Major engineering complexity dynamic evaluation model based on Markov chain and entropy theory

Abstract

The invention discloses a major engineering complexity dynamic evaluation model based on a Markov chain and an entropy theory, and belongs to the technical field of major engineering complexity dynamic evaluation. The invention discloses a major engineering complexity dynamic evaluation model based on a Markov chain and an entropy theory. The major engineering complexity dynamic evaluation model comprises a subcategory identification module, a scoring module and a Markov chain-entropy model. The method solves the problems that in the prior art, the state transition and entropy change process is difficult to reflect, the reliability of the complexity evaluation result is low, and the dynamic evolution rule of the complexity in the full life cycle of the project is difficult to reveal. The Markov chain modeling state transition probability is combined to reveal the complexity dynamic evolution path, and the entropy theory is used to quantify the system disorder degree, so that the dynamic monitoring of the full life cycle complexity of the major engineering project is realized, and a scientific basis is provided for project management decision. And the risks of construction period delay and cost hyper-branch caused by out-of-control complexity are effectively reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of dynamic evaluation of major engineering complexity, and in particular to a dynamic evaluation model of major engineering complexity based on Markov chain and entropy theory. Background Art

[0002] Complexity management has always been a challenge in the field of major engineering project management. Existing technologies mainly include traditional complexity management methods, such as qualitative assessment based on expert experience and simple quantitative analysis methods. However, these methods have obvious limitations:

[0003] 1. Lack of dynamism: Unable to capture the dynamic evolution of complexity. The technological, environmental, and organizational dimensions of major engineering systems exhibit nonlinear interactions at different stages, making it difficult for traditional static models to reflect state transitions and entropy changes.

[0004] 2. Insufficient quantification: Existing methods are mostly based on subjective scoring and lack objective mathematical modeling support, resulting in low credibility of complexity assessment results.

[0005] 3. Limitations of traditional methods: It is difficult to reveal the dynamic evolution of complexity throughout the project life cycle and cannot provide a scientific basis for project management decisions.

[0006] To address the above problems, the present invention proposes a dynamic evaluation model that integrates Markov chain and entropy theory, which can quantitatively analyze complexity from multiple dimensions and multiple stages, and reveal the dynamic laws of complexity through state transition matrix and entropy value calculation. Summary of the Invention

[0007] The purpose of the present invention is to provide a dynamic evaluation model for the complexity of major engineering projects based on Markov chain and entropy theory. By constructing a complexity indicator system covering six dimensions of technology, environment, organization, goal, information and progress, combining the state transition probability of Markov chain modeling to reveal the dynamic evolution path of complexity, and using entropy theory to quantify the system disorder, dynamic monitoring of the complexity of major engineering projects throughout their life cycle can be achieved, providing a scientific basis for project management decisions, effectively reducing the risks of construction delays and cost overruns caused by uncontrolled complexity, and solving the problems raised in the above-mentioned background technology.

[0008] To achieve the above objectives, the present invention provides the following technical solutions: a dynamic evaluation model for the complexity of major projects based on Markov chains and entropy theory, comprising:

[0009] The subcategory identification module is used to define and classify the complexity of the engineering projects to be evaluated from multiple dimensions based on complexity theory;

[0010] a scoring module, configured to quantitatively evaluate the complexity degree of each complexity sub-category at different time points;

[0011] a Markov chain-entropy model, configured to construct a dynamic evaluation model combining Markov chain and entropy theory according to the evaluation result of the evaluation module, and dynamically analyze the complexity of the whole life cycle of the engineering project to be evaluated.

[0012] Preferably, the sub-category identification module specifically comprises:

[0013] The complexity of the engineering project to be evaluated is divided into six dimensions of technology, environment, organization, target, information and schedule;

[0014] An analysis model of the whole life cycle from the investment decision-making to the operation is established, and the relative complexity at different time points is dynamically sorted to reveal the evolution characteristics of the complexity;

[0015] The relative importance ranking of the sub-categories in the life cycle of the engineering project to be evaluated is obtained.

[0016] Preferably, the Markov chain-entropy model specifically comprises:

[0017] a construction unit, configured to introduce Markov chain theory, construct a state transition probability matrix, and describe the state transition rule of the engineering project to be evaluated at different time points;

[0018] a quantification unit, configured to quantitatively evaluate the disorder degree of the engineering project to be evaluated by combining the state transition rule of the engineering project to be evaluated at different time points with the entropy theory;

[0019] a calculation and evaluation unit, configured to evaluate the complexity level of the engineering project to be evaluated by calculating the maximum entropy, the standard entropy and the weighted entropy, and obtain the complexity evaluation result of the engineering project to be evaluated according to the calculation result.

[0020] Preferably, the working process of the Markov chain-entropy model specifically comprises:

[0021] obtaining the relative importance ranking of the sub-categories in the life cycle of the engineering project to be evaluated;

[0022] obtaining the sub-category ranking of two adjacent time points in the life cycle of the engineering project to be evaluated;

[0023] introducing Markov chain theory, constructing a state transition probability matrix, and describing the state transition rule of the engineering project to be evaluated at different time points;

[0024] obtaining the Markov chain conditional probability ranking by using the state transition rule of the engineering project to be evaluated at different time points;

[0025] The Markov chain conditional probability of the engineering project to be evaluated is used to rank the conditional transition matrix;

[0026] An entropy model is introduced to calculate the complexity of the engineering project to be evaluated according to the calculation result.

[0027] Preferably, the entropy model is introduced to calculate the complexity of the engineering project to be evaluated according to the calculation result.

[0028] The complexity level is calculated by the entropy model, and the complexity level corresponds to the weight entropy;

[0029] The maximum complexity is calculated by the entropy model, and the maximum complexity corresponds to the maximum entropy;

[0030] The relative complexity level is calculated by the entropy model, and the relative complexity level corresponds to the standard entropy;

[0031] The complexity of the engineering project to be evaluated is evaluated according to the calculated entropy value. The greater the entropy value, the higher the disorder degree of the engineering project to be evaluated, and the greater the complexity.

[0032] Preferably, the complexity level of the major project is calculated, and the complexity level of the major project corresponds to the weight entropy, and the specific formula is as follows:

[0033]

[0034] Wherein, H is the actual entropy value, H ij is the weight entropy, p ij is the conditional transition probability of the Markov chain, 0≤p ij ≤1, 1≤i, j≤n.

[0035] Preferably, the maximum complexity level is calculated, and the maximum complexity level corresponds to the maximum entropy, and the calculation formula is as follows:

[0036]

[0037] Wherein, H ijmax is the maximum entropy.

[0038] Preferably, the relative complexity level is calculated, and the relative complexity level corresponds to the standard entropy, and the calculation formula is as follows:

[0039]

[0040] Wherein, H ijnormalized is the standard entropy.

[0041] Preferably, the Markov chain theory is introduced, and the state transition probability matrix is constructed, which specifically includes:

[0042] A fixed probability P ijSo that:

[0043] P(X (n+1) = i|X (n) = j,X (n-1) = i n-1 ,…,X (0) = i (0) ) = P ij ,n>0

[0044] Wherein i, j, i0, i1, …, i n-1 ∈ M, M is a set comprising all possible states of the Markov chain, which satisfies P ij ≥ 0,

[0045] The Markov chain transition probability matrix is constructed, and the Markov chain transition probability matrix is specifically as follows:

[0046]

[0047] Preferably, the complexity degree of each complexity sub-category at different time points is quantitatively evaluated, and specifically includes:

[0048] Based on the identified complex sub-categories, the project whole life cycle is divided into six main stages of investment decision, survey and design, procurement bidding, construction, acceptance and delivery and operation;

[0049] Two observation time points are selected in each stage, and the complexity degree of each sub-category at different time points is quantitatively evaluated by expert scoring method.

[0050] Compared with the prior art, the beneficial effects of the present application are:

[0051] 1. The present application can comprehensively and dynamically evaluate the complexity of a major engineering project by constructing a complexity index system covering six dimensions of technology, environment, organization, target, information and progress, consider various aspects of project complexity from multiple dimensions, and reveal the dynamic evolution law of complexity;

[0052] 2. The present application reveals the dynamic evolution path of complexity by combining Markov chain modeling state transition probability, quantifies the degree of system disorder by using entropy theory, and improves the objectivity and accuracy of evaluation by using quantitative evaluation method and model calculation, thereby avoiding subjectivity and ambiguity;

[0053] 3. The present application provides a scientific basis for project management decision, helps project managers better understand and cope with project complexity, improves management efficiency and reduces management cost, thereby realizing dynamic monitoring of the complexity of the whole life cycle of a major engineering project, providing a scientific basis for project management decision, and effectively reducing the risk of time delay and cost overrun caused by complexity out of control. BRIEF DESCRIPTION OF DRAWINGS

[0054] Fig. 1 A major engineering complexity dynamic evaluation model framework based on Markov chain and entropy theory of the present application;

[0055] Fig. 2 A project sub-category complexity ranking visualization diagram of the present application;

[0056] Fig. 3 A major engineering complexity dynamic evaluation model module schematic diagram based on Markov chain and entropy theory of the present application. DETAILED DESCRIPTION

[0057] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0058] In order to solve the problems that the prior art is difficult to reflect state transition and entropy change process, lacks objective mathematical modeling support, and leads to low reliability of complexity evaluation results and difficulty in revealing the dynamic evolution law of complexity in the whole life cycle of a project, please refer to Figs. 1-3 The technical solutions of the present embodiments are as follows:

[0059] The major engineering complexity dynamic evaluation model based on Markov chain and entropy theory comprises:

[0060] A sub-category identification module is used for complexity definition and classification of the engineering project to be evaluated. Based on complexity theory, the complexity of the engineering project to be evaluated is defined and classified from multiple dimensions, including technology, environment, organization, target, information and schedule dimensions. Each dimension is further subdivided into complexity sub-categories, such as multi-unit coordination and resource allocation difficulty under the organization dimension, so as to more comprehensively cover various aspects of project complexity.

[0061] A scoring module is used for quantitatively evaluating the complexity degree of each complexity sub-category at different time points. The complexity degree of each complexity sub-category at different time points is quantitatively evaluated, and the scoring range is 1-4 points. The higher the score is, the greater the complexity is. The evaluation result is used as a state space of the Markov chain model for calculating a state transition probability matrix.

[0062] A Markov chain-entropy model is used for constructing a dynamic evaluation model integrating Markov chain and entropy theory according to the evaluation result of the evaluation module, and dynamically analyzing the complexity of the whole life cycle of the engineering project to be evaluated.

[0063] The sub-category identification module specifically comprises:

[0064] The complexity of the engineering project to be evaluated is divided into six dimensions of technology, environment, organization, target, information and schedule, and each dimension is further subdivided into complexity sub-categories, such as multi-unit coordination and resource allocation difficulty under the organization dimension, so as to more comprehensively cover various aspects of project complexity;

[0065] An analysis model is established for the whole life cycle from the investment decision to the operation, and the relative complexity at different time nodes is dynamically sorted, so as to reveal the evolution characteristics of complexity;

[0066] The relative importance ranking of the sub-categories in the life cycle of the engineering project to be evaluated is obtained.

[0067] The Markov chain-entropy model specifically comprises:

[0068] The construction unit is used to introduce the Markov chain theory, construct a state transition probability matrix, describe the state transition law of the engineering project to be evaluated at different time points, and quantitatively evaluate the complexity degree of each complexity sub-category at different time points;

[0069] The quantification unit is used to quantitatively evaluate the degree of disorder of the engineering project to be evaluated by using the state transition law of the engineering project to be evaluated at different time points in combination with the entropy theory;

[0070] The calculation and evaluation unit is used to evaluate the complexity level of the engineering project to be evaluated by calculating the maximum entropy, standard entropy and weight entropy, and the greater the entropy value, the higher the degree of disorder of the engineering project to be evaluated, and the greater the complexity, and the complexity evaluation result of the engineering project to be evaluated is obtained according to the calculation result.

[0071] The workflow of the Markov chain-entropy model specifically comprises:

[0072] The relative importance ranking of the sub-categories in the life cycle of the engineering project to be evaluated is obtained;

[0073] The ranking of the sub-categories of the adjacent two time points in the life cycle of the engineering project to be evaluated is obtained;

[0074] The Markov chain theory is introduced, a state transition probability matrix is constructed, and the state transition law of the engineering project to be evaluated at different time points is described;

[0075] The Markov chain conditional probability ranking is obtained by using the state transition law of the engineering project to be evaluated at different time points;

[0076] The conditional transition matrix is obtained by using the Markov chain conditional probability ranking of the engineering project to be evaluated;

[0077] An entropy model is introduced for calculation, and complexity of the engineering project to be evaluated is evaluated according to the calculation result.

[0078] An entropy model is introduced for calculation, and complexity of the engineering project to be evaluated is evaluated according to the calculation result

[0079] The complexity level is calculated by using the entropy model, and the complexity level corresponds to the weight entropy;

[0080] The maximum complexity is calculated by using the entropy model, and the maximum complexity corresponds to the maximum entropy;

[0081] The relative complexity level is calculated by using the entropy model, and the relative complexity level corresponds to the standard entropy;

[0082] The complexity of the engineering project to be evaluated is evaluated according to the calculated entropy value, and the greater the entropy value, the higher the disorder degree of the engineering project to be evaluated, and the greater the complexity.

[0083] The complexity level of the major project is calculated, and the complexity level of the major project corresponds to the weight entropy, and the specific formula is as follows:

[0084]

[0085] H is the actual entropy value, H ij is the weight entropy, p ij is the conditional transition probability of the Markov chain, 0≤p ij ≤1, 1≤i, j≤n.

[0086] The maximum complexity level is calculated, and the maximum complexity level corresponds to the maximum entropy, and the calculation formula is as follows:

[0087]

[0088] Where, H ijmax is the maximum entropy.

[0089] The relative complexity level is calculated, and the relative complexity level corresponds to the standard entropy, and the calculation formula is as follows:

[0090]

[0091] Where, H ijnormalized is the standard entropy.

[0092] The Markov chain theory is introduced, and the state transition probability matrix is constructed, which specifically includes:

[0093] A fixed probability P ij independent of time is set, so that:

[0094] P(X (n+1) =i|X (n) =j, X(n-1) = i n-1 ,…,X (0) = i (0) ) = P ij ,n > 0

[0095] Wherein i, j, i0, i1, …, i n-1 ∈ M, M is a set comprising all possible states of Markov chain, M can also be called state space, elements in M are called states of random process; probability P ij represents the probability of transition from the given current state j to state i, that is, transition probability, which satisfies P ij ≥ 0,

[0096] The Markov chain transition probability matrix is constructed, and the Markov chain transition probability matrix is as follows:

[0097]

[0098] The complexity degree of each complexity subcategory at different time points is quantitatively evaluated, specifically including:

[0099] Based on the identified complex subcategories, the project full life cycle is divided into investment decision, survey and design, procurement bidding, construction, acceptance and operation six main stages;

[0100] Two observation time points are selected in each stage, and the complexity degree of each subcategory at different time points is quantitatively evaluated by expert scoring method.

[0101] The major engineering complexity dynamic evaluation model based on Markov chain and entropy theory is used to evaluate the complexity of the project, specifically including:

[0102] The complexity of the project is divided into six dimensions of technology, environment, organization, target, information and schedule, and an analysis model of the six-stage full life cycle from investment decision to operation is established, and the relative complexity at different time nodes is dynamically sorted to reveal the evolution characteristics of complexity, and finally 24 representative complexity influence subcategories are extracted through systematic analysis of literature and project files, which provides a quantitative basis for subsequent complexity level measurement;

[0103] The complexity degree of each complexity subcategory at different time points is quantitatively evaluated, and the score range is 1-4;

[0104] According to the expert scoring results, a state transition probability matrix is constructed, and the entropy value, maximum entropy value, relative complexity level and weighted entropy value of the project at different time points are calculated;

[0105] The theoretical maximum entropy value Hmax The actual entropy value H is 8.4015, the relative complexity level is 78%, and the weighted entropy value WH is 21.5655. The results show that the project as a whole is in a state of high complexity, and the dimensions of technology, environment, organization, target, information, and schedule all show significant complexity characteristics.

[0106] Based on the identified complex sub-categories, the project full life cycle is divided into investment decision-making, survey and design, procurement bidding, construction, acceptance and handover, and operation six main stages, and two observation time points are selected in each stage, a total of 12 evaluation points are set. The complexity degree of each sub-category at different time points is quantitatively evaluated by expert scoring method, and finally the complexity dynamic evolution analysis result shown in Table 2 is formed, which clearly presents the relative complexity change trend of the six complex sub-categories in the project process.

[0107]

[0108]

[0109] Table 2 is the complexity ranking of project sub-categories

[0110] The ranking in Table 2 is visualized as a graph Fig. 2 , and the complexity change trend of each complex sub-category at 24 observation time points can be more clearly seen. Through the analysis of Table 2 and Fig. 2 , it can be seen that in the full life cycle of the project, the complexity ranking change between adjacent time nodes occurs a total of 129 times, which significantly improves the complexity degree of the overall project management. This embodiment further sets 12 time nodes for the 6 key stages of the project whole process, and quantifies the relative importance of each complexity dimension at different time points through expert scoring method, and the final analysis result is shown in Table 3.

[0111]

[0112] Table 3 shows the ranking change of the six dimensions of project complexity

[0113] Based on the dynamic evaluation results of the six key dimensions, this embodiment statistics the sorting change of each complexity index between adjacent observation nodes, as shown in Table 4, which clearly presents the evolution characteristics of the relative importance of different complexity dimensions in the project process:

[0114]

[0115]

[0116] The probability distribution of the ranking change of each dimension of the project is represented by the following matrix:

[0117]

[0118] In the consideration of the system with a certain complex dimension, the transition probability between the state levels presents the characteristics of uniform distribution, that is, the possibility of the system jumping from a certain state level to any other state level is the same, that is, p ij = 0.166667. The data processing is carried out by using the natural logarithmic conversion method, and the result can be expressed as follows:

[0119] H = 8.4015

[0120] H max = 10.751

[0121]

[0122] Combined with the formula WH ij = WR ij H ij and the ranking change matrix, the weight entropy WH of the project complexity level can be calculated as:

[0123] WH = 21.5655

[0124] After completing the calculation of the weight entropy value of the overall project complexity, the weight entropy of the complexity level of each sub-class can be calculated, and the actual entropy H and the weight entropy WH of each sub-project complexity level can be further calculated, and the calculation results are shown in Table 5:

[0125]

[0126]

[0127] Table 5 Actual entropy H and weight entropy WH of complex sub-class

[0128] According to the data shown in Table 5, the complexity level weight values of the six complexity subsystems in the project present significant differences, the actual entropy value (H = 4.6755) and the weight entropy value (WH = 9.5691) of the organizational complexity are both in the first place, followed by the progress complexity, the information complexity, the technical complexity, the target complexity and the environmental complexity. This quantitative analysis result shows that among the project complexity subsystems, the organizational complexity and the progress complexity have higher system importance and management difficulty. Through the empirical research, it is shown that the application of the model in the project has achieved remarkable results, verifying the effectiveness and practicality of the model. The maximum entropy value H max of the project theory is 10.751, the actual entropy value H is 8.4015, the relative complexity level is 78%, and the weighted entropy value WH is 21.5655. These specific data provide strong evidence for the advantages of the model.

[0129] It is to be understood that the terminology used herein such as first and second, and the like, is only used to distinguish one entity or action from another entity or action, and does not necessarily require or imply any such actual relationship or order between such entities or actions. Moreover, the terms "comprises", "comprising", or any other variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can include other elements not expressly listed or inherent to such process, method, article, or apparatus.

[0130] While the embodiments of the application have been shown and described, it is to be understood that the embodiments can be modified, altered, replaced, and varied without departing from the principles and spirit of the application.

Claims

1. A dynamic evaluation model for major engineering complexity based on Markov chain and entropy theory, characterized by: include; The subcategory identification module is used to define and classify the complexity of the engineering projects to be evaluated from multiple dimensions based on complexity theory; Scoring module, used to quantitatively evaluate the complexity of each complexity subcategory at different points in time; The Markov chain-entropy model is used to construct a dynamic evaluation model that integrates Markov chain and entropy theory based on the evaluation results of the evaluation module, and dynamically analyze the complexity of the entire life cycle of the engineering project to be evaluated.

2. The dynamic evaluation model for major engineering complexity based on Markov chain and entropy theory according to claim 1 is characterized in that: The subcategory identification module specifically includes: The complexity of the engineering project to be evaluated is divided into six dimensions: technology, environment, organization, goal, information and schedule. Each dimension is further subdivided into complexity subcategories. Establish an analytical model covering the entire life cycle of six stages, from investment decision to operation, and dynamically sort the relative complexity of the analytical model at different time nodes to reveal the evolutionary characteristics of complexity; Obtain the relative importance ranking of subcategories within the life cycle of the project to be evaluated.

3. The dynamic evaluation model for major engineering complexity based on Markov chain and entropy theory according to claim 1 is characterized in that: The Markov chain-entropy model specifically includes: The construction unit is used to introduce the Markov chain theory, construct the state transition probability matrix, and describe the state transition rules of the engineering project to be evaluated at different time points; A quantification unit is used to quantify the disorder of the project to be evaluated by combining the state transition law of the project to be evaluated at different time points with entropy theory; The calculation and evaluation unit is used to evaluate the complexity level of the engineering project to be evaluated by calculating the maximum entropy, standard entropy and weighted entropy, and obtain the complexity evaluation result of the engineering project to be evaluated according to the calculation result.

4. The dynamic evaluation model for major engineering complexity based on Markov chain and entropy theory according to claim 3 is characterized in that: The workflow of the Markov chain-entropy model specifically includes: Obtain the relative importance ranking of subcategories within the life cycle of the project to be evaluated; Obtain the subcategory rankings of the subcategory at two adjacent time points within the life cycle of the project to be evaluated; Introducing Markov chain theory, constructing a state transition probability matrix to describe the state transition rules of the project to be evaluated at different time points; The Markov chain conditional probability ranking is obtained by using the state transition rules of the engineering project to be evaluated at different time points; Utilize the Markov chain conditional probability ranking conditional transfer matrix of the engineering project to be evaluated; The entropy model is introduced for calculation, and the complexity of the engineering project to be evaluated is evaluated based on the calculation results.

5. The dynamic evaluation model for major engineering complexity based on Markov chain and entropy theory according to claim 4 is characterized in that: The entropy model is introduced to perform calculations, and the complexity of the project to be evaluated is evaluated based on the calculation results. The entropy model is used to calculate the complexity level, which corresponds to the weighted entropy; The maximum complexity is calculated using the entropy model, and the maximum complexity corresponds to the maximum entropy; The relative complexity level is calculated using the entropy model, and the relative complexity level corresponds to the standard entropy; The complexity of the engineering project to be evaluated is evaluated based on the calculated entropy value. The larger the entropy value, the higher the disorder and complexity of the engineering project to be evaluated.

6. The dynamic evaluation model for major engineering complexity based on Markov chain and entropy theory according to claim 5 is characterized in that: The calculation of the complexity level of major projects, the complexity level of major projects corresponds to the weighted entropy, and the specific formula is as follows: Among them, H is the actual entropy value, H ij is the weight entropy, p ij is the conditional transition probability of the Markov chain, 0≤P ij ≤1, 1≤i, j≤n.

7. The dynamic evaluation model for major engineering complexity based on Markov chain and entropy theory according to claim 5 is characterized in that: The maximum complexity level is calculated, and the maximum complexity level corresponds to the maximum entropy, and the calculation formula is as follows: Among them, H ijmax is the maximum entropy.

8. The dynamic evaluation model for major engineering complexity based on Markov chain and entropy theory according to claim 5 is characterized in that: The relative complexity level is calculated, and the relative complexity level corresponds to the standard entropy, and the calculation formula is as follows: Among them, H ijnormalized is the standard entropy.

9. The dynamic evaluation model for major engineering complexity based on Markov chain and entropy theory according to claim 1 is characterized in that: The introduction of Markov chain theory and the construction of state transition probability matrix specifically include: Set a fixed probability P that is independent of time ij , such that: P(X (n+1) =i|X (n) =j,X (n-1) =i n-1 ,…,X (0) =i (0) )=P ij ,n>0 where i,j,i0,i1,…,i n-1 ∈M, M is the set of all possible states of the Markov chain that satisfies P ij ≥0, j=0,1,...; Construct the Markov chain transfer probability matrix. The Markov chain transfer probability matrix is ​​as follows:

10. The dynamic evaluation model for major engineering complexity based on Markov chain and entropy theory according to claim 1 is characterized in that: The quantitative evaluation of the complexity level of each complexity subcategory at different time points specifically includes: Based on the identified complex subcategories, the project life cycle is divided into six stages: investment decision-making, survey and design, procurement and bidding, construction, acceptance and handover, and operation; Two observation time points were selected in each stage, and the complexity of each subcategory at different time points was quantitatively evaluated using the expert scoring method.

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