A high arch dam construction scheme optimization method based on prospect theory

Abstract

This invention discloses a method for optimizing high arch dam construction schemes based on prospect theory. First, it comprehensively considers the development characteristics of construction indicators at each stage and proposes a dynamic reference point evolution method to achieve multi-stage, multi-attribute, and continuous random variable optimization of high arch dam construction schemes. Then, by establishing the weights of indicators and time weights at each stage, and finally based on the prospect stochastic criterion, it achieves intelligent optimization of the high arch dam construction scheme, effectively improving the scientific nature of decision-making. Compared with existing technologies, this invention comprehensively considers the development characteristics of construction indicators at each stage, achieving multi-stage, multi-attribute, and continuous random variable optimization of high arch dam construction schemes; it realizes intelligent optimization of high arch dam construction schemes, effectively improving the scientific nature of decision-making and solving the problem of low accuracy in current construction scheme optimization results.

Description

Technical Field

[0001] This invention relates to the field of high arch dam construction simulation, and in particular to a method for optimizing high arch dam construction schemes based on prospect theory. Background Technology

[0002] The construction of high arch dams is a complex stochastic dynamic process, and construction process simulation provides an important tool for optimizing and deciding on construction schemes. Based on the simulation results of different construction schemes, and considering various construction progress control indicators, intelligent optimization methods are used to obtain the optimal construction scheme, which can provide an important basis for on-site construction progress control. The optimization of high arch dam construction schemes needs to address the characteristics of multi-stage, multi-attribute, and continuous random variables, which existing research struggles to optimize. Currently, there is no method that comprehensively considers multi-attribute random indicators at each construction stage to optimize the construction scheme, and there are few targeted methods for multi-stage, multi-attribute optimization of continuous random variables. Summary of the Invention

[0003] To address the shortcomings of the existing technologies, this invention proposes a method for optimizing the construction scheme of high arch dams based on prospect theory. It comprehensively considers the development characteristics of construction indicators at each stage and proposes a dynamic reference point evolution method. Based on the prospect stochastic criterion and by establishing the weights of indicators and time weights at each stage, it achieves intelligent optimization of the high arch dam construction scheme, thereby improving the accuracy of the optimization.

[0004] This invention is achieved using the following technical solution:

[0005] This invention discloses a method for optimizing the construction scheme of high arch dams based on prospect theory, the method comprising the following steps:

[0006] Step 1: Based on the engineering characteristics of high arch dam construction, set up several construction plans and determine the decision indicators for the construction plans;

[0007] Step 2: Use the intelligent simulation system for high arch dam construction to perform simulation analysis and obtain the key parameters of each construction scheme at each stage.

[0008] Step 3: Normalize the various decision indicators of the construction plan, transforming each indicator value into a benefit-type indicator, and establish it as the key parameter x of the current stage decision indicator j plan i. ijt The model is as follows:

[0009]

[0010] Where, x ijt X is the key parameter of decision indicator j for scheme i at the current stage t. jt Let be the sample set of index j for each construction scheme in stage t;

[0011] Step 4: Based on the development and changes of different attributes of various decision indicators during the execution of the high arch dam construction plan, establish dynamic reference points for the decision indicators at each stage of each construction plan using the concept of average development speed. Subtract the dynamic reference points from the decision indicators at each stage of each construction plan, and establish the following model of the dynamic reference point change process based on the concept of average development speed:

[0012]

[0013]

[0014]

[0015]

[0016]

[0017] Where, x jt h represents the coordinates of the reference point for index j at stage t. t The parameters for setting the reference point at stage t, Let x be the reference point for index j at time t. jt The expected mean, p ijt Let j be the probability function of decision index j for option i at stage t. Let s be the average growth rate of indicator j. jt For the growth rate of indicator j under stage t, x jl x when t = l jt x jt-1 The coordinates of the reference point for index j in the previous stage t-1;

[0018] Step 5: Based on the prospect stochastic dominance theory, establish the value functions for each indicator at each stage of each construction scheme; the value function model based on the prospect stochastic dominance theory is as follows:

[0019] V ijt =∫π(p ijt )v(Δx k (7)

[0020]

[0021]

[0022] Δx k =x ijt -x jt (10)

[0023]

[0024] Among them, V ijtLet π() be the value function, ν() be the probability weight function, and Δx be the value function. k For the key parameter x ijt The difference from the dynamic reference point, k is the index of Δx, α and β are the concavity and convexity of the power functions of the gain and loss regions, respectively, θ is the characteristic that the loss region is steeper than the gain region, γ is the risk-reward attitude coefficient, δ is the risk-loss attitude coefficient, and x jt For the stage t The reference point for indicator j, W jt W represents the weight of the indicator attribute for indicator j in the current stage t. t V represents the time series weights. i Foreground value for scheme i;

[0025] Step 6: Using the CRITIC method, establish the weights of each indicator attribute and time weight for each scheme at each stage;

[0026] Step 7: Calculate the value function model shown in formulas (7) to (11) in step 5 according to prospect theory. The calculation results are used as the prospect values ​​of each construction scheme. Optimize each construction scheme. The larger the prospect value, the better the scheme.

[0027] Compared with the prior art, the present invention can achieve the following specific technical effects:

[0028] 1) Taking into account the development characteristics of construction indicators at each stage, the random variable optimization of the high arch dam construction scheme is achieved in multiple stages, with multiple attributes and continuity;

[0029] 2) It realizes intelligent optimization of the construction plan for high arch dams, effectively improves the scientific nature of decision-making, and solves the problem of low accuracy of the current construction plan optimization results. Attached Figure Description

[0030] Figure 1 This is an overall flowchart of a method for optimizing a high arch dam construction scheme based on prospect theory, according to an embodiment of the present invention.

[0031] Figure 2 This is a schematic diagram of a preferred construction scheme for a high arch dam based on prospect theory, according to an embodiment of the present invention. Detailed Implementation

[0032] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0033] like Figure 1 The diagram shown is an overall flowchart of a method for optimizing a high arch dam construction scheme based on prospect theory, according to the present invention. Figure 2 The diagram shown is a schematic model of a preferred construction scheme for a high arch dam based on prospect theory, according to an embodiment of the present invention.

[0034] Based on the engineering characteristics of high arch dam construction, several reasonable construction schemes were established, and decision indicators for each scheme were determined. For example, when optimizing the construction scheme for the cantilever height of the dam, three construction schemes with different cantilever heights were set up: an overall cantilever height of 60m + a cantilever height of 50m at the orifice (hereinafter referred to as Scheme C1), an overall cantilever height of 70m + a cantilever height of 60m at the orifice (hereinafter referred to as Scheme C2), and an overall cantilever height of 80m + a cantilever height of 70m at the orifice (hereinafter referred to as Scheme C3). The decision indicators for each construction scheme included "number of days to reach the critical node appearance ahead of schedule", "maximum pouring intensity from the start of simulation", "balance index of maximum pouring intensity from the start of simulation", and "average interval and proportion of concrete dam blocks exceeding 14 days". The intelligent simulation system for high arch dam construction was used for simulation analysis to obtain the key construction parameters for each stage of each construction scheme.

[0035] The overall process of the proposed method for optimizing the construction scheme of a high arch dam based on prospect theory includes the following steps:

[0036] Step 1: Normalize each decision indicator to convert each indicator value into a benefit-type indicator, meaning that the larger the indicator value, the better the overall performance. The normalization algorithm used is expressed as follows:

[0037]

[0038] Where, x ijt X is the key parameter of scheme i for phase t index j. jt Let be the sample set of index j for each construction scheme in stage t;

[0039] Step 2: Based on the development and changes of different attributes of various decision indicators during the execution of the high arch dam construction plan, establish dynamic reference points for decision indicators at each stage of each construction plan using the concept of average development speed.

[0040] In this embodiment, the model for the dynamic establishment of the reference point change process based on the concept of average growth rate is as follows:

[0041]

[0042]

[0043]

[0044]

[0045]

[0046] Where, x jt h represents the coordinates of the reference point for index j at stage t.t The parameters for setting the reference point at stage t, Let x be the reference point for index j at the current time t. jt The expected mean, p ijt Let j be the probability function of decision index j for option i at stage t. Let s be the average growth rate of indicator j. jt For the growth rate of indicator j under stage t, x jl x when t = l jt x jt-1 The coordinates of the reference point for index j in the previous stage t-1;

[0047] Step 3: Based on the prospect stochastic dominance theory, establish the value functions of each indicator at each stage of each construction scheme;

[0048] In this embodiment, the value function model established based on the prospect stochastic dominance theory is as follows:

[0049] V ijt =∫π(p ijt )v(Δx k (7)

[0050]

[0051]

[0052] Δx k =x ijt -x jt (10)

[0053]

[0054] Among them, V ijt Let π() be the value function, ν() be the probability weight function, and Δx be the value function. k For the key parameter x ijt The difference from the dynamic reference point, k is the index of Δx, α and β are the concavity and convexity of the power functions of the gain and loss regions, respectively, θ is the characteristic that the loss region is steeper than the gain region, γ is the risk-reward attitude coefficient, δ is the risk-loss attitude coefficient, and x jt For the stage t The reference point for indicator j, W jt W represents the weight of the indicator attribute for indicator j in the current stage t. t V represents the time series weights. i Foreground value for scheme i;

[0055] In this embodiment, α and β are 0.88, θ is 2.25, γ is 0.61, and δ is 0.72. All of these values ​​have been experimentally verified to be reasonable.

[0056] Step 4: Using the CRITIC method, establish the weights of each indicator attribute and time weight for each scheme at each stage;

[0057] In this embodiment, the stage weights for each stage are established as W1, W2, W3, and W4, as follows:

[0058] W1=(0.187,0.159,0.307,0.295,0.0507)

[0059] W2=(0.221,0.141,0.311,0.177,0.150)

[0060] W3=(0.272,0.098,0.266,0.168,0.196)

[0061] W4=(0.476,0.107,0.337,0.0218)

[0062] And, time weight: W t =(0.300,0.129,0.290,0.281)

[0063] Step 5: Calculate the value function model shown in formulas (7) to (11) in Step 5 according to prospect theory. The calculation results are used as the prospect values ​​of each construction scheme. Optimize each construction scheme. The larger the prospect value, the better the scheme.

[0064] In this embodiment, the decision index for each stage is V = (-0.454, 0.228, 0.146) according to prospect theory. Therefore, Scheme 2 is the optimal one.

[0065] This invention first comprehensively considers the development characteristics of construction indicators at each stage and proposes a dynamic reference point evolution method to achieve multi-stage, multi-attribute, and continuous random variable optimization of high arch dam construction schemes. Then, by establishing the indicator weights and time weights for each stage, and finally based on the prospect stochastic criterion, it achieves intelligent optimization of high arch dam construction schemes, effectively improving the scientific nature of decision-making.

[0066] Those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for optimizing the construction scheme of a high arch dam based on prospect theory, characterized in that, The method includes the following steps: Step 1: Based on the engineering characteristics of high arch dam construction, set up several construction plans and determine the decision indicators for the construction plans; Step 2: Use the intelligent simulation system for high arch dam construction to perform simulation analysis and obtain the key parameters of each construction scheme at each stage. Step 3: Normalize the various decision indicators of the construction plan, transforming each indicator value into a benefit-type indicator, and establish it as the key parameter x of the current stage decision indicator j plan i. ijt The model is as follows: Where, x ijt X is the key parameter of decision indicator j for scheme i at the current stage t. jt Let be the sample set of index j for each construction scheme in stage t; Step 4: Based on the development and changes of different attributes of various decision indicators during the execution of the high arch dam construction plan, establish dynamic reference points for the decision indicators at each stage of each construction plan using the concept of average development speed. Subtract the dynamic reference points from the decision indicators at each stage of each construction plan, and establish the following model of the dynamic reference point change process based on the concept of average development speed: Where, x jt h represents the coordinates of the reference point for index j at stage t. t The parameters for setting the reference point at stage t, Let x be the reference point for index j at time t. jt The expected mean, p ijt Let j be the probability function of decision index j for option i at stage t. Let s be the average growth rate of indicator j. jt For the growth rate of indicator j under stage t, x jl x when t = l jt x jt-1 The coordinates of the reference point for index j in the previous stage t-1; Step 5: Based on the prospect stochastic dominance theory, establish the value functions for each indicator at each stage of each construction scheme; the value function model based on the prospect stochastic dominance theory is as follows: In ijt =∫π(p ijt )v(Δx k ) (7) Δx k =x ijt -x jt (10) Among them, V ijt Let π() be the value function, ν() be the probability weight function, and Δx be the value function. k For the key parameter x ijt The difference from the dynamic reference point, k is the index of Δx, α and β are the concavity and convexity of the power functions of the gain and loss regions, respectively, θ is the characteristic that the loss region is steeper than the gain region, γ is the risk-reward attitude coefficient, δ is the risk-loss attitude coefficient, and x jt For the stage t The reference point for indicator j, W jt W represents the weight of the indicator attribute for indicator j in the current stage t. t V represents the time series weights. i Foreground value for scheme i; Step 6: Using the CRITIC method, establish the weights of each indicator attribute and time weight for each scheme at each stage; Step 7: Calculate the value function model shown in formulas (7) to (11) in step 5 according to prospect theory. The calculation results are used as the prospect values ​​of each construction scheme. Optimize each construction scheme. The larger the prospect value, the better the scheme.

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