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Regression

Regression. *************************************************************************** Y = Y0 + sum(Bi*deltaXi) + sum(Ci*deltaXi*deltaXi) Y -- output variable Y0 -- constant regression coefficient Bi -- linear regression coefficient for ith input

barbara-acevedo
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Regression

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  1. Regression *************************************************************************** Y = Y0 + sum(Bi*deltaXi) + sum(Ci*deltaXi*deltaXi) Y -- output variable Y0 -- constant regression coefficient Bi -- linear regression coefficient for ith input Ci -- quadratic regression coefficient for ith input delatXi = (Xi - mean(Xi))/ Dev(Xi) Di = (Bi * Mean(i) / Dev(i)) / 100 Di -- the ouput variable will change by D units if the ith input changes by 1% Mean(i) -- Sample mean value of ith input variable Dev(i) -- Sample deviation value of ith input variable Ei = Bi*Bi / (sum(Bi*Bi)) Ei -- Percentage of the total variance this input i contributes ***************************************************************************

  2. Regression TOBI ID Seal = RSFL4011 Sample Mean = 0.375581 Sample Deviation = 0.0137519 Y0 (constant regression coefficient) = 0.375538 R Squared (ideal value = 1) = 0.999681 Parameter Sample_Mean Sample_Dev ABS(Bi) Ci Di Ei CLEA4011 0.0080 0.0004 0.0117 -0.0001 0.0026 73.1132 MXRI4011 6.0000 0.1056 0.0053 -0.0000 0.0030 15.0546 RSRF4014 0.7000 0.0308 0.0033 0.0001 0.0007 5.7203 RSAR4061 0.5986 0.0105 0.0032 0.0000 -0.0018 5.6043 RSRF4028 1.2300 0.0541 0.0006 0.0000 0.0001 0.1737 RSRF4012 0.5000 0.0220 0.0005 0.0000 0.0001 0.1274 RSAR4010 1.0000 0.0132 0.0003 0.0000 -0.0002 0.0389 RSAR4036 1.0000 0.0440 0.0003 -0.0000 0.0001 0.0355 RSAR4034 1.0000 0.0440 0.0002 -0.0000 0.0001 0.0326 CLEA4015 0.0120 0.0016 0.0002 -0.0000 0.0000 0.0290 RSAR4035 1.0000 0.0440 0.0002 -0.0000 0.0000 0.0228 RSAR7002 0.0040 0.0002 0.0002 -0.0000 0.0000 0.0145 RSAR7001 0.0040 0.0002 0.0002 0.0000 0.0000 0.0139 RSAR7000 0.0040 0.0002 0.0002 0.0000 0.0000 0.0134 RSAR4049 0.2006 0.0088 0.0001 -0.0000 0.0000 0.0022 MXRI4015 7.5600 0.1330 0.0000 0.0000 0.0000 0.0010 RSAR4027 9.2040 0.1619 0.0000 -0.0000 0.0000 0.0005 RSAR4002 0.0018 0.0000 0.0000 0.0000 -0.0000 0.0004 RSAR4030 0.0815 0.0036 0.0000 0.0000 0.0000 0.0002 RSRF4000 0.3250 0.0143 0.0000 -0.0000 0.0000 0.0002 RSAR8591 5.8900 0.1036 0.0000 0.0000 0.0000 0.0002 RSRF4016 0.5000 0.0220 0.0000 0.0000 0.0000 0.0002 RSAR4017 0.0030 0.0001 0.0000 0.0000 -0.0000 0.0002 RSAR4076 6.7210 1.4782 0.0000 -0.0000 0.0000 0.0001 RSAR4081 0.0001 0.0000 0.0000 -0.0000 0.0000 0.0001

  3. Regression TOBI Discharge Pressure 29 Output Parameter = PRES4004 Sample Mean = 203.7838 Sample Deviation = 2.9065 Y0 (constant regression coefficient) = 203.7555 R Squared (ideal value = 1) = 0.9989 Parameter Sample_Mean Sample_Dev ABS(Bi) Ci Di Ei RSRF4028 1.2300 0.0541 2.0775 -0.0431 -0.4723 51.0759 RSAR4010 1.0000 0.0132 0.9900 0.0046 0.7502 11.5973 RSAR4036 1.0000 0.0440 0.9607 0.0120 -0.2184 10.9230 RSAR4034 1.0000 0.0440 0.8748 0.0183 -0.1989 9.0552 CLEA4015 0.0120 0.0016 0.8715 0.0219 -0.0660 8.9880 RSAR4035 1.0000 0.0440 0.7583 0.0099 -0.1724 6.8054 RSAR4049 0.2006 0.0088 0.2193 0.0021 -0.0499 0.5693 MXRI4015 7.5600 0.1330 0.1738 -0.0007 -0.0988 0.3573 RSRF4014 0.7000 0.0308 0.1378 -0.0039 -0.0313 0.2248 RSAR4027 9.2040 0.1619 0.1149 0.0057 -0.0653 0.1561 RSAR4030 0.0815 0.0036 0.1064 -0.0011 -0.0242 0.1339 RSRF4018 0.5000 0.0220 0.0538 -0.0025 -0.0122 0.0343 RSAR4069 0.0267 0.0012 0.0324 0.0006 -0.0074 0.0124 RSRF4032 1.0000 0.0440 0.0279 0.0006 -0.0063 0.0092 RSRF4019 0.4800 0.0211 0.0264 0.0015 -0.0060 0.0082 PPERF5 388.4330 0.3417 0.0255 0.0004 0.2894 0.0077 RSAR4061 0.5986 0.0105 0.0232 0.0028 0.0132 0.0064 RSRF4029 1.0000 0.0440 0.0215 -0.0009 -0.0049 0.0055 CLEA4011 0.0080 0.0004 0.0191 0.0008 0.0043 0.0043 RSRF4020 0.4800 0.0211 0.0190 -0.0005 -0.0043 0.0043 RSRF4050 1.0000 0.0440 0.0177 0.0016 -0.0040 0.0037 RSRF4016 0.5000 0.0220 0.0149 0.0017 -0.0034 0.0026 PPERF6 97.2510 0.0856 0.0147 0.0002 0.1673 0.0026 RSAR4022 1.0000 0.0176 0.0137 -0.0015 -0.0078 0.0022 MXRI4011 6.0000 0.1056 0.0123 -0.0026 0.0070 0.0018

  4. Regression TOBI Discharge Temp 30 Output Parameter = CTMP4004 Sample Mean = 953.3461 Sample Deviation = 0.3713 Y0 (constant regression coefficient) = 953.3333 R Squared (ideal value = 1) = 0.9943 Parameter Sample_Mean Sample_Dev ABS(Bi) Ci Di Ei CLEA4015 0.0120 0.0016 0.1968 0.0019 -0.0149 29.6447 RSRF4028 1.2300 0.0541 0.1858 0.0062 0.0422 26.4037 RSAR4010 1.0000 0.0132 0.1452 0.0016 -0.1100 16.1325 RSRF4014 0.7000 0.0308 0.1061 0.0026 -0.0241 8.6185 RSAR4036 1.0000 0.0440 0.0859 -0.0009 0.0195 5.6452 RSAR4034 1.0000 0.0440 0.0776 -0.0010 0.0176 4.6102 RSAR4035 1.0000 0.0440 0.0677 -0.0008 0.0154 3.5029 CLEA4011 0.0080 0.0004 0.0621 0.0001 0.0141 2.9462 MXRI4015 7.5600 0.1330 0.0391 0.0001 -0.0222 1.1686 MXRI4011 6.0000 0.1056 0.0285 -0.0001 0.0162 0.6215 RSAR4049 0.2006 0.0088 0.0198 -0.0002 0.0045 0.2993 RSRF4018 0.5000 0.0220 0.0122 -0.0008 -0.0028 0.1144 RSAR4027 9.2040 0.1619 0.0099 -0.0005 0.0056 0.0753 RSAR4030 0.0815 0.0036 0.0093 0.0013 0.0021 0.0663 RSAR4002 0.0018 0.0000 0.0070 0.0002 0.0040 0.0374 RSRF4000 0.3250 0.0143 0.0055 0.0000 -0.0013 0.0234 PPERF5 388.4330 0.3417 0.0035 -0.0001 0.0393 0.0092 RSAR7584 0.1533 0.0027 0.0033 -0.0000 -0.0019 0.0084 RSRF4019 0.4800 0.0211 0.0033 -0.0001 -0.0007 0.0082 RSRF4016 0.5000 0.0220 0.0032 0.0002 -0.0007 0.0080 RSAR4061 0.5986 0.0105 0.0032 -0.0005 -0.0018 0.0079 RSRF4032 1.0000 0.0440 0.0031 -0.0007 0.0007 0.0071 RSRF4020 0.4800 0.0211 0.0029 -0.0002 -0.0007 0.0064 RSAR4069 0.0267 0.0012 0.0029 -0.0001 0.0007 0.0063 RSRF4012 0.5000 0.0220 0.0028 -0.0007 0.0006 0.0061

  5. Regression 1Blade TE Rim Cavity Temperature 34 Output Parameter = CTMP4013 Sample Mean = 1002.3014 Sample Deviation = 2.5490 Y0 (constant regression coefficient) = 1002.1736 R Squared (ideal value = 1) = 0.9421 Parameter Sample_Mean Sample_Dev ABS(Bi) Ci Di Ei CLEA4015 0.0120 0.0016 1.7293 -0.0647 0.1310 49.6090 RSAR4049 0.2006 0.0088 0.8851 0.0123 -0.2012 12.9962 RSRF4028 1.2300 0.0541 0.8343 -0.0550 -0.1897 11.5459 RSRF4051 1.0000 0.0440 0.5376 0.0387 0.1222 4.7936 RSAR4045 0.1230 0.0271 0.4754 0.0413 0.0216 3.7489 RSRF4050 1.0000 0.0440 0.4656 0.0134 0.1058 3.5956 RSAR4013 0.0841 0.0185 0.4625 0.0274 0.0210 3.5478 RSRF4032 1.0000 0.0440 0.4038 0.0305 0.0918 2.7043 RSAR4044 0.0690 0.0152 0.3648 0.0009 0.0166 2.2075 MXRI4015 7.5600 0.1330 0.3394 -0.0112 0.1929 1.9111 RSAR4030 0.0815 0.0036 0.2975 0.0069 -0.0676 1.4679 RSRF4014 0.7000 0.0308 0.1691 0.0083 0.0384 0.4743 RSAR4036 1.0000 0.0440 0.1037 -0.0007 0.0236 0.1784 RSRF4018 0.5000 0.0220 0.1022 0.0047 0.0232 0.1732 RSAR4034 1.0000 0.0440 0.0945 0.0059 0.0215 0.1482 RSAR4035 1.0000 0.0440 0.0809 0.0093 0.0184 0.1085 RSRF4029 1.0000 0.0440 0.0804 -0.0025 -0.0183 0.1071 RSAR4082 0.0631 0.0139 0.0713 0.0262 0.0032 0.0843 RSAR4043 0.0120 0.0026 0.0618 -0.0121 0.0028 0.0633 RSAR4063 0.0094 0.0021 0.0565 -0.0030 0.0026 0.0529 RSAR4042 0.0360 0.0079 0.0530 0.0194 0.0024 0.0467 RSAR4010 1.0000 0.0132 0.0502 0.0089 -0.0380 0.0417 RSAR4040 0.0302 0.0067 0.0458 0.0043 0.0021 0.0349 RSRF4000 0.3250 0.0143 0.0457 0.0108 -0.0104 0.0346 RSAR4002 0.0018 0.0000 0.0418 -0.0079 0.0238 0.0290

  6. Regression 33 Output Parameter = PRES4013 Sample Mean = 81.1058 Sample Deviation = 0.1531 Y0 (constant regression coefficient) = 81.0750 R Squared (ideal value = 1) = 0.9593 Parameter Sample_Mean Sample_Dev ABS(Bi) Ci Di Ei RSAR4076 6.7210 1.4782 0.1009 0.0344 -0.0046 47.8331 PPERF6 97.2510 0.0856 0.0878 -0.0003 0.9978 36.2294 RSAR4045 0.1230 0.0271 0.0370 0.0009 0.0017 6.4512 RSAR4013 0.0841 0.0185 0.0338 0.0012 0.0015 5.3621 RSAR4044 0.0690 0.0152 0.0219 0.0000 0.0010 2.2629 PPERF5 388.4330 0.3417 0.0181 -0.0007 -0.2053 1.5328 RSAR4063 0.0094 0.0021 0.0042 0.0000 0.0002 0.0811 RSAR4043 0.0120 0.0026 0.0033 -0.0003 0.0001 0.0503 RSAR4062 0.0075 0.0016 0.0031 0.0001 0.0001 0.0460 RSRF4028 1.2300 0.0541 0.0028 0.0000 -0.0006 0.0371 RSAR4034 1.0000 0.0440 0.0018 -0.0008 -0.0004 0.0154 RSAR4047 0.4200 0.0924 0.0013 -0.0009 0.0001 0.0084 CLEA4015 0.0120 0.0016 0.0013 -0.0003 -0.0001 0.0077 RSAR4082 0.0631 0.0139 0.0012 -0.0001 -0.0001 0.0066 RSAR4058 0.0021 0.0005 0.0011 0.0005 0.0001 0.0062 RSAR7000 0.0040 0.0002 0.0010 0.0001 0.0002 0.0051 RSAR4038 0.0631 0.0139 0.0010 -0.0002 -0.0000 0.0048 RSAR4010 1.0000 0.0132 0.0010 0.0004 0.0008 0.0048 RSAR4036 1.0000 0.0440 0.0010 0.0002 -0.0002 0.0044 RSAR4060 0.0300 0.0066 0.0010 0.0001 0.0000 0.0043 RSAR4002 0.0018 0.0000 0.0009 0.0001 -0.0005 0.0041 RSAR4081 0.0001 0.0000 0.0009 0.0001 -0.0002 0.0036 RSAR4053 0.0920 0.0040 0.0008 -0.0002 -0.0002 0.0032 RSAR4059 10.7250 2.3588 0.0008 -0.0008 0.0000 0.0031 RSRF4001 0.1200 0.0053 0.0008 -0.0008 -0.0002 0.0029

  7. %Total Variance

  8. Probability Density Function (PDF) serves to represent a probability distribution in terms of integrals. A probability density function can be seen as a 'smoothed out' version of a histogram.

  9. Cumulative Distribution Density (CDF) is defined by cdf (y) = Probability (x < y) = integral from -infinity to y over pdf (x) 90% of pressures will be less than this value 10% of pressures will be less than this value

  10. Cumulative Distribution Density (CDF) is defined by cdf (y) = Probability (x < y) = integral from -infinity to y over pdf (x) 90% of pressures will be less than this value 10% of pressures will be less than this value

  11. Cumulative Distribution Density (CDF) is defined by cdf (y) = Probability (x < y) = integral from -infinity to y over pdf (x) 90% of pressures will be less than this value 10% of pressures will be less than this value

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