**4. Applications on Rocket Engine engineering**

This section presents two solutions in applying GAs in the aerospace area, both concerning the fuel pumping in liquid propellant rocket engines. There are many choices to be done in the design of a high performance fuel pump, being one of them the type of pump.

Two different types of pumps were modelled: the Harrington pumps and the turbo pumps. Both present a complex design methodology, which includes: tabled functions interpolations, numerical integrals and constructive material choices.

 1 http://physics.nist.gov/PhysRefData/ASD/index.html

<sup>2</sup> http://kurucz.harvard.edu 4 and http://wwwuser.oat.ts.astro.it/castelli/

The Search for Parameters and Solutions:

*Harrington Pumps* (Caetano & Hetem 2011).

understanding of these concerns).

stages on space missions.

and constructive details are explained in next section.

k2. Valves k7 and k8 serve as ventilation for the chambers.

**4.1.1 Pump description and operation** 

controlled by a small processor.

**4.1.2 The model: Pump constructive details** 

Applying Genetic Algorithms on Astronomy and Engineering 171

This subsection is based on the published work *Artificial Intelligence Parametrization of* 

Since the beginning of liquid engine spacecraft history, the choices on pumping were the turbo pumps (Neufeld 1995). However, turbo pumps present many difficulties to design and to achieve their optimum performance. Good and experienced designers can project specialized turbo pumps that can deliver 70-90% efficiency, but figures less than half that are not uncommon. Low efficiency may be acceptable in some applications, but in rocketry this is a severe problem. Common problems include: 1) excessive flow from the high pressure rim back to the low pressure inlet along the gap between the casing of the pump and the rotor; 2) excessive recirculation of the fluid at inlet; 3) excessive vortexing of the fluid as it leaves the casing of the pump; 4) damaging cavitation to impeller blade surfaces in low pressure zones; and 5) critical shaping of the rotor itself is hardly precise (see the many examples and demonstrations presented by Dixon & Hall (2010) for a better

On the other end, the options are the pressurized tanks. In this choice, the fuel and oxidizer reservoir are filled charged with a high pressure gas (helium or nitrogen) that pushes the fluid to the thrust chamber. So, it is easy to see that the tank output fuel pressure drops as the rocket engine consumes its content. As an option, the designer can increase the inside pressure, but this came also with a high cost in material (due to tank thickness) and instability. Actually, pressurized propellant tanks are used on small rockets like the last

As an elegant intermediate solution between these two extremes, Harrington (2003) presented a design fills the gap between the pressure fed and the turbo pumps. This solution also has the advantage of lowering the costs of a rocket project, keeping low weight and without the high complexity of a turbo pump, whose operation, theoretical concerns

The construction consists of two chambers (B1 and B2 on figure 9) and a set of 8 valves. The chambers are connected to the main tank (Mt) through valves k3 and k4. These chambers also deliver propellant to the combustion chamber (CB) through valves k5 and k6. There is a high pressure gas generator (Hp) that is connected to the chambers through valves k1 and

The pumps work alternating two states. In state 1, B1 is being filled by Mt and B2 is feeding the combustion chamber; and in state 2 their role is inverted, say B2 is being filled by Mt and B1 is feeding the combustion chamber. The state change is done by opening and closing the valves, as presented in figure 9 and table 2. The opening and closing of the valves is

Designing a Harrington pump is simple, but the optimization process is not (as expected: a P-problem and a NP-problem respectively). A pump with a small chamber must be filled

**4.1 Using GA to parameterize the design of Harrington pumps** 

Fig. 7. Main screen of the program GASpectrum after five generations. The upper panel presents the spectra: the blue line represents the observed spectrum and the red line represents the best individual spectrum (adapted from Hetem & Gregorio-Hetem 2009).

Fig. 8. Main results for stars HD202746, PDS054 and TW Hydra, on calcium, iron, titanium and cobalt lines (adapted from Hetem & Gregorio-Hetem 2009).

170 Bio-Inspired Computational Algorithms and Their Applications

Fig. 7. Main screen of the program GASpectrum after five generations. The upper panel presents the spectra: the blue line represents the observed spectrum and the red line represents the best individual spectrum (adapted from Hetem & Gregorio-Hetem 2009).

Fig. 8. Main results for stars HD202746, PDS054 and TW Hydra, on calcium, iron, titanium

and cobalt lines (adapted from Hetem & Gregorio-Hetem 2009).

### **4.1 Using GA to parameterize the design of Harrington pumps**

This subsection is based on the published work *Artificial Intelligence Parametrization of Harrington Pumps* (Caetano & Hetem 2011).

Since the beginning of liquid engine spacecraft history, the choices on pumping were the turbo pumps (Neufeld 1995). However, turbo pumps present many difficulties to design and to achieve their optimum performance. Good and experienced designers can project specialized turbo pumps that can deliver 70-90% efficiency, but figures less than half that are not uncommon. Low efficiency may be acceptable in some applications, but in rocketry this is a severe problem. Common problems include: 1) excessive flow from the high pressure rim back to the low pressure inlet along the gap between the casing of the pump and the rotor; 2) excessive recirculation of the fluid at inlet; 3) excessive vortexing of the fluid as it leaves the casing of the pump; 4) damaging cavitation to impeller blade surfaces in low pressure zones; and 5) critical shaping of the rotor itself is hardly precise (see the many examples and demonstrations presented by Dixon & Hall (2010) for a better understanding of these concerns).

On the other end, the options are the pressurized tanks. In this choice, the fuel and oxidizer reservoir are filled charged with a high pressure gas (helium or nitrogen) that pushes the fluid to the thrust chamber. So, it is easy to see that the tank output fuel pressure drops as the rocket engine consumes its content. As an option, the designer can increase the inside pressure, but this came also with a high cost in material (due to tank thickness) and instability. Actually, pressurized propellant tanks are used on small rockets like the last stages on space missions.

As an elegant intermediate solution between these two extremes, Harrington (2003) presented a design fills the gap between the pressure fed and the turbo pumps. This solution also has the advantage of lowering the costs of a rocket project, keeping low weight and without the high complexity of a turbo pump, whose operation, theoretical concerns and constructive details are explained in next section.

#### **4.1.1 Pump description and operation**

The construction consists of two chambers (B1 and B2 on figure 9) and a set of 8 valves. The chambers are connected to the main tank (Mt) through valves k3 and k4. These chambers also deliver propellant to the combustion chamber (CB) through valves k5 and k6. There is a high pressure gas generator (Hp) that is connected to the chambers through valves k1 and k2. Valves k7 and k8 serve as ventilation for the chambers.

The pumps work alternating two states. In state 1, B1 is being filled by Mt and B2 is feeding the combustion chamber; and in state 2 their role is inverted, say B2 is being filled by Mt and B1 is feeding the combustion chamber. The state change is done by opening and closing the valves, as presented in figure 9 and table 2. The opening and closing of the valves is controlled by a small processor.

#### **4.1.2 The model: Pump constructive details**

Designing a Harrington pump is simple, but the optimization process is not (as expected: a P-problem and a NP-problem respectively). A pump with a small chamber must be filled

The Search for Parameters and Solutions:

the fuel pressure, *Pf*, the fuel mass density,

*c*, and stress coefficient,

(1989), the chamber walls thickness can be obtained by

ρ

and the total chamber mass by

where *g* represents the gravity acceleration.

ρ

(Griffinand & French 1991; Sutton 1986).

through the vent.

mass density,

and:

ratio:

obtained by *m Q*=

Applying Genetic Algorithms on Astronomy and Engineering 173

The choice of pump tanks material plays an important role, as its mass density and stress coefficients are the main keys in the pump design. The main tank pressure (about 300 kPa) and the area of the inlet valves set up the limits for the maximum inflow rate. If the inflow velocity is increased this can cause the propellant to be aerated, what is not desirable for the proper working of the engine. The extra volume of pressurized gas in the pump chamber should be small to minimize gas usage, but if it is too small, there will be a loss of propellant

The primary parameters for the calculations are the state changing cycle, *tcy*, the volume flow determined by the rocket engine needs, *Q*, the specific impulse of the propellants, *Isp*, at

*<sup>f</sup>*, the thrust, T, and the material properties: the

*<sup>c</sup>*. From these parameters, considering the pump

<sup>=</sup> , (4)

<sup>=</sup> , (5)

. (6)

, (7)

<sup>=</sup> , (8)

ρ

<sup>3</sup> <sup>0</sup> 6 *cy t*

where the integral results in the chamber volume, and for the simplest case of steady flow, it resumes to *Vc*=*Q.tcy*. Knowing the diameter and applying the stress formulae from Young

*Qdt*

π

*f c*

*c P D*

ρ

σ

<sup>2</sup> *M tD c wcc* = π

To obtain the thrust, one can apply the momentum equation for the case of ideal expansion,

*T gQI* = *sp f* ρ

Manipulation of these expressions and an estimative of the relative weight of the valves and other accessories lead to expression 7 from Harrington (2003), the pump thrust to weight

> 0.43 *sp f <sup>c</sup> f cy c*

that is to be optimized. The total pump mass is *Mp*=1.56 *Mc*, and the mass flow can be easily

of this set of equations as a model. Table 3 presents the results obtained for typical parameter values. These results are in agreement with rocket engine pump literature

ρ σ

ρ

*<sup>f</sup>* . The expressions (4)-(8) were coded in a program to test the feasibility

*T gI W PT*

σ

chambers are spherical, one can instantly obtain the diameter of one chamber:

*c*

*w*

*t*

*D*

and vented quickly, with minimal head loss through the gas and liquid valves and plumbing. Making the pump cycle as fast as possible would make it lightweight, but higher flow velocities cause problems (Harrington 2003).

Fig. 9. Schematic view and operation of a Harrington pump, with its chambers (B1 and B2) and valves (k1-8). The main rocket fuel tank is represented by Mt whereas Hp represents a high pressure gas generator. The two states are presented. Left: B1 is being filled by Mt while B2 is feeding the combustion chamber. Right: B1 is feeding the combustion chamber while B2 is being filled by Mt. the arrows indicate the flow. (Caetano & Hetem 2011).


Table 2. Derived model parameters for the sample (Caetano & Hetem 2011).

172 Bio-Inspired Computational Algorithms and Their Applications

and vented quickly, with minimal head loss through the gas and liquid valves and plumbing. Making the pump cycle as fast as possible would make it lightweight, but higher

Fig. 9. Schematic view and operation of a Harrington pump, with its chambers (B1 and B2) and valves (k1-8). The main rocket fuel tank is represented by Mt whereas Hp represents a high pressure gas generator. The two states are presented. Left: B1 is being filled by Mt while B2 is feeding the combustion chamber. Right: B1 is feeding the

combustion chamber while B2 is being filled by Mt. the arrows indicate the flow. (Caetano

valve state 1 state 2

k1 closed open

k2 open closed

k3 open closed

k4 closed open

k5 closed open

k6 open closed

k7 open closed

k8 closed open

Table 2. Derived model parameters for the sample (Caetano & Hetem 2011).

flow velocities cause problems (Harrington 2003).

& Hetem 2011).

The choice of pump tanks material plays an important role, as its mass density and stress coefficients are the main keys in the pump design. The main tank pressure (about 300 kPa) and the area of the inlet valves set up the limits for the maximum inflow rate. If the inflow velocity is increased this can cause the propellant to be aerated, what is not desirable for the proper working of the engine. The extra volume of pressurized gas in the pump chamber should be small to minimize gas usage, but if it is too small, there will be a loss of propellant through the vent.

The primary parameters for the calculations are the state changing cycle, *tcy*, the volume flow determined by the rocket engine needs, *Q*, the specific impulse of the propellants, *Isp*, at the fuel pressure, *Pf*, the fuel mass density, ρ*<sup>f</sup>*, the thrust, T, and the material properties: the mass density, ρ*c*, and stress coefficient, σ*<sup>c</sup>*. From these parameters, considering the pump chambers are spherical, one can instantly obtain the diameter of one chamber:

$$D\_c = \sqrt[3]{6} \frac{\int\_0^{t\_{cy}} Qdt}{\pi} \,\tag{4}$$

where the integral results in the chamber volume, and for the simplest case of steady flow, it resumes to *Vc*=*Q.tcy*. Knowing the diameter and applying the stress formulae from Young (1989), the chamber walls thickness can be obtained by

$$t\_w = \frac{P\_f D\_c}{\sigma\_c} \,\,\,\,\,\tag{5}$$

and the total chamber mass by

$$M\_c = \pi t\_w D\_c^2 \rho\_c \,. \tag{6}$$

To obtain the thrust, one can apply the momentum equation for the case of ideal expansion, and:

$$T = \mathcal{g}Q\mathcal{l}\_{sp}\mathcal{p}\_f \,. \tag{7}$$

where *g* represents the gravity acceleration.

Manipulation of these expressions and an estimative of the relative weight of the valves and other accessories lead to expression 7 from Harrington (2003), the pump thrust to weight ratio:

$$\frac{T}{\mathcal{W}} = 0.43 \frac{\text{g} \mathbf{I}\_{sp} \rho\_f}{P\_f T\_{cg}} \frac{\sigma\_c}{\rho\_c} \,\text{,}\tag{8}$$

that is to be optimized. The total pump mass is *Mp*=1.56 *Mc*, and the mass flow can be easily obtained by *m Q*= ρ *<sup>f</sup>* . The expressions (4)-(8) were coded in a program to test the feasibility of this set of equations as a model. Table 3 presents the results obtained for typical parameter values. These results are in agreement with rocket engine pump literature (Griffinand & French 1991; Sutton 1986).

The Search for Parameters and Solutions:

(parameter set, adaptation level, <sup>2</sup>

expression given by Press et al. (1995):

χ

Applying Genetic Algorithms on Astronomy and Engineering 175

Now we explain how the GA method was implemented in the Harrington pump model described above. We first clarify the GA nomenclature in the field of pump design. A *parameter* (e.g. volume flow) corresponds to the concept of a 'gene', and a change in a parameter is a 'mutation'. A parameter set that yields a possible solution corresponds to a 'chromosome', our Λ. An 'individual' is a solution that is composed of one parameter set and two additional GA control variables. One of these variables is χ2, which refers to the 'adaptation' level. The other control variable is Φ, the genetic operator. The term 'generation' means 'all the individuals' (or all the solutions) present in a given iteration.

method presented herein implements a *χ*2 minimization of the comparison between the desired results <sup>0</sup> { } Γ = *V ,D ,t ,M ,M ,T,T / W,m c cw c p* , and the results obtained by the application of expressions (4) to (8), the model results. There are three main advantages of using a GA for this task: (i) the GA method potentially browses the whole permitted parameter space, better avoiding the 'traps' of local minima; (ii) the method is not affected by changes in the model; (iii) the GA implementation does not need to compute the derivatives of *χ*2 (such as ∂*χ*2/∂*P*f, for example) required by the usual methods. This fact

The main structures used to manipulate the data are linked lists containing the solutions

*<sup>i</sup>* , and the genetic operator, Φ*i*, expressed by 2 { , , ,( , )} *Si ii i i* = ΨΛ Γ Φ

Hetem & Gregorio-Hetem (2007), the code starts with the construction of the first generation, where all parameters are randomly chosen within an allowed range (for example, 15 cm < *D*c < 30 cm). Here, the number of parameter sets in the first generation is assumed to be 100. In the next step, the evaluation function runs the model for each solution, and compares the synthetic Γ*i* with the desired data, Γ0, to find *χ*2, using a modified

2 0

which we want to optimize, it is enough to establish a corresponding to Γ0*<sup>j</sup>* very high.

χ

considers the solutions and the genetic operators. Formally,

*<sup>i</sup> np j <sup>j</sup>*

=

1 *np*

1 0

where *np* is the number of values in the result set, Γ0*<sup>j</sup>*, is the desired value on position *j* (e.g. Γ01=*Vc*), and Γ*ij* is the calculated value for the solution *Si*. The smallest *χ*2 corresponds to the goodness-of-fit, or simply *gof.* The *gof* values express how each individual is adapted, or how close each solution is, to the best solution (Bentley & Corne 2002). For the value of *T/W*,

A judgment function then determines the genetic operator Φ to be applied to a solution. Its values can be 'copy': the individual remains the same in the next generation; 'crossover': the individual is elected to change a number of genes (parameters) with another individual, creating a new one; 'mutation': one of its genes is randomly changed; or 'termination': none of the genes continue to subsequent generations. The chosen action is expressed by the Φ*<sup>i</sup>* variable, associated with each individual. The next step is to evolve the current generation (*k*) to the next (*k* + 1) one, which is done through a multi-dimensional function β that

*j ij*

, where *Si* denotes the *i*th solution. Following Goldberg (1989) and

2

Γ −Γ <sup>=</sup> <sup>Γ</sup> , (12)

simplifies the code and minimizes computer errors caused by gradient calculations.

χ

ρ σ

. Essentially, the GA

The code uses the parameters described in (9), namely {,,,} *cy f c c* Λ = *t P*


1 Propellant mixture: LOX/RP-1 2 2219 Aluminum alloy

Table 3. Test values for the pump model and results.

#### **4.1.3 GA optimization method**

Here we describe de Genetic Algorithm (GA) optimization method and the formalism applied to code the problem to its needs.

The pump parameters we want to find are a subset of those described as primary parameters: the state changing cycle, *tcy*, the fuel pressure, *Pf*, the fuel mass density, ρ*<sup>f</sup>*, and the material properties: the mass density, ρ*c*, and stress coefficient, σ*<sup>c</sup>*. These are the GA free parameters, formally

$$
\Lambda = \{t\_{cy'}P\_{f'}\rho\_{c'}\sigma\_c\}\,. \tag{9}
$$

known as the parameter set. The technique used to work with the material parameters, ρ*c* and σ*<sup>c</sup>*, are explained in sub-section 4.1.4.

The obtained pump must deliver a desired mass rate, , of a given propellant, ρ*<sup>f</sup>*, and must be made of a given material, ρ*c* and σ*<sup>c</sup>*. Some variables are project dependent, like the volume flow, *Q*, the specific impulse of the propellants, *Isp*, at the fuel pressure, and the thrust, *T*. These three parameters are those the rocket engine designer should define to specify the pump he needs. Differently from the first parameters described on the above paragraph, these values cannot be altered by the algorithm, and can be included in another group, the constant set:

$$\Psi = \{Q, I\_{sp}, T\} \,. \tag{10}$$

Another group of variables is need: the result set. These are the values that are obtained by running the model code:

$$
\Gamma = \{V\_{\bf c}, D\_{\bf c}, t\_{w}, M\_{\bf c}, M\_{p}, T, T \;/\text{V}, \dot{m}\}\,. \tag{11}
$$

To satisfy the GA formalism, one must write down the model that describes the necessary transformations to obtain Γ from Ψ and Λ, or Λ= Ψ Γ *f* ( ,) .

174 Bio-Inspired Computational Algorithms and Their Applications

Entry parameters Model results *tcy* 5 s *Vc* 0,016667 m3 *Q* 200 l/min *Dc* 31,69203 cm *Isp* 285 s *tw* 0,090549 cm

*<sup>f</sup>* <sup>1</sup> 935 kg/m3 *Mc* 0,8 kg *Pf* 4 Mpa *Mp* 1,248 kg *T* 8800 N *T* 8704,85 N

*<sup>c</sup>*<sup>2</sup> 2,8 g/cm3 *m* 3,116667 kg/s

Here we describe de Genetic Algorithm (GA) optimization method and the formalism

The pump parameters we want to find are a subset of those described as primary

{,,,} *cy f c c* Λ = *t P* ρ σ

known as the parameter set. The technique used to work with the material parameters,

flow, *Q*, the specific impulse of the propellants, *Isp*, at the fuel pressure, and the thrust, *T*. These three parameters are those the rocket engine designer should define to specify the pump he needs. Differently from the first parameters described on the above paragraph, these values cannot be altered by the algorithm, and can be included in another group, the

Another group of variables is need: the result set. These are the values that are obtained by

To satisfy the GA formalism, one must write down the model that describes the necessary

The obtained pump must deliver a desired mass rate, , of a given propellant,

*c*, and stress coefficient,

σ

*<sup>c</sup>*. Some variables are project dependent, like the volume

{, ,} Ψ = *QI T sp* . (10)

{ } Γ = *V ,D ,t ,M ,M ,T,T / W,m c cw c p* . (11)

*,* (9)

ρ*<sup>f</sup>*, and

*<sup>f</sup>*, and must be

ρ*c*

*<sup>c</sup>*. These are the GA free

ρ

parameters: the state changing cycle, *tcy*, the fuel pressure, *Pf*, the fuel mass density,

ρ

*<sup>c</sup>*<sup>2</sup> 350 MPa *T/W* 8718,8

ρ

σ

ρ

Table 3. Test values for the pump model and results.

1 Propellant mixture: LOX/RP-1 2 2219 Aluminum alloy

**4.1.3 GA optimization method** 

parameters, formally

made of a given material,

running the model code:

and σ

constant set:

applied to code the problem to its needs.

the material properties: the mass density,

*<sup>c</sup>*, are explained in sub-section 4.1.4.

ρ*c* and σ

transformations to obtain Γ from Ψ and Λ, or Λ= Ψ Γ *f* ( ,) .

Now we explain how the GA method was implemented in the Harrington pump model described above. We first clarify the GA nomenclature in the field of pump design. A *parameter* (e.g. volume flow) corresponds to the concept of a 'gene', and a change in a parameter is a 'mutation'. A parameter set that yields a possible solution corresponds to a 'chromosome', our Λ. An 'individual' is a solution that is composed of one parameter set and two additional GA control variables. One of these variables is χ2, which refers to the 'adaptation' level. The other control variable is Φ, the genetic operator. The term 'generation' means 'all the individuals' (or all the solutions) present in a given iteration.

The code uses the parameters described in (9), namely {,,,} *cy f c c* Λ = *t P* ρ σ . Essentially, the GA method presented herein implements a *χ*2 minimization of the comparison between the desired results <sup>0</sup> { } Γ = *V ,D ,t ,M ,M ,T,T / W,m c cw c p* , and the results obtained by the application of expressions (4) to (8), the model results. There are three main advantages of using a GA for this task: (i) the GA method potentially browses the whole permitted parameter space, better avoiding the 'traps' of local minima; (ii) the method is not affected by changes in the model; (iii) the GA implementation does not need to compute the derivatives of *χ*2 (such as ∂*χ*2/∂*P*f, for example) required by the usual methods. This fact simplifies the code and minimizes computer errors caused by gradient calculations.

The main structures used to manipulate the data are linked lists containing the solutions (parameter set, adaptation level, <sup>2</sup> χ *<sup>i</sup>* , and the genetic operator, Φ*i*, expressed by 2 { , , ,( , )} *Si ii i i* = ΨΛ Γ Φ χ , where *Si* denotes the *i*th solution. Following Goldberg (1989) and Hetem & Gregorio-Hetem (2007), the code starts with the construction of the first generation, where all parameters are randomly chosen within an allowed range (for example, 15 cm < *D*c < 30 cm). Here, the number of parameter sets in the first generation is assumed to be 100. In the next step, the evaluation function runs the model for each solution, and compares the synthetic Γ*i* with the desired data, Γ0, to find *χ*2, using a modified expression given by Press et al. (1995):

$$\mathcal{X}\_i^2 = \frac{1}{n\_p} \sum\_{j=1}^{n\_p} \left( \frac{\Gamma\_{0j} - \Gamma\_{ij}}{\Gamma\_{0j}} \right)^2,\tag{12}$$

where *np* is the number of values in the result set, Γ0*<sup>j</sup>*, is the desired value on position *j* (e.g. Γ01=*Vc*), and Γ*ij* is the calculated value for the solution *Si*. The smallest *χ*2 corresponds to the goodness-of-fit, or simply *gof.* The *gof* values express how each individual is adapted, or how close each solution is, to the best solution (Bentley & Corne 2002). For the value of *T/W*, which we want to optimize, it is enough to establish a corresponding to Γ0*<sup>j</sup>* very high.

A judgment function then determines the genetic operator Φ to be applied to a solution. Its values can be 'copy': the individual remains the same in the next generation; 'crossover': the individual is elected to change a number of genes (parameters) with another individual, creating a new one; 'mutation': one of its genes is randomly changed; or 'termination': none of the genes continue to subsequent generations. The chosen action is expressed by the Φ*<sup>i</sup>* variable, associated with each individual. The next step is to evolve the current generation (*k*) to the next (*k* + 1) one, which is done through a multi-dimensional function β that considers the solutions and the genetic operators. Formally,

The Search for Parameters and Solutions:

can benefit of GA robustness and reliability.

a candidate to solution it is easy to verify if it is a good solution.

pumps with Genetic Algorithms (Burian et al. 2011).

efficiency).

Applying Genetic Algorithms on Astronomy and Engineering 177

evolutions and increasing complexity of the model, like thermal transfer and realistic valves,

The next step in this work is to enhance the model with more realistic and specific trends. It is expected to incorporate non-linear functions, differential equations and integrals. Also tabled functions are not far from what can be found in a pump project, with its intrinsic interpolations. The overall problem of finding parameters for a pump design can easily turn to a NP-Problem, that is a problem that is very difficult to find a solution, but, once one has

**4.2 Using GA to parameterize the design of turbo pumps to be used in rocket engines**  This subsection is based on the published work Parametric Design of Rocket Engine Turbo

Turbo pumping in high-thrust, long-duration liquid propellant rocket engine applications, generally results in lower weights and higher performance when compared to pressurized gas feed systems. Turbo pump feed systems require only relatively low pump-inlet pressures, and thus propellant-tank pressures, while the major portion of the pressure required at the thrust chamber inlets is supplied by the pumps, saving considerable vehicle weight. As stated by Huzel & Huang (1967) the best performing turbo pump system is defined as that which affords the heaviest payload for a vehicle with a given thrust level, range or velocity increment: gross stage take-off weight; and thrust chamber specific impulse (based on propellant combination, mixture ratio, and chamber operating

The particular arrangement or geometry of the major turbo pump components is related to their selection process (Logan & Roy 2003). Some complex designs, like the SSME-Space Shuttle Main Engine, have a multiple stage pump, but most propellant pumps have a singlestage main impeller. Eventually, one or more design limits are reached which requires more iteration, each with a new changed parameter or approach. For a better example, see table 5

which presents some data from the V2 (II world war German missile) alcohol pump.

Parameter value

impeller diameter 34 cm

rotation 5000 rpm

performance 265 kW

delivery 50 kg/s

delivery pressure 25 atm

This subsection considers the development of a software tool based on GA to assist the determination of the excellent parameters for the configuration of turbo pumps in engines

Table 5. Parameters from the alcohol V2 pump, adapted from Sutton & Biblarz (2001).

$$\left[\left(S\_{1'}, S\_{2'}, \dots, S\_N\right)\_{k+1} = \beta\right] \left[\left(S\_{1'}, \Phi\_1\right), \left(S\_{2'}, \Phi\_2\right), \dots, \left(S\_{N'}, \Phi\_N\right)\right]\_k. \tag{13}$$

As soon as a new generation is ready, the evaluation function is reapplied, and the algorithm repeats the described actions until an end-of-loop condition is reached. The end condition can be based on the number of iterations or the quality (a low level for the <sup>2</sup> χ *i* values).

#### **4.1.4 The choice of chamber constructive material**

The main material properties, the mass density, ρ*c*, and stress coefficient, σ*<sup>c</sup>*, can also be chosen by the GA. Instead of working directly with these parameters, it was created a material parameter, *Kc*, an integer that points to a density-stress database. So, our new parameter set becomes

$$\Lambda = \{t\_{cy'}P\_{f'}\rho\_c(\mathbf{K}\_c)\_\prime \sigma\_c(\mathbf{K}\_c)\}\,' \,. \tag{14}$$

or simply

$$
\Lambda = \{t\_{cy}, P\_{f'}K\_c\}\,. \tag{15}
$$

As *Kc* is a discrete value, it was needed to build special routines to manipulate the genes in the first generation and in mutation events.

#### **4.1.5 Results and conclusion**

Table 4 presents the main results for a GA run of 20 generations. The values are in agreement with the expected for the pump. The material chosen for the chambers was cooper 99.9%. A typical running with about 100 generation is achieved in ~5 seconds in a simple laptop computer.


1 Propellant mixture: LOX/RP-1

2 Copper 99.9% Cu

Table 4. GA result values for the pump model.

The GA proved to be efficient, and due to the method itself being independent of model complexity, it certainly can be used in future implementations of pump design. Future 176 Bio-Inspired Computational Algorithms and Their Applications

[ 1 2 ] <sup>1</sup> ( )( ) ( ) 11 22 ,,, , , , ,, , *N N <sup>k</sup> <sup>N</sup> <sup>k</sup> SS S S S S*

As soon as a new generation is ready, the evaluation function is reapplied, and the algorithm repeats the described actions until an end-of-loop condition is reached. The end condition can be based on the number of iterations or the quality (a low level for the <sup>2</sup>

chosen by the GA. Instead of working directly with these parameters, it was created a material parameter, *Kc*, an integer that points to a density-stress database. So, our new

> { , , ( ), ( )} *cy f c c c c* Λ = *tP K K* ρ

As *Kc* is a discrete value, it was needed to build special routines to manipulate the genes in

Table 4 presents the main results for a GA run of 20 generations. The values are in agreement with the expected for the pump. The material chosen for the chambers was cooper 99.9%. A typical running with about 100 generation is achieved in ~5 seconds in a

> tcy 8.2 s Vc 0.00393786 m3 Q 200 l/min Dc 0.195924 cm Isp 285 s tw 0,089 cm ρf 1 935 kg/m3 Mc 0.957973 kg Pf 4 Mpa Mp 1.49444 kg

σc 2 350 MPa T/W 843.227

ρc 2 2,8 g/cm3 *m* 0.448098 kg/s

The GA proved to be efficient, and due to the method itself being independent of model complexity, it certainly can be used in future implementations of pump design. Future

ρ

σ

<sup>+</sup> = ΦΦ Φ . (13)

*c*, and stress coefficient,

{,,} *cy f c* Λ = *t PK* . (15)

σ

, (14)

χ*i*

*<sup>c</sup>*, can also be

β

**4.1.4 The choice of chamber constructive material**  The main material properties, the mass density,

the first generation and in mutation events.

**4.1.5 Results and conclusion** 

simple laptop computer.

1 Propellant mixture: LOX/RP-1

Table 4. GA result values for the pump model.

2 Copper 99.9% Cu

values).

or simply

parameter set becomes

evolutions and increasing complexity of the model, like thermal transfer and realistic valves, can benefit of GA robustness and reliability.

The next step in this work is to enhance the model with more realistic and specific trends. It is expected to incorporate non-linear functions, differential equations and integrals. Also tabled functions are not far from what can be found in a pump project, with its intrinsic interpolations. The overall problem of finding parameters for a pump design can easily turn to a NP-Problem, that is a problem that is very difficult to find a solution, but, once one has a candidate to solution it is easy to verify if it is a good solution.

### **4.2 Using GA to parameterize the design of turbo pumps to be used in rocket engines**

This subsection is based on the published work Parametric Design of Rocket Engine Turbo pumps with Genetic Algorithms (Burian et al. 2011).

Turbo pumping in high-thrust, long-duration liquid propellant rocket engine applications, generally results in lower weights and higher performance when compared to pressurized gas feed systems. Turbo pump feed systems require only relatively low pump-inlet pressures, and thus propellant-tank pressures, while the major portion of the pressure required at the thrust chamber inlets is supplied by the pumps, saving considerable vehicle weight. As stated by Huzel & Huang (1967) the best performing turbo pump system is defined as that which affords the heaviest payload for a vehicle with a given thrust level, range or velocity increment: gross stage take-off weight; and thrust chamber specific impulse (based on propellant combination, mixture ratio, and chamber operating efficiency).

The particular arrangement or geometry of the major turbo pump components is related to their selection process (Logan & Roy 2003). Some complex designs, like the SSME-Space Shuttle Main Engine, have a multiple stage pump, but most propellant pumps have a singlestage main impeller. Eventually, one or more design limits are reached which requires more iteration, each with a new changed parameter or approach. For a better example, see table 5 which presents some data from the V2 (II world war German missile) alcohol pump.


Table 5. Parameters from the alcohol V2 pump, adapted from Sutton & Biblarz (2001).

This subsection considers the development of a software tool based on GA to assist the determination of the excellent parameters for the configuration of turbo pumps in engines

The Search for Parameters and Solutions:

obtained by

where ϕ

where ψ

and

we adopt this value.

The shaft speed is given by

Then, the absolute positive head can be obtained by

Applying Genetic Algorithms on Astronomy and Engineering 179

*Q v dA* <sup>=</sup> . (20)

*H HHH* <sup>1</sup> =+− *tef* (21)

*HHHH H stef v* =+− − , (22)

= , (22)

*u dN* = *rad s* . (23)

Δ = , (24)

, (25)

. (27)

, (26)

ψ= 1.0,

1 1 *A eff*

and the net positive suction head or available suction head above vapor pressure can be

where *Hv* is the combustible vapor pressure. The required suction head will be taken as 80% of the available suction head in order to provide a margin of safety for cavitation, or *HSR*=0.8*H*1. To avoid pump cavitation, *Hs* has to be higher than *HSR*. If additional head is required by the pump, the propellant may have to be pressurized by external means, such as by the addition of another pump in series (a booster pump) or by gas pressurization of the propellant tanks. A small value of *HSR* is desirable because it may permit a reduction of the

*SR*

=3/4 and *uSI*=17.827459 are constants. *uSI* is necessary due to SI convertions (see

*SI*

Sutton & Biblarz 2001, eq. 10-7). This last expression allows us to obtain *Nrad/s*, the shaft

1 2 *u Q* φ

2 /

2

*<sup>u</sup> <sup>H</sup>* ψ*g*

has values between 0.90 and 1.10 for different designs. As for many pumps,

*P H* 1 10 = *g*

2 1 <sup>0</sup> *P HH* =Δ + ( )*g*

*m Q* = ρ

0

ρ

ρ

requirements for tank pressurization and, therefore, a lower inert tank mass.

speed in radians per second. The impeller vane tip speed is given by

At this point, we are able to obtain all the final results, 1 2 Γ = { , , }: *mP P*

With *u*, we can evaluate the head delivered by the pump

*rpm*

*SH <sup>N</sup>*

for liquid propellant rockets. We present the first version, which considers the calculation of the main parameters of a compressor stage.

#### **4.2.1 The model**

The pump compressor model used in this work is based on chapter 10 of Sutton & Biblarz (2001). This model provides a coherent basis for the modeling, and is sufficiently complex to be used as a valid test on the further parameter optimizing step.

The pump parameters we want to find are: the inlet compressor diameter, d1, the compressor outlet diameter, *d*2, the fluid input velocity, *v*1, the suction specific speed, *S*, the shaft cross section, *AS*1, the pressure in the main tank, *Pt*, the total fluid friction (viscosity included) due to flow through the pipes, valves, etc, *Pf*, the pressure due to the tank elevation from the pump inlet, *Pe*. In particular, this last parameter leads to project insights concerning the pump position inside the rocket. These are the GA free parameters, formally Λ= {*d*1,*d*2,*v*1,*S*,*dS*1,*Pt*,*Pf*,*Pe*}, known as the parameter set. The obtained compressor must deliver a desired mass rate, *m* , and, from an input pressure *P*1, generate a flow with an output pressure *P*2. Some constants shall be considered, like the fluid mass density, ρ, and the external gravity, *g*0. We assumed as fluid the ethanol (C2H6OH) due to its green properties and green results. These three parameters are those the rocket engine designer should define to specify the compressor he needs. Differently from the first eight parameters described on the above paragraph, these values cannot be altered by the algorithm, and can be included in another group, the result set 1 2 Γ = {, , } *mP P* .

To satisfy the GA formalism, one must write down the model, or the formalism that describes the necessary transformations to obtain Γ from Λ, or Γ=*f* (Λ). One can obtain these expressions following Sutton & Biblarz (2001) model and converting their expressions. First, the pressures should be converted to heads, or the height necessary to the fluid to cause a given pressure, so we define *Ht*, *He* and *Hf*, the tank head, the elevation head and the friction head, respectively, that can be obtained by

$$P\_t = \int\_{H\_t} g\_0 \rho d\mathbf{h} \tag{16}$$

$$P\_e = \int\_{H\_e} g\_0 \rho d\mathbf{h} \,\prime \,\tag{17}$$

and

$$P\_f = \int\_{\mathcal{H}\_f} \mathcal{g}\_0 \rho d\mathcal{H} \,. \tag{18}$$

The effective area of the inlet is given by

$$A\_{1\text{eff}} = \frac{1}{4} \frac{d\_1^2}{\pi} - A\_{\text{S1}} \tag{19}$$

which determines the volume flow

$$Q = \iint\_{A\_{1g}} v\_1 dA \,. \tag{20}$$

Then, the absolute positive head can be obtained by

$$H\_t = H\_t + H\_e - H\_f \tag{21}$$

and the net positive suction head or available suction head above vapor pressure can be obtained by

$$H\_s = H\_t + H\_e - H\_f - H\_v \, \, \, \, \tag{22}$$

where *Hv* is the combustible vapor pressure. The required suction head will be taken as 80% of the available suction head in order to provide a margin of safety for cavitation, or *HSR*=0.8*H*1. To avoid pump cavitation, *Hs* has to be higher than *HSR*. If additional head is required by the pump, the propellant may have to be pressurized by external means, such as by the addition of another pump in series (a booster pump) or by gas pressurization of the propellant tanks. A small value of *HSR* is desirable because it may permit a reduction of the requirements for tank pressurization and, therefore, a lower inert tank mass.

The shaft speed is given by

178 Bio-Inspired Computational Algorithms and Their Applications

for liquid propellant rockets. We present the first version, which considers the calculation of

The pump compressor model used in this work is based on chapter 10 of Sutton & Biblarz (2001). This model provides a coherent basis for the modeling, and is sufficiently complex to

The pump parameters we want to find are: the inlet compressor diameter, d1, the compressor outlet diameter, *d*2, the fluid input velocity, *v*1, the suction specific speed, *S*, the shaft cross section, *AS*1, the pressure in the main tank, *Pt*, the total fluid friction (viscosity included) due to flow through the pipes, valves, etc, *Pf*, the pressure due to the tank elevation from the pump inlet, *Pe*. In particular, this last parameter leads to project insights concerning the pump position inside the rocket. These are the GA free parameters, formally Λ= {*d*1,*d*2,*v*1,*S*,*dS*1,*Pt*,*Pf*,*Pe*}, known as the parameter set. The obtained compressor must deliver a desired mass rate, *m* , and, from an input pressure *P*1, generate a flow with an output pressure *P*2. Some constants shall be considered, like the fluid mass density,

the external gravity, *g*0. We assumed as fluid the ethanol (C2H6OH) due to its green properties and green results. These three parameters are those the rocket engine designer should define to specify the compressor he needs. Differently from the first eight parameters described on the above paragraph, these values cannot be altered by the algorithm, and can

To satisfy the GA formalism, one must write down the model, or the formalism that describes the necessary transformations to obtain Γ from Λ, or Γ=*f* (Λ). One can obtain these expressions following Sutton & Biblarz (2001) model and converting their expressions. First, the pressures should be converted to heads, or the height necessary to the fluid to cause a given pressure, so we define *Ht*, *He* and *Hf*, the tank head, the elevation head and the friction

> 0 *t t H P g dh* = ρ

> > 0 *e*

0 *f*

2 1 1 1 1 4 *eff <sup>S</sup> <sup>d</sup> <sup>A</sup> <sup>A</sup>* π

*e H P g dh* = ρ

*f H P g dh* = ρ

, (16)

, (17)

. (18)

= − , (19)

ρ, and

the main parameters of a compressor stage.

be used as a valid test on the further parameter optimizing step.

be included in another group, the result set 1 2 Γ = {, , } *mP P* .

head, respectively, that can be obtained by

The effective area of the inlet is given by

which determines the volume flow

and

**4.2.1 The model** 

$$N\_{\gamma \mu u} = \frac{S H\_{\rm SR}^{\rho}}{\mu\_{\rm sl} \sqrt{Q}},\tag{22}$$

where ϕ=3/4 and *uSI*=17.827459 are constants. *uSI* is necessary due to SI convertions (see Sutton & Biblarz 2001, eq. 10-7). This last expression allows us to obtain *Nrad/s*, the shaft speed in radians per second. The impeller vane tip speed is given by

$$
\mu = \frac{1}{2} d\_2 \mathcal{N}\_{nd/s} \,. \tag{23}
$$

With *u*, we can evaluate the head delivered by the pump

$$
\Delta H = \frac{\mu^2}{\mathcal{W}\mathcal{S}\_0} \,'\,\tag{24}
$$

where ψ has values between 0.90 and 1.10 for different designs. As for many pumps, ψ = 1.0, we adopt this value.

At this point, we are able to obtain all the final results, 1 2 Γ = { , , }: *mP P*

$$P\_1 = H\_1 \mathbb{g}\_0 \rho \text{ , \tag{25}}$$

2 1 <sup>0</sup> *P HH* =Δ + ( )*g* ρ, (26)

and

$$
\dot{m} = \rho Q \,. \tag{27}
$$

The Search for Parameters and Solutions:

Applying Genetic Algorithms on Astronomy and Engineering 181

This problem is entirely based on discrete elements – there are no floating point parameters. So, the main discussion here is how to build a chromosome syntax that can be used under the GA rules, and still be meaningful for the model. Besides, as the problem is fully discretized, there are high probabilities of finding different solutions that are equally evaluated in their adaptation function. This leads to new enhancements in the model to better evaluate the solutions, enhancing the separation between different individuals.

This subsection is based on the published work Automatic Allocation of Electric Power

The measurement of how well the electric power distribution system can provide a secure and adequate supply of power to satisfy the customer's requirements is called "reliability". Regarding electric power distribution systems, the electric utilities companies are responsible for the most reliable service as possible, reflecting the most advanced state of technology with reasonable cost to the end product that is the electric power3. Most utilities record outage information such as the number of outages, elapse time, and the number of customers interrupted. These data and statistics may be reported for each circuit or operating division, for comparison purposes, using the standard performance

The performance indices provide historical *datum* which can be used to determine increasing or decreasing trends and to measure whether system improvement plans have

The quality model we consider in this subsection uses the following indices, based on the

1. SAIDI (System Average Interruption Duration Index): defined by the rate of average interruption duration per customer served per year. This index is commonly referred to

Sum of Customer Interruption Durations SAIDI

2. SAIFI (System Average Interruption Frequency Index): that defined by the rate of average number of times that a customer's service is interrupted during a reporting period per customer served in a given period (usually one year). A customer

Total Number of Customer Interruptions SAIFI

It is easy to see that what is desired is a circuit with minimal SAIDI and SAIFI with the smaller cost in protective installed devices. The resulting circuit with these characteristics

interruption is defined as one sustained interruption to one customer:

Total Number of Customers Served <sup>=</sup> (29)

Total Number of Customers Served <sup>=</sup> (30)

sustained outage data: the SAIDI and SAIFI indexes, explained as follows:

**5.1 Using GA in the allocation of electric power protective devices** 

Distribution Protective Devices (Burian et al. 2010).

as minutes of interruption per customer.

3 instead of guarantying continuous service to their customers…

indices.

yielded expected results.

will the optimized circuit.

It is also interesting to evaluate the shaft specific speed

$$N\_s = \frac{\mu\_{\text{SI}} \sqrt{Q}}{H\_{\text{SR}}^{\theta}} \, \text{} \tag{28}$$

which, with the aid of table 10-2 of Sutton & Biblarz (2001), defines the pump and impeller type.

#### **4.2.2 Results and conclusion**

We built a computer code to optimize equations in the same way it was done to the Harrington pumps (see subsection 4.1). The resulting parameters obtained from the GA code where in good agreement with what is expected for this kind of project. Some comparisons between GA results and correct results are presented in table 6.


Table 6. Comparison between obtained results (GA) and correct answer (Γ0) for an ethanol compressor.

Evidently, for the simple definitions presented for this model, one does not need a sophisticated method as described to obtain a good result. But, as all designers know very well, there are no simple projects, especially concerning rocket engine pumps. The next step in this work is to enhance the model with more realistic and specific trends. It is expected to incorporate non-linear functions, differential equations and integrals. Also tabled functions are not far from what can be found in a pump project, with its intrinsic interpolations. The overall problem of finding parameters for a pump design can easily turn to a NP-Problem, that is a problem that is very difficult to find a solution, but, once one has a candidate to solution it is easy to verify if it is a good solution. Again, the GA proved to be efficient, and due to the method itself being independent of model complexity, it certainly can be used in future implementations. Future evolutions and increasing complexity of the model can benefit of GA robustness and reliability.

#### **5. Applications on energy distribution**

The application described in this section solves the problem of allocation of protective devices in electric power distribution plants. For a given power plant distribution, it is necessary to choose in which points one must place equipment for the net protection, or not.

180 Bio-Inspired Computational Algorithms and Their Applications

*SI*

which, with the aid of table 10-2 of Sutton & Biblarz (2001), defines the pump and impeller

We built a computer code to optimize equations in the same way it was done to the Harrington pumps (see subsection 4.1). The resulting parameters obtained from the GA code where in good agreement with what is expected for this kind of project. Some

Correct answer 226,8 342669 6816870 (%)

Table 6. Comparison between obtained results (GA) and correct answer (Γ0) for an ethanol

Evidently, for the simple definitions presented for this model, one does not need a sophisticated method as described to obtain a good result. But, as all designers know very well, there are no simple projects, especially concerning rocket engine pumps. The next step in this work is to enhance the model with more realistic and specific trends. It is expected to incorporate non-linear functions, differential equations and integrals. Also tabled functions are not far from what can be found in a pump project, with its intrinsic interpolations. The overall problem of finding parameters for a pump design can easily turn to a NP-Problem, that is a problem that is very difficult to find a solution, but, once one has a candidate to solution it is easy to verify if it is a good solution. Again, the GA proved to be efficient, and due to the method itself being independent of model complexity, it certainly can be used in future implementations. Future evolutions and increasing complexity of the model can

The application described in this section solves the problem of allocation of protective devices in electric power distribution plants. For a given power plant distribution, it is necessary to choose in which points one must place equipment for the net protection, or

*m* (kg/s) P1 (Pa) P2 (Pa) mean error

10 228,1 342345 6816450 0,22 20 227,5 342360 6816440 0,13 50 227,1 342601 6816890 0,05 100 226,9 342670 6816880 0,01

*u Q <sup>N</sup> H*φ

*SR*

= , (28)

*s*

comparisons between GA results and correct results are presented in table 6.

It is also interesting to evaluate the shaft specific speed

type.

**4.2.2 Results and conclusion** 

generations

benefit of GA robustness and reliability.

**5. Applications on energy distribution** 

compressor.

not.

This problem is entirely based on discrete elements – there are no floating point parameters. So, the main discussion here is how to build a chromosome syntax that can be used under the GA rules, and still be meaningful for the model. Besides, as the problem is fully discretized, there are high probabilities of finding different solutions that are equally evaluated in their adaptation function. This leads to new enhancements in the model to better evaluate the solutions, enhancing the separation between different individuals.

#### **5.1 Using GA in the allocation of electric power protective devices**

This subsection is based on the published work Automatic Allocation of Electric Power Distribution Protective Devices (Burian et al. 2010).

The measurement of how well the electric power distribution system can provide a secure and adequate supply of power to satisfy the customer's requirements is called "reliability". Regarding electric power distribution systems, the electric utilities companies are responsible for the most reliable service as possible, reflecting the most advanced state of technology with reasonable cost to the end product that is the electric power3. Most utilities record outage information such as the number of outages, elapse time, and the number of customers interrupted. These data and statistics may be reported for each circuit or operating division, for comparison purposes, using the standard performance indices.

The performance indices provide historical *datum* which can be used to determine increasing or decreasing trends and to measure whether system improvement plans have yielded expected results.

The quality model we consider in this subsection uses the following indices, based on the sustained outage data: the SAIDI and SAIFI indexes, explained as follows:

1. SAIDI (System Average Interruption Duration Index): defined by the rate of average interruption duration per customer served per year. This index is commonly referred to as minutes of interruption per customer.

$$\text{SAIDI} = \frac{\text{Sum of Customer Interpretution Duration}}{\text{Total Number of Customer Served}} \tag{29}$$

2. SAIFI (System Average Interruption Frequency Index): that defined by the rate of average number of times that a customer's service is interrupted during a reporting period per customer served in a given period (usually one year). A customer interruption is defined as one sustained interruption to one customer:

$$\text{SAIFI} = \frac{\text{Total Number of Customer Interpretations}}{\text{Total Number of Customer served}} \tag{30}$$

It is easy to see that what is desired is a circuit with minimal SAIDI and SAIFI with the smaller cost in protective installed devices. The resulting circuit with these characteristics will the optimized circuit.

<sup>3</sup> instead of guarantying continuous service to their customers…

The Search for Parameters and Solutions:

Applying Genetic Algorithms on Astronomy and Engineering 183

Fig. 11. Representation of the circuit of figure 10 with the nodes with all the possible

The first step is to provide formalism in such a way that the protective devices net could be represented by a set of genes in a chromosome Λ, and that the Bishop (1997) model could be

The solution chosen was to code the circuit as a series of nodes, designed by N*i*, with *i* being an integer number, and to build a list of links between the nodes (see figure 11). The special node N0 is the main protective switch in the substation (which is present in all solutions). Each link between nodes can have a protective device, and its location is designed as *Pi,j*, with *i* and *j* being the two nodes that define the link. Special data structure is provided to the nodes to storage information about the number of phases, number of consumers,

The adopted solution considers *S* as a ordered list of tokens, and the position in the ordered

0,1 1,2 1,3 2,4 2,5 2 ,6 6,7 6,12 7 ,8

,,,,,,, ,,

. (31)

7 ,9 9,10 9,11 12,13 12,14 14,15 14,16

So, Λ is a finite set of tokens, and its number of elements is much smaller than the number of nodes squared4, that assumes the role of parameter set in the P-problem. These tokens can represent a protective device to be placed in its respective circuit position. The possible devices are: main substation switch, only possible in location *P*0,1 (S); fuse (F), automatic

*PPPPPPPP P*

,,, , , ,

*PP P P P P P* Λ = 

4 Of course! When representing an electric circuit one does not link one node to all the other nodes…

list corresponds to a location as *Pi,j*. Then, for the circuit of figure 11, one has

locations for protective devices (adapted from Burian et al. 2010).

**5.1.2 The methodology: Converting to a GA application** 

expressed as a P-problem whose parameters are given by Λ.

distance to neighbours nodes, etc.

reclose switch (R) and nothing (no device).

Fig. 10. Circuit with Circuit Breaker in the Electric Power Substation without Reclosing Capability, based on Bishop (1997).

#### **5.1.1 The model**

The chosen model was based in the work developed by Bishop (1997) whose circuit has multiple laterals with customer's numbers and load KVA values seen on the figure 10. To perform the analysis one needs some statistics, like: number of customers; placement of protective devices on the electric power utility; good possibilities to implement protective devices; distribution circuit response to the quality indices; and traditional values of repair and recover in accordance with Bishop's indices.

The initial circuit used to the analysis is presented by figure 10, where it was considered the values of Bishop (1997) to the indices in circuits of electric power distribution with similar features in North American solutions. The used general statistical parameters are presented in table 7. As a base case analysis, the system was modelled with no reclosing of substation device. This is intended only to yield values for relative comparison with other circuits, with protective devices like recloses and fuses placed on the circuit, achieving the comparison landscape with the SAIDI and SAIFI indices.


Table 7. General statistical parameters used in the model.

182 Bio-Inspired Computational Algorithms and Their Applications

Fig. 10. Circuit with Circuit Breaker in the Electric Power Substation without Reclosing

The chosen model was based in the work developed by Bishop (1997) whose circuit has multiple laterals with customer's numbers and load KVA values seen on the figure 10. To perform the analysis one needs some statistics, like: number of customers; placement of protective devices on the electric power utility; good possibilities to implement protective devices; distribution circuit response to the quality indices; and traditional values of repair

The initial circuit used to the analysis is presented by figure 10, where it was considered the values of Bishop (1997) to the indices in circuits of electric power distribution with similar features in North American solutions. The used general statistical parameters are presented in table 7. As a base case analysis, the system was modelled with no reclosing of substation device. This is intended only to yield values for relative comparison with other circuits, with protective devices like recloses and fuses placed on the circuit, achieving the comparison

> Faults per circuit mile per year 0.22 Percent of permanent faults 20% Percent of temporary faults 80%

Manual restoration time 2.0 hours Repair time for 30 lines 3.0 hours Repair time for 10 lines 2.5 hours

Capability, based on Bishop (1997).

and recover in accordance with Bishop's indices.

landscape with the SAIDI and SAIFI indices.

Table 7. General statistical parameters used in the model.

**5.1.1 The model** 

Fig. 11. Representation of the circuit of figure 10 with the nodes with all the possible locations for protective devices (adapted from Burian et al. 2010).

#### **5.1.2 The methodology: Converting to a GA application**

The first step is to provide formalism in such a way that the protective devices net could be represented by a set of genes in a chromosome Λ, and that the Bishop (1997) model could be expressed as a P-problem whose parameters are given by Λ.

The solution chosen was to code the circuit as a series of nodes, designed by N*i*, with *i* being an integer number, and to build a list of links between the nodes (see figure 11). The special node N0 is the main protective switch in the substation (which is present in all solutions). Each link between nodes can have a protective device, and its location is designed as *Pi,j*, with *i* and *j* being the two nodes that define the link. Special data structure is provided to the nodes to storage information about the number of phases, number of consumers, distance to neighbours nodes, etc.

The adopted solution considers *S* as a ordered list of tokens, and the position in the ordered list corresponds to a location as *Pi,j*. Then, for the circuit of figure 11, one has

$$\Lambda = \begin{Bmatrix} P\_{0,1'}P\_{1,2'}P\_{1,3'}P\_{2,4'}P\_{2,5'}P\_{2,6'}P\_{6,7'}P\_{6,12'}P\_{7,8'} \\ P\_{7,9'}P\_{9,10'}P\_{9,11'}P\_{12,13'}P\_{12,14'}P\_{14,15'}P\_{14,16'} \end{Bmatrix} \cdot \tag{31}$$

So, Λ is a finite set of tokens, and its number of elements is much smaller than the number of nodes squared4, that assumes the role of parameter set in the P-problem. These tokens can represent a protective device to be placed in its respective circuit position. The possible devices are: main substation switch, only possible in location *P*0,1 (S); fuse (F), automatic reclose switch (R) and nothing (no device).

<sup>4</sup> Of course! When representing an electric circuit one does not link one node to all the other nodes…

The Search for Parameters and Solutions:

**6. Acknowledgments** 

**7. References** 

Program; FAPESP and CNPq.

Francisco.

Conference & Electric Expo.

IEEE, 2010. v. 1. p. 22-22.

ISBN 978-1-85617-793-1.

*completeness*. W. H. Freeman.

Dullemond C. P., Dominik C., Natta A. (2001) ApJ, 560, 957

Applying Genetic Algorithms on Astronomy and Engineering 185

Fig. 12. Optimized circuit obtained with the GA method (adapted from Burian et al. 2010).

The author wants to thank UFABC/CECS - Engineering, Modeling and Social Sciences Center of Federal University do ABC; AEB – Brazilian Space Agency / UNIESPAÇO

Bentley, P.J., & Corne D.W. (2002) *Creative Evolutionary Systems*. Morgan-Kaufmann, San

Bishop, M.T. (March 1997) *Establishing Realistic Reliability Goals*. The Tech Advantage 97

Burian, R.; Hetem, A., Caetano, C. A. C. *Automatic Allocation of Electric Power Distribution* 

Caetano, C.A.C., & Hetem, A. (2011) *Artificial Intelligence Parametrization of Harrington Pumps*, to be submitted to International Journal of Heat and Fluid (in preparation). Cook, Stephen (1971) *The complexity of theorem proving procedures*. Proceedings of the Third

Ertmer, W., Johann, U., Penselin, S., & Stinner, P. 1979, Z. Phys. A, 291, 207 Dixon, S. L.,Hall,C. A. (2010) *Fluid mechanics and thermodynamics of turbomachinery* 6th ed.

Garey, M. R., & Johnson, D. S. (1979) *Computers and Intractability: A Guide to the Theory of NP-*

Dominik C., Dullemond C. P., Waters L. B. F. M., Walch S. (2003) A&A, 398, 607

*Protective Devices* (2010) Opatija. 33rd International Convention on Information and Communication Technology, Electronics and Microelectronics. Opatija / Abbazia :

Annual ACM Symposium on Theory of Computing. pp. 151–158.Dembczyński, J.,

André P., Ward-Thompson D., Barsony M., (1993), ApJ, 406, 122

The kind of device defines the algorithm to be used to obtain the overall cost of protective devices, and the SAIDI and SAIFI indexes according to Bishop (1997). So, each set Λ*<sup>i</sup>* represents a different circuit, and applying the Bishop's algorithms one obtains a result set

$$
\Gamma\_i \left( \Lambda\_i \right) = \left\{ \text{SAIDI}\_i \text{SAIFI}\_i \, \mathcal{c}\_{\text{Si}} \, \mathcal{c}\_{\text{Ri}} \, \mathcal{c}\_{\text{fi}} \right\}. \tag{32}
$$

where *cS*, *cR* and *cf* are the costs of the main switch reclose switch and fuses, which are expressed in monetary "units", being one unit the cost of the a monophasic fuse.

As the set Γ*i* itself cannot express the degree of adaptation the individual Λ*i* to the problem we want to solve, we must provide an expression to summarize Γ*i* in a more convenient, single valued variable, like the *gof* value, described in subsection 3.1. The definition of this *gof* should have a monotonic behaviour as the costs and the SAIDI and SAIFI index increase. We adopted the simple expression

$$
\kappa\_{\mathcal{S}} \circ f = \kappa\_{\mathfrak{s}} \left( \mathsf{SAIDI} + \mathsf{SAIFI} \right) + \kappa\_{\mathfrak{b}} \left( \mathcal{c}\_{\mathbb{S}} + \mathcal{c}\_{\mathbb{R}} + \mathcal{c}\_{\mathcal{f}} \right). \tag{33}
$$

where κ*a* and κ*<sup>b</sup>* are constant scale converters. Then, one can say that optimized circuit will be that one that offers the smaller *gof*. With this, our inverted NP-problem can be solved by looking for the individual Λ*i* that presents the smaller *gof*. As all the parameters are limited range integer numbers (tokens), some special care must be taken in the GA routines that deal with new individuals and mutation. So, these routines where rebuild taking into account the discrete character of the chromosomes. The overall behaviour of the GA optimization code follows the algorithm proposed in figure 2.

#### **5.1.3 Results and conclusion**

The resulting optimized circuit is shown in figure 12, and its corresponding indexes are presented in table 8. The GA code performed the ranging of large number of solutions and configurations, within the universe of about 50 generations of configurations. This demonstrates the GA potential in this kind of analysis and application to discrete allocation equipment's. GA optimization techniques has been showed to be an effective technique to optimize the allocation of protective devices inside the electrical distribution systems.


Table 8. Indexes values for optimized circuit.

Fig. 12. Optimized circuit obtained with the GA method (adapted from Burian et al. 2010).

#### **6. Acknowledgments**

The author wants to thank UFABC/CECS - Engineering, Modeling and Social Sciences Center of Federal University do ABC; AEB – Brazilian Space Agency / UNIESPAÇO Program; FAPESP and CNPq.

#### **7. References**

184 Bio-Inspired Computational Algorithms and Their Applications

The kind of device defines the algorithm to be used to obtain the overall cost of protective devices, and the SAIDI and SAIFI indexes according to Bishop (1997). So, each set Λ*<sup>i</sup>* represents a different circuit, and applying the Bishop's algorithms one obtains a result set

where *cS*, *cR* and *cf* are the costs of the main switch reclose switch and fuses, which are

As the set Γ*i* itself cannot express the degree of adaptation the individual Λ*i* to the problem we want to solve, we must provide an expression to summarize Γ*i* in a more convenient, single valued variable, like the *gof* value, described in subsection 3.1. The definition of this *gof* should have a monotonic behaviour as the costs and the SAIDI and SAIFI index increase.

*a b* ( ) SAIDI SAIFI ( ) *<sup>S</sup> <sup>R</sup> <sup>f</sup> gof* = + + ++

be that one that offers the smaller *gof*. With this, our inverted NP-problem can be solved by looking for the individual Λ*i* that presents the smaller *gof*. As all the parameters are limited range integer numbers (tokens), some special care must be taken in the GA routines that deal with new individuals and mutation. So, these routines where rebuild taking into account the discrete character of the chromosomes. The overall behaviour of the GA

The resulting optimized circuit is shown in figure 12, and its corresponding indexes are presented in table 8. The GA code performed the ranging of large number of solutions and configurations, within the universe of about 50 generations of configurations. This demonstrates the GA potential in this kind of analysis and application to discrete allocation equipment's. GA optimization techniques has been showed to be an effective technique to optimize the allocation of protective devices inside the electrical distribution systems.

> Index value SAIDI 2.7694 SAIFI 1.04385 Cost S 60 units Number S 1 Cost R 280 units Number R 3 Cost F 25 units Number F 9 Total Cost 365 units

 κ

*<sup>b</sup>* are constant scale converters. Then, one can say that optimized circuit will

expressed in monetary "units", being one unit the cost of the a monophasic fuse.

κ

optimization code follows the algorithm proposed in figure 2.

We adopted the simple expression

**5.1.3 Results and conclusion** 

Table 8. Indexes values for optimized circuit.

where κ*a* and κ ( ) {SAIDI ,SAIFI , , , } *i i i i Si Ri fi* ΓΛ = *ccc* . (32)

*ccc* . (33)

André P., Ward-Thompson D., Barsony M., (1993), ApJ, 406, 122


**10** 

*1Turkey 2USA* 

**Fusion of Visual and Thermal Images** 

Biometric technologies such as fingerprint, hand geometry, face and iris recognition are widely used to identify a person's identity. The face recognition system is currently one of the most important biometric technologies, which identifies a person by comparing individually acquired face images with a set of pre-stored face templates in a database.

Though the human perception system can identify faces relatively easily, face reorganization using computer techniques is challenging and remains an active research field. Illumination and pose variations are currently the two obstacles limiting performances of face recognition systems. Various techniques have been proposed to overcome those limitations in recent years. For instance, a three dimensional face recognition system has been investigated to solve the illumination and pose variations simultaneously [Bowyer et al., 2004; S. Mdhani et al., 2006]. The illumination variation problem can also be mitigated by additional sources such as infrared (IR) images [D. A. Socolinsky & A. Selinger, 2002].

Thermal face recognition systems have received little attention in comparison with recognition in visible spectra partially due to the high cost associated with IR cameras. Recent technological advances of IR cameras make it practical for face recognition. While thermal face recognition systems are advantageous for detecting disguised faces or when there is no control over illumination, it is challenging to recognize faces in IR images because 1) it is difficult to segment faces from background in low resolution IR images and 2) intensity values in IR images are not consistent due to the fact that different body

The overall goal of this research is to develop computational methods for obtaining efficiently improved images. The research objective will be accomplished by integrating enhanced visual images with IR Images through the following steps: 1) Enhance optical images, 2) Register the enhanced optical images with IR images, and 3) Fuse the optical and

Section 2 surveys related work for IR imaging, image enhancement, image registration and image fusion. Section 3 discusses the proposed nonlinear image enhancement methods.

temperatures result in different intensity values in IR images.

IR images with the help of Genetic Algorithm.

**1. Introduction** 

 **Using Genetic Algorithms** 

*1Turkish Air Force Academy, 2Old Dominion University,* 

Sertan Erkanli1,2, Jiang Li2 and Ender Oguslu1,2

