+1-415-670-9189

info@expertsmind.com

# Application Of Particle Swarm Optimisation Algorithm In Reliability Optimisation Problem Assignment Help

###
Nature Inspired Optimisation Tools - Application Of Particle Swarm Optimisation Algorithm In Reliability Optimisation Problem
**Application Of Particle Swarm Optimisation Algorithm In Reliability Optimisation Problem**

A gas turbine system has been studied in such section to relevant information pertaining for the functional performance of the system with its system dependability or reliability is explained also. The most normally witnessed gas turbine system is as given:

Seem the over speed protection system for a gas turbine as represented in following diagram. The over speed detection system is similar as it is depicted in diagram, in most of the gas turbines. Whereas operating it, whenever an over speed happens it is essential to cut off the fuel supply. For this cause, five control valves (V1-V5) should be closed from security point of view. Thus, control system can then be modeled like five stage series system. The objective is to find the number of redundant components at all stages i, weight, subjected to design constraints on the cost and the product of volume and weight. The objective function for this specific system is as given:

** Figure: The Over-speed Protection System of a Gas Turbine**

Here,

c_{i} = Cost of all components in subsystem i,

i = Index for sub-systems, i = 1 . . . s,

p_{i} = weight-volume of all components in subsystem i,

w_{i} = Weight of all components in subsystem i,

c_{i} = Cost of all components in subsystem i,

R_{i} = Reliability of all components in subsystem i,

P_{max} = Maximum weight-volume of system,

P_{min} = Minimum weight-volume of system,

W_{max} = Maximum weight of system,

W_{min} = Minimum weight of system, and

Δw, Δp and Δc = Magnitude of cost, weight and weight-volume constraint violation

The factors exp(x_{i}/4) xi in Eqs. 24 and 25 accounts for the interconnecting hardware.

The innovative problem was presented by Tillman. The problem's objective function has been appropriately modified to combine multiple objectives related with the components. Moreover, a self adaptive penalty function is embedded also in function of objective consequently best solution is searched effectively and efficiently by the penalizing in-feasible solutions. For the five stage sequence gas turbine system the input data is describe in Table no.4.

To implement the customized Particle Swarm Optimization algorithm in aforementioned reliability optimization problem and a solution string, represented in diagram, has been constructed here, x_{i,j} = Number of redundant component j utilized in subsystem i.

*x**1*

*x**2*

*x**3*

*....*

*....*

*x**i*

*....*

*x**s*

** Figure: showing of a Solution String that is employed in the modified Particle Swarm Optimization Algorithm**

** Table no.4: Input Data for Gas Turbine System**

*j*

*R**ij*

*p**ij*

*P*

*c**ij*

*C*

*w**ij*

*W*

1

0.80

0.85

0.90

0.65

0.75

1

2

3

4

2

110

7

7

5

9

4

175

7

8

8

6

9

200

2

3

4

5

In order to implement the Particle Swarm Optimization algorithm in the aforementioned Gas turbine system illustrated pseudo-code described in Programme no.4.

**Start**

initialize the population

while (iter < max_iter)// whereas termination criterion is not reached

do

for (i = 1 to number of particles)

evaluate J_{obj_function} //compute the objective function for all particles

Update p_{id} and p_{gd} // update the global best and self best position

for (j=1 to number of dimensions)

Calculate new velocity according to eq15 without previous velocity term

**// compute velocity of particle using chaotic random generators.**

if (v_{ij} = 0)

if (crand3(.)<0.5)

v_{ij} = crand4(.)*v //velocity is reinitialized

else

v_{ij} = - crand5(.)*v //velocity is reinitialized

endif

endif

v_{ij} = sign(v_{ij})*min (abs(v_{ij} , v_{max}))//if velocity goes above v_{max}

//then it is allocated the velocity equal to v_{max}

update the particle's position X_{ij}

increase j

increase i

**//calculate Time Varying Acceleration Coefficients for next**

** **

** //generation **

Update the parameters ?_{1} and ?_{2} as per eqn(21) and (22)

iter=iter+1;

enddo

end

**Programme no.4: Pseudo Code for the Particle Swarm Optimization Applied to the Reliability Optimization Problem or ROP.**

Expertsmind’s world class education services

We at www.expertsmind.com offer email based assignment help – homework help and projects assistance from k-12 academic level to college and university level and management and engineering studies. Our experts are helping students in their studies and they offer instant tutoring assistance giving their best practiced knowledge and spreading their world class education services through e-Learning program.

- Quality assignment help assistance 24x7 hrs

- Best qualified tutor’s network

- Time on delivery

- Quality assurance before delivery

- 100% originality and fresh work

**Application Of Particle Swarm Optimisation Algorithm In Reliability Optimisation Problem**

**Figure: The Over-speed Protection System of a Gas Turbine**_{i}= Cost of all components in subsystem i,

_{i}= weight-volume of all components in subsystem i,

_{i}= Weight of all components in subsystem i,

_{i}= Cost of all components in subsystem i,

_{i}= Reliability of all components in subsystem i,

_{max}= Maximum weight-volume of system,

_{min}= Minimum weight-volume of system,

_{max}= Maximum weight of system,

_{min}= Minimum weight of system, and

_{i}/4) xi in Eqs. 24 and 25 accounts for the interconnecting hardware.

_{i,j}= Number of redundant component j utilized in subsystem i.

*x**1*

*x**2*

*x**3*

*....*

*....*

*x**i*

*....*

*x**s*

**Figure: showing of a Solution String that is employed in the modified Particle Swarm Optimization Algorithm**

**Table no.4: Input Data for Gas Turbine System***j*

*R**ij*

*p**ij*

*P*

*c**ij*

*C*

*w**ij*

*W*

1

0.80

0.85

0.90

0.65

0.75

1

2

3

4

2

110

7

7

5

9

4

175

7

8

8

6

9

200

2

3

4

5

**Start**

_{obj_function}//compute the objective function for all particles

_{id}and p

_{gd}// update the global best and self best position

**// compute velocity of particle using chaotic random generators.**

_{ij}= 0)

_{ij}= crand4(.)*v //velocity is reinitialized

_{ij}= - crand5(.)*v //velocity is reinitialized

_{ij}= sign(v

_{ij})*min (abs(v

_{ij}, v

_{max}))//if velocity goes above v

_{max}

_{max}

_{ij}

**//calculate Time Varying Acceleration Coefficients for next**

**//generation**

_{1}and ?

_{2}as per eqn(21) and (22)

**Programme no.4: Pseudo Code for the Particle Swarm Optimization Applied to the Reliability Optimization Problem or ROP.**