Artificial immune system for optimal design of composite hydrogen storage vessel

doi:10.1016/j.commatsci.2009.07.015

Computational Materials Science

Volume 47, Issue 1, November 2009, Pages 261-267

https://doi.org/10.1016/j.commatsci.2009.07.015 Get rights and content

Abstract

Based on the clonal selection principle in the biological immunology, an artificial immune system (AIS) is proposed to optimize the weight of Al-carbon fiber/epoxy composite hydrogen storage vessels under burst pressure constraint. The AIS simulates the generation of the antigens, the combination of the antigens and antibodies, and the selection, cloning and hypermutation of B cells, the maintenance of diverse antibody cells, the generation of the memory cells with high affinities and the death of the antibody cells with low affinities. Effects of the antibody size and the iterative number on the optimization results are explored. By comparison, the AIS shows higher search velocity and precision than the genetic algorithm and simulated annealing.

Introduction

Economical and efficient hydrogen storage technology plays an important role in dominating the new energy utilization such as the hydrogen fuel cell vehicle all over the world. Due to a series of advantages of high stiffness, high strength and low density, carbon fiber/epoxy composites are increasingly used to develop the lightweight high pressure hydrogen storage vessels [1], [2].

Because of the low density of hydrogen and the limited space available on the vehicle, the basic requirements for the composite vessels put forward by the hydrogen fuel cell system are small volume, low weight, low cost, safe and reliable. However, the composite vessels may generally be subjected to complex environment such as high pressure and high temperature. This not only presents a strong challenge to the physical and mechanical performance of structure and material, but also to the excellent design about how to achieve a perfect combination of favorable safety performance and low cost under a certain design condition [3], [4].

By introducing the simple mathematical models or the gradient-based search methods [5], [6], [7], [8], several research is performed to optimize the composite laminates for different objectives of stiffness, strength and weights. However, in view of the complexity of structural sizes and material properties, they can hardly be competent for the optimal design of laminated structures with large-scale discrete design space with a lot of design parameters. Currently, various intelligent optimization algorithms that simulate the evolutionary principles in the disciplines of computational biology, physics and immunology, have been successfully applied to optimize the composite structures with large-scale design space. The popular algorithms are genetic algorithm, simulated annealing and artificial immune system. The genetic algorithm, which is originally proposed by Holland [9] to simulate the evolution of biology, has been widely used to conduct the optimal design of composite laminated structures [10], [11], [12], [13], [14], [15], [16], [17], [18]. However, the local search ability is relatively weak in contrast with its strong global search ability. In addition, the genetic algorithm is confronted with the problem of “prematurity” for solving the multi-peak optimization space, which may provide the erroneous optimum results. Since Kirkpatrick et al. [19] first proposed the simulated annealing to describe the annealing process of the high-temperature metal particles in statistical thermodynamics, several work is performed with respect to the optimal design of composite structures [20], [21], [22], [23], [24]. However, the search velocity and calculation precision are not high due to the critical damand for large iterative number.

In this paper, the artificial immune system (AIS) based on the clonal selection principle in the biological immunology is applied to the optimal design of composite hydrogen storage vessels. The AIS defends against the invasion of the foreign pathogeny and protects the body through the antigen recognization, the cloning and hypermutation of B cells, the generation of memory cells and the death of antibody cells with low affinities. The AIS compares the objective function and constraint conditions to the antigens, and compares the applicable results to the antibodies, and compares the applicable objective to the affinity between the antigen and antibody. The remarkable advantages of the AIS over the genetic algorithm lie in the maintenance of diverse antibody cells and the presence of memory cells with high affinities. Already, Omkar et al. [25] proposed an AIS to perform the optimal design of simple composite laminated structures. Yet, the unconstrained optimization appears to be imperfect for practical engineering application. In terms of the Al-carbon fiber/epoxy composite hydrogen storage vessels, an AIS in this analysis is proposed to solve the weight minimum problem under the burst pressure constraint. A penalty function is proposed to deal with the constrained problem. Effects of the antibody size and the iterative number are explored. The optimization results using the AIS are also compared with those obtained using the genetic algorithm and simulated annealing.

Section snippets

The structure of composite hydrogen storage vessels

The following analysis concentrates on a composite hydrogen storage vessel, as shown in Fig. 1. The vessel is composed of a 6061-T6 aluminum liner and $n_{s}$ T700 fiber/0164 epoxy composite layers. For the carbon fiber/epoxy composite layers, the spiral and hoop winding occurs at the cylinder of vessel, but only the spiral winding appears at the head of vessel.

The spiral winding angle $α_{0}$ at the cylinder is determined by [26] $α_{0} = \arcsin (r / R_{0})$ where r represents the radius of the polar axis, which is

Basic design conditions

The basic design conditions are summarized as

(1)
The working pressure is P_w;
(2)
The capacity of composite vessel is V;
(3)
Minimize $W = f (h, r), (h \in F_{1}, r \in F_{2})$

P (h, r) \geq q * P_{w}

where the weight W and actual burst pressure P of composite vessels are functions of the thickness h and the polar radius r. F₁ and F₂ are the variable ranges for h and r, respectively. q is the stress ratio of the actual burst pressure P to the working pressure P_w.

Biological immune system

The biological immune system is a complex, adaptive, pattern-recognition system which is composed of the interrelated organs, tissues, cells and molecules. These components collectively protect the body from bacterial, parasitic, fungal, viral infections and from the growth of tumor cells. The substance which causes the response of the immune system to defend against the pathogeny is called antigen. An antigen may be a foreign substance from the environment such as the chemicals, bacteria,

Results and discussion

The constant parameters in the optimization analysis of composite vessels are chosen as: the capacity of the composite vessels V = 0.01 m³, the inner radius and length of the cylinder are 100 mm and 220 mm, respectively, the number of composite layers is n_s = 10, the thickness of the liner is 3 mm, the thickness of each composite layer at the cylinder is h $\in$ [1.2,1.6] mm, the radius of the polar axis is r $\in$ [30,45] mm, the work pressure of composite vessels is $P_{w} = 70 MPa$ , the stress ratio is q = 2.35, the

Conclusions

An artificial immune system (AIS) based on the biological clonal selection principle is proposed to optimize the weight of composite vessels under burst pressure constraint. A penalty function is proposed to deal with the constrained problem. The AIS takes into account the affinity between the antigen and antibody, the cloning, hypermutation of B cells, the generation of the memory cells and the death of the antobodies with low affinities. By comparison, the proposed AIS exhibits more favorable

Acknowledgements

This research is supported by the Chinese postdoc science funding (Number: 20070411175), high-technology research and development program (863 program) of China (Numbers: 2006AA05Z143, 2006AA11A188 and 2006AA11A187) and the key project of national programs for fundamental research and development (973 program) of China (Number: 2007CB209706).

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Artificial immune system for optimal design of composite hydrogen storage vessel

Abstract

Introduction

Section snippets

The structure of composite hydrogen storage vessels

Basic design conditions

Biological immune system

Results and discussion

Conclusions

Acknowledgements

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