**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**21

# Search results for: Hypercube

##### 21 Improvement of Central Composite Design in Modeling and Optimization of Simulation Experiments

**Authors:**
A. Nuchitprasittichai,
N. Lerdritsirikoon,
T. Khamsing

**Abstract:**

_{2}liquefaction based on external refrigeration with two refrigeration circuits was used as a simulation case study. Latin Hypercube Sampling (LHS) was purposed to combine with existing Central Composite Design (CCD) samples to improve the performance of CCD in generating the second order model of the system. The second order model was then used as the objective function of the optimization problem. The results showed that adding LHS samples to CCD samples can help capture surface curvature characteristics. Suitable number of LHS sample points should be considered in order to get an accurate nonlinear model with minimum number of simulation experiments.

**Keywords:**
Central composite design,
CO2 liquefaction,
Latin Hypercube Sampling,
simulation – based optimization.

##### 20 Considerations for Effectively Using Probability of Failure as a Means of Slope Design Appraisal for Homogeneous and Heterogeneous Rock Masses

**Authors:**
Neil Bar,
Andrew Heweston

**Abstract:**

Probability of failure (PF) often appears alongside factor of safety (FS) in design acceptance criteria for rock slope, underground excavation and open pit mine designs. However, the design acceptance criteria generally provide no guidance relating to how PF should be calculated for homogeneous and heterogeneous rock masses, or what qualifies a ‘reasonable’ PF assessment for a given slope design. Observational and kinematic methods were widely used in the 1990s until advances in computing permitted the routine use of numerical modelling. In the 2000s and early 2010s, PF in numerical models was generally calculated using the point estimate method. More recently, some limit equilibrium analysis software offer statistical parameter inputs along with Monte-Carlo or Latin-Hypercube sampling methods to automatically calculate PF. Factors including rock type and density, weathering and alteration, intact rock strength, rock mass quality and shear strength, the location and orientation of geologic structure, shear strength of geologic structure and groundwater pore pressure influence the stability of rock slopes. Significant engineering and geological judgment, interpretation and data interpolation is usually applied in determining these factors and amalgamating them into a geotechnical model which can then be analysed. Most factors are estimated ‘approximately’ or with allowances for some variability rather than ‘exactly’. When it comes to numerical modelling, some of these factors are then treated deterministically (i.e. as exact values), while others have probabilistic inputs based on the user’s discretion and understanding of the problem being analysed. This paper discusses the importance of understanding the key aspects of slope design for homogeneous and heterogeneous rock masses and how they can be translated into reasonable PF assessments where the data permits. A case study from a large open pit gold mine in a complex geological setting in Western Australia is presented to illustrate how PF can be calculated using different methods and obtain markedly different results. Ultimately sound engineering judgement and logic is often required to decipher the true meaning and significance (if any) of some PF results.

**Keywords:**
Probability of failure,
point estimate method,
Monte-Carlo simulations,
sensitivity analysis,
slope stability.

##### 19 Efficiency of Robust Heuristic Gradient Based Enumerative and Tunneling Algorithms for Constrained Integer Programming Problems

**Authors:**
Vijaya K. Srivastava,
Davide Spinello

**Abstract:**

This paper presents performance of two robust gradient-based heuristic optimization procedures based on 3^{n} enumeration and tunneling approach to seek global optimum of constrained integer problems. Both these procedures consist of two distinct phases for locating the global optimum of integer problems with a linear or non-linear objective function subject to linear or non-linear constraints. In both procedures, in the first phase, a local minimum of the function is found using the gradient approach coupled with hemstitching moves when a constraint is violated in order to return the search to the feasible region. In the second phase, in one optimization procedure, the second sub-procedure examines 3^{n} integer combinations on the boundary and within hypercube volume encompassing the result neighboring the result from the first phase and in the second optimization procedure a tunneling function is constructed at the local minimum of the first phase so as to find another point on the other side of the barrier where the function value is approximately the same. In the next cycle, the search for the global optimum commences in both optimization procedures again using this new-found point as the starting vector. The search continues and repeated for various step sizes along the function gradient as well as that along the vector normal to the violated constraints until no improvement in optimum value is found. The results from both these proposed optimization methods are presented and compared with one provided by popular MS Excel solver that is provided within MS Office suite and other published results.

**Keywords:**
Constrained integer problems,
enumerative search algorithm,
Heuristic algorithm,
tunneling algorithm.

##### 18 A Hypercube Social Feature Extraction and Multipath Routing in Delay Tolerant Networks

**Authors:**
S. Balaji,
M. Rajaram,
Y. Harold Robinson,
E. Golden Julie

**Abstract:**

Delay Tolerant Networks (DTN) which have sufficient state information include trajectory and contact information, to protect routing efficiency. However, state information is dynamic and hard to obtain without a global and/or long-term collection process. To deal with these problems, the internal social features of each node are introduced in the network to perform the routing process. This type of application is motivated from several human contact networks where people contact each other more frequently if they have more social features in common. Two unique processes were developed for this process; social feature extraction and multipath routing. The routing method then becomes a hypercube–based feature matching process. Furthermore, the effectiveness of multipath routing is evaluated and compared to that of single-path routing.

**Keywords:**
Delay tolerant networks,
entropy,
human contact networks,
hyper cubes,
multipath Routing,
social features.

##### 17 Hamiltonian Related Properties with and without Faults of the Dual-Cube Interconnection Network and Their Variations

**Authors:**
Shih-Yan Chen,
Shin-Shin Kao

**Abstract:**

**Keywords:**
Hypercubes,
dual-cubes,
fault-tolerant
hamiltonian property,
dual-cube extensive networks,
dual-cube-like
networks.

##### 16 FEM Models of Glued Laminated Timber Beams Enhanced by Bayesian Updating of Elastic Moduli

**Authors:**
L. Melzerová,
T. Janda,
M. Šejnoha,
J. Šejnoha

**Abstract:**

Two finite element (FEM) models are presented in this paper to address the random nature of the response of glued timber structures made of wood segments with variable elastic moduli evaluated from 3600 indentation measurements. This total database served to create the same number of ensembles as was the number of segments in the tested beam. Statistics of these ensembles were then assigned to given segments of beams and the Latin Hypercube Sampling (LHS) method was called to perform 100 simulations resulting into the ensemble of 100 deflections subjected to statistical evaluation. Here, a detailed geometrical arrangement of individual segments in the laminated beam was considered in the construction of two-dimensional FEM model subjected to in fourpoint bending to comply with the laboratory tests. Since laboratory measurements of local elastic moduli may in general suffer from a significant experimental error, it appears advantageous to exploit the full scale measurements of timber beams, i.e. deflections, to improve their prior distributions with the help of the Bayesian statistical method. This, however, requires an efficient computational model when simulating the laboratory tests numerically. To this end, a simplified model based on Mindlin’s beam theory was established. The improved posterior distributions show that the most significant change of the Young’s modulus distribution takes place in laminae in the most strained zones, i.e. in the top and bottom layers within the beam center region. Posterior distributions of moduli of elasticity were subsequently utilized in the 2D FEM model and compared with the original simulations.

**Keywords:**
Bayesian inference,
FEM,
four point bending test,
laminated timber,
parameter estimation,
prior and posterior
distribution,
Young’s modulus.

##### 15 Fault-Tolerant Optimal Broadcast Algorithm for the Hypercube Topology

**Authors:**
Lokendra Singh Umrao,
Ravi Shankar Singh

**Abstract:**

**Keywords:**
Fault tolerance,
hypercube,
broadcasting,
link/node
faults,
routing.

##### 14 Construction of Space-Filling Designs for Three Input Variables Computer Experiments

**Authors:**
Kazeem A. Osuolale,
Waheed B. Yahya,
Babatunde L. Adeleke

**Abstract:**

**Keywords:**
Computer Experiments,
Latin Squares,
Latin
Hypercube Designs,
Orthogonal Array,
Space-filling Designs.

##### 13 Sensitivity Analysis of Principal Stresses in Concrete Slab of Rigid Pavement Made From Recycled Materials

**Authors:**
Aleš Florian,
Lenka Ševelová

**Abstract:**

Complex sensitivity analysis of stresses in a concrete slab of the real type of rigid pavement made from recycled materials is performed. The computational model of the pavement is designed as a spatial (3D) model, is based on a nonlinear variant of the finite element method that respects the structural nonlinearity, enables to model different arrangements of joints, and the entire model can be loaded by the thermal load. Interaction of adjacent slabs in joints and contact of the slab and the subsequent layer are modeled with the help of special contact elements. Four concrete slabs separated by transverse and longitudinal joints and the additional structural layers and soil to the depth of about 3m are modeled. The thickness of individual layers, physical and mechanical properties of materials, characteristics of joints, and the temperature of the upper and lower surface of slabs are supposed to be random variables. The modern simulation technique Updated Latin Hypercube Sampling with 20 simulations is used. For sensitivity analysis the sensitivity coefficient based on the Spearman rank correlation coefficient is utilized. As a result, the estimates of influence of random variability of individual input variables on the random variability of principal stresses s1 and s3 in 53 points on the upper and lower surface of the concrete slabs are obtained.

**Keywords:**
Concrete,
FEM,
pavement,
sensitivity,
simulation.

##### 12 Maximum Induced Subgraph of an Augmented Cube

**Authors:**
Meng-Jou Chien,
Jheng-Cheng Chen,
Chang-Hsiung Tsai

**Abstract:**

Let max_{ζG}(*m*) denote the maximum number of edges in a subgraph of graph *G *induced by *m* nodes. The *n*-dimensional augmented cube, denoted as *AQn*, a variation of the hypercube, possesses some properties superior to those of the hypercube. We study the cases when *G* is the augmented cube *AQn*.

**Keywords:**
Interconnection network,
Augmented cube,
Induced subgraph,
Bisection width.

##### 11 Reliability Evaluation of Composite Electric Power System Based On Latin Hypercube Sampling

**Authors:**
R. Ashok Bakkiyaraj,
N. Kumarappan

**Abstract:**

This paper investigates the suitability of Latin Hypercube sampling (LHS) for composite electric power system reliability analysis. Each sample generated in LHS is mapped into an equivalent system state and used for evaluating the annualized system and load point indices. DC loadflow based state evaluation model is solved for each sampled contingency state. The indices evaluated are loss of load probability, loss of load expectation, expected demand not served and expected energy not supplied. The application of the LHS is illustrated through case studies carried out using RBTS and IEEE-RTS test systems. Results obtained are compared with non-sequential Monte Carlo simulation and state enumeration analytical approaches. An error analysis is also carried out to check the LHS method’s ability to capture the distributions of the reliability indices. It is found that LHS approach estimates indices nearer to actual value and gives tighter bounds of indices than non-sequential Monte Carlo simulation.

**Keywords:**
Composite power system,
Latin Hypercube sampling,
Monte Carlo simulation,
Reliability evaluation,
Variance analysis.

##### 10 Independent Spanning Trees on Systems-on-chip Hypercubes Routing

**Authors:**
Eduardo Sant'Ana da Silva,
Andre Luiz Pires Guedes,
Eduardo Todt

**Abstract:**

Independent spanning trees (ISTs) provide a number of advantages in data broadcasting. One can cite the use in fault tolerance network protocols for distributed computing and bandwidth. However, the problem of constructing multiple ISTs is considered hard for arbitrary graphs. In this paper we present an efficient algorithm to construct ISTs on hypercubes that requires minimum resources to be performed.

**Keywords:**
Hypercube,
Independent Spanning Trees,
Networks
On Chip,
Systems On Chip.

##### 9 Optimization of Parametric Studies Using Strategies of Sampling Techniques

**Authors:**
Lenka Ševelová,
Aleš Florian

**Abstract:**

**Keywords:**
Concrete,
pavement,
simulation,
reliability,
Latin Hypercube Sampling,
parametric studies.

##### 8 Statistical Analysis of Stresses in Rigid Pavement

**Authors:**
Aleš Florian,
Lenka Ševelová,
Rudolf Hela

**Abstract:**

**Keywords:**
concrete,
FEM,
pavement,
simulation.

##### 7 Cycle Embedding in Folded Hypercubes with More Faulty Elements

**Authors:**
Wen-Yin Huang,
Jia-Jie Liu,
Jou-Ming Chang

**Abstract:**

Faults in a network may take various forms such as hardware/software errors, vertex/edge faults, etc. Folded hypercube is a well-known variation of the hypercube structure and can be constructed from a hypercube by adding a link to every pair of nodes with complementary addresses. Let FFv (respectively, FFe) be the set of faulty nodes (respectively, faulty links) in an n-dimensional folded hypercube FQn. Hsieh et al. have shown that FQn - FFv - FFe for n ≥ 3 contains a fault-free cycle of length at least 2n -2|FFv|, under the constraints that (1) |FFv| + |FFe| ≤ 2n - 4 and (2) every node in FQn is incident to at least two fault-free links. In this paper, we further consider the constraints |FFv| + |FFe| ≤ 2n - 3. We prove that FQn - FFv - FFe for n ≥ 5 still has a fault-free cycle of length at least 2n - 2|FFv|, under the constraints : (1) |FFv| + |FFe| ≤ 2n - 3, (2) |FFe| ≥ n + 2, and (3) every vertex is still incident with at least two links.

**Keywords:**
Folded hypercubes,
interconnection networks,
cycle embedding,
faulty elements.

##### 6 The Spanning Laceability of k-ary n-cubes when k is Even

**Authors:**
Yuan-Kang Shih,
Shu-Li Chang,
Shin-Shin Kao

**Abstract:**

**Keywords:**
container,
Hamiltonian,
k-ary n-cube,
m*-connected.

##### 5 Accurate And Efficient Global Approximation using Adaptive Polynomial RSM for Complex Mechanical and Vehicular Performance Models

**Authors:**
Y. Z. Wu,
Z. Dong,
S. K. You

**Abstract:**

**Keywords:**
Global approximation,
polynomial response surface,
domain decomposition,
domain combination,
multiphysics modeling,
hybrid powertrain optimization

##### 4 A Systematic Approach for Finding Hamiltonian Cycles with a Prescribed Edge in Crossed Cubes

**Authors:**
Jheng-Cheng Chen,
Chia-Jui Lai,
Chang-Hsiung Tsai,

**Abstract:**

The crossed cube is one of the most notable variations of hypercube, but some properties of the former are superior to those of the latter. For example, the diameter of the crossed cube is almost the half of that of the hypercube. In this paper, we focus on the problem embedding a Hamiltonian cycle through an arbitrary given edge in the crossed cube. We give necessary and sufficient condition for determining whether a given permutation with n elements over Zn generates a Hamiltonian cycle pattern of the crossed cube. Moreover, we obtain a lower bound for the number of different Hamiltonian cycles passing through a given edge in an n-dimensional crossed cube. Our work extends some recently obtained results.

**Keywords:**
Interconnection network,
Hamiltonian,
crossed cubes,
prescribed edge.

##### 3 A Hamiltonian Decomposition of 5-star

**Authors:**
Walter Hussak,
Heiko Schröder

**Abstract:**

Star graphs are Cayley graphs of symmetric groups of permutations, with transpositions as the generating sets. A star graph is a preferred interconnection network topology to a hypercube for its ability to connect a greater number of nodes with lower degree. However, an attractive property of the hypercube is that it has a Hamiltonian decomposition, i.e. its edges can be partitioned into disjoint Hamiltonian cycles, and therefore a simple routing can be found in the case of an edge failure. The existence of Hamiltonian cycles in Cayley graphs has been known for some time. So far, there are no published results on the much stronger condition of the existence of Hamiltonian decompositions. In this paper, we give a construction of a Hamiltonian decomposition of the star graph 5-star of degree 4, by defining an automorphism for 5-star and a Hamiltonian cycle which is edge-disjoint with its image under the automorphism.

**Keywords:**
interconnection networks,
paths and cycles,
graphs andgroups.

##### 2 The Panpositionable Hamiltonicity of k-ary n-cubes

**Authors:**
Chia-Jung Tsai,
Shin-Shin Kao

**Abstract:**

**Keywords:**
Hamiltonian,
panpositionable,
bipanpositionable,
k-ary n-cube.

##### 1 CSOLAP (Continuous Spatial On-Line Analytical Processing)

**Authors:**
Taher Omran Ahmed,
Abdullatif Mihdi Buras

**Abstract:**

**Keywords:**
Continuous Data,
Data warehousing,
DecisionSupport,
SOLAP