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The paper aims to accurately measure the key motion parameters, such as velocity, azimuth and pitch angle, of the small flying object with a non-uniform curve trajectory. It proposes a measurement method and its calculation model of non-uniform curve trajectory using a photoelectric sensor array.

First, the basic composition of the measurement system and mechanism of photoelectric sensor array are described, respectively. Second, a non-uniform curve mathematical measurement model is constructed differently from the traditional linear trajectory, taking into account the influence of gravity and air resistance. Third, the measurement error of the system is analyzed through numerical simulation. Finally, the accuracy and feasibility of the approach are verified by live-ammunition experiments.

The results show that the systematic error of the hitting point coordinates can be reduced by 9% compared to the traditional linear measurement model. Consequently, this method can meet the higher measurement requirement for the key motion parameters of the small flying object under the non-uniform curve trajectory. Research limitations/implications (if applicable)- although the approach itself is generalizable, the method is unable to detect the motion parameters of multiple small flying objects.

Although the approach itself is generalizable, the method is unable to detect the motion parameters of the multiple small flying objects.

It is evident that the proposed non-uniform curve measurement model is more precise in quantifying the essential characteristics of the small flying object, particularly in consideration of the environmental conditions.

The precise measurement of the key motion parameters of the small flying object can facilitate the enhancement of the protective performance of protective materials.

A novel approach to measurement is proposed, which differs from the conventional uniform trajectory model. To this end, the space construction of the photoelectric sensor array is optimized. The number of the sensors is revised.

The construction industry has been investigating “where Henry Ford is in the industry system.” Given that listed construction enterprises are the backbone of the promotion of the high-quality development of the industry, their research and innovation are of considerable importance. This study aims to comprehensively assess the research and development (R&D) status quo and trends within various types of construction enterprises in order to identify effective strategies to enhance R&D efficiency in the construction industry.

Based on the data won from annual reports and the CSMAR database for the period 2016–2020, this study examines 104 listed construction enterprises in China. By applying both the data envelopment analysis (DEA) method and the Malmquist productivity index, this research compares and analyzes the static and dynamic differences in R&D efficiency across different types of construction enterprises.

Results suggest that the magnitude of change in the Malmquist decomposition index of 104 listed construction enterprises gradually narrowed, but the comprehensive technological level remained relatively low. Although state-owned enterprises had an advantage in scale efficiency, meaning they could maximize output with given inputs, their technological progress efficiency, also known as the degree of technological innovation, was significantly lower than that of private enterprises. As one finding, state-owned enterprises in comparison with private enterprises experience significant R&D inefficiency. It represents the main cause of their low degree of technological innovation and efficiency.

This study assesses the R&D efficiency of listed construction enterprises in China from the perspective of different market segments, state-owned and private enterprises and suggests approaches to improve strategies for various corporate types. Thus, the study’s new findings contribute to addressing the challenge of low R&D levels in the construction industry in the fields of engineering, construction and architectural management.