Experimental Research on Rapid Localization of Acoustic Source in a Cylindrical Shell Structure without Knowledge of the Velocity Profile

Acoustic source localization in a large pressure vessel or a storage tank-type cylindrical structure is important in preventing structural failure. However, this can be challenging, especially for cylindrical pressure vessels and tanks that are made of anisotropic materials. The large area of the cylindrical structure often requires a substantial number of sensors to locate the acoustic source. This paper first applies conventional acoustic source localization techniques developed for the isotropic, flat plate-type structures to cylindrical structures. The experimental results show that the conventional acoustic source localization technique is not very accurate for source localization on cylindrical container surfaces. Then, the L-shaped sensor cluster technique is applied to the cylindrical surface of the pressure vessel, and the experimental results prove the applicability of using this technique. Finally, the arbitrary triangle-shaped sensor clusters are attached to the surface of the cylindrical structure to locate the acoustic source. The experimental results show that the two acoustic source localization techniques using sensor clusters can be used to monitor the location of acoustic sources on the surface of anisotropic cylindrical vessels, using a small number of sensors. The arbitrarily triangle-shaped sensors can be arbitrarily placed in a cluster on the surface of the cylindrical vessel. The results presented in this paper provide a theoretical and experimental basis for the surface acoustic source localization method for a cylindrical pressure vessel and lay a theoretical foundation for its application.

On Triangles with Sides That Form an Arithmetic Progression

Properties of triangles such that the squares of their sides form an arithmetic progression were studied in 2018. In this paper, triangles with sides that form an arithmetic progression are described. Let a, b, c be sides of an arbitrary triangle ABC. If sides b, a, c of the triangle ABC form an arithmetic progression then, for example, the equality a=(b+c)/2 (b<a<c) holds. The class of triangles for which a=(b+c)/2 is greater than the class of triangles for which b, a, c form an arithmetic progression. In this paper, we study the properties of triangles for which this equality holds. Thus, triangles with sides that form an arithmetic progression are described with the help of the parameters p, R, r. Classes of rectangular triangles, triangles with angle 30°, triangles with angle 60°, triangles with angle 120° are studied and described.

Two New Equilateral Triangles Associated with a Triangle

In this short paper, we study two new equilateral triangles associated with an arbitrary triangle and further generalizations.

Faces of 2-Dimensional Simplex of Order and Chain Polytopes

Each of the descriptions of vertices, edges, and facets of the order and chain polytope of a finite partially ordered set are well known. In this paper, we give an explicit description of faces of 2-dimensional simplex in terms of vertices. Namely, it will be proved that an arbitrary triangle in 1-skeleton of the order or chain polytope forms the face of 2-dimensional simplex of each polytope. These results mean a generalization in the case of 2-faces of the characterization known in the case of edges.

Comparison Analysis of Fuzzy AHP and AHP in Multiple-Decision Making Problem Using Statistic Approach

Analytic Hierarchy Process (AHP) is a robust approach for decision making under complex criteria. Decision makers express their opinions differently and arbitrarily, giving rise to uncertainty in the ranking of alternatives. Fuzzy AHP was then developed and applied under those circumstances to reduce the uncertainty. This paper generates a string of randomly simulated data to represent completely arbitrary triangle fuzzy number, and based on these data compare Fuzzy AHP with classical AHP in statistical manner. Then the paper conducts a series of SPSS linear regressions for this comparison with two critical factors: the pairwise comparison weight value of AHP and the fuzzy value range of Fuzzy AHP. The regression shows how these two factors affect the differences between the two approaches. Results indicate that the pairwise comparison weight value of AHP significantly influences the difference while the fuzzy value range does not. In general, Fuzzy AHP narrows the final weights between each criterion, but in some extreme situations, this conclusion does not exist any more.