## 1 Introduction  
Cities serve as crucial platforms for advancing high-quality development, efficient governance and high-quality living in the new era. Within China's ongoing pursuit of New-Type Urbanization, a national strategy explicitly prioritizing urban quality and connotative development over mere physical expansion [1], enhancing urban vitality and promoting intensive urban development emerge as central priorities. These objectives represent key focal points for the thorough implementation of urban renewal initiatives and the comprehensive practice of the people-centered philosophy underpinning New-Type Urbanization [2]. As of 2024, China's urbanization rate has reached 67%. The acceleration of urbanization and the rapid population growth in central areas have significantly altered urban spatial structures. The rapid urbanization process and global population growth have led to an increase in the number of urban residents to 56% by 2021. Urban management has become one of the most severe development challenges facing the world in the 21 st century. At the same time, it has caused inefficient and fragmented spatial functional layouts, manifested as the decline in old urban areas, uneven distribution of public services, traffic congestion, separation of living and working spaces and social stratification [3], ultimately disrupting the orderly distribution of urban vitality. Urban growth and the steady rise in living standards have propelled the advancement of urban vitality to the forefront of modern urban planning priorities [4]. In China, this is both driven by the intrinsic impetus of urban development and the national demand for sustainable and high-quality urban environments under the backdrop of new urbanization. Therefore, it is crucial to conduct in-depth research on strategies to enhance urban spatial vitality in order to achieve sustainable urban progress, improve residents' well-being and strengthen the overall competitiveness of cities. Urban vitality encompasses diverse and profound connotations. [PERSON] was the first to propose that the city's vitality stems from the close integration of residents' daily lives and living spaces, which creates rich diversity in life [5]. [PERSON] defined vitality as the degree to which an urban environment fosters essential human activities, ecological needs and capacity development, and regarded vitality as a key element for evaluating the form of space and social sustainability [6]. [PERSON] argued that the vitality of urban public spaces derives from the presence of people and their activities [7]. [PERSON] et al. conceptualized urban vitality as a city's ability to foster a human-centered living environment, where the concentration of people gives qualities similar to those of living organisms, acting as the fundamental source of urban vitality [8]. [PERSON] et al. indicated that urban vitality is mainly reflected in the appeal of public spaces to diverse groups of people [9]. Collectively, these perspectives emphasize the central role of human activities and their interaction with the environment as the main drivers of urban vitality. The Natural Resources and Planning Bureau of Qingdao has set forth development goals aimed at achieving comprehensive enhancement of regional functions and environmental quality, establishing a new engine for urban growth, and stimulating urban vitality. Therefore, examining the interplay between urban vitality and the built environment is critical for informing urban design and management approaches aimed at strengthening urban vitality. The quantitative assessment of urban vitality has attracted significant interest across diverse fields such as urban planning, urban geography and the social sciences. Early methodologies relied on field surveys to collect data on individual activities, interaction behaviors and lived experiences to characterize urban vitality.