOOD PRODUCTION.
STUDENTS LEARN ABOUT AND UNDERSTAND:
THE FORMALISM AND ABSTRACT REPRESENTATION TOOLS, THE CLASSIFICATION CRITERIA AND THE DEVELOPMENT TECHNIQUES OF MATHEMATICAL MODELS, THE MINIMUM ABILITY TO DISCERN THE LEVEL OF COMPLEXITY APPROPRIATE FOR THE SYSTEMIC DESCRIPTION OF THE PLANTS OF THE FOOD INDUSTRY;
NUMERICAL RESOLUTION OF MATHEMATICAL MODELS CONSISTING OF PARTIAL DIFFERENTIAL EQUATIONS OF THE PARABOLIC TYPE;
SOLVING LINEAR PROGRAMMING PROBLEMS.

APPLIED KNOWLEDGE AND UNDERSTANDING - ENGINEERING ANALYSIS
BEING ABLE TO OBTAIN, SELECT, RE-ELABORATE AND CRITICALLY ANALYZE ENGINEERING DATA.
KNOWING HOW TO CLASSIFY MATHEMATICAL MODELS.
ABILITY TO SELECT AND USE MATHEMATICAL MODELS PREDICTIVE OF THE BEHAVIOR OF TYPICAL PROCESSES OF THE FOOD AND PROCESS INDUSTRY.
DESCRIBE A LINEAR OPTIMIZATION PROBLEM ACCORDING TO THE FORMALISM AND THE BASIC HYPOTHESES FOR LINEAR PROGRAMMING.

APPLIED KNOWLEDGE AND UNDERSTANDING - ENGINEERING DESIGN
RECOGNIZE THE SPECIFIC CHARACTERISTICS AND THE MOST FREQUENT CONNOTATIONS IN THE MATHEMATICAL MODELS REPRESENTATIVE OF PROCESSES IN THE FOOD INDUSTRY.
RECOGNIZE PHENOMENA AND PROCESSES THAT ARE BEST DESCRIBED BY A MATHEMATICAL MODEL BASED ON THE CONCEPT OF POPULATION BALANCE, AND POSSESS THE FOUNDATIONS FOR DEVELOPING IT.
SOLVE A DYNAMIC MODEL DESCRIBED THROUGH A PARTIAL DIFFERENTIAL EQUATION (PDE) OF PARABOLIC TYPE THROUGH THE METHOD OF FINITE DIFFERENCES, CONSCIOUSLY USING SOFTWARE.
DESCRIBE A LINEAR OPTIMIZATION PROBLEM ACCORDING TO THE FORMALISM AND THE BASIC HYPOTHESES FOR LINEAR PROGRAMMING AND SOLVE IT WITH STANDARD ALGORITHMS, KNOWINGLY USING SOFTWARE.

AUTONOMY OF JUDGMENT - ENGINEERING PRACTICE
- KNOWING HOW TO CLASSIFY MATHEMATICAL MODELS.
- DISTINGUISH THE DIFFERENCES IN BEHAVIOR, CONCEPTUAL AND PRACTICAL, UNDER STEADY-STATE OR DYNAMIC CONDITIONS, BETWEEN LINEAR AND NON-LINEAR SYSTEMS.
- KNOWING HOW TO RECOGNIZE LIMITS AND DIFFICULTIES RELATED TO THE USE OF SPECIFIC CALCULATION SOFTWARE.
- KNOWING HOW TO DISTINGUISH THE LEVEL OF COMPLEXITY APPROPRIATE FOR THE SYSTEM DESCRIPTION OF THE PROCESS INDUSTRY PLANTS.
- KNOWING HOW TO CLASSIFY AND SOLVE OPTIMIZATION PROBLEMS.

TRANSVERSAL SKILLS - ABILITY TO LEARN
UNDERSTAND THE TERMINOLOGY USED IN ENGLISH IN THE DEVELOPMENT AND APPLICATIONS OF MATHEMATICAL MODELS.
LEARN TO DEAL WITH MASTERY AND ENHANCEMENT OF A SOFTWARE, THE SOLUTION OF A PROBLEM AND THE EFFECTIVE REPRESENTATION OF THE RESULTS.

TRANSVERSAL SKILLS - COMMUNICATION SKILLS
ABILITY TO PRESENT, WITH LANGUAGE PROPERTIES, A SIMPLE CASE STUDY TYPICAL OF THE FOOD INDUSTRY CAPABLE OF BEING MODELED AND, USING DEDICATED SOFTWARE (SUCH AS MATLAB® AND MUC®), TO DISCUSS THE RESULTS OF THE MATHEMATICAL RESOLUTION, EVEN IN A TIME OF LIMITED EXPOSURE.
TRANSVERSAL SKILLS - INVESTIGATION SKILLS
KNOWING HOW TO APPLY THE KNOWLEDGE ACQUIRED TO CONTEXTS OTHER THAN THOSE PRESENTED DURING THE COURSE, AND TO DEEPEN THE TOPICS COVERED USING STUDY MATERIALS OTHER THAN THOSE PROPOSED.
DISTINGUISH THE DIFFERENCES IN BEHAVIOR, CONCEPTUAL AND PRACTICAL, UNDER STEADY-STATE OR DYNAMIC CONDITIONS, BETWEEN LINEAR AND NON-LINEAR SYSTEMS.
DISTINGUISHING THE IMPLICATIONS OF A NONLINEAR OPTIMUM PROBLEM PRESENTS WITH RESPECT TO A LINEAR ONE.
Prerequisites
FOR THE SUCCESSFUL ACHIEVEMENT OF THE SET OBJECTIVES, BASIC MATHEMATICAL KNOWLEDGE IS REQUIRED, IN PARTICULAR FOR ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS, MASTERY OVER MATERIAL AND ENERGY BALANCES IN NON-STATIONARY CONDITIONS AND THE FUNDAMENTALS OF TRANSPORT PHENOMENA.
Contents
AFTER A BRIEF PRESENTATION OF THE COURSE SYLLABUS AND THE PROCEDURE FOR LEARNING ASSESSMENT, THE COURSE WILL FOCUS ON THE FOLLOWING TOPICS:

• INTRODUCTION TO MATLAB® LANGUAGES AND TECHNICAL USES (1H TH, 0H EX, 2H LAB).
• CLASSIFICATIONS OF MODELS IN GENERAL, AND OF MATHEMATICAL MODELS IN PARTICULAR (2H TH, 0H EX, 0H LAB).
• FIRST-PRINCIPLE MODELS: BASIC MODELS; MODELS INVOLVING TRANSPORT PHENOMENA; MODELS BASED ON THE “POPULATION BALANCE APPROACH”(8H TH, 3H EX, 0H LAB).
• EMPIRICAL MODELS AND DATA FITTING (3H TH, 0H EX, 5H LAB).
• DYNAMICAL MODELS: DYNAMIC MODELS WITH “INPUT-OUTPUT REPRESENTATION”; STATE-SPACE DYNAMIC MODELS; BLACK BOX DYNAMIC MODELS (6H TH, 0H EX, 0H LAB).
• TIME SERIES (2H TH, 0H EX, 0H LAB). .
• NUMERICAL METHODS FOR PARABOLIC PDES. USE OF MUC 1.0 - PARABOLIC PDE SOLVER CODE IN LABVIEW® (6H TH, 1H EX, 2H LAB). .
• INTRODUCTION TO OPTIMIZATION (3H TH, 0H EX, 0H LAB).
• LINEAR PROGRAMMING: THE GRAPHICAL METHOD AND THE ONE AND TWO PHASES SIMPLEX ALGORITHM (9H TH, 1HEX, 6H LAB).
Teaching Methods
THE COURSE INCLUDES A TOTAL OF 60H DIVIDED INTO 36H OF THEORY, 18 OF EXERCISES AND 6 OF THE LABORATORY WITH INTERACTIVE SOFTWARE.
TEACHING IS PROVIDED "IN ATTENDANCE" AND IN ENGLISH.
ATTENDANCE TO TEACHING COURSES IS STRONGLY RECOMMENDED.
THE TEACHING INCLUDES THEORETICAL LESSONS CARRIED OUT BY THE TEACHER WITH EXTENSIVE USE OF SLIDES AND COMPUTERIZED ANIMATIONS, CLASSROOM EXERCISES CARRIED OUT BY THE TEACHER ON THE BLACKBOARD AND COMPUTER LAB ACTIVITIES CARRIED OUT BY THE TEACHER INTERACTIVELY WITH THE STUDENTS, THROUGH THE USE OF APPROPRIATE TEACHING SOFTWARE. EACH STUDENT IS ASSIGNED A USER NAME AND A PASSWORD, AND THEREFORE ACCESS IN THE COMPUTER ROOM TO PCS CONNECTED TO THE NETWORK AND EQUIPPED WITH THE MATLAB®¸ LICENSE WITH HIS CURVE FITTING TOOLBOX, AND THE EXECUTABLE MUC® ARE ALLOWED. EACH STUDENT CAN INSTALL AND USE THE LICENSE OF THE UPDATED VERSION OF MATLAB® OF THE UNIVERSITY, BY DOWNLOADING IT FROM HTTPS://WEB.UNISA.IT/SERVIZI-ON-LINE/MATLAB-X-UNISA. IN ADDITION, EACH STUDENT WILL BE GIVEN THE FREEWARE CODE MUC 1.0 - PARABOLIC PDE SOLVER AND SOME MATLAB® SCRIPTS.
ALL COURSE PRESENTATIONS, OTHER NOTES AND TEXTS FROM PREVIOUS WRITTEN EXAMS ARE MADE AVAILABLE BY THE TEACHER ON THE UNIVERSITY PLATFORM MS TEAMS®.
Verification of learning
THE EVALUATION OF THE ACHIEVEMENT OF THE SET OBJECTIVES IS MADE BY WRITTEN TEST OF THE 2H DURATION. IT INCLUDES:
AN "APPLICATION AND PRACTICAL" PART BASED ON THE USE OF MATLAB®, CONSISTING IN THE PROCESSING OF PROBLEMS DESCRIBED IN THE ENGLISH LANGUAGE OF LINEAR PROGRAMMING, RESOLUTION OF PDE AT THE FINITE DIFFERENCES, CONSTRUCTION OF A MODEL OF DATA FITTING AND SIMPLIFIED ANALYSIS OF A TIME SERIES,
A "THEORY" PART WITH OPEN OR QUIZ QUESTIONS ON MATHEMATICAL MODELING.
THE TEST INVOLVES PROVIDING AND ASSEMBLING THE ANSWERS DIRECTLY ON PC IN A MS WORD® FILE, WITH THE RESULTS OBTAINED FROM MATLAB® AND/OR MUC®, WHILE KEEPING ALL THE TEACHING MATERIALS OF THE COURSE AVAILABLE.
THE TEST IS INTENDED TO BE PASSED WITH THE MINIMUM SCORE (18/30) IF THE STUDENT HAS CARRIED OUT AT LEAST TWO OF THE THREE PROBLEMS, AND AT THE SAME TIME HAS PROVIDED VALID ANSWERS TO 60% OF THE QUESTIONS. IF THE STUDENT SHOWS COMPARATIVE KNOWLEDGE, APPLIED UNDERSTANDING AND CRITICAL AUTONOMY OF JUDGMENT AND REASONING, DESCRIBED IN THE PREVIOUS PARAGRAPHS, THEY ACHIEVE THE MAXIMUM SCORE (30/30). FOR THE PURPOSE OF THE PRAISE, THE QUANTITY (COMPLETE AND CORRECT ANSWER ALSO NUMERICALLY TO ABOUT 90% OF THE QUESTIONS) WILL BE TAKEN INTO ACCOUNT BUT ALSO THE QUALITY (APPROPRIATE SCIENTIFIC LANGUAGE AND MASTERY OF THE MATTER) OF THE EXPOSURE.
Texts
1. SNIEDER R., “A GUIDED TOUR OF MATHEMATICAL METHODS FOR THE PHYSICAL SCIENCES”, 2ND EDITION, CAMBRIDGE UNIVERSITY PRESS, ISBN-13: 9780521834926, ISBN-10: 0521834929, 2004
2. HIMMELBLAU D.M. E BISCHOFF K.B., “PROCESS ANALYSIS AND SIMULATION”, WILEY,1967
3. ZONDERVAN E., A NUMERICAL PRIMER FOR THE CHEMICAL ENGINEER, SECOND EDITION, TAYLOR & FRANCIS, 2020
4. PRESENTATIONS AND LECTURE NOTES PROVIDED BY THE LECTURER.
More Information
THE COURSE IS IN ENGLISH.
WEB SITE FOR BOTH PERSONAL STUDY AND EXAMINATION MARKS:
HTTP://COMET.ENG.UNIPR.IT/~MICCIO
MS TEAMS® UNIVERSITY PLATFORM “MATHEMATICAL MODELING OF PROCESSES IN FOOD INDUSTRIES – 0622800009”
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