Parametric Optimization of System Modes for Nozzle Turbine Vane by Means of Costimulated Artificial Immune System
Abstract
:Featured Application
Abstract
1. Introduction
2. Materials and Methods
2.1. Formulation of the Optimization Function
- n—number of design variables (geometrical parameters);
- xi—ith design variable from design domain ,
- —optimization function;
- X—design variable vector.
- —model area;
- —set of geometrical design variables;
- —penalty function defined according to constraint .
2.2. Artificial Immune System with Costimulation Effect
- t—iteration index (population);
- j—number of B-cells;
- N—number of B-cells in the population;
- —j-th B-cell in population t,
- n—number of paratopes in the B-lymphocyte;
- —i-th paratope in the j-th B-lymphocyte.
- —number of clones of j-th B-cell;
- —number of clones defined as algorithm parameter;
- —lymphocyte rank basing on the fitness function result: ;
- —number of B-cells defined as algorithm parameter.
- —mutation coefficient for j-th B-lymphocyte;
- —mutation coefficient.
- RND(−1,1)—random number from −1 to 1 with uniform probability;
- —lower range for design parameter ;
- —upper range for design parameter .
- r—distance between lymphocytes (memory cells).
2.3. FEM Model Description and Optimization Framework
3. Results
4. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameter | Value |
---|---|
Frequency of T-cell refresh, fitness function evaluations | 20 |
T-cell margin for criterion O1 | 5% |
Parameter | Value |
---|---|
Memory cells | 3 |
Clone number | 6 |
Termination criteria—number of iterations | 10 |
Mutation probability | 0.75 |
Parameter | Lower Bound, in | Upper Bound, in |
---|---|---|
Casing shell A | 0.080 | 0.120 |
Casing shell B | 0.080 | 0.180 |
Casing shell C | 0.080 | 0.120 |
Forward hook thickness | 0.100 | 0.200 |
Rear hook thickness | 0.090 | 0.120 |
Nozzle shell thickness | 0.060 | 0.120 |
Forward hook position | −0.040 | 0.040 |
Rear hook position | −0.050 | 0.050 |
Parameter | Lower Bound, deg. | Upper Bound, deg. |
---|---|---|
Forward hook leaning | 80 | 100 |
Rear hook leaning | 80 | 100 |
Parameter | Value |
---|---|
Lymphocyte number (memory cells) | 3 |
Clone number | 6 |
Termination criteria, iteration quantity | 40 |
Probability of mutation | 0.75 |
Number of design variables | 10 |
Parameter Name | Genetic Algorithm (GA) | Artificial Immune System (AIS) | Costimulated Artificial Immune System (CAIS) |
---|---|---|---|
Casing shell A [in] | 0.110 | 0.099 | 0.098 |
Casing shell B [in] | 0.165 | 0.142 | 0.150 |
Casing shell C [in] | 0.111 | 0.120 | 0.120 |
Forward hook thickness [in] | 0.183 | 0.200 | 0.200 |
Rear hook thickness [in] | 0.107 | 0.111 | 0.111 |
Forward hook leaning [°] | 92.1 | 100.0 | 96.4 |
Rear hook leaning [°] | 82.3 | 80.0 | 82.8 |
Nozzle shell thickness [in] | 0.083 | 0.063 | 0.061 |
Forward hook position [in] | 0.036 | 0.040 | 0.040 |
Rear hook position [in] | −0.048 | −0.050 | −0.050 |
Genetic Algorithm (GA) | Artificial Immune System (AIS) | Costimulated Artificial Immune System (CAIS) | |
---|---|---|---|
Number of fitness function evaluations | 1374 | 443 | 380 |
Model area, in2 | 19.163 | 19.109 | 19.114 |
Natural frequency | 125.0 | 125.1 | 125.0 |
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Robak, R.; Szczepanik, M.; Rulik, S. Parametric Optimization of System Modes for Nozzle Turbine Vane by Means of Costimulated Artificial Immune System. Appl. Sci. 2024, 14, 3991. https://doi.org/10.3390/app14103991
Robak R, Szczepanik M, Rulik S. Parametric Optimization of System Modes for Nozzle Turbine Vane by Means of Costimulated Artificial Immune System. Applied Sciences. 2024; 14(10):3991. https://doi.org/10.3390/app14103991
Chicago/Turabian StyleRobak, Rafał, Mirosław Szczepanik, and Sebastian Rulik. 2024. "Parametric Optimization of System Modes for Nozzle Turbine Vane by Means of Costimulated Artificial Immune System" Applied Sciences 14, no. 10: 3991. https://doi.org/10.3390/app14103991
APA StyleRobak, R., Szczepanik, M., & Rulik, S. (2024). Parametric Optimization of System Modes for Nozzle Turbine Vane by Means of Costimulated Artificial Immune System. Applied Sciences, 14(10), 3991. https://doi.org/10.3390/app14103991