美国麻省理工大学：《航空航天学讲义》教学资源（讲义，英文版）8 testmatrices

Test matrices 16.621 Prof earl murman

Test Matrices 16.621 Prof. Earll Murman

Variables o Independent Variable: a quantity that you will vary and control E. G. angle of attack, chamber pressure or temperature, coefficient in algorithm, luminosity, gain O Parameter: a quantity that is set or otherwise determined which you will not vary but which needs to be recorded E. G. atmospheric pressure, constant in algorithm, battery voltage,… O Dependent Variable: A measureable output quantity of your experiment which is a function of the input variables and parameters E. G. reaction time, force, energy consumed temperature

2 Variables z Independent Variable: A quantity that you will vary and control – E.G.; angle of attack, chamber pressure or temperature, coefficient in algorithm, luminosity, gain, ... z Parameter: A quantity that is set or otherwise determined, which you will not vary but which needs to be recorded – E.G.; atmospheric pressure, constant in algorithm, battery voltage,... z Dependent Variable: A measureable output quantity of your experiment which is a function of the input variables and parameters – E.G.; reaction time, force, energy consumed, temperature

Exercise With your partner, write down your expected variables and parameters o Independent variables ● Parameters ● Dependent variables

3 Exercise z With your partner, write down your expected variables and parameters. z Independent Variables z Parameters z Dependent variables

Test matrices A graphical display of your experimental independent variables to help Covey the scope of your experiment to your audience Plan and execute your experiment e Each cell represents a data point for your experiment for which you will collect values for the dependent variables Propeller RPM TVS O RPM 1000 RPM 2000 RPM 3000 RPM 4000 RPM eeds 0 mph mp KDVs 10 mph 15 mph Courtesy of Cyndi vongvanith and Lester McCoy 4

4 Test Matrices z A graphical display of your experimental independent variables to help: – Covey the scope of your experiment to your audience – Plan and execute your experiment z Each cell represents a “data point” for your experiment for which you will collect values for the dependent variables. 4000 RPM 0 mph 5 mph 10 mph 15 mph 0 RPM 1000 RPM 2000 RPM 3000 RPM Propeller RPM Speed . Courtesy of Cyndi Vongvanith and Lester McCoy IVs DVs

Multi-Variable experiments Factor= Number of independent variables Four-Factor experiment has 4 independent variables Level a given value of an independent variable Numerical -200 300 400 Qualitative- Brand x, brand y, brand z Full-Factorial Experiment All factors at all levels May lead to a huge number of data points Fractional-Factorial Experiment Expert judgement: carefully selected subset Adaptive: decide as you get some data Design of Experiments Taguchi, orthogonal arrays Beyond scope of 16.62X

5 Multi-Variable Experiments – Factor = Number of independent variables • Four-Factor experiment has 4 independent variables – Level = A given value of an independent variable • Numerical – 200, 300, 400 … • Qualitative – Brand x, Brand y, Brand z … – Full-Factorial Experiment • All factors at all levels • May lead to a huge number of data points. – Fractional-Factorial Experiment • Expert judgement: carefully selected subset • Adaptive: decide as you get some data • Design of Experiments: Taguchi, orthogonal arrays – Beyond scope of 16.62X

Presentation of test matrices: full factorial Test matrix used for graphical representation of test plan Define.A=nth level of factor A IV DVI DV2 DV3 One variable matrix A A,B, A,B 2 AB Two variable matrix A,B1 AB AO A2B n M A,. 2 AAmB mm Three variable matrix A4 B C2 A,B,CI

6 Presentation of Test Matrices: Full Factorial – Test matrix used for graphical representation of test plan • Define: A n = nth level of factor A – One variable matrix – Two variable matrix – Three variable matrix m 1 m 2 m m 2 1 2 2 2 n 1 1 1 2 1 n A B A B A B A B A B A B A B A B A B Λ Μ Μ Ο Μ Λ Λ A1 B1 C1 A4 B3 C 2 IV A1 ... A n DV1 DV2 DV3

Presentation of test matrices: full factorial N-variable matrix Creativity needed Stamina will probably also be required For A, B D,E,FI For A2 By DEF 312 D,E,F 7

7 – N- variable matrix • Creativity needed • Stamina will probably also be required! D1 E1 F1 D4 E3 F2 D1 E1 F1 D4 E3 F2 For A1 B1: For A2 B7: Presentation of Test Matrices: Full Factorial

Expert Judgement Approach Eliminate some combinations of independent variables to reduce the total number of data points Often required to make experiment feasible within time and budget constraints Strategies for elimination · Insight from previous theory or experiments Wisdom from advisor or other subject matter expert Logical thought about interrelationship of variables on the physics of the problem

8 Expert Judgement Approach – Eliminate some combinations of independent variables to reduce the total number of data points – Often required to make experiment feasible within time and budget constraints – Strategies for elimination • Insight from previous theory or experiments • Wisdom from advisor or other subject matter expert • Logical thought about interrelationship of variables on the physics of the problem

Adaptive approach Preliminary runs Production runs Use theory to bracket range Data range and spacing 2 or 3 test cases to check set-up May not be uniform Compare with theory Cluster samples in interesting S Ru un Ri un

9 Adaptive Approach – Preliminary Runs • Use theory to bracket range • 2 or 3 test cases to check set-up • Compare with theory – Production Runs • Data range and spacing • May not be uniform – Cluster samples in “interesting areas” Run Data Run Data

Additional considerations o Repeatability: Is there reason to believe that the measurement accuracy will be increased if multiple runs are made with the same independent variables and parameters? o Hysteresis: Is there reason to believe the physical effect being studied may depend upon the sequence or rate in which you vary the independent variable o Learning: Is the reason to believe your human subjects or intelligent software will become more capable during the experiment through learning? Fatigue: Will your subjects become less capable during the test due to tiring? Refer to backup slides for more information

10 Additional Considerations z Repeatability: Is there reason to believe that the measurement accuracy will be increased if multiple “runs” are made with the same independent variables and parameters? z Hysteresis: Is there reason to believe the physical effect being studied may depend upon the sequence or rate in which you vary the independent variable? z Learning: Is the reason to believe your human subjects or intelligent software will become more capable during the experiment through learning? z Fatigue: Will your subjects become less capable during the test due to tiring? Refer to backup slides for more information