My Digital Twins: from Simple Life Simulation to Development through Evolution. Part 2

Reads: 50  | Likes: 0  | Shelves: 0  | Comments: 0

  • Facebook
  • Twitter
  • Reddit
  • Pinterest
  • Invite

Status: In Progress  |  Genre: Non-Fiction  |  House: Booksie Classic

In this essay, I plan to discuss the issues of creating the best digital twins as a problem of structural optimization and show how natural selection in the form of a genetic algorithm is used for this purpose.

1. Introduction

 

Of course, you know that the digital twin is nothing else but the digital replica of the physical entity as it is explained by Wiki and how it was shown in many examples of Part 1 of this essay. The digital replica is created before its physical twin and, as we discussed, lives a digital life during numerical tests and optimization being used later for manufacturing, repair, modernization, and even for decision making about decommissioning of its physical twin. As we discussed in Part 1, the most important role of the digital twin is to be the best, which means to satisfy all imposed requirements and constraints, before its physical twin will be born. It means that even today the digital twin is the older sibling of the physical one and not the digital model, but the real object is a replica in this case. And there is no “chicken or egg” dilemma. This is an axiom: the modern artificially created structure is the replica of its digital twin; the digital twin is the first, its physical replica is the second. In the near future all physical entities, created by a human being, by artificial intelligence, or by their combination, will be replicas of their digital models.

Let's have a look, which way, how, it can be provided that the digital twin and the future physical replica of this twin are the best. I do not want to discuss the whole scope of twins and refer to other digital models, for example, models of organizational structure or business processes ones, which can be and often are simulated today too; only structures, the major area of my expertise, will be covered by this essay. And, if we are speaking about the best structure, then we should have some kind of criteria to judge which of existing competitors is the best. At the design stage, we use optimization techniques. But if we look at the living structures, for example, flying insects, like a dragonfly, and compare their capabilities with artificial flying objects, like a helicopter, we will see, that the perfection is on the insect's side. It means that Mother Nature has a very effective optimization tool. And we even know the name of this tool, which is natural selection.

In this essay, I plan to discuss the issues of creating the best digital twins as a problem of structural optimization and show how natural selection in the form of a genetic algorithm is used for this purpose.

 

2. Problem Formulation

 

At the beginning let's have a look at my idea of dividing the structural design variables (DV) into three groups: (1) genes or concept parameters of the structure; (2) skeleton, parameters of the shape and frame; (3) muscles, parameters of the load-bearing material distribution, cross-section areas and thicknesses of structural elements; and use of Genetic Algorithm (GA) combined with Sequential Linearization in Optimality Criteria (SLOCM) methods for every genetically identified individual in the artificially created generation of different individuals, imitating the life of every particular specimen, starting with conceiving of a structural embryo by GA, developing its skeleton and muscles systems and training for competition by SLOCM, competing for being selected into a mating pool to be processed by GA, mating, giving offsprings with possible mutation, creating a new generation.

 

The first time this idea was described here: Zarubin, Adaptive Strategy Based on the Genetic Algorithm and a Sequence of Discrete Models in Aircraft Structural Optimization, published in Adaptive Computing in Design and Manufacture, Edited by I.C. Parmee, Springer-Verlag, 1998, ISBN 3-540-76254-X. You can find the article here: https://books.google.ca/books?id=yc3TBwAAQBAJ&pg=PA254&lpg=PA254&dq=ripak+software&source=bl&ots=6q8Z4_ODpc&sig=gLhLqV86zFrklF6pGkh2LcLaWCk&hl=en&sa=X&ved=0ahUKEwjajtamt_TbAhWAIDQIHUtFCik4ChDoAQhMMAc#v=onepage&q=ripak%20software&f=false 

 

Nervous system parameters in the form of the coupling steering system and structure for active load control can be added easily, same as parameters of engine, fuel and electrical systems, landing gears, runway profile for landing/taxi load cases, etc. Modern supercomputing techniques, cluster computing, in particular, give a chance to parallelize a problem solution and provide separate processor to every individual structure for simulating life as a process of new airframe conceiving and embryo development to its sexually mature state via preprocessing of the concept into the coupled finite element (FE), aerodynamic (in the form of computational fluid dynamics or CFD), landing gear, control system, etc. models, design loads and other constraints definition, optimization as a kind of individual structure growing up via skeleton development (shape-skeleton optimization) and muscles system training (material distribution optimization) by SLOCM. The SLOCM is well presented here: Zarubin, Structural sensitivity analysis and optimization in the RIPAK package. Part I, Structural Optimization, Vol.8, No. 2/3, Springer Verlag International, 1994

 

During structural design, we have to satisfy many demands and constraints imposed upon the structure. Models of coupled FE/CFD analysis allow us to calculate values of many constraint functions like stresses, displacements, frequencies, critical loads, critical velocities, etc. Preventing violation of these constraints results in a structural mass increase. Therefore a minimum of structural mass is a very important demand for a successful structure. Usually, variations of m- and r-type parameters are used for structural mass minimization subject to all constraints. The parameters of s-type, as it was said before and is demonstrated below, have to be defined on the basis of more general criteria or goal function, like aircraft efficiency.

 

Goal function, or fitness as we call it in GA, is an important issue. If main parameters {s} are defined and fixed it is a common practice to use structural mass as a goal function of {m} and {r} design variables, but for {s} parameters this function doesn't work properly. For example, the wing aspect ratio ? has a positive sensitivity coefficient for the structural mass, which means that ??increase leads to structural mass increase. But there is a desire to make ??it bigger with the purpose to reduce the induced drag. Structural mass in the role of goal function doesn't allow to do this and ??will be placed to its minimum value in such optimization.

 

There are many other main parameters from the s-type group which in the case of structural mass minimization take its boundary values. For example, another three parameters: wing profile thickness will try to attain its maximum, angle of sweepback - minimum, fuselage length aspect ratio - minimum too. But these three parameters influence drag, cruise velocity, fuel, and transportation efficiency with opposite effect to structural mass. It may happen that the reduction of structural mass will lead to a reduction of aircraft efficiency.

 

I do not want to go for more details and put here only the fact that the criteria of transportation efficiency in the form of relative expenses were taken as a fitness after consideration and comparison of many others. The optimization task was formulated as

 

Minimize Relative Expenses (function of x, r, s) subject to all constraints (functions of x, r, s)

3. Solution Method

 

The solution method is based on the aircraft models' adaptation to optima conditions during the design process. The mechanisms of adaptation provide a progressive modification of some parameters which in the GA approach are considered as a set of genes combined in a chromosome. It means that only principal DVs are treated like genes, other DVs are the parameters that describe not the set of chromosomes, but the sizes of the object. It is very natural to propose that the s-type of the DVs are the principal parameters, which have to be encoded and treated as genes. And other DVs are the parameters of structural "skeleton" (r-type) and "muscular" systems (m-type) which have to be developed and trained accordingly (V.A. Zarubin, Multidisciplinary large-scale structural optimization and the place of genetic algorithms in it, Proceedings of 1st Int. Conf. on Evolutionary Computation and Its Application "EvCA'96", Presidium of the Russian Academy of Science, Moscow, 1996).

Another distinctive peculiarity of my approach is the presence of special procedures of structural development in the form of structural shape-skeleton optimization and sizing, interpreted in “V.A. Zarubin, Genetic algorithm in the role of a shell for structural evolution simulation at the conceptual design stage, Proc. of the 1st on-line workshop on soft computing, WSC1, Nagoya University, Nagoya, August 19-30, 1996” as life simulation and training resulted in development and correction of body (not genes) parameters by the SLOCM's mechanisms of adaptation.

In short, GA is used for creating initial generation, crossbreeding, and conceiving new individuals in the form of an embryo. Each embryo is growing and developing by SLOCM before taking part in a competition to be selected into the mating pool. Crossbreeding and mutation happen in the mating pool by GA and a new generation is created. The process is repeated until convergence.
 

4. Example

 

The short-range passenger aircraft was taken as a subject for numerical demonstration.

Preliminary research revealed that the 100-seat plane with the range of 1500-2000 km would be in demand for the next 20 years.

The main requirements to the aircraft under designing prescribe cabin layout, crew staff of 2 pilots and 3 stewards, 800 km/h of cruise speed, 10000 m of cruise flight height, 1800 m of runway length, 220 km/h of landing speed, 2000 km of range with 12000 kg of payload. Other demands define the levels of reliability, safe damages, safety, and comfort. Technological, maintenance, and environmental restrictions are formulated too.

The optimal problem was formulated as relative expenses minimization subject to minimum structural mass and a broad spectrum of constraints mentioned above.

Vector {s} consists of the following parameters: arw is wing aspect ratio; arf is fuselage aspect ratio; c0 is relative airfoil thickness; nw is wing's narrowing; bs is back-sweep angle; Hcr is cruise height; Vcr is cruise speed; mat is a type of material.

 

Genotype relations are presented in Tables 1 and 2.

 

 

Table 1. Genotype relations, 2 bits strings

DV:

c0

nw

arf

mat

String:

--

--

--

--

00

0.10

2

6.5

D16

01

0.11

2.5

7.5

B95

10

0.12

3

8.5

AlLi1

11

0.13

3.5

10

AlLi2

 

Table 2. Genotype relations, 3 bits strings

DV:

arw

Hcr

Vcr

bs

String:

---

---

---

---

000

7

3

500

0

001

8

6

600

5

010

9

7

650

10

011

10

7.5

700

15

100

10.5

8

750

20

101

11

8.5

800

25

110

11.5

9

850

30

111

12

10

900

35

 

The initial population of 50 individuals was created randomly. The best individual in this generation has the parameters shown in Table 3. The parameters of the worst one are placed in Table 4. Fitness is a value of goal function in our case.

 

Table 3. The best individual of the initial population

arw

arf

Vcr

bs

c0

nw

Hcr

mat

Fitness

10

8.5

700

35

0.11

2.0

10

D16

0.222507

 

Table 4. The worst individual of the initial population

arw

arf

Vcr

bs

c0

nw

Hcr

mat

Fitness

10.5

6.5

900

35

0.13

3.0

8

AlLi1

0.593151

 

Then algorithm described in the fourth section of “Zarubin, Adaptive Strategy Based on the Genetic Algorithm and a Sequence of Discrete Models in Aircraft Structural Optimization, published in Adaptive Computing in Design and Manufacture” is implemented. For the demonstration in this essay, the algorithm is reduced and steps 3.8-3.12 are excluded, which means that structural optimization is done by the FSD approach as a part of the SLOCM algorithm. Each genotype is decoded into grown phenotype and known practical empirical models are used for aircraft appearance forming and take-off mass evaluation. The finite element model and loads are determined for each individual.

Several examples of FE models are presented in fig.1. Then each individual is optimized by SLOCM, its structural and take-off masses of second approximation are calculated and goal function, fitness in the form of relative expenses, is evaluated too. The diagram of fitness values is presented in fig.2.
 

 

Fig.1. Examples of FE-models of six individuals from an initial population

 

Fig.2. Fitness diagram of the initial population


Fig.3. The process of fitness changes during iterations

 

In the initial population maximum value of the goal function was equal to 0.593151, the minimum was equal to 0.222507. During the first 7 generations, the maximum goal function value had big alterations. After this, the tendency for maximum value decrease appeared. Minimum had the reduction tendency from the beginning. The best individual appeared in the ninth generation. Then it disappeared in the 11th generation and appeared again in the 12th one. The 30th generation has the worst individual with 0.2278966 and the best one with 0.2146728 value of goal function. There are 26 individuals in the population with such value of goal function. The fitness diagram on the 30th generation is presented in fig. 4.

Fig.4. Fitness diagram of the thirtieth generation

 

The best and the worst individuals in this generation are presented in Tables 5 and 6.

 

Table 5. The best individual of the thirties population

arw

arf

Vcr

bs

c0

nw

Hcr

mat

Fitness

10.5

6.5

750

35

0.10

2.0

10

D16

0.21

 

Table 6. The worst individual of the thirties population

arw

arf

Vcr

bs

c0

nw

Hcr

mat

Fitness

9

6.5

750

35

0.10

2.0

8.5

D16

0.2278966

 

Aerodynamic and elastic (finite element) models of the second level are shown in fig.5 and 6.


Fig.5. Aerodynamic model of the second level (three projections)

Fig. 6. FE-model of the second level

 

5. Conclusions and further works.

 

There was no ability and sufficient computer power to realize the technology described above at the end of the 90s in full scale. But the essay demonstrates the ability of the natural selection technique in the form of GA-SLOCM combination to be implemented for aircraft structural optimization. The process of conceptual design based on simulation of airframe model evolution via natural selection is presented. There are at least two distinctive features in this approach of GA-SLOCM natural selection method usage in structural optimization.

 

1. Fitness is a function of the set of DVs that consists of genes, skeleton, and muscular variables. For the airframe structure the division of the whole vector {x} into subvectors {s}, {r} and {m} is natural and well-reasoned by their influence upon a structural model. Structural material distribution parameters or m-type of DVs don’t change FE-mesh. These parameters or sizes of element cross-sections play the role of structural muscles. Shape and skeleton parameters or r-type of DVs change FE-mesh geometry. For example, wing ribs may be perpendicular to the forward or rear spar. The orientation influences coordinates of the rib's nodes. But it doesn't change mesh topology (elements spacious relations), element types, material features. And only s-type or conceptual DVs influence airframe and a model appearance. For example, a stabilizer can be a canard, T-tail, or normal; wing may have or may have not the inner strut beam in its structure; rear part of the fuselage may be truss or semimonocoque; different type of structural materials may be implemented and so on. These parameters may change structural appearance, its global features, and FE-mesh radically. Only these s DVs play a role in structural genes.

 

2. Genotype developing has a training phase during which each grown individual is developing before taking part in a competition for a place in the mating pool and a chance to give birth for the offspring. Aviation structures are defined and shaped by aerodynamic and other loads they create and bear. These aerodynamic, landing, taxi, and other loads are dependent on the structure itself. Therefore in aviation structural design, it's natural to have a sequence of structural models used in the iteration process with a more clear definition of structural parameters first and loads then. The life of each individual is simulated as structural development to meet the constraints and satisfy the demands imposed.

 

Now when powerful supercomputers and grid systems are available, the near future works on this subject can be continued in three directions.

 

1. Control system, engine, and landing gear models have to be added to the FE/CFD combination and additional DVs are introduced to the optimization problem accordingly.

 

2. The processing of each individual at the training SLOCM phase is formed as a standalone task available for parallelization at supercomputers and/or computer grids. After breeding by GA and new generation creation each individual is treated in a separate processor. The set of discrete models for accurate structural behavior simulation is implemented at these tasks. The set of models is used to solve such complicated problems as the flutter critical speed evaluation, load distribution determination, aircraft balancing during the maneuver, dynamic response during landing and taxi, etc. The aerodynamic model (CFD) allows evaluating the aerodynamic pressure distribution on aircraft lifting surfaces. The inertia model describes the non-structural (payload, fuel, equipment, engines, etc.) mass distribution. This model defines inertia forces, a center of mass position, and other inertia characteristics. The finite element model (FEM) describes the elastic features of the structure, integrates the loads created by aerodynamic and inertia models, and defines the angles of attack of the wing's panels for aerodynamic analysis. Displacements, strains, stresses, critical load factors, natural modes, and frequencies of the structure are evaluated by finite element analysis. All this was demonstrated in the simplified example above. Now it has to be done for the full-scale tasks.

 

3. The idea of a special environment for structural evolution presented as the Net Shell for Designing Control (NSDC) and described in V.A. Zarubin, Genetic algorithm in the role of a shell for structural evolution simulation at the conceptual design stage, Proc. of the 1st on-line workshop on soft computing, WSC1, Nagoya University, Nagoya, August 19-30, 1996, has to be realized. The shell provides engineers with the possibilities to present the design process as a set of subprocesses and tasks distributed through departments, teams, personnel, and their desks; to prescribe the technology, databases, data input, processing by particular software and output at each desk; to organize these data flow; to define time-table and responsibility, etc. The NSCD must be a fully portable program that can be parallelized for usage in supercomputers and computer grids. Expert systems, discussed in Part 1, have to be developed as a part of NSCD to provide a smart interface between NSCD and the end-users. Business process models can be added to this environment too, but it's a different story :) But if this branch of digital twins is interesting for you, there is some information here: Fundamentals of the process approach to open system management, Proceedings of the 5th international “Complex systems: control and modeling problems” conference, Samara, 2003. Imitation models and optimization were used in the research described there.

 

 

 

 

 


Submitted: May 28, 2021

© Copyright 2021 slava zarubin. All rights reserved.

  • Facebook
  • Twitter
  • Reddit
  • Pinterest
  • Invite

Add Your Comments:


Facebook Comments