Comparative Study Setup Mathematical methods and models1

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8.2.1 “Heavy-Duty” Diesel

The results of the ANN training and verification are given in Figure 8.3, in a fashion similar to that used for the ROHR model results given in Chapter 4. Evident from an engineering point of view is the excellent agreement of measured and simulated ϕ SOC , ϕ 10 , ϕ 50 , and ϕ 90 characteristics for the training operating conditions c.f. Figure 8.5 a. However, for approximately half of the verification operating condi- tions no correlation between the measured and simulated values is noted. From the correlation coefficients r given in Table 8.2, both the excellent agree- ment for ANN training r 0.95 and the weak correlation for ANN verification r 0.5 are confirmed. Although the correlation coefficients are smaller than 0.5 for the ANN verification, the fact that the measured and simulated results do agree for 10 out of the 20 verification operating conditions results in correlation coefficients significantly higher than 0 1 . As an example of verification operating conditions with both good and poor agreement, the ROHR characteristics and operating condition data for four condi- tions - two training and two verification conditions - are given in Figure 8.4 and Table 8.1, respectively. The four operating conditions have identical engine speeds and brake mean effective pressures, as well as similar injection pressures p Inj = 350 or 400 [bar] and SOIs SOI = 350, 356 or 357 [°CA aTDC]. Whereas almost no dis- crepancy is noted between the measured and simulated characteristics for operating conditions 4, 16, and 20, ROHR characteristics for operating condition 35 determined from ANN simulations are delayed by approximately 40 °CA. Although the effects of an advanced SOI timing are correctly reproduced for 4 SOI = 350 [°CA aTDC], the one degree change in SOI from 357 to 356 [°CA aTDC] between 20 and 35 causes the neural network to fail. a b Fig. 8.3 Heavy-Duty Diesel ROHR ANN Training Verification: a Sequential Operating Conditions Plot, b “1-to-1” Scatter Plot 1. r = 0 : no linear correlation between two variables. The two variables are considered to be statisti- cally independent. C ra n k A n g le ϕ [° C A a T D C ] 300 320 340 360 380 400 420 440 460 Heavy-Duty Operating Conditions [-] 5 10 15 20 25 30 35 40 Verificat ion Training ϕ SOC Sim Meas ϕ 10 Sim Meas ϕ 50 Sim Meas ϕ 90 Sim Meas ϕ S im u la ti o n [° C A a T D C ] 300 320 340 360 380 400 420 440 460 ϕ Measurment [° CA aTDC] 300 320 340 360 380 400 420 440 460 Training Verificat ion St art of Combustion 10 Energy Release 50 Energy Release 90 Energy Release