7.5 Neural Network based Fuel Optimization
7.5.5 Adaption for Output Consistency
The numerical optimization of the fuel consumption has a significant influence on the perfor- mance of the dynamic map which is identified based on the inverse optimal data. In order to achieve a well optimized and reliable result, first of all sufficient iterations in the numerical optimization should be conducted in order to guarantee that a satisfactory causal optimal behaviour of the system can be found. Secondly the identifiability of the obtained engine control optimal inputs should be considered to ensure that the causal system behaviour can be represented by an inverse identified dynamic model. Moreover since the constrained fuel optimization is based on engine models, it is crucial to apply the obtained optimal signals to the real system and evaluate the consistency of the resulting system outputs to the simulated outputs. Figure 7.14 displays the profiles of the optimal outputs collected from the NN mod- els and the virtual engine, where the fitness of the RT output to the demanded constraints is:
R2T opt= 79.96% R2λopt=−222.86% (7.16)
Since the segment method is selected, the NN outputs have spikes at the connecting points but meet the constraints closely at other points. However in the RT outputs the spikes are filtered but large errors exist at points across the whole output sequence. Comparing to the validation results in Section 7.4.4, the fitness of the optimal RT output is remarkably small.
CHAPTER 7. DYNAMIC CALIBRATION AND CONTROLLER DESIGN 153 This indicates that the identified NN models could represent the system dynamics accurately if tested with inputs that are similar to the identification signals however the models may not be qualified to simulate the system behavior accurately if tested with the optimal inputs. In the time domain the optimal inputs change much more quickly and drastically than the signal used for identification as shown in Figure 7.12.
0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 20 40 60 80 100 120 Time(0.03s) torque constraint RT output 1st iteration RT output 2nd iteration 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 0.5 1 1.5 2 2.5 3 Time(0.03s) λ constraint RT output 1st iteration RT output 2nd iteration
Figure 7.15: Optimal outputs on RT model by iterations
To improve the output consistency two approaches can be employed. The first approach is to reidentify the engine models using the obtained optimal inputs and then to repeat the fuel optimization with the revised models. It is well known a model can easily represent the system behaviour accurately in the validation if the validation signals have similar properties to the identification signals in the time domain and frequency domain.
Assuming the identification signals are chosen as the initial data signals used in the optimization, the resulting optimal inputs which are considered as validation signals must necessarily be different from the initial signals since the inputs must be adjusted to optimize the fuel consumption. However the difference between the signals can be reduced asymp- totically by running the identification and optimization iteratively. Figure 7.15 and Table 7.6 illustrate an example of the effect of this approach. In the first iteration there is a large discrepancy between the resulting RT output and the desired constraint while this distinction is significantly reduced in the second iteration and the output fitness is enhanced correspond-
CHAPTER 7. DYNAMIC CALIBRATION AND CONTROLLER DESIGN 154 ingly. As no additional constraint is added to the optimization, the search region in each iteration is not further limited. Theoretically the true optimal value is always achievable pro- viding sufficient iterations are conducted in the identification and optimization. Nevertheless the major disadvantage here is the large amount of experimental time required to repeat this comprehensive procedure.
Table 7.6: The fitness of RT output to desired constraints in iterations
1st iteration 2nd iteration R2T 79.96% 88.16% R2λ -222.86% -79.88% 0 200 400 600 800 1000 1200 1400 1600 1800 2000 5 10 15 20 25 30 Time(0.03s) SA( ° )
Optimal SA without rate constraint Optimal SA with rate constraint
Figure 7.16: Optimal SA obtained with/without rate constraint
Table 7.7: The fitness of RT output to desired constraints with/without rate constraint
No rate constraint With rate constraint
R2T 79.96% 94.66%
R2λ -222.86% 28.43%
Besides processing the model identification and the fuel optimization iteratively, ad- ditional constraints can be applied to the optimization with the purpose of improving the output consistency. The major difference between the identification signal and the optimal signal is the time interval and the rate of change. To compensate for the dissimilarity, a constraint on the rate of input change would be effective however it should be implemented on the inputs selectively since additional constraints may compromise the optimization re-
sult and computational time. In the dynamic calibration procedure, the INJ and θ values
CHAPTER 7. DYNAMIC CALIBRATION AND CONTROLLER DESIGN 155 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 20 40 60 80 100 120 Time(0.03s) torque constraint
RT output wihtout rate constraint RT output with rate constraint
0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 0.5 1 1.5 2 2.5 3 Time(0.03s) λ constraint
RT output without rate constraint RT output with rate constraint
Figure 7.17: Optimal outputs on RT model with/without rate constraints
controllers. On the other hand the SA is only controlled by the feedforward compensator consequently a SA map with good accuracy is crucial for the fuel economy. A rate constraint
∆u=u(t)−u(t−1) = 1 was applied to SA and the optimal signal obtained with and without
the rate constraint is shown in Figure 7.16. The corresponding outputs on the RT model are illustrated in Figure 7.17 and the validation result is given in Table 7.7, proving that the rate constraint has a significant effect on the consistency of the output.