Research on Range of Appropriate Spatial Scale of Underground Commercial Street Based on Psychological Perception Evaluation

Featured Application: (1) Interdisciplinary interaction between environmental psychology and architectural design theory. (2) Application of virtual reality technology for human perception evaluation. (3) Mastery of the appropriate length range and related laws of human perception change in underground commercial street spaces. (4) Confirmation of significant perception impact under different scale combinations on human perception


Introduction
The rapid increase in urban population has presented a new challenge to the spatial capacity of large cities.Consequently, the expansion of underground space has emerged as a critical option for future urban development [1].However, recent underground space developments face issues such as poor systematic planning and outdated methodologies [2].In developing urban underground commercial streets, focusing on creating more human-centered spatial scales is essential.However, the current design of street space at the metropolitan scale, influenced by modern architectural theories and the predominance of subjective creativity, has led to a disconnection between theory and practice, resulting in a lack of human-centered design and disorder in the spatial environment.This study takes the appropriateness of spatial scale as one of the essential means of judging spatial quality.
Early spatial research explored the human scale as a crucial metric for assessing street spaces [3].Scholars conducted spatial perception experiments focusing on emotional experiences [4], psychological problems [5], and comfort [6].They introduced environmental psychology theory, integrating human subjective feelings with design.However, spatial quality evaluation suffers from redundancy, limited research approaches, and a lack of integration with real-world settings for experimentation.Most studies have looked at street space in terms of individual dimensions, such as the percentage of sky on the street [7] and the quality of greenery [8], consequently lacking systematic and scientific rigor.
Spatial appropriateness, regarded as a crucial criterion in assessing the human scale [9], is progressively garnering research attention.MATZARAKIS A examines individuals' comfort levels by analyzing their physiological parameters alongside environmental factors [10].Fang Zhiguo investigates the appropriateness of the street space scale through SPSS and SD analysis [11].D Hudec (2023) developed a methodology for calculating space capacity parameters and assessing shared space appropriateness, focusing on transportation aspects [12].However, the research on the specific impact of the appropriateness on the spatial quality of streets lacks more direct empirical evidence.Increasingly, scholars have integrated field research and street maps into their studies, exemplified by Liu Qing, who studied the walking perceptual experience of urban street space [13].Jingxian Tang and Ying Long employed image segmentation techniques to segment the streetscape to evaluate the five dimensions of spatial quality proposed by Ewing and Clement [14].Zhang F (2018) conducted empirical studies in Beijing and Shanghai to explore the correlation between perceived quality and visual elements [15].Zhang L (2019) [16] and Vukmirovic, Milena (2022) [17], among others, utilized web-based data such as location-based data (LBS), Twitter data, and points of interest (POIs) to investigate the relevance of these data for urban design and pedestrian space enhancement.Conducting research on street space quality solely through field research overlooks potential interfering factors in natural environments, leading to highly variable research outcomes.Similarly, utilizing street maps and big data fails to integrate with actual scenes for in-depth analysis.To increase the experiment's realism and compensate for the inability to analyze the scenarios in context, this study employs a virtual reality experimental platform to construct street scene models, enabling subjects to evaluate spatial quality in a virtual reality setting.This approach aims to minimize the impact of irrelevant factors while obtaining precise data.
Environmental differences between aboveground and underground spaces may impact human perception differently.With the increasing influence of underground space development on urban development, most scholars have been researching humanized spatial quality.Elena Romanova (2016) explored underground buildings, analyzing the problems related to the negative psychology of users [18], and Jisun Kim (2016) [19] explored the psychological impact of underground transport spaces on passengers [12].In both of the above studies, the psychological feelings of the users were considered mainly in terms of the functional dimension, with the additional impacts caused by influencing factors being neglected.Li Z (2017) made design recommendations for the exterior design of underground shopping streets using case studies [20].Still, the study was detached from people's subjective perception evaluation and lacked objective experimental support.Ding Shanmin investigated the psychological perception of side interfaces in underground streets through the efficient simulation properties of VR [21].However, they did not consider the relationship between the spatial scale combinations and the influence of psychological perceptions.Xu Yao took the underground commercial street guidance sign as the research object [22].The two-dimensional street image simulated the actual threedimensional visual guidance situation.The experiment ignored the perception difference between stereo and planar in the simulation problem.Despite their significant correlation with human psychology, scant research addresses the optimal length of underground commercial streets [23].An appropriate length can enhance individuals' time engaging in activities within street spaces.Moreover, alterations in the spatial scale of underground commercial streets can influence people's perceptions of the environment.Studying the evaluation of scale combinations in space helps to analyze the perception differences between three-dimensional and flat surfaces from a human perspective.
In the research on scale combinations, Yoshinobu Ashihara [24] studied scale combinations such as D/H in two-dimensional scale combinations, forming a particular theoretical foundation.However, more needs to be done to research spatial scale combinations in other dimensions.In the underground commercial street space scene, in addition to two-dimensional scale combinations, three-dimensional scale combinations can reflect depth perception.The validation of the two-dimensional scale requires the value of the one-dimensional scale.The three scale combinations are closely connected.The length element is consistent with the direction of the pedestrians' behavioral paths, so the appropriate lengths under different spatial scale combinations are worth in-depth research.
This study will be guided by environmental psychology and architectural theory, taking the urban underground commercial street as the primary research object, cutting in from the perspective of scale combination, obtaining the perception evaluation data under different modeling scenarios, and researching the relationship between the influence of one-dimensional, two-dimensional, and three-dimensional scale combinations on the appropriate spatial lengths, to explore the appropriate length range and scale combinations of the underground commercial street.

Research Scope
The research objective of this paper focuses on the scale combinations of underground commercial streets.The author collected essential scale data on underground commercial streets in urban areas to create a more realistic experimental model.The research locations mainly include underground streets in commercial complexes, and the research objects are the underground commercial streets that connect nodes in these underground streets.Shanghai, situated in eastern China, stands as a global metropolis interweaving international economy, finance, and trade, boasting a plethora of expansive underground commercial avenues.Nanjing, the capital city of Jiangsu Province, serves as a pivotal transportation nexus within the Yangtze River Delta, experiencing rapid commercial growth in recent years and offering significant reference value.Xuzhou, situated in the northwestern region of Jiangsu Province, anchors the Huaihai Economic Zone, boasting substantial potential for commercial advancement.Chengdu, a significant economic and cultural epicenter in southwest China, doubles as a trade and logistics hub and a comprehensive transportation nexus, showcasing a robust underground commercial street infrastructure that offers valuable inspiration for the study.Therefore, 62 underground commercial streets in the above cities were selected for scale measurements, which included their length, width, and height (Figure 1).

Experiment Content and Steps
This paper explores the appropriate range of underground commercial street lengths, based on the scale research data, to complete the following two virtual simulation experiments (Figure 3): Based on the scale data collected from the actual underground commercial street research, virtual reality technology was used to construct underground commercial street models with different scale combinations.In the virtual simulation model, participants were instructed to assess various street scale combinations using a questionnaire comprising six adjectives rated on a 7-point scale.This approach aimed to assess spatial perception evaluation data quantitatively.Subsequently, mathematical and statistical analyses were employed to investigate the impact of one-dimensional and two-dimensional scales on the perception evaluation, considering parameters such as length, width, and height.This analysis identified the most influential elements, clarifying their correlation with perception scale data.Verification was conducted through coverage analysis.Finally, based on these findings, an appropriate length range was deduced using a combination of one-dimensional and two-dimensional scales.
Experiment 2: three-dimensional scale combination-appropriate length selection experiment.
Based on the scale data collected from the actual underground commercial street research, virtual reality technology was used to construct underground commercial street models with different scale combinations.Subjects with helmets and handles could travel and stay in the underground commercial street with fixed width and height values.The selection of the appropriate length in the virtual scene was recorded in real time.A holistic three-dimensional range of appropriate scale combinations was obtained through the superposition analysis and visualization of the data.
In this study, we will combine the appropriate length range obtained from the perception evaluation experiment of Experiment 1 and the appropriate length selection results of Experiment 2 to verify each other, determine the typical characteristics of the appropriate scales, and finally obtain the appropriate length range and scale combinations affecting the spatial perception of the underground commercial street.

Questionnaire Setting and Evaluation Index Establishment
The sub-experiment used the Delphi method [25] to determine the evaluation indicators of spatial perception.A leading group of three researchers, twenty students, and ten in-service teachers of architecture and related disciplines formed a panel of experts to select and evaluate the indicators.In the first consultation, the study categorized the indicators in the assessed articles regarding past streets: scale perception and ambiance perception.The experts screened 30 common adjective pairs describing spatial perception, including indicators such as safe [26], lively [27], comfort [28], and beautifully [29], from the articles to evaluate them.In the second consultation, several anonymous evaluations were provided regarding the content of the first consultation to obtain a consistent opinion.Six of the fifteen adjective pairs were finally selected as the spatial perception evaluation indexes for this experiment, and the questionnaire was set up using the SD method, as shown in Table 1.This study utilized an immersive virtual reality system as the platform, comprising an optical position-tracking system, a head-mounted display (HMD), an orientationtracking device, and a graphic workstation for monitoring and maintaining the virtual environment (VE) status (Figure 4).The laboratory room had dimensions of 6 m × 7 m, and to accommodate the scale of the experimental model scene, subjects were asked to use the Oculus Rift DK2, a virtual reality headset manufactured by Oculus VR Inc. from San Francisco, CA, USA., in conjunction with the system's joystick to navigate seamlessly throughout the experimental model.

Participants
The experiment was conducted in the VR laboratory of the China University of Mining and Technology.Considering that the existing main consumer population comprises young people and the experimental field is located in this school, the researchers weighed the coverage and practical operability of the experiment and decided to recruit school students with a significant age span.Data from college student populations in a related experiment on street assessment proved to be valid [30,31].
The experiment was announced in the school's community through a paid form.The recruitment scope was for college students, considering that the imaging with the virtual reality device uses a 3D virtual space.Some people will have physiological reactions such as vertigo and nausea, affecting the accuracy of the perceptual data collected in the experiment.Therefore, we chose physically and mentally healthy people with normal or corrected vision who would not experience 3D vertigo as subjects for this experiment.Before the start of the formal experiment, the participants were asked whether they had participated in virtual reality experiments in the past, of which 49.51% denied any contact with VR.In comparison, 50.49% said that they had at least one experience.The participants were allowed to have a sneak preview of the virtual reality scene, with those with regular physical sensations being chosen as the subjects and those with an adverse reaction being excluded from the experiment.The final number of subjects was 53, with an age span of 18 to 29 years.Thirteen samples had low credibility and were screened out after the screening.Finally, 40 valid data samples were retained, of which 24 were male, and 16 were female, with an average age of 24 years old, and the subjects' majors covered architecture, urban and rural planning, civil engineering, interior design, accounting, computers, foreign languages, etc., among which 18 people were majoring in architecture-related professions and 22 people were majoring in non-architecture-related professions.In addition, multiple professional backgrounds enable the subject group to have richer hobbies and aesthetic preferences, realizing the diversity of the sample.The subjects' cognitive ability was within the normal range.The experimental scenes, labeled I to V, gradually increased in height, resulting in 15 underground commercial street spaces with varying length and width combinations in each scene.The model spaces predominantly consisted of rectilinear shapes, using white plaster as the street material and maintaining a light intensity of approximately 700 lx, as shown in Table 2.Both virtual simulation experiments in this study shared the same 15 scenes.The primary focus of this study was to examine the appropriate range of lengths.Thus, in experiment two, the maximum length selection range was set at 70 m to provide more options for the subjects.Based on the analysis of previous research, this paper utilized high-frequency data to construct various street models for underground commercial streets.These models were formed by combining five different heights (H), three different widths (D), and four different lengths (L).As a result, 60 underground commercial street models were obtained through combinations of one-dimensional and two-dimensional scales.The values of the one-dimensional and two-dimensional scale variables can be found in Table A1 of Appendix A.

Experimental Procedure
The experiment standardized the subjects' visual height at 167 cm, reflecting the average height of the participants.Within the virtual scene, offering a 360° panoramic view, measures were taken to mitigate subjects' vertigo by setting the walking speed of the handle to 1 m/s during pre-experimentation.The detailed experimental procedure is outlined as follows: Experiment 1: one-dimensional and two-dimensional scale combination-perception evaluation experiment.
In this experiment, the subjects could navigate a virtual model of an underground commercial street using a handle.After familiarizing themselves with the environment, they were asked to return to the starting point of the street space.Subsequently, they were asked to complete a scale, where the experimenter recorded their perceptual ratings of different scale combinations of the underground commercial street.The entire experimental process lasted approximately 30 min.
Experiment 2: three-dimensional scale combination-appropriate length selection experiment.
After allowing the participants to navigate through a virtual scene of an underground commercial street using a handle, they were required to use the handle to select a more appropriate street length to stay on.For this experiment, the experimenter randomly presented the subjects with different scale combinations of the virtual underground commercial street scene.Initially, the subjects were allowed to explore the street entirely using the handle and choose the most appropriate length to stay on.The experimenter recorded the data length, and the complete experimental process took approximately 30 min.

One-Dimensional Scale Combination
As shown in Table 3, there is a strong correlation between one-dimensional scale combinations and perception.Each scale element is strongly correlated with its corresponding scale perception.Specifically, the correlation between the width element and the height perception is negative (p = −0.836),suggesting that as the width increases, the height of the street decreases significantly.On the other hand, the width element is positively correlated with the perception of openness (p = 0.823), indicating that as the width increases, the perceived openness of the space also increases.Therefore, among the onedimensional scale elements, the width element significantly impacts the perception of underground commercial streets, as it is highly correlated with width, height, and openness perception.Data with a background colour is data with a pearson index higher than 0.8

Two-Dimensional Scale Combination
In the two-dimensional scale combination of length (L) and width (D), the top and bottom interfaces are controlled by L and D, respectively.The area of the interface is represented by L × D, while the aspect ratio of the interface is represented by L/D.Table 4 shows a strong positive correlation between L/D and the length perception (p = 0.854).This means that the larger the L/D value, the longer people perceive the distance of the street space.On the other hand, there is a highly negative correlation between L/D and the perception of stability (p = −0.801).This indicates that as the L/D value increases, people perceive less stability in the street space.
In the two-dimensional scale combination of length (L) and height (H), L and H control the side interface of the underground commercial street.The area of the side interface is represented by L × H, while L/H represents the length-to-height ratio of the side interface.As shown in Table 4, there is a strong correlation between L/H and the length perception (p = 0.763).This suggests that the larger the L/H value, the longer the distance of the street space is perceived to be.
In the two-dimensional scale combination of width (D) and height (H), D and H control the positive interface of the underground commercial street space.The area of the positive interface is represented by D × H, while D/H represents the width-to-height ratio of the positive interface.According to Table 4, D/H has significant correlation coefficients (p = 0.960; p = −0.941;p = 0.849) for width, height, and the perception of openness.This means that as the D/H value increases, the perceived width of the street space becomes longer, the height becomes lower, and the perception of the openness of the street space increases.D/H has a stronger correlation with spatial perception than the one-dimensional scale combinations.Data with a background colour is data with a pearson index higher than 0.8.

Summary Table of Factors of Maximum-Relevance Scale Combinations
By analyzing the correlation between the one-dimensional and two-dimensional scale combinations and the six spatial perceptions, this paper summarizes the scales with the highest correlation factor with individual perceptions, as shown in Table 5.The findings reveal that the two-dimensional scale combinations correlate more strongly with overall spatial perception compared to the one-dimensional scale.Specifically, the L/D scale combination demonstrates a high correlation with length perception (p = 0.854) and stability perception (p = −0.801),and a significant correlation with comfort perception (p = −0.679).On the other hand, the D/H scale combination shows a high correlation with width perception (p = 0.960), height perception (p = 0.941), and openness perception (p = 0.849).These results indicate that the combination of two-dimensional scales, particularly L/D and D/H, significantly impacts the overall spatial perception.

Regression Analysis of Maximum-Correlation Scale Factors and Spatial Perception
This paper investigates the influence of two scale combinations, aspect ratio L/D and aspect ratio D/H, which are considered the most influential.The study examines the relationship between each scale factor and its highly correlated perception to determine the appropriate range.The analysis uses SPSS, where the three two-dimensional scale combinations with the highest correlation coefficients are regressed against their corresponding highly correlated perceptions, and fitting curves are plotted.Since the independent variable consists of two scale elements, it is possible to categorize it based on one of the remaining scale elements, resulting in multiple fitted curves on the graph.The corresponding range of appropriateness under the scale difference can be derived by applying the judgment law of appropriate perception states.The derived range of appropriateness is presented in Table 6 (a-e).Based on the judgment law of the appropriate perception state and combined with the fitting curve diagram, calculations were made to determine the L/D ranges when the length perception and the stability perception reached the appropriate state individually, as well as the L/D range when both of them reached the appropriate state together.Additionally, the overall appropriateness range at different heights was also determined.Table 7 presents these findings.For a height of 3 m, the appropriate range of L/D was found to be 9.2-14.3.Similarly, for a height of 3.5 m, the appropriate range of L/D was 8.5-13.0.The appropriate range for a height of 4.0 m was 8.3-11.6;for a height of 4.5 m, it was 7.6-11.2;and for a height of 5.0 m, it was 7.0-10.0.By examining the intersection of these ranges, it was discovered that the L/D range of 9.0-10.0was achieved when both types of perception reached the appropriate state across all height ranges.Therefore, the final determined L/D range was 9.2-10.0.Based on the judgment law of the appropriate perception state and combined with the fitting curve diagram, the D/H range was calculated when the width perception, height perception, and openness perception reached the appropriate state, respectively, under different lengths.Table 8 shows the calculated D/H range when all three reached the appropriate state together and the overall appropriate range.For a length of 35 m, the appropriate range of D/H was 1.1-1.3.For a length of 45 m, the appropriate range of D/H was 1.1-1.4.For a length of 55 m, the appropriate range of D/H was 1.2-1.5.For a length of 70 m, the appropriate range of D/H was 1.2-1.6.The intersection of these ranges formed the range of D/H when the three kinds of perception reached the appropriate state for all lengths, which was 1.2-1.3.Through a correlation analysis of one-dimensional and two-dimensional scale combinations, as well as spatial perception, it was found that the two-dimensional scale combination had a stronger correlation with the six types of perception.Specifically, the length/width ratio (L/D) and width/height ratio (D/H) showed the highest correlation coefficient with spatial perception.The appropriate range for the length/width ratio (L/D) gradually decreased with an increase in heigh.In contrast, the appropriate range for the width/height ratio (D/H) gradually increased with an increase in length.Moreover, as the length increased, its appropriate range also gradually increased.

Coverage Analysis of Appropriate Scope of Two-Dimensional Scale Combinations
This paper analyzed the range of appropriate two-dimensional scale combinations in terms of coverage, specifically focusing on their applicability to different scale combinations of underground commercial streets.To enhance the feasibility of the study, the perception trend of two scale elements was examined by varying another scale element.The variable length (L) allowed for a comprehensive exploration of three-dimensional scale combinations.By determining the appropriate range of aspect ratio (L/D) for different heights (H), the corresponding lengths (L) for three widths (D) of underground commercial streets within this range could be identified.The perception appropriateness within this range reflected the coverage of the two-dimensional scale combinations.If a majority of the length perceptions and stability perceptions fell within the appropriate range of L/D, then this indicated good coverage.If some of the length perceptions and stability perceptions were within the appropriate range of L/D, then this suggested general coverage.However, if the length and stability perceptions did not fall within the appropriate range of L/D, then this indicated a lack of coverage.
Firstly, the appropriate lengths (L) corresponding to the three widths (D) were obtained based on the appropriate range of aspect ratios (L/D) for five different heights (H).This information is presented in Table 9.Subsequently, a regression analysis was performed in SPSS, considering the scale combination changes and the quantified perception evaluation data from Experiment 1.The fitting curves for the six kinds of spatial perception were obtained and integrated into a single graph, creating an overall perception change graph.To further explore the coverage of different three-dimensional scale combination streets by the two-dimensional scale combination fit range, the overall perception change map was combined with the obtained length (L) fit range.This combined information is shown in Table 10,the shaded part indicates the range of suitability of the zone.As shown in Table 10, the underground commercial street with a width (D) of 3.3 m had appropriate lengths for heights of 3 m and 3.5 m, resulting in general coverage.Similarly, in the underground commercial street with a width (D) of 5.4 m, most of the length and stability perceptions were appropriate within the obtained appropriate lengths, indicating good coverage of the length-to-width ratio (L/D).On the other hand, for the heights of 4.5 m and 4 m, some of the lengths and stability perceptions reached the appropriate state with general coverage.While some streets had lengths exceeding the experimental length range, most streets achieved appropriate perception.Therefore, the two-dimensional scale combination L/D effectively covered most of the street space with different three-dimensional scale elements.Determining experimental length values through a statistical analysis of previous research data adds practical significance to the findings.

Analysis of Selection Range of Appropriate Length of Three-Dimensional Scale Combinations
This paper conducted a three-dimensional-scale appropriate length selection experiment to explore the spatial scale comprehensively.The experiment aimed to determine the appropriate length selection range for underground commercial streets with different width and height values.By doing so, the study identified the appropriate range of threedimensional scale combinations and their corresponding change rules.
In this study, a total of 600 selection points were recorded by 40 subjects in 15 virtual underground commercial streets.The selection points were determined based on the acceptable street lengths for the subjects, and the appropriate length ranges were derived from the lengths chosen by all subjects.The author created a plan view of each street scenario to visually represent the aggregation of length values.The author marked the street length range of 35-70 m, determined through actual research, and overlaid the selected appropriate length values from all subjects onto the graph.The darkness of the colors in the graph indicates the number of people who chose the respective lengths, with darker colors representing a higher cumulative number of people.The colored ranges on the graph represent the appropriate length ranges, while the darker parts indicate the most appropriate length ranges (see Table 11).Finally, a summary table presenting the appropriate and optimal length ranges was generated, as shown in Table 12.

Comparison Analysis of Appropriate Length Range
The appropriate length range was determined through two experiments: one using the appropriate L/D range and the other using a combination of three-dimensional scales.The experimental data from Tables 10 and 13 were used to control the interval range.The overlapping range of the two groups of experiments is shown in Figure 5; after removing the interval range that did not intersect, the best appropriate length range was obtained, resulting in a total of eight groups, as shown in Table 13.

Research Innovation
Research on enhancing the quality of street spaces has traditionally emphasized street spatial scale, a crucial aspect even within the virtual realm of platforms like Google Street View.Prior studies by Kashiwagi [32] and Matsumoto [33] have illustrated the close relationship between physical factors such as the street aspect ratio and spatial perception through perceptual models.Similarly, Liu (2020) utilized street length and width as research indices to investigate their impact on pedestrian travel [34].However, the existing literature predominantly examines scale elements along a single dimension within spatial scale analysis.Departing from this approach, the current study extends the analysis from a one-dimensional to a three-dimensional scale, yielding more comprehensive and direct insights.By analyzing the significant influence of spatial scale on perception evaluation, enhanced recommendations for improving street spatial quality are provided.
In regards to the measurement of street perception data, this study also constructed a virtual reality platform for behavioral recording and perception evaluation concerning Cipresso [35], which was previously primarily applied in clinical research [36], where subjects were able to achieve the awareness and comparison of multiple scenarios in a virtual scenario, and which also allowed for the real-time recording of the subjects' behavioral data.The study learned from Ge's method of investigating street scene environments [37], where the perception appraisal was measured by presenting the street scenes to the subjects as adjective pairs for scoring.Unlike previous studies, the study conducted two experiments simultaneously to obtain perception evaluation data and appropriate length selection data, which are conducive to validating the final results.
In the research on the appropriate range of street length, Xiao Y showed that the appropriate length of above-ground streets is 249 m.In this study, underground streets were used as the object of research, and the study concluded that the length of underground streets ranges from 43 to 66 m, which makes up for the research gap in the underground area [38].Yu Z found that the appropriate ratio of street width and height is 1~2, which is basically in line with the value of 1.2~1.3 of the width-to-height ratio in this experiment when researching the interface morphology of streets [39].It is worth noting that Zhan L et al. (2019) used psycho-perception evaluation to analyze the appropriate scale of the space and obtain the appropriate values under different width-to-height, length-to-height, and width-to-length scale indicators [40].However, an analysis of the impact of one-dimensional and three-dimensional scale data is needed.Ultimately, the data obtained could only be based on the two-dimensional scale of the appropriate scale evaluation recommendations.
In contrast, the methodology of the present study can infer the range values of the remaining two scales through one scale indicator.Different from the previous research, the above study considered that when the width is about 5.4, the appropriate length is about 55 m, but the results of this study show that when the width is 5.4 m, with the change in height, the length value can reach the appropriate requirement within the range of 46~66 m.Therefore, when researching the appropriate scale of street space, the three dimensions should be fully considered, and the impact of changes in each dimension on the quality of street space should be observed.
In addition, the results of this research can be combined with other related articles to obtain more diverse spatial design parameters.For example, H Yang (2020) calculated the effect of the street aspect ratio on carbon monoxide diffusion, and a sustainable public space can be obtained through the combination of perception evaluation and carbon emission issues from a human perspective [41].Zhai, Y (2023) investigated the color distribution of building façades and colors involved in street functions, and combined with the scale research results in this study, a more diversified combination of street space elements can be obtained [42].In summary, this study provides a variety of threshold ranges for the most appropriate spatial scale combinations, establishes an experimental scenario of appropriate scale dimensions, and can offer more possibilities for researching the integrated impact of spatial elements in urban planning and architectural design.In future urban design and planning, it is also necessary to combine multiple dimensions in spatial design and include the subjective perception of pedestrians, spatial carbon emissions, and traffic efficiency in the scope of the comprehensive consideration.

Limitations and Future Directions
At the level of experimental tools, this study uses a virtual reality modeling platform to model the experiment, but it has yet to fully exploit its advantage of realism.The experiment only takes spatial scale indicators as the object of study, and the constructed scene itself is relatively simple, with some differences from natural street scenes, which may only partially allow subjects to immerse themselves in the environment for evaluation.
At the level of the research sample, the subjects selected for this survey were mainly a group of college students with a relatively similar age, which may indicate the uniformity of the education and other attributes of the subjects and may lead to the convergence of the results of this study in some aspects.Considering that the use of VR equipment is not yet widespread, 50.49% of people had experienced VR equipment before the experiment without considering factors such as habits and preferences, which may affect the experiment's results.In addition, considering the acceptance and comprehension issues, there are some difficulties in data collection for both younger and older subjects.Head-mounted VR devices may also make subjects feel emotions such as stress and anxiety, and in the future, more advanced devices are needed to mitigate such effects as much as possible.
At the level of spatial perception evaluation, although the study covered all the indicators related to the spatial scale as much as possible and filtered them, adjectives such as beautiful, lively, engaging, etc., which are highly associated with the quality of street space, could not be used as evaluation indicators to measure the spatial scale.The study only focused on the factors that influence the spatial scale.
Therefore, in future research on street space appropriateness, we can add as many research objects as possible to improve the experimental model, increase the fidelity of the model, and take into account the visual, acoustic, and thermal comfort environments, in order to record the state of the research objects from more dimensions and collect multimodal perceptual evaluation data to conduct interactive analyses and validate the accuracy of the experiments.

Suggestion of Design and Application
From the above research, the influence of spatial scale on the design of underground commercial streets is highlighted, providing designers with specific data references on the range of appropriate lengths and scale combinations, which can help to improve the design quality and user experience of underground commercial streets.We propose the following recommendations for the appropriate length range of underground commercial streets: In terms of three-dimensional scale combination optimization, according to the results of the study, the design of the underground commercial street should give priority to the scale combination with a width of 5.4 m, combined with an experimental height of 3.0 m to 5.0 m, to obtain the most appropriate range of lengths (62-66 m, 58-63 m, 49-53 m, and 46-52 m).Such a design can improve the comfort of space perception and instill better feelings in the users.
In terms of the optimization of two-dimensional scale combinations, the width-toheight ratio should be optimized as much as possible in the design, especially for a width of 5.4 m.A scale combination with a more extensive range of the most appropriate length can be chosen to improve the user's spatial perception experience.
In terms of appropriate length range planning, designers should comprehensively consider the relationship between width and height when planning underground commercial streets and design according to the reference value of the appropriate length range provided in the study to improve the overall perception appropriateness.
Meanwhile, the study of the virtual reality modeling platform reveals the shortcomings of the current design model in terms of realism and provides a direction of improvement for future research.The potential applications of the research are as follows: In future street space planning, factors such as sightscape, soundscape, and the thermal comfort environment can be considered comprehensively to achieve a design that better meets people's perception needs.
By studying the changing law of spatial scale combination, the spatial layout can be optimized in the actual design to improve the overall perception appropriateness of the underground commercial street and people's comfort.
Introducing multimodal perception evaluation data for interactive analysis helps assess the street space's appropriateness more comprehensively and improves the scientific and practicality of design decisions.

Conclusions
Through the analysis and verification of perception evaluation experiments combining one-dimensional and two-dimensional scales and appropriate length selection experiments combining three-dimensional scales, data were obtained on the optimal appropriate length range and scale combination for underground commercial streets.Through the one-dimensional and two-dimensional scale combination of perception evaluation experiments and the three-dimensional scale combination of appropriate length selection experiments of data testing and analysis, the best underground commercial street was finally obtained with an appropriate length range and scale combination of data with a width of 3.3 m, an experimental height of the value of dimensions of 3 m, and an appropriate length range of about 43-46 m.When the experimental height was 3.5 m, the appropriate length range was about 37-41 m; in the underground commercial street with a width of 5.4 m, when the experimental height was 3.0 m, the appropriate length range was about 62-66 m, and when the experimental height was 3.5 m, the appropriate length range was about 58-63 m.When the experimental height was 4.0 m, the appropriate length range was about 49-53 m.When the experimental height was 5.0 m, the most appropriate length range was about 46-52 m; compared with other widths, the spatial perception of the underground commercial street with a width of about 5.4 m generally reached an appropriate state within the appropriate length range, indicating that this value should be used as the recommended width of the underground commercial street; in the underground commercial street with a width of 8.7 m, the experimental height was 5 m, and the most appropriate length range was about 60-65 m.In the perception research of underground commercial streets, experiments have been conducted to derive eight sets of three-dimensional scale combinations that can provide the most comfortable feeling.
The relationship between the appropriate width-to-height ratio of an underground commercial street and the overall perception of its space can be summarized as follows: a more appropriate ratio will result in a higher overall perception of appropriateness and a more extensive range of appropriate length options.The variation pattern of the appropriate range of three-dimensional scale combinations is as follows: when the width is 3.3 m, the appropriate length range will initially decrease and then increase with the increase in height; when the width is 5.4 m, the appropriate length range will gradually decrease with the increase in height; when the width is 8.7 m, the appropriate length range will also gradually decrease with the increase in height.

Figure 1 .
Figure 1.Location of the research object.

2. 2 .
Data Processing In this paper, an experimental model was constructed by analyzing the fundamental data information of 62 underground commercial streets in five cities for frequency analysis.The high-frequency scale values, representing the scale values of the underground commercial streets in our research, were identified based on the frequency histogram (Figure 2).For further analysis, higher-frequency values were selected for length, width, and height.Specifically, the values chosen for length were 35 m, 45 m, 55 m, and 70 m; for width, they were 3.3 m, 5 m, and 8.7 m; and for height, they were 3 m, 3 m, 5 m, and 4 m.Additionally, the values of 35 m, 45 m, 55 m, and 70 m for length, 3.3 m, 5.4 m, and 8.7 m for width, and 3 m, 3.5 m, 4 m, 4.5 m, and 5 m for height were also included.The scale model of the underground commercial street constructed using these data serves as the foundation for our experimental study, enabling us to draw more practical conclusions.
(a) High-frequency length (b) High-frequency width (c) High-frequency height

Figure 2 .
Figure 2. Frequency diagram of length, width, and height of underground commercial street.

Figure 3 .
Figure 3. Research methods and processes.Experiment 1: one-dimensional and two-dimensional scale combination-perception evaluation experiment.Based on the scale data collected from the actual underground commercial street research, virtual reality technology was used to construct underground commercial street models with different scale combinations.In the virtual simulation model, participants were instructed to assess various street scale combinations using a questionnaire comprising six adjectives rated on a 7-point scale.This approach aimed to assess spatial perception evaluation data quantitatively.Subsequently, mathematical and statistical analyses were employed to investigate the impact of one-dimensional and two-dimensional scales on the perception evaluation, considering parameters such as length, width, and height.This analysis identified the most influential elements, clarifying their correlation with perception scale data.Verification was conducted through coverage analysis.Finally, based on these findings, an appropriate length range was deduced using a combination of one-dimensional and two-dimensional scales.Experiment 2: three-dimensional scale combination-appropriate length selection experiment.Based on the scale data collected from the actual underground commercial street research, virtual reality technology was used to construct underground commercial street models with different scale combinations.Subjects with helmets and handles could travel and stay in the underground commercial street with fixed width and height values.The selection of the appropriate length in the virtual scene was recorded in real time.A holistic three-dimensional range of appropriate scale combinations was obtained through the superposition analysis and visualization of the data.In this study, we will combine the appropriate length range obtained from the perception evaluation experiment of Experiment 1 and the appropriate length selection results of Experiment 2 to verify each other, determine the typical characteristics of the appropriate scales, and finally obtain the appropriate length range and scale combinations affecting the spatial perception of the underground commercial street.

2. 5 . 3 .
Construct an Experimental Model Based on the results of the survey collection, the data on the experimental model size were constructed.The high-frequency values for length were 35 m, 45 m, 55 m, and 70 m.The selected high-frequency values for width were 3.3 m, 5.4 m, and 8.7 m.Similarly, for height, the selected high-frequency values were 3 m, 3.5 m, 4 m, 4.5 m, and 5 m.When selecting the scale elements for the experimental model, high-frequency values were chosen for the width and height scale elements.
(a) Aspect ratio L/D and perception of length.(b) Aspect ratio L/D and perception of stability.(c) Aspect ratio D/H and perception of width.(d) Aspect ratio D/H and perception of height.(e) Aspect ratio D/H and perception of openness.

Author
Contributions: Conceptualization, T.Y. and Y.Z.; data curation, S.D. and X.X.; formal analysis, X.C., Z.L., and Y.H.; funding acquisition, L.S. and Z.L.; investigation, L.S.; methodology, T.Y., Y.X., and K.H.; project administration, Y.H. and J.W.; resources, L.S.; software, X.C., Y.X., and Kuntao Hu; supervision, T.Y., Y.Z., and L.S.; validation, S.D., X.X., and J.W.; visualization, T.Y.; writing-original draft, T.Y. and Y.Z.; writing-review and editing, S.D. and Y.X.All authors have read and agreed to the published version of the manuscript.Funding: This study has been financially supported by "International Science and Technology Cooperation Fund of Jiangsu Collaborative Innovation Center for Building Energy Saving and Construction Technology (grant no.SJXTGJ2102)" and funded by "the Graduate Innovation Program of China University of Mining and Technology (Grant No. 2023WLJCRCZL315)" and "2023 Funded by the Postgraduate Research and Practice Innovation Program of Jiangsu Province (Grant No. SJCX23_1270)".

Table 2 .
Schematic table of experimental scenarios I-V.

Table 3 .
Table of correlation coefficients between the combination of one-dimensional scale variables and perception evaluation.

Table 4 .
Table of correlation coefficients between two-dimensional scale variable combinations and perception evaluation.

Table 5 .
Summary of maximum-relevance scale combination factors.

Table 6 .
Maximum-correlation scale factors and spatial perception regression analyses.

Table 7 .
Appropriate range of L/D for aspect ratios.

Table 8 .
Appropriate range of aspect ratio D/H.

Table 9 .
Appropriate L range derived from appropriate L/D range.

Table 10 .
Graph of the overall perception curve corresponding to the appropriate length.

Table 11 .
Overlay with appropriate length selection.

Table 12 .
Summary table of appropriate length range and most appropriate length range.

Table 13 .
Summary of optimum length ranges.

Table A1 .
One-and two-dimensional scale combination variables taking values.