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So far, the research on topology optimization against noise has mainly addressed frequency-domain problems, while time-domain analysis is also widely used in practical engineering. Nonetheless, the topology optimization work on the latter was rarely reported due to its complexity. This article presents a new topology optimization scheme of bi-material curved shell structure to reduce the time-domain noise generated by transient vibration. A finite element formulation for an eight-node curved shell element is presented. The Newmark integral method is employed to calculate transient responses, and the obtained results are input into the time-domain boundary element method to predict transient sound pressure. In the optimization model, the volumetric densities of material in a bi-material interpolation model constructed by the solid isotropic material with penalization model are chosen as the design variables; the time integral of the squared sound pressure on structural surfaces or prescribed reference points in acoustic medium over a specified time interval of interest is taken as the objective function; and the constraint on material volume is considered. A volume-preserving Heaviside penalization is introduced to suppress gray elements. Furthermore, the calculation of time-domain sound radiation sensitivity is transformed into the following two processes: (a) the derivation of transient response based on the Newmark integral method; (b) the derivation of transient sound pressure based on the discrete time-domain boundary integral equation. Numerical examples demonstrate the validity of the approach proposed in this article. The influences of volume-preserving Heaviside penalization, volume constraint, loading position and form, and selection of objective function on the optimal design are discussed.

In this paper, resource flow variables are extracted from the internal structural features of the logistics distribution process and a new method for optimizing the internal structure of the logistics distribution system by using the characteristic state space is proposed. The characteristic state equation is constructed to represent the input and output resources of each basic logistics activity. The basic logistics activity equation is iterated according to the resource flow, and the implementation of the basic logistics process is visually and quantitatively expressed in the form of the characteristic state matrix. According to the nature of the characteristic state space, the optimization problem of the logistics distribution system is transformed into a critical path-planning problem, the gradient calculation of the objective function is solved, and an improved genetic algorithm is proposed. This accelerates the convergence speed of the algorithm and reduces the running time of the optimization process. Taking a listed logistics distribution enterprise as an example, the optimization algorithm is verified, which proves the advantages of the algorithm and provides a new method and theoretical basis for the analysis and optimization of the logistics distribution system.

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A reasonable rain gauge network layout can provide accurate regional rainfall data and effectively support the monitoring, development and utilization of water resources. Currently, an increasing number of network design methods based on entropy targets are being applied to network design. The discretization of data is a common method of obtaining the probability in calculations of information entropy. To study the application of different discretization methods and different entropy-based methods in the design of rain gauge networks, this paper compares and analyzes 9 design results for rainy season rain gauge networks using three commonly used discretization methods (A1, SC and ST) and three entropy-based network design algorithms (MIMR, HT and HC) from three perspectives: the joint entropy, spatiality, and accuracy of the network, as evaluation indices. The results show that the variation in network information calculated by the A1 and ST methods for rainy season rain gauge data is too large or too small compared to that calculated by the SC method, and also that the MIMR method performs better in terms of spatiality and accuracy than the HC and HT methods. The comparative analysis results provide a reference for the selection of discrete methods and entropy-based objectives in rain gauge network design, and provides a way to explore a more suitable rain gauge network layout scheme.