Bid Evaluation Method of Railway Green Construction Based on Improved PCA-Gray Variable Weight Clustering Model

The current bid evaluation method can no longer meet the needs of green construction of railway construction projects, so a bid evaluation method based on an improved PCA-gray variable weight clustering model is proposed. A bid evaluation index system for railway green construction projects with a hierarchical structure was constructed from three aspects: basic construction ability, business ability and green construction ability, and the index evaluation criteria were given. Considering the high dimensional complexity of the bid evaluation system, the improved PCA method was used to reduce the dimension of the bid evaluation system, and on this basis, an improved linear weighted comprehensive evaluation function was constructed to preliminarily evaluate the construction ability of bidders. Then, the grey variable weight clustering model is used to construct the definite weighted function to further analyze the green construction ability of the bidders and select the optimal bidder. Finally, the method was applied to the bid evaluation of railway engineering projects from Lanzhouxi to Zhongchuan Airport, and the conclusion is consistent with the actual bidders, which proves the applicability and effectiveness of the model.


Introduction
Railway green construction, as a new type of sustainable development concept, aims to meet the basic requirements of construction projects such as quality and time limit while protecting the environment, saving resources and energy, and eventually achieve the goal of harmonious development of human and nature. As the primary link to select the best bidder, bid evaluation of railway green construction project is an important guarantee to promote the smooth development of railway green construction, and also a necessary condition to accelerate the construction of green railway. Therefore, in order to encourage railway construction enterprises to actively carry out green construction, it is necessary to conduct green construction bid evaluation for railway construction projects. At present, there are a lot of researches on project bid evaluation and related aspects at home and abroad. Puri and Tiwari (2014) analyzed the relevant theoretical methods for contractor evaluation and examined the actual criteria for the selection of contractors, and then determined bid evaluation methods. Padhi and Mohapatra (2010) proposed a binary goal programming model to solve the multi-objective decision-making problem in bid evaluation. Shrestha (2014) proposed average bid method to alternate low bid method in public sector construction procurement. Zhang (2015) integrated fuzzy theory, data envelopment analysis (DEA) and grey relational analysis and proposed a systematic decision-making method of bid evaluation based on fuzzy DEA and grey relation for choosing proper bidders. Geng and Ren (2014) applied fuzzy comprehensive evaluation in the bid evaluation of municipal engineering construction projects. Liu et al. (2016) aimed large construction projects to propose the method of Partial Least Squares (PLS) path modeling and develop a Sequence-Multi-Criteria System. Yang and Zhang (2017) proposed using DEA model to study bidding evaluation of projects and verified the applicability of the model with specific cases. Turskis (2008) presented the multi-attribute contractors ranking method and an illustrative example of contractor selection is used to demonstrate the feasibility and practicability of the proposed model.  proposed bid evaluation optimal model of engineering project based on ELECTRE-I and ELECTRE-II, respectively.
Through learning the existing research results, the following problems are found: (1) The bid evaluation system established is not perfect enough, the influence of railway green construction elements has not been comprehensively considered, and it cannot reflect the green construction ability of bidders.
(2) Although the bid evaluation system has been widely recognized worldwide, there are still many shortcomings in the bid evaluation process. The study of most of the factors is still in qualitative research, lack of quantitative research, such as corporate credibility, management level, and so on. Therefore, it is difficult to accurately select the best bidder that meets the requirements in the specific bid evaluation practice.
In view of the above problems, based on traditional bid evaluation system, this paper supplemented the green construction factors and established a more perfect bid evaluation system. Then, the improved PCA method and gray variable weight clustering model are introduced to realize the quantitative research of railway green construction project bid evaluation, making the process of bid evaluation more scientific and operable.

Construction of index system
(1) Establishment of index pre-selection set We collected the bid evaluation factors of railway engineering projects in Guangzhou, Shanghai, Beijing, Jiangsu, Gansu and many other places by extensive investigations, and then the connotation and extension of the involved bid evaluation indexes and all the indexes between logical relationships are analyzed. Then merge or decompose some indexes to establish a pre-selection set of bid evaluation indexes, which can be divided into three categories of basic construction ability, business ability and green construction ability.
(2) Index screening The number of index pre-selection sets obtained through the above extensive collection is very large, so it is necessary to screen them. The pre-selection set indexes are screened, in this paper, with the help of relevant knowledge of management statistics, i.e., all pre-selection set indexes are first input to establish the database of bid evaluation indexes, then the frequency and weight of each index in the bid evaluation method were calculated, and the indexes with high frequency and heavy weight were selected to form a set of screened bid evaluation indexes.
(3) Construction of bid evaluation system Based on the general goals of railway green construction bid evaluation, the green construction bid evaluation are sorted into three sub-targets, namely: (1) Review of basic construction ability-the evaluation of the bidder's own basic construction ability and reputation.
(2) Review of business ability-analysis and comparison of bidding price and financial ability of bidders (3) Review of green construction ability-review of green construction design plans and green construction experience.
Then, the bid evaluation of railway green construction projects is taken as the target layer, the basic construction ability, business ability, and green construction ability are used as the criterion layer (i.e., three sub-targets), and the indexes selected in step (2) is used as the index layer. Among them, the index layer is a further detailed explanation of the criterion layer, and it is also the basis for determining the general goals. The indexes at all layers are progressively advanced, thereby constructing a multi-level green construction project evaluation system. Figs. 1 to 4 show the process of establishing the bid evaluation system.

Basis for determination of evaluation level standard
The evaluation level standards should follow the principles of feasibility, advancedness, and economy, and comply with China's current railway green construction codes and related regulations, such improves the persuasiveness of the evaluation level standards. The basis for formulating the evaluation level standards for each evaluation index is as follows:

Fig. 5 Basis for the establishment of evaluation level standards
The opinions of a large number of experts were collated through field surveys and visits, and the specific description of the index evaluation standard was formed with reference to the relevant specifications and regulations in Fig. 5, as shown in Table 1. It is mainly evaluated by the enterprise's credit ability, management personnel ability, enterprise construction technology level, and typical project performance.

Enterprise construction performance U12
Refers to the bidder's completion on time and a certain social reputation and project performance in previous projects

Construction experience of similar projects U13
The bidder's historical completion of the quality, safety, progress, cost, civilized construction of similar construction projects.
Financial status of the business U14 Use cash flow analysis to evaluate the financial status of construction enterprises.

Enterprise reputation level U15
It is mainly reflected in the credit rating, law-abiding consciousness, service consciousness and quality concept of construction enterprises.

Quality of project management staff U16
It is mainly reflected in the sense of responsibility of managers, the ability of organization and scheduling, and the awareness of safety management.
Engineering quality assurance measures U17 Engineering quality assurance measures mainly include quality assurance systems, quality supervision agency, quality control procedures, and quality responsibility implementation systems.

Rationality of the construction schedule U18
On the premise of ensuring the safety and quality of the project, reasonably arrange the logical relationship of the construction procedures, and reasonably allocate management personnel, operators and construction machinery.

Scientificity of construction plans U19
The rationality of the construction plan layout in the construction organization design, and the use of wasteland at the construction site

Rationality of labor arrangement plan U110
Reasonable arrangement of management personnel and construction personnel

Rationality of construction machinery plans U111
Whether the number and model of mechanical equipment are reasonably equipped to maximize the technological progress and the applicability of mechanical equipment.

Application of four new technologies U112
The use of new technologies, new processes, new products and new materials in the construction process.
Safe and civilized construction measures U113 1. The extent of compliance with the requirements of the Regulations on the Administration of Work Safety in Construction Engineering. 2. Whether to regularly conduct safety education for personnel engaged in hazardous operations in accordance with the provisions of the Safety Production Law, and whether a feasible protection plan has been formulated.
Total engineering quotation U21 Economics of the total price of the proposed project proposed by the bidder Rationality of the quote structure U22 Whether the cash inflow and cash outflow estimates during the construction phase are reasonable, and whether the adopted capital use plan maintains sufficient liquidity and a reasonable capital structure.

Rationality of the capital flow plan U23
Reasonableness of sub-item project quotation costs, measure project costs and other project costs Preferential conditions U24 Preferential conditions for equipment, technology, patents, etc.
New technology and new measures for water saving in construction U31

Use of new water-saving technologies and measures in construction
Use of water-saving appliances in living and production areas U32 The ratio of the number of water-saving appliances used to the total number of water facilities in the project Water saving management system U33 Establishment and soundness of water-saving management system According to the Green Building Evaluation Standards (GB / T 50378-2014), the proportion of the amount of materials used within 500km from the construction site to the total amount of materials Recycling of waste building materials U311 The ratio of the amount of waste materials actually recycled at the construction site to the total waste Use of recyclable materials U312 The proportion of recyclable materials in the total use of building materials Measures to reduce physical material loss U313 According to the Technical Indicators of Green Construction Technology Demonstration Project of the Ministry of Housing and Urban-Rural Development (2013), the ratio of physical material savings to planned usage Use of intensive production materials U314 The proportion of construction materials of intensive production to the total construction materials of the project

Usage of energy-saving lamps U315
With reference to the Technical Indicators for Green Construction Technology Demonstration Project of the Ministry of Housing and Urban-Rural Development (2013), the proportion of energy-saving lamps used in the total number of project lighting fixtures.

Use of energy-saving electrical equipment U316
The proportion of energy-saving machinery and equipment used in the total number of machinery and equipment during construction In order to comprehensively consider the impact of all indexes on the bid evaluation of railway green construction projects, there should be a unified evaluation level standard for all indexes. However, although some green construction specifications have been issued in some local areas, far from reaching the purpose of bid evaluation for railway green construction projects, and cannot be evaluated with specific quantitative standards. Therefore, based on the Fig.5 and Table 1, combined with the maximum resolvability of human thinking, supposing a score of 10 is the highest score, the standard evaluation level is divided into five-levels of excellent, good, general, qualified, and disqualified. As shown in Table 2.

Subjective weighting
The specific calculation steps of G1 method (Zhou et al. 2018;Xie et al. 2010) are as follows: a. Determine the order relationship Assuming that according to the evaluation standard, indexes Xi and Xj have the relationship: First, select the most important index from the index set   1 2 , , , m X X X and mark it as * 1 X . Then, select the most important index from the remaining m-1 indexes and mark it as * 2 X , and so on, the last index left after n-1 screening is marked as * n X . From this, the order relationship of the indexes is determined as, Supposing the ratio of the relative importance of * 1 k X − and * k X is rk, and the standard scales of rk are shown in Table 3: Then, according to the weight * n w , the weights of n-1th, n-2th, …, and 2nd indexes can be calculated as, Finally, the weight vector of the index set can be expressed by

Objective weighting
The entropy weight method (EWM) (Tiwar et al. 2019;Gao et al. 2017;Hamid et al. 2016) refers to reflecting the relative importance of each index in the system according to certain regularity among the index data. The smaller the index's entropy value, the more useful information it provides, and the larger the weight; otherwise, the smaller the index's weight.
Step 1: Data standardization The positive index can be calculated as, The negative index can be calculated as, where xij is the original data of jth index of ith research object, yij is normalized data, n is the number of research object, p is the number of index.
The matrix formed by the normalized data is expressed as Y, Step 2: According to the entropy principle and matrix Y, the entropy value Hj of the index is calculated as, In order to make lnfij meaningful, fij is defined as, Step 3: Calculate the entropy weight wj of the jth index, and the index entropy weight vector j W  is expressed as,

Building the combined weighting model
Both subjective and objective weighting methods have their own advantages and disadvantages. In order to give full play to the advantages of the two methods, this paper uses moment estimation method (Ji et al. 2018) to integrate the two methods to construct the combined weighting method.
The combined weighting model: based on G1 method and EWM to determine the subjective and objective weights respectively, moment estimation method is used to calculate the importance coefficient of subjective and objective weights, namely j  and j  , and the combined weight j W of the index is calculated by using Eq. (12). indexes with a linear combination, expressed by   (13)). The linear combination is based on the principle of retaining main information, so that the new index includes most information of the original index as much as possible, and the new indexes are independent of each other.   14) shows that the relative importance of the new indexes decreases successively. Therefore, the principal components need to be screened to simplify the complexity of the analysis process in practical applications.

Calculation procedure of PCA method
(1) Construct the original data matrix X where xij is the value of the jth index of the ith research object Dimensionless processing of elements in matrix X, the positive index can be calculated using min max min , and the negative index can be calculated using max max min (2) Form a standardized matrix Z The dimensionless matrix is transformed by using Z-Score method (Eq. (16)) to obtain the standardized matrix Z, which is expressed by Eq. (17),

) Calculate eigenvalues and eigenvectors
The Jacobi method is used to solve the characteristic equation 0 IR  −= to obtain non-negative eigenvalues λi (i = 1, 2, …, p), and these eigenvalues are arranged in order from large to small: Substituting the eigenvalue λi into the characteristic equation to obtain the corresponding eigenvector ai (i = 1,2,…, p) (Eq.20), and satisfy ( ) 12 , , , 1, 2, , It should be noted that when SPSS 22.0 software was used for principal component analysis, it was not aij that was obtained, but the load lij of the original data matrix the relationship between them is ij i ij l a  = .
(5) Calculate contributing rate and cumulative contribution rate The number of selected principal components is determined by the cumulative contribution rate of the principal components, which reflects the degree of coverage of the original variables. The larger the cumulative contribution rate is, the less the loss of data information is. Usually, 85%~95% (This paper takes 85%) of the cumulative contribution rate is selected. Contributing rate of principal component i  and cumulative contribution rate i  are calculated as,

Improved PCA
Although the traditional PCA method calculates the variance and correlation coefficient of the index and the difference in the degree of variation of the index is eliminated, the principal component extracted according to the correlation coefficient only contains part of the information that each index, which cannot completely reflect all the information contained in the original index data. Therefore, the traditional PCA method is improved by the averaging method (Yang et al. 2015) in this paper, which can effectively make up for this defect.
Assume that the averaged index value and covariance are recorded as yij and uij, respectively. The process of improving the traditional PCA using the averaging method is as follows: (1) Averaging the original data  (25), the covariance between the indexes is obtained as, where sij is the covariance of the original data.
Assume that the correlation coefficients of the indexes for the averaged data are It can be seen that the averaging does not change the correlation coefficient among the indexes, i.e., the new covariance matrix can reflect not only all the information of the correlation matrix, but also the variation information of each index.
(3) Constructing an improved linear weighted comprehensive evaluation function The averaged index is converted into a new principal component by the traditional PCA method, and an improved linear weighted comprehensive evaluation function is obtained as, where μpi is the weighted principal component coefficient (i = 1, 2, …, m), m is the number of selected principal components, and Yi is the ith principal component.

Grey clustering theory
The grey system theory (Fidan and Yuksel 2019;Voskoglou 2018) is to analyze the known information to fully dig out the laws of the original data itself, so as to achieve an accurate description of future trends.
The bid evaluation process of railway green construction project is characterized by high-dimensional complexity, uncertainty and system fuzziness, so the bid evaluation process can be regarded as a gray system. And the indexes of railway green construction bid evaluation involve a wide range of areas and a high information uncertainty, which completely conforms to the characteristics of the gray system.

Principles of grey clustering method
The principle of the gray clustering method (Delgado and Romero 2017;) is to use the gray relational degree matrix to construct the gray definite weighted function to perform cluster analysis on the evaluation indexes.
(1) Construct definite weighted function Definition 1 Suppose there are n research objects, p evaluation indexes, and s different gray class levels. And the observation value of the jth (j=1, 2, …, p) index of the ith (i =1, 2, …, n)research object is xij . The ith research object belongs to the kth gray class level.
, and the image is shown in Fig. 6.
The calculation of the critical value k j  of the jth index belonging to the kth is related to the type of definite weighted function. The calculation of the specific critical value k j  is divided into the following types: (1) The critical value of a typical definite weighted function is calculated as, (2) The definite weighted function of the lower limit measure has no level critical values ( ) The definite weighted function of the lower limit measure corresponding to Fig.7 is expressed as, 0 0, (4) (1) ( ) (1), (2) (2) (1) (4) (2), (4) (4) (2) (4) The definite weighted function for upper limit measure has no level critical values ( ) The definite weighted function of upper limit measure corresponding to Fig.9 is expressed as, 0 (1)

Grey variable weight clustering model
Based on the analysis of the gray clustering method described above, this paper selects the gray variable weight clustering model (Zhu et al. 2018;Liu and Yang 2017;He and Mao 2016) for evaluation. The specific steps are as follows: (1) Construct the definite weighted function ( ) ( 1, 2, , ; 1, 2, , ) of k subclass of the index j.
(2) Determine gray evaluation weight matrix Q experts were invited to rate the research subjects. Assuming that the tth where m is the number of criterion layers, w is the weight of the index, k ig R is the membership degree of the kth gray class of the gth criterion layer of the ith research object.
Finally, calculate the comprehensive evaluation matrix of the target layer. Assuming k i R is the degree of the ith research object belongs to the kth gray class, then where Wg is the weight of the criterion layer g. The comprehensive evaluation weight matrix of the target layer is 12 ( , , , ) (4) Identification criteria for maximum membership Knowing the evaluation matrix of the target layer, the maximum membership degree identification criterion is used to determine that the ith research object belongs to the gray class k  .

Project Overview
The new high-speed railway from Lanzhouxi to Zhongchuan Airport is 63.136 km, and new stations are Santan, Chenguanying, Fuliqu , Xigu, Shuping (reserved), Zhongchuan and Lanzhou Airport stations. The total length of the bridge and tunnel is 44.656 km, accounting for 70.88% of the total length of the whole line. The main line covers 18 large and medium-sized bridges with a total length of 40.881 km and 7 tunnels with a total length of 3.775 km. The total static investment is 9182.883 million yuan.

Source of initial data
In the construction process of the new high-speed railway from Lanzhouxi to Zhongchuan airport, the standards of green construction should be observed. Now, five railway construction enterprises with a qualification level of not lower than the first-level qualification of general construction contractors and green construction ability are invited to submit bids nationwide. Meanwhile, 5 companies engaged in green building construction and green construction scientific research institutions were hired in Gansu region, and each company was asked to send 5 experts to form a bid evaluation committee. And based on table 2, five bidders (respectively marked A to E) were scored according to the actual situation of the bid evaluation index, and the average value was taken, as shown in Table 4.

Analysis on Improved PCA Method
The normalization equation for positive index was adopted to normalize the index data, and then the Eq. (16) was used to further standardize the index data. Then based on standardized index data, the dimension of the bid evaluation index was reduced, and the corresponding eigenvalues and contribution rate were calculated. Finally, determine the number of principal components to be selected according to the "85% principle". The results showed that the first three principal components (M11, M12, M13 and M31, M32, M33, respectively) were selected for U1 and U3. And U2 selects the first two principal components (M21 and M22, respectively), as shown in table 5. The coefficient of principal component score is calculated by factor loading using SPSS22.0 software. The factor loading is the correlation coefficient between the principal component and the initial variable. It can objectively reflect the degree of correlation between the principal component and each initial variable. The specific values are shown in Table 6.
The ratio of variance contribution rate corresponding to each principal component and the sum of variance contribution rate of all principal components is taken as the weight of each principal component, and the comprehensive score of U1, U2 and U3 of different bidders are calculated respectively, which are expressed as S1, S2 and S3. The scores of each principal component are substituted into the expressions of S1 to S3, and the comprehensive scores of the criteria layers U1, U2, and U3 of each bidder are calculated, as shown in Table 7. Because the relative importance of the criteria layers U1, U2, and U3 are different, the moment estimation combination weighting method is used to determine the index combination weights, as shown in Table 8. The specific values S1, S2 and S3 of the 5 bidders are respectively substituted into the above formula to obtain the final comprehensive score of each enterprise (denoted as S), as shown in table 9. By comparing the results in table 9, it is concluded that the comprehensive score size of the five bidders is SB >SD > SA >SE >SC. Thus, the best bidder was preliminarily determined as the B enterprise.

Analysis of grey variable weight clustering model
Although the improved PCA model has preliminarily determined the optimal bidder, it cannot accurately reflect the green construction ability level of each bidder. Therefore, this paper uses the grey variable weight clustering model evaluate the green construction level of the five bidders (1) Determination of weights Since the original data are scored by experts, the subjectivity is high, so the EWM is used to calculate the index weight to increase the objectivity. Substituting the datas in table 4 into Eqs. (4) to (10) to calculate the weight of indexes, the results are shown in table 10. Considering that the qualitative index is highly subjective and the possibility of error is large, in order to make up for this shortcoming, we choose to build an interval trapezoid definite weighted function. Then, the five-levels of excellent, good, general, qualified, and disqualified are quantitatively described, (i.e., table 2), and the functions and images of each level is shown in Table 11.
3.5 ,10 3.5 / 3 3.5 ,6.5 = 1 6.5 ,8 10 / 2 8 ,10 9.5 2 / 3 2 ,5 = 1 5 ,6.5 9.5 / 3 6.5 ,9.5 The dates in table 4 and the expressions of definite weighted functions in table 11 were used to calculate the membership degree of each evaluation index of enterprise A and determine the gray evaluation matrix of enterprise The membership degree of the target layer can be obtained by using the formula ii R W R =, and then the comprehensive gray evaluation matrix of the target layer is determined. Based on the above calculation results, combined with Eq. (45), the green construction level of 5 bidders can be identified. Specifically, the green construction levels of the five bidders are respectively: A is level III, B is levelⅠ, C is level Ⅲ, D is levelⅡ, and E is level Ⅲ. Therefore, the optimal bidder can be finally determined as bidder B.

Discussion
The bid evaluation system established in this paper considers the bidder's green construction ability, which is more perfect compared with the traditional evaluation system, so the evaluation results are convincing to some extent. However, there are still some indexes cannot find relevant industry norms or national standards as the basis for scoring. They can only rely on the experience of experts to score, which is too subjective. Therefore, how to measure these indexes needs further research to improve the accuracy of the bid evaluation results.
The advantage of this paper is a combined weighting model was built to determine the weighting, such that the weight not only considers the impact of subjective human factors, but also the impact of objective data, which makes the weight distribution more reasonable. And compared with the commonly used AHP method, G1 method has the advantages of no consistency test. If using the AHP method, when the calculated matrix order is large, in the process of establishing the judgment matrix, the comparison judgment between the elements ( ) 1 / 2 nn − times needs to be made, which requires a large amount of calculation, moreover, when the number of factors being compared exceeds nine, the accuracy of such judgments is difficult to guarantee, according to psychologists. For the bid evaluation model, because of the use of the improved PCA method, the complexity of the calculation process was simplified, the bid evaluation efficiency was improved, but it cannot accurately reflect their green construction level. Therefore, the grey variable weight clustering method is used to evaluate the green construction ability of bidders by making full use of the gray information through the internal relationship between the internal data of the bidding documents.
However, due to limited space, this paper only established the bid evaluation system, proposed a bid evaluation model, and did not study the details and process issues of bid evaluation. Further research is needed on the development of the standard bid evaluation process, which is also the focus of the later research.
In general, we will continue to follow up the actual railway green construction projects, track and in-depth research on new issues emerging in the bid evaluation process, and propose more accurate quantitative methods for railway green construction bid evaluation.

Conclusion
(1) As the current bid evaluation system can no longer meet the requirements of the development of railway green construction, so based on the traditional bid evaluation system of railway construction projects, this paper supplemented the factor of green construction ability, and then reconstructed a more comprehensive bid evaluation system of railway green construction.
(2) The moment estimation method was used to integrate the G1 method and the EWM, and a combined weighting model was constructed to determine the weight of the bid evaluation index. The dimension of the bid evaluation index system was reduced through the improved PCA method, and the bid evaluation results were calculated with as few main indexes as possible, the best bidders was preliminarily obtained. Then, the grey variable weight clustering model was used to evaluate the green construction level of the bidders, and finally select the optimal bidder.
(3) Five bidders of Lanzhouxi to Zhongchuan airport intercity high-speed railway were evaluated by the proposed method, the selected bidder are consistent with the actual situation. Through the case analysis, it can be seen that this method can not only make up for the defects of the current bid evaluation method, but also guide the development of the bidding system of railway engineering green construction project towards the direction of standardized management, which lay a theoretical foundation for ensuring the smooth implementation of the railway green construction project.