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This paper aims to use the crankshaft-bearing system of a four-cylinder internal combustion engine as the studying object, and develop a multi-objective optimization design of the crankshaft-bearing. In the current optimization design of engine crankshaft-bearing, only the crankshaft-bearing was considered as the studying object. However, the corresponding relations of major structure dimensions exist between the crankshaft and the crankshaft-bearing in internal combustion engine, and there are the interaction effects between the crankshaft and the crankshaft-bearing during the operation of internal combustion engine.

The crankshaft mass and the total frictional power loss of crankshaft-bearing s are selected as the objective functions in the optimization design of crankshaft-bearing. The Particle Swarm Optimization algorithm based on the idea of decreasing strategy of inertia weight with the exponential type is used in the optimization calculation.

The total frictional power loss of crankshaft-bearing and the crankshaft mass are decreased, respectively, by 26.2 and 5.3 per cent by the multi-objective optimization design of crankshaft-bearing, which are more reasonable than the ones of single-objective optimization design in which only the crankshaft-bearing is considered as the studying object.

The crankshaft-bearing system of a four-cylinder internal combustion engine is taken as the studying object, and the multi-objective optimization design of crankshaft-bearing based on the crankshaft-bearing system is developed. The results of this paper are helpful to the design of the crankshaft-bearing for engine. There is universal significance to research the multi-objective optimization design of crankshaft-bearing based on the crankshaft-bearing system. The research method of the multi-objective optimization design of crankshaft-bearing based on the crankshaft-bearing system can be used to the optimization design of the bearing in the shaft-bearing system of ordinary machinery.

Prior studies have confirmed market segmentation as an important shackle to China's macroeconomy upgrade, but the systematic analysis of microenterprise upgrade remains inadequate. This paper aims to investigate the nonlinear impact of market segmentation on microenterprise upgrade.

The price method was applied to calculate China's provincial market segmentation, including commodity, capital, labor and energy. The generalized method of moments was employed to examine the nonlinear impact of market segmentation on the upgrading of manufacturing enterprises based on microenterprise data from 2003 to 2019.

First, China’s heterogeneous market segmentations have been significantly reduced. Macroeconomics and policies are critical factors in market integration. Second, there is an inverted U-shaped relationship between China’s total market segmentation and the upgrading of manufacturing enterprises. Third, the relationship between the commodity market segmentation, labor market segmentation, energy market segmentation and manufacturing enterprises' upgrade is shown as an inverted U-shaped. Nevertheless, the relationship between the capital market segmentation and upgrading of manufacturing enterprises exhibits a U-shape.

The impact of market segmentation on the upgrading of manufacturing enterprises in China performs nonlinearly. An inverted U-shaped relationship exists between market segmentation in commodity, labor and energy and the upgrading of manufacturing enterprises, while a U-shaped relationship prevails between capital market segmentation and the upgrading of manufacturing enterprises.