industrial heritage sites, totaling 2500 hectares and generally possessing multiple groups of architectural monuments.

**Figure 2.** Industrial heritage reuse evaluation system indicators.

Although Beijing has made some progress in the preservation of industrial heritage, a large number of industrial buildings and structures are still inevitably demolished and severely damaged during urban construction. Due to their advantageous location and low demolition costs, a large number of industrial buildings and structures in Beijing's older urban areas have been demolished [26]. In addition, there is a lack of rational and scientific development and utilization of industrial heritage, as well as a lack of policy guidance for the reuse of individual industrial heritage properties, resulting in a uniform pattern of reuse and imitation. The reuse of industrial heritage must be developed appropriately, taking into consideration its own potential for adaptive reuse and the actual urban development situation [27].

This paper selects the first group of eight representative and typical parks, including Shougang Industrial Heritage Park and 798 Art Park, which Beijing announced in January 2019 as cultural and creative industrial parks transformed from industrial architecture heritage. They have multiple building clusters, are close in scale, contribute significantly to the development of Beijing's cultural industries through adaptive reuse, and best represent Beijing's industrial architecture heritage conservation in its current state. Figure 3 illustrates the distribution of the parks' locations. They are currently employed as evaluation objects for measuring and verifying the potential for reuse of industrial architecture heritage.

#### *3.3. Calculation of Reuse Potentiality Based on Improved Entropy TOPSIS*

The quantitative measurement of reuse potential usually begins by assigning weights to the evaluation indicator system, including criteria weights and order weights. Based on the linearly weighted composite weights, the reuse potential size is compared via ranking after the composite potential evaluation value is calculated based on the indicator weights using Improved Entropy TOPSIS [28].

**Figure 3.** Distribution of industrial parks' locations.

3.3.1. Combined Weighting of Indicators Assignment of Order Weights

The C-OWA method was used to calculate the order weights of the reuse potential evaluation indicators. The specific calculation steps are as follows:

1. A number of expert groups were invited to score the importance of the indicators according to the existing evaluation system. Scoring set A for the original indicators of the re-evaluation program was obtained.

$$\mathbf{A} = (a\_1, a\_2, \dots, a\_n)$$

2. The new importance scores were obtained by arranging the scored data from the largest to the smallest to obtain the evaluation set B:

$$\mathcal{B} = (b\_0, \ b\_1, \dots, \ b\_{n-1}) \ (b\_0 \succeq^\* b\_1 \succeq^\* \dots \succeq^\* b\_{n-1})$$

3. The weighting vector *ϕm*+<sup>1</sup> for each value in the evaluation index was determined based on the combination number *C<sup>m</sup> <sup>n</sup>*−1:

$$\boldsymbol{\rho}\_{m+1} = \frac{\mathbf{C}\_{n-1}^{m}}{\sum\_{m=0}^{n-1} \mathbf{C}\_{n-1}^{m}} = \frac{\mathbf{C}\_{n-1}^{m}}{2^{n-1}},\tag{1}$$

$$m = 0, \ 1, \ \dots, \ l-1 \ \sum\_{m=0}^{n-1} \boldsymbol{\rho}\_{m+1} = 1.$$

4. Set B of the importance scores of the evaluation indicators was weighted to obtain the absolute weight *ϑj*:

$$\overline{\theta\_j} = \sum\_{m=0}^{n-1} \varphi\_{m+1} b\_m(j=1,2,\ldots,n) \tag{2}$$

5. The relative weights of the evaluation indicators *ϑ<sup>j</sup>* were calculated:.

$$\theta\_{\vec{\jmath}} = \frac{\overline{\theta\_{\vec{\jmath}}}}{\sum\_{j=0}^{p} \overline{\theta\_{\vec{\jmath}}}} (\vec{\jmath} = 1, \, 2, \, \dots, n) \tag{3}$$

Assignment of Criteria Weights

The Entropy Weight Method was used to calculate the criteria weights of the reuse potential evaluation indicators. The specific calculation steps are as follows:

1. The corresponding values of different program indicators *aij* were determined, and they were homogenized according to the available expert importance evaluation scoring data to avoid the influence of different levels of evaluation indicators:

$$a'\_{\text{ij}} = \frac{a\_{\text{ij}} - \min\{a\_{\text{i}j}, \dots, a\_{\text{mj}}\}}{\max\{a\_{\text{i}j}, \dots, a\_{\text{mj}}\} - \min\{a\_{\text{i}j}, \dots, a\_{\text{mj}}\}} (\text{i} = 1, \dots, m \text{ j} = 1, \dots, n) \tag{4}$$

2. The weight of the different evaluation values of each indicator in the total value *δij* were calculated:

$$\delta\_{\vec{i}\vec{j}} = \frac{a'\_{\vec{i}\vec{j}}}{\sum\_{i=1}^{m} a'\_{\vec{i}\vec{j}}} (\vec{i} = 1, \dots, m \,\, \vec{j} = 1, \dots, n) \tag{5}$$

3. The entropy of each indicator *ej* was calculated:

$$\epsilon\_j = -\mathbf{k} \sum\_{i=1}^{m} \delta\_{ij} \ln \left( \delta\_{ij} \right) \left( i = 1, \dots, m \; j = 1, \dots, n \right) \tag{6}$$

4. The information entropy redundancy of each indicator *dj* was calculated:

$$d\_{\hat{\jmath}} = 1 - e\_{\hat{\jmath}} \tag{7}$$

5. The weights of the graded indicators *μ<sup>j</sup>* were calculated:

$$\mu\_j = \frac{d\_j}{\sum\_{i=1}^n d\_j} (j = 1, \dots, n) \tag{8}$$

Determination of Comprehensive Weights

In order to avoid the negative influence of a single weight on the calculation of the evaluation indexes, the comprehensive weights must consider both the relative importance of the indexes and the influence of the index factors in the order of the evaluation results. The criteria weights and the order weights must be linearly weighted to obtain the comprehensive weights *ωj*.

$$
\omega\_{\dot{j}} = \alpha \mu\_{\dot{j}} + (1 - \alpha) \theta\_{\dot{j}} \quad \text{a} \in [0, 1], \tag{9}
$$

$$
\omega\_{\vec{\jmath}} \ge 0 \\
\sum\_{j=1}^{n} \omega\_{\vec{\jmath}} = 1. \tag{10}
$$

3.3.2. Determination of the Reuse Adaptive Potentiality Using TOPSIS Method

The exact calculation procedure is as follows:


$$z\_{ij} = \omega\_{ij} x'\_{ij\prime}$$

$$\mathbf{Z} = \begin{bmatrix} z\_{11} & \cdots & z\_{1j} \\ \vdots & \ddots & \vdots \\ z\_{i1} & \cdots & z\_{ij} \end{bmatrix} . \tag{11}$$

3. The optimal evaluation value for each evaluation scenario was determined as a positive ideal solution *z*+, and the worst evaluation value was determined as a negative ideal solution *z*−:

$$z^{+} = [z\_{i1}^{+}, z\_{i2}^{+}, \dots, z\_{ij}^{+}](j = 1, 2, \dots, n),$$

$$z^{-} = [z\_{i1}^{-}, z\_{i2}^{-}, \dots, z\_{ij}^{-}](j = 1, 2, \dots, n).$$

4. the Euclidean distance, the distance to the optimal solution *D*<sup>+</sup> *<sup>i</sup>* , and the distance to the worst value *D*− *<sup>i</sup>* were calculated:

$$D\_i^+ = \sqrt{\sum\_{j=1}^n \left(z\_{ij}^+ - z\_{ij}\right)^2} (i = 1, 2, \dots, m \ j = 1, 2, \dots, n), \tag{12}$$

$$D\_i^- = \sqrt{\sum\_{j=1}^n \left(z\_{ij}^- - z\_{i\bar{j}}\right)^2} (i = 1, 2, \dots, m \ j = 1, 2, \dots, n). \tag{13}$$

5. The relative proximities *C*∗ *<sup>i</sup>* of each evaluation option to the optimum value and rank were calculated and compared to determine the size of the recycling potentiality;

$$\mathbb{C}\_{i}^{\*} = \frac{D\_{i}^{-}}{D\_{i}^{+} + D\_{i}^{-}} \quad 0 \le \mathbb{C}\_{i}^{\*} \le 1 (i = 1, 2, \dots, m) \tag{14}$$

The closer the value of the relative proximity *C*∗ *<sup>i</sup>* is to 1, the more effective the corresponding solution is and the greater the reuse potentiality is.

#### **4. Calculation**

The specific reuse potential calculations have been omitted due to space limitations, and the results are presented in table form. The building evaluation process is as follows:

1. The evaluation criteria were developed using empirical data and industry norms, as well as the specific indicator content of the reuse potential evaluation system, and experts scored the importance using the evaluation criteria, as shown in Table 1.

**Table 1.** Evaluation index importance scoring basis.




**Table 2.** Combined weighting calculation results.

#### **(a) Evaluation Indicator System Campus Case Measurement Primary Indicators Secondary Indicator Shougang Industrial Park 751D**·**PARK No. 27 Factory 1897 Science and Technology Innovation City Laijin Cultural and Creative Industrial Park Weighted Data Weighted Data Weighted Data Weighted Data** Intrinsic Value (Building Dimension) Landscape Integrity 0.0248 0.1215 0.0195 0.1050 0.0178 0.0808 0.0244 0.1056 Structural Reliability 0.0362 0.0349 0.0107 0.0287 Heritage Authenticity 0.0294 0.0156 0.0185 0.0180 Safety 0.0311 0.0349 0.0337 0.0345 Intrinsic Value (Regional Dimension) Location 0.0142 0.0614 0.0332 0.1049 0.0140 0.1115 0.0242 0.1194 Surrounding Environment 0.0000 0.0066 0.0116 0.0160 External Space 0.0095 0.0308 0.0336 0.0273 Planning Restrictions 0.0229 0.0172 0.0169 0.0254 Infrastructure 0.0149 0.0173 0.0352 0.0264 Retrofit Value (Building Dimension) Functional Variability 0.0246 0.1015 0.0237 0.0951 0.0187 0.0700 0.0250 0.0609 Architectural Sustainability 0.0158 0.0143 0.0066 0.0183 User Attitude 0.0321 0.0367 0.0190 0.0112 Construction Technology Implementation 0.0290 0.0205 0.0257 0.0064 Retrofit Value (Regional Dimension) Expected Results 0.0334 0.1322 0.0209 0.0657 0.0248 0.1069 0.0000 0.1007 Economic Conditions 0.0198 0.0000 0.0117 0.0167 Political Context 0.0351 0.0115 0.0232 0.0318 Participants' Attitudes 0.0177 0.0051 0.0272 0.0272 Legal Policies 0.0263 0.0281 0.0200 0.0250 Potential Benefits (Building Dimension) Humanistic Values 0.0300 0.1683 0.0100 0.1241 0.0207 0.0933 0.0267 0.1113 Artistic Value 0.0243 0.0195 0.0231 0.0303 Expected Impact 0.0372 0.0345 0.0346 0.0319 Scientific and Technological Value 0.0368 0.0276 0.0000 0.0058 Representation and Scarcity 0.0400 0.0325 0.0148 0.0167 Potential Benefits (Regional Dimension) History Continuity 0.0356 0.1718 0.0189 0.1228 0.0211 0.1279 0.0040 0.0682 Cultural Evaluation 0.0257 0.0277 0.0328 0.0197 Social Effects 0.0420 0.0262 0.0380 0.0233 Value-added Location 0.0335 0.0293 0.0223 0.0130 Future Earnings 0.0351 0.0208 0.0137 0.0082

#### **Table 3.** Standardization of indicator evaluation data.


#### **Table 3.** *Cont.*

4. The relative size of the reuse potential was obtained by calculating the relative proximity *C*∗ *<sup>i</sup>* according to the TOPSIS method, and the final potentiality ranking is shown in Table 4.



**Figure 4.** Graphical representation of the integrated weight calculation results.

The potentiality validation step was a continuation of the reuse potential evaluation system, with the combined weights obtained via the linear weighting of the order weights and the criteria weights. Step 3.invited park users to score the secondary evaluation indicators for which the standardization is shown in Tables A1 and A2 in the Appendix A. The TOPSIS method was used to quantify the magnitude of the reuse potential of the eight parks as per the users, as shown in Table A3.

#### **5. Results and Discussion**

The calculation results of the relative size ranking of the potential of the eight parks are as follows: Shougang Industrial Heritage Park > 798 Art Park > 751D·PARK > No. 27 Factory 1897 Science and Technology Innovation City > Laijin Cultural and Creative Industry Heritage Park > 768 Cultural and Creative Industry Heritage Park > Xinhua 1949 Cultural and Financial Industry Heritage Park > Beijing Langyuan Cultural Creative Park. The calculation results with respect to the reuse potential from the user's perspective are as follows: Shougang Industrial Heritage Park > 798 Art Park > 751D-PARK > No. 27 Factory 1897 Science and Technology Innovation City > Laijin Cultural and Creative Industrial Park > Xinhua 1949 Cultural and Financial Industrial Heritage Park > 768 Cultural and Creative Industrial Heritage Park > Beijing Langyuan Cultural Creative Park.

According to the radar map derived from the potentiality measurements and evaluation data of the eight parks, the results of the actual measurements and user evaluations in six dimensions, such as building ontology and the urban dimension, for measuring the potential distribution do not differ significantly. The final ranking results of the relative

value of the potential size remain unchanged, indicating that the potentiality evaluation system and quantitative measurement procedure are feasible.

The evaluation results indicate that: (1) the potentiality of the regional dimension needs to be taken into account. With the exception of Shougang Industrial Park and 798 Industrial Park, the urban dimension has a greater potential for utilization than the building dimension in the remaining parks. The scarcity of both Shougang Industrial Heritage Park and 798 Art Park increases the value of the building ontology because their distinct designs represent the characteristics of their respective industries. According to the findings, the potentiality value of the regional dimension largely determines the ranking of the final reuse potentialities of industrial parks with less distinct shapes, and the higher the actual measured potential value, the higher the ranking of the industrial park's reuse potentiality. Due to insufficient utilization of the potentiality of the urban dimension, the current paradigm of transformation is rather homogeneous. In order to promote sustainable urban development, it is necessary to devise a targeted industrial heritage reuse strategy that takes the urban dimension into account. (2) These eight successful reuse cases of industrial parks demonstrate that an important prerequisite for the reuse of industrial heritage is that the buildings are objectively adaptable, so structural reliability and architectural safety provide significant advantages in terms of intrinsic value assessment. Furthermore, the expected impact of the building and the social utility of the urban dimension highlight its potentiality value. As the location of industrial heritage will be the new environment for functional use after renewal, the location's potential has a significant impact on the future development of the reuse project. The added-value conditions of the location, such as the anticipated increased impact and the social benefit of the industrial heritage prior to use, are essential in determining the reuse strategy.

798 Art Park was the first industrial heritage park in China to be redeveloped spontaneously without planning; 751 D·PARK was redeveloped through planning; and Shougang Industrial Heritage Park was the largest industrial heritage park to be redeveloped through planning. Due to space limitations, we will briefly discuss the assessment results using the three industrial heritage parks with the greatest potential for reuse and the most representative examples.

Figure 5 depicts the measured results of Shougang Industrial Heritage Park, and the actual measurement is essentially consistent with the results of the user evaluation potential; its reuse potential primarily emphasizes the potentiality value in the building and urban dimension, and the renovation strategy indicates the potential ability to bring actual benefits to the region and the city following adaptive reuse. Most of the buildings and structures in the park have strong industrial characteristics, and their distinctive forms and volumes are highly representative and scarce for the regional and urban environments [29]. To preserve its scientific and technological value, Shougang Industrial Heritage Park must retain a greater number of heritage categories and quantities, as well as several significant process nodes and a large number of surviving muscles, and contribute to the preservation of collective memory [30]. Because it is not in a central location with well-developed urban functions or a commercial environment, the urban dimension's inherent value prior to adaptive use is low.

Figure 6 depicts the results of 798 Art Park's evaluation potential. The user evaluation of the urban dimension's autologous value and retrofitting value is less than the actual potential measured potential benefit value, indicating that its renovation brings expectations to the urban area that fall short of the actual predicted potential value. The urban dimension of the park's autologous value is more prominent.

798 Art Park epitomizes the value of art and its driving force. As its adaptive reuse adds new artistic and cultural values to its industrial heritage, it presents rich and diverse cultural values to visitors and provides better artistic experiences through the atmosphere of the art district, resulting in economic value for the area in which it is located [31]. The interior and outdoor space characteristics of the old building are utilized rationally in the building space, and emphasis is placed on the transformation of space. The indoor and outdoor spaces and flow lines are reorganized so that the spaces form various levels and depths. Nevertheless, according to feedback from actual users, the park's building environment and sanitation facilities are less satisfactory, and the sanitary conditions are more concerning. In addition, because some functions overlap and business introductions are comparable [32], the users' evaluation of the transformation value of the urban dimension is lower than anticipated.

**Figure 5.** Comparison of potential evaluation distribution in Shougang Industrial Heritage Park. (**a**) Distribution of reuse potential of primary indicators; (**b**) distribution of reuse potential for secondary indicators.

**Figure 6.** Comparison of potential evaluation distribution in 798 Art Park. (**a**) Distribution of reuse potential of primary indicators; (**b**) distribution of reuse potential for secondary indicators.

Figure 7 depicts the potential measurement results for 751D-PARK. The user evaluation has a higher value than the actual measurement potential among the autologous and retrofitting values of the urban dimension, indicating that its renovation has a larger impact on the urban area than the actual predicted potential size. The potential benefits of the urban dimension and the building itself stand out more.

The primary function of 751D-PARK was to ensure the supply of living and production energy for the construction and development of the electronic city. Later, it was transformed into an international cultural and creative park with a fashion design theme, establishing a trading platform for the design industry in the original factory compound and serving as a cultural gathering place for numerous domestic and foreign fashion design groups and well-known companies. The transformed industrial space resources serve as a venue for high-end brand launches and original design exhibitions, and the brand's activities have a far-reaching influence, culminating in an anticipated impact on the urban area that exceeds its actual predicted potential size. The retention of iconic and representative buildings and structures reflects the potential value response for the building proper, and the renovation preserves the original environment, develops new functions, and transforms old industrial equipment into new art spaces, making it an important area for the fusion of fashion and art [33].

**Figure 7.** Comparison of potential evaluation distribution in 751 D·PARK. (**a**) Distribution of reuse potential of primary indicators; (**b**) distribution of reuse potential for secondary indicators.

The potentiality measurements for the remaining parks are shown in Figure 8.

**Figure 8.** *Cont*.

**Figure 8.** Comparison of the radar map of the distribution of potential of the remaining industrial heritage parks. (**a**) Distribution of indicators of reuse potential in No. 27 Factory 1897 Science and Technology Innovation City; (**b**) distribution of indicators of reuse potential in Laijin Cultural and Creative Industry Heritage Park; (**c**) distribution of indicators of reuse potential in Xinhua 1949 Cultural and Financial Industrial Heritage Park; (**d**) distribution of indicators of reuse potential in 768 Cultural and Creative Industry Heritage Park; (**e**) distribution of indicators of reuse potential in Beijing Langyuan Cultural Creative Park.

Its evaluation method is more compatible than a conventional reuse potentiality evaluation, and the evaluation process is applicable not only to measuring the adaptive reuse potential of the entire industrial heritage park but also to determining the development timing of individual industrial architecture heritage and the relative sizes of their respective reuse

potentials within a park. To increase the compatibility of the evaluation methods, the system of evaluation of reuse potential proposed in this paper includes the evaluation of the potential of renovated and reused industrial architecture heritage, determining the advantages and disadvantages of their potential and defining the possibility of future adjustment.
