1. S5-1 ADM730, Section 5, September 2005 Copyright  2005 MSC.Software Corporation SECTION 5 RESULTS INTERPRETATION Response = 3 + 7X 1 + X 2 + 4X 1 X 2 + 5X 2 2 -5 <= X 1 <= 5 -5 <= X 2 <= 5

2. S5-2 ADM730, Section 5, September 2005 Copyright  2005 MSC.Software Corporation

3. S5-3 ADM730, Section 5, September 2005 Copyright  2005 MSC.Software Corporation RESULTS INTERPRETATION n This module includes: u Equation Order u Exporting and Importing u The Work Space Column Calculator u Analyzing Results

4. S5-4 ADM730, Section 5, September 2005 Copyright  2005 MSC.Software Corporation EQUATION ORDER n What equation order should be used? ADAMS/Insight lets you model your system as a fit of the responses with respect to the factors. The fits are: u Linear u Interactions u Quadratic u Cubic

5. S5-5 ADM730, Section 5, September 2005 Copyright  2005 MSC.Software Corporation EQUATION ORDER… You can easily visualize Linear, Quadratic, and Cubic least-squares regression fits for 1 factor and 1 response. The following are examples of these fits: Linear Quadratic Cubic

6. S5-6 ADM730, Section 5, September 2005 Copyright  2005 MSC.Software Corporation EQUATION ORDER… The order of fit, corresponding equations, and minimum number of data points (trials) are shown below: Fit Type:Equation:Unknowns: LinearA + BX 1 + CX 2 3 InteractionsA + BX 1 + CX 2 + DX 1 X 2 4 QuadraticA + BX 1 + CX 2 + DX 1 X 2 + EX 1 2 + FX 2 2 6 CubicA + BX 1 + CX 2 + DX 1 X 2 + EX 1 2 + FX 2 2 + GX 1 X 2 2 + HX 2 X 1 2 + IX 1 3 + JX 2 3 10

7. S5-7 ADM730, Section 5, September 2005 Copyright  2005 MSC.Software Corporation EXPORTING AND IMPORTING n Exporting a design space u ADAMS/Insight lets you export a design space to a file as comma- separated values (csv). You can then fill in the response values using another tool, such as a spreadsheet or custom application. u This is typically used for physical DOEs, such as the tuning of a physical prototype at a testing track. This isn’t usually applicable if you’re using ADAMS/Insight solely with the other MSC.ADAMS products. n Importing a work space u After filling in the response values, you can then import a csv file into ADAMS/Insight as a work space. You can perform the fitting on the data that you entered for the responses.

8. S5-8 ADM730, Section 5, September 2005 Copyright  2005 MSC.Software Corporation THE WORK SPACE COLUMN CALCULATOR The Work Space Column Calculator is a built-in tool for manipulating factor or response column data. It is used when you want to scale a factor’s column value, or create a user-defined response value from a simple algebraic expression. It is easy to assign a known response value: Response = 3 + 7X1 + X2 + 4X1X2 + 5X2^2 Or, scale a factor by a constant: Factor_1 = Factor_1 * 2 The expression language is standard Python syntax. Press F1 in the calculator window for more information on: u Python syntax u Examples u Variables available in your expressions

9. S5-9 ADM730, Section 5, September 2005 Copyright  2005 MSC.Software Corporation THE WORK SPACE COLUMN CALCULATOR…

10. S5-10 ADM730, Section 5, September 2005 Copyright  2005 MSC.Software Corporation ANALYZING RESULTS n Graphical indicators u ADAMS/Insight provides graphical indicators that appear next to computed statistics of interest. The indicators are defined as follows: Entity needs investigation Entity isn’t necessarily bad, but could use some consideration Entity is likely appropriate

11. S5-11 ADM730, Section 5, September 2005 Copyright  2005 MSC.Software Corporation ANALYZING RESULTS… n Statistics u ADAMS/Insight compares the assumed solution to the actual data and provides a wealth of statistical information. Refer to the ADAMS/Insight online help for definitions of the terms, including: l The model fit l Term significance l Coefficients l Residual values n Rules-of-thumb-summary u Provides a quick overview of the three main indicators for each response in the model. Indicates important quantities to focus on for each response.

12. S5-12 ADM730, Section 5, September 2005 Copyright  2005 MSC.Software Corporation ANALYZING RESULTS… n Goodness-of-fit u How do the predicted values in the model compare with the actual data? u R-squared and R-squared-adjusted indicate the variance in the predicted results versus the real data. A score of 1 is a perfect fit. u Regression Significance (P) is the probability that the fitted model has no useful terms. Small values of P (less than 0.02) indicate that the fit does have useful terms. u R/V: Range-to-Variance values greater than 10 mean that the fit likely predicts values well. R/V scores less than 4 means that values may not have high confidence.

13. S5-13 ADM730, Section 5, September 2005 Copyright  2005 MSC.Software Corporation ANALYZING RESULTS… n Goodness-of-fit example u One dataset, two regression fits. The statistics back up the visual effect. The linear response fit to the dataset is fine, but ADAMS/Insight flags the R-squared value as suspicious. The quadratic response fit to the dataset is much better, earning very high scores for all indicators. Visually, the fit is much better.

14. S5-14 ADM730, Section 5, September 2005 Copyright  2005 MSC.Software Corporation ANALYZING RESULTS… n Term Significances u Term significances estimate the probability that the term is insignificant in the calculated fit. Very low scores mean that the term is highly significant in the fit. u The example below is the quadratic fit from the previous page. Note that the constant term and factor_01 squared are most significant. Is it possible for a valid fit without including the second (factor_1) term?

15. S5-15 ADM730, Section 5, September 2005 Copyright  2005 MSC.Software Corporation ANALYZING RESULTS… n Studentized Residuals, Cook’s statistics u These quickly show the influence of each run on the fit. They can help identify outlier results that can be removed before the model is re-fit. The first trial appears to affect the fit more than the others, hence the caution indicator.

16. S5-16 ADM730, Section 5, September 2005 Copyright  2005 MSC.Software Corporation ANALYZING RESULTS… n Term coefficients u Summarizes the fitted model characteristics. For each response, it shows the coefficient (multiplier) for each term used in the fit. This means: Response_2 = 3.2567 * 1 – 1.1103*X1 – 1.4707*X2 + 3.1864*X3 + 1.451*X1*X2 + 0.68597*X1*X3 + 1.0783*X2*X3 and, Response_1 = 3*X1 + 4*X2 + 5*X1*X Each row has the term definition (constant, factor, factor*factor, factor squared, and so on) with the coefficient in front of each factor coming from the fit process.