First, the global error used as the threshold value for screening solutions was unknown. Then, we evaluated all 300 cases from iteration 1 to the last iteration and screened them for HM solutions. The percentage of relative discrepancies between the current and previous proxy versus iteration number ( Tripoppoom et al., 2019).Īfter that, the proxy-based MCMC algorithm generated the last iteration cases with a different filtering scheme using the lowest global error value for all 25 cases. The objective is to maximize this determinant (if there is no correlation at all, it is equal to 1 and the design is orthogonal).įigure 4.8. This criterion is calculated using the determinant of the parameter correlation matrix. This means that they are as uncorrelated as possible (if there is a correlation between two parameters A and B, it is difficult to separate the effect of A from the effect of B). Independence: it is desirable for the parameters to be as orthogonal as possible. The objective is to maximize this distance − This criterion is calculated using the distance between the closest two points on the design. Space-filling: the trials of the LHS DOE should fill the input domain as much as possible. The main characteristics of LHS designs are: − This design is not unique and the space-filling and independence criteria are relative. In this case, a very high number of designs are generated and the design which contains the best space-filling and independence criteria is selected. LHS designs are particularly suitable for numerical designs of experiments. The objective is to maximize this determinant (if there is no correlation at all, it is equal to 1 and the design is orthogonal). This means that they are as uncorrelated as possible (if there is correlation between two parameters A and B, it is difficult to separate the effect of A from that of B). The objective is to maximize this distance – Space-filling: it is desirable for the design’s test to fill the input domain as much as possible. The main properties expected for LHS designs are: – However, the names of higher-order hypercubes do not appear to be in common use for higher powers.* Values in parenthesis are design values. As a result, the act of raising a number to 2 or 3 is more commonly referred to as " squaring" and "cubing", respectively. Similarly, the exponent 3 will yield a perfect cube, an integer which can be arranged into a cube shape with a side length of the base. For example, the exponent 2 will yield a square number or "perfect square", which can be arranged into a square shape with a side length corresponding to that of the base. Generalized hypercubesĪny positive integer raised to another positive integer power will yield a third integer, with this third integer being a specific type of figurate number corresponding to an n-cube with a number of dimensions corresponding to the exponential. A unit hypercube's longest diagonal in n dimensions is equal to n. It is a closed, compact, convex figure whose 1- skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length. In geometry, a hypercube is an n-dimensional analogue of a square ( n = 2) and a cube ( n = 3). For the four-dimensional object known as “the” hypercube, see Tesseract. For internetwork topology, see Hypercube internetwork topology.
For the computer architecture, see Connection Machine. This article is about the mathematical concept.
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