Application of computational intelligence technique for estimating superconducting transition temperature of YBCO superconductors

doi:10.1016/j.asoc.2016.02.005

Applied Soft Computing

Volume 43, June 2016, Pages 143-149

https://doi.org/10.1016/j.asoc.2016.02.005 Get rights and content

Highlights

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We developed CIM for estimating T_C of doped YBCO superconductors.
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The developed CIM is characterized with high degree of accuracy.
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The results of the developed CIM agree well with the experimental results.
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T_C of any doped YBCO superconductor can be accurately estimated using CIM.

Abstract

Yttrium barium copper oxide (YBCO) is a high temperature superconductor with excellent potential for long distance power transmission applications as well as other applications involving generation of high magnetic field such as magnetic resonance imaging machines in hospitals. Among the uniqueness of this material is its perpetual current carrying ability without loss of energy. Practical applications of YBCO superconductor depend greatly on the value of the superconducting transition temperature (T_C) attained by YBCO superconductor upon doping with other external materials. The number of holes (i.e. doping) present in an atom of copper in CuO₂ planes of YBCO superconductor controls its T_C. Movement of the apical oxygen along CuO₂ planes due to doping gives insight to the way of determining the effect of doping on T_C using the bound related quantity (lattice parameter) that is easily measurable with reasonable high precision. This work employs excellent predictive and generalization ability of computational intelligence technique via support vector regression (SVR) to develop a computational intelligence-based model (CIM) that estimates the T_C of thirty-one different YBCO superconductors using lattice parameters as the descriptors. The estimated superconducting transition temperatures agree with the experimental values with high degree of accuracy. The developed CIM allows quick and accurate estimation of T_C of any fabricated YBCO superconductor without the need for any sophisticated equipment.

Graphical abstract

Introduction

YBCO superconductors are antiferromagnetic insulators with half-filled CuO₂ planes and characterized with high T_C as well as critical current density which make them useful for several practical applications such as magnetic resonance imaging machines. The temperature at which this material exhibits its superconducting nature (that is, carrying current without loss of energy) is known as superconducting transition temperature (T_C) and plays a significant role in its applications. YBCO superconductor having high T_C indicates that little effort is to be done before putting it into applications. Adequate understanding of their charge reservoir layer and the mechanism of charge transfer is required for improving their superconducting transition temperature [1]. Incorporation of dopants such as B, Ce, Al, Ca, Ag and Ni among others into the CuO₂ planes weakens the antiferromagnetic ordering. The concentration of holes in CuO₂ planes as well as the level of the charge of oxygen within the plane contribute enormously to the value of the T_C of this superconducting materials [2]. Meanwhile, ionic substitution has been established as one of the ways of controlling the level of the charge of oxygen within the planes [2] and affects the T_C as a result of the strain and disorder created by the dopants in the lattice [3]. The dependence of doping on the properties paves ways for improving the superconducting properties, in particular, the T_C, since the effect of many external materials on the value of T_C can be easily observed through change in lattice parameters. However, doping dependence on T_C of YBCO superconductors is very difficult to determine since the doping information is not directly contained in their chemical formula. To crown it all, YBCO is characterized with chain and plane sites [Cu(1) and Cu(2) respectively] which makes the distribution of holes between the two sites more difficult to analyze. This present work provides accurate way of determining the effect of dopants on the value of T_C through a computational intelligent technique that has demonstrated excellent predictive and generalization ability in the presence of few descriptive features [4], [5].

The number of holes in every atom of copper in CuO₂ planes of YBCO superconductors can be accounted for by comprehending the movement of apical oxygen {O(4)} along the CuO₂ planes as consequent upon doping. Increase in the level of doping moves the apical oxygen toward the plane. This observed effect of holes on the apical oxygen is easily determined from bounding related properties such as Raman frequency and bound lengths which are not conveniently measurable. Another bound related quantity that can be conveniently measured with reasonable precision is the lattice parameter which sums the bound lengths Cu(1) single bond O(4), Cu(2)Cu(2) and Cu(2)O(4) together. This present work directly relates the lattice parameters to the T_C through computational intelligence technique using SVR. The success of this model paves significant way for quick and accurate estimation of T_C of doped YBCO superconductor and eventually eases the usual high demanding experimental procedures that involve the use of expensive cryostat.

Support vector regression represents a special class of support vector machines which adopts loss function to control the maximum tolerable deviation of its estimates from the target values. It is characterized with absence of local minima and utilization of kernels. It seeks to optimize the generalization bounds by defining the loss function called epsilon intensive loss function which ignores possible errors located within certain distance of the true value [6]. Its excellent predictive and generalization ability is utilized in solving many non-linear real life complex problems that are difficult to approach using conventional means. SVR has been reported as a novel tool of estimating superconducting properties [5], [7] as well as other properties of materials at large [4], [8], [9], [10], [11], [12], [13]. Application of SVR extends to medical diagnosis [14], [15], oil and gas industries [16] and other fields of study [17], [18]. The success of SVR in solving many complex problems and the need to have a novel means of estimating the T_C of doped YBCO superconductors, serve as motivations for carrying out this research work. The choice of SVR as the computational intelligent technique used in this research work is due to its ability to generalize well in the presence of few descriptive features and data-points since limited data-points available in the literatures [4], [6], [19], [20], [21].

The results of our modeling and simulations indicate that the developed CIM is capable of estimating the T_C of doped YBCO superconductors with high degree of accuracy as can be deduced from high coefficients of correlation of 96.65% and 95.75% during the training and testing periods of the model respectively.

The remaining part of this work is organized as follows. Section 2 describes the proposed computational intelligent technique, the test-set-cross validation optimization technique and the generalization performance evaluation of the developed model. Section 3 contains empirical studies that include the description of the dataset, computational methodology and the effect of SVR parameters on the performance of the developed model. Section 4 presents and discuses results while Section 5 states the conclusions and recommendation.

Section snippets

Brief description of the proposed computational intelligent technique

SVR stems from support vector machines which is derived from statistical learning theory and structural risk minimization principle [22], [23]. It employs mapping function called kernel function to map non-linear regression to high dimensional feature space where linear regression is conducted. The complete regression function is presented in Eq. (1) with the inclusion of the mapping function K〈 x_i, x 〉. $f (x) = \sum_{i = 1}^{k} (λ_{i}^{*} - λ_{i}) K 〈 x_{i}, x 〉 + b$ where $λ_{i}^{*}$ and λ_i represent Lagrangian multipliers.

Eq. (1) is

Description of dataset

The development of CIM that estimates the T_C of doped YBCO involves thirty-one lattice parameters and their corresponding T_C. Table 4 presents the dataset as drawn from the literatures [1], [2], [18], [36], [37], [38]. The data-set includes various lattice parameters obtained when dopants such as aluminum (Al), nickel (Ni), calcium (Ca), silver (Ag), boron (B), cobalt (Co) and cerium (Ce) among others were incorporated in the lattice structure of the parent compound YBCO superconductor. The

Result and discussion

SVR was modeled to estimate the T_C of doped YBCO superconductors by training and testing the model using lattice parameters as descriptors. High correlation coefficients were obtained in the course of training and testing the model. The correlation graphs for both training and testing phases are presented in Fig. 9, Fig. 10 respectively. The closeness of the points in both figures indicates minimum deviation of the estimated values from experimental results.

The measures of estimation accuracy

Conclusion and recommendation

We developed CIM for estimating the T_C of doped YBCO superconductors by training and testing SVR using optimum parameters obtained through test-set-cross validation technique. High correlation coefficients of 96.65% and 95.75% were obtained in the course of training and testing the model. The estimated superconducting transition temperatures are very close to the experimental results. This suggests that SVR is capable of estimating T_C of doped YBCO superconductors with high degree of accuracy

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Application of computational intelligence technique for estimating superconducting transition temperature of YBCO superconductors

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

Brief description of the proposed computational intelligent technique

Description of dataset

Result and discussion

Conclusion and recommendation

Phys. Proc.

J. Nat. Gas Sci. Eng.

Comput. Mater. Sci.

Appl. Soft Comput.

Expert Syst. Appl.

Phys. C Supercond.

Phys. C

Comput. Ind.

Inf. Sci.

Inf. Sci.

Phys. C Supercond.

Cryog. Guildf.

Ag-doping-induced coordination incompatibility and its effect on superconductivity in YBCO

J. Supercond.

Structure, microstructure and transport properties of B-doped YBCO system

Phys. C Supercond.

Estimation of superconducting transition temperature TC for superconductors of the doped MgB2 system from the crystal lattice parameters using support vector regression

J. Supercond. Nov. Magn.

Superconducting transition temperature Tc estimation for superconductors of the doped MgB2 system using topological index via support vector regression

J. Supercond. Nov. Magn.

Support vector regression

Neural Inf. Process.

Prediction of superconducting transition temperatures for Fe-based superconductors using support vector machine

Adv. Phys. Theor. Appl.

Investigating the effect of correlation-based feature selection on the performance of neural network in reservoir characterization

J. Nat. Gas Sci. Eng.

Estimation of superconducting transition temperature T_C for superconductors of the doped MgB₂ system from the crystal lattice parameters using support vector regression

Superconducting transition temperature T_c estimation for superconductors of the doped MgB₂ system using topological index via support vector regression