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Aim: Optimization modelling of 4-cycle DI pulse rated engine. Objective: Explore Example- Diesel_4cyl_DIpulse_injratemap and write a detailed report Parameters-SOI, Rail Pressure Response- NO and bsfc minimum Run all designs for a case and find the optimum values Comment on your observations Theory: In a genetic…
Soudip Hazra
updated on 06 Mar 2021
Aim:
Optimization modelling of 4-cycle DI pulse rated engine.
Objective:
Explore Example- Diesel_4cyl_DIpulse_injratemap and write a detailed report
Theory:
In a genetic algorithm, a population of candidate solutions (called individuals, creatures, or phenotypes) to an optimization problem is evolved toward better solutions. Each candidate solution has a set of properties (its chromosomes or genotype) which can be mutated and altered; traditionally, solutions are represented in binary as strings of 0s and 1s, but other encodings are also possible.
The evolution usually starts from a population of randomly generated individuals, and is an iterative process, with the population in each iteration called a generation. In each generation, the fitness of every individual in the population is evaluated; the fitness is usually the value of the objective function in the optimization problem being solved. The more fit individuals are stochastically selected from the current population, and each individual's genome is modified (recombined and possibly randomly mutated) to form a new generation. The new generation of candidate solutions is then used in the next iteration of the algorithm. Commonly, the algorithm terminates when either a maximum number of generations has been produced, or a satisfactory fitness level has been reached for the population.
A typical genetic algorithm requires:
a genetic representation of the solution domain,
a fitness function to evaluate the solution domain.
A standard representation of each candidate solution is as an array of bits. Arrays of other types and structures can be used in essentially the same way. The main property that makes these genetic representations convenient is that their parts are easily aligned due to their fixed size, which facilitates simple crossover operations. Variable length representations may also be used, but crossover implementation is more complex in this case. Tree-like representations are explored in genetic programming and graph-form representations are explored in evolutionary programming; a mix of both linear chromosomes and trees is explored in gene expression programming.
Once the genetic representation and the fitness function are defined, a GA proceeds to initialize a population of solutions and then to improve it through repetitive application of the mutation, crossover, inversion and selection operators.
Simulation model:
Boundary conditions:
Case setup as a function of rail pressure and start of ignition angle
Injection timing
Design optimization:
Algorithm: Genetic algorithm
Multi objective pareto design
Factors: SOI and rail pressure
Response: BSFC and NOx ppm
GT POST
Effect of BSFC on rail pressure
We observe here that a single optimal point for lower bsfc is not available in case of rail pressure due to the presence of other important factors. Optimal point for bsfc can be selected by selecting suitable operating point.
Effect of BSFC on SOI
From the plot we observe that delay in start of injection results in increase in bsfc. Therefore early SOI is needed for maintaining lower bsfc.
Effect of NOx on rail pressure
We observe here that a single optimal point for lower nox is not available in case of rail pressure due to the presence of other important factors. Optimal point for nox can be selected by selecting suitable operating point
Effect of NOx on SOI
From the plot we see that earlier the fuel is injected more is the nox produced. So start of injection should be delayed to reduce the inline cylinder pressure thereby reducing nox level.
Pareto design plot
From the plot we observe that if we aim for minimum bsfc, higher nox is seen. Similarly for lower nox high bsfc will be seen. So these outputs are inversely proportional to each other. Some compromise is necessary and the best selection is done based on the necessity of consumer of product.
Pareto design cases
Sensitivity analysis for BSFC
Sensitivity analysis for Nox ppm
From the plot we can observe that bot SOI and rail pressure have almost equal sensitivity on bsfc and nox emission. But SOI has higher sensitivity for nox than compared to bsfc. And rail pressure has high sensitivity for bsfc than nox. Comparing the relative sensitivity of SOI and rail pressure SOI has 0.75 and rail pressure has 0.25. therefore SOI is more sensitive than rail pressure in case of minimizing nox and bsfc.
BSFC contour plot
Nox contour plot
Multi objective Pareto design table
Conclusions:
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