Optimization method of co-addition of thickener and water reducer based on polyvinyl alcohol fiber concrete

Abstract

The present application discloses a method for optimizing the co-addition of thickeners and water reducers in polyvinyl alcohol fiber concrete, comprising: step S1) constructing a multi-level pre-analysis framework model; step S2) considering the input and output data of all decision-making units based on the pre-analysis framework model, obtaining the optimal effect site and effect frontier through boundary constraints and planning solution, and evaluating the relative efficiency of homogeneous decision-making units under multiple input indicators and effect indicators; step S3) judging effectiveness / ineffectiveness based on the efficiency score of the decision-making unit, accurately adjusting the dosage configuration of the thickener and water reducer for the ineffective decision-making unit, and gradually optimizing to the efficiency frontier calibrated in the final goal. The present application can overcome the defects of the prior art in the design of the co-addition of thickeners and water reducers in polyvinyl alcohol fiber concrete, such as non-standard methods, inaccurate data, and limited application, and improve the systematicness and accuracy of the co-addition scheme of thickeners and water reducers in polyvinyl alcohol fiber concrete.

Description

Technical Field

[0001] The present application relates to the technical field of building materials, and in particular to a method for optimizing the compounding of a thickener and a water reducer based on polyvinyl alcohol fiber concrete. Background Art

[0002] Polyvinyl alcohol fiber concrete is a composite material made by adding polyvinyl alcohol fiber to ordinary concrete to improve its mechanical properties, durability, and stability. During the preparation of polyvinyl alcohol fiber concrete, water reducers play a role in adsorption, dispersion, wetting, and lubrication, while thickeners reduce the mutual attraction and cohesion between cement particles by changing the properties of the particle surface and lowering the surface tension of the mixture. Together, they enhance the overall performance of polyvinyl alcohol fiber concrete by improving its fluidity and cohesion. Due to the complex compatibility and adsorption behaviors of thickeners and water reducers with cementitious materials, fine aggregate, and polyvinyl alcohol fibers, as well as the complex compatibility and adsorption behaviors between the thickeners and water reducers, the reinforcing effect of polyvinyl alcohol fiber concrete varies depending on the co-addition scheme of thickeners and water reducers.

[0003] In the current existing technical solutions, the design of the compounding scheme of thickener and water reducer in polyvinyl alcohol fiber concrete is mainly manifested in three aspects:

[0004] One approach involves testing flow properties such as fluidity and slump in the laboratory, using the parameters at which the material exhibits optimal fluidity and consistency as the appropriate blending ratio for the thickener and water reducer. This approach suffers from size effects, differences in test standardization and reproducibility, and has limitations in solving the problem and inaccurate data results.

[0005] The second is to refer to existing industry standards and empirical formulas to determine the composite ratio of thickener and water reducer; this scheme relies on empirical preference design and lacks standardization, rationality and universality;

[0006] The third approach involves using computer simulation software to simulate the fluidity and stability of PVA fiber-reinforced concrete, thereby predicting the effects of different additive ratios. This approach relies heavily on the accuracy of the simulation, and the validity and applicability of the data remain questionable. Currently, common design methods suffer from nonstandard methods, inaccurate data, and limited application, making them incapable of optimizing the combined addition of thickeners and water reducers in PVA fiber-reinforced concrete.

[0007] Therefore, the optimization of the co-addition scheme of thickeners and water reducers suitable for polyvinyl alcohol fiber reinforced concrete has become one of the decision-making challenges faced by the field of building materials. Summary of the Invention

[0008] In order to solve the above technical problems, the embodiment of the present application provides a method for optimizing the co-blending of thickeners and water reducers in polyvinyl alcohol fiber concrete, which overcomes the defects of "non-standard methods", "inaccurate data" and "not widely used" in the prior art design of co-blending of thickeners and water reducers in polyvinyl alcohol fiber concrete, and improves the systematicness and accuracy of the co-blending scheme of thickeners and water reducers in polyvinyl alcohol fiber concrete.

[0009] The present invention provides a method for optimizing the compounding of a thickener and a water reducer in polyvinyl alcohol fiber concrete, comprising the following steps:

[0010] Step S1) constructing a multi-level pre-analysis framework model, which includes an overall target unit, a decision unit, an input indicator unit, and an effect indicator unit, wherein the overall target unit is the ultimate goal of optimizing the composite ratio of thickener and water reducer in polyvinyl alcohol fiber concrete;

[0011] The decision-making unit includes several groups, including different composite mixing ratio schemes of thickener and water reducer in polyvinyl alcohol fiber concrete; each decision-making unit corresponds to a composite mixing ratio scheme of thickener and water reducer;

[0012] The input indicator unit is the mass mixing ratio of thickener and water reducer in each group of decision units;

[0013] The effect index unit is the flow expansion degree set of the corresponding polyvinyl alcohol fiber concrete in each group of decision units;

[0014] Step S2) Based on the pre-analysis framework model, the input and output data of all decision-making units are considered, and the maximum efficiency index parameters of each group of decision-making units are obtained through the planning model and boundary constraints. The effectiveness of homogeneous decision-making units is evaluated under various input and effect index conditions. Homogeneity means that the decision-making units being compared have similar properties or characteristics to ensure the fairness and rationality of the comparison process. Homogeneous decision-making units represent different composite ratios of thickener and water reducer in polyvinyl alcohol fiber concrete under the same design principle and comparison environment.

[0015] Step S3) Based on the efficiency scores of all decision-making units, valid / invalid decision-making units are identified, and the dosage configuration of the thickener and water reducer of the invalid decision-making units is precisely adjusted, and the optimization is gradually carried out to the efficiency frontier (efficiency index parameter equals 1), thereby optimizing the thickener and water reducer co-addition scheme in polyvinyl alcohol fiber reinforced concrete.

[0016] Furthermore, step 2) includes the following steps:

[0017] Step S21) establishing the mixing ratios of various thickeners and water reducers for polyvinyl alcohol fiber reinforced concrete;

[0018] Step S22) Constructing n groups of decision making units by combining different compounding ratios of thickener and water reducer;

[0019] The dosage of thickener and water reducer corresponding to each decision-making unit is used as input elements to construct the input vector X of the production process represented by the decision-making unit;

[0020] The flow expansion degree corresponding to each group of decision-making units is used as the effect element to construct the effect vector Y in the production process of the decision-making units;

[0021] Define (X, Y) as the possible set of all possible decisions;

[0022] Step S23) Obtain the input comprehensive evaluation index P and output comprehensive evaluation index P of each group of decision units ' The effect evaluation index parameter K is obtained; the efficiency is evaluated by the effect evaluation index parameter K of each group of decision units. The larger the K is, the better the effect of the combined dosage of thickener and water reducer in this group of schemes on the fluidity of polyvinyl alcohol fiber concrete is.

[0023] Furthermore, step S23) specifically includes:

[0024] Each decision-making unit contains two input variables, thickener and water reducer, and one effect variable, flow expansion. Let: , , , , ;

[0025] Among them, i represents the i-th scheme of co-adding thickener and water reducer, with a total of n groups of decision units; represents the dosage of thickener in the jth decision plan, represents the dosage of water reducer in the jth decision plan; represents the flow expansion of PVA fiber reinforced concrete in the jth decision scheme; Represents the corresponding weight coefficient of thickener input variable, Represents the corresponding weight coefficient of the water reducer input variable; Represents the weight coefficient of the flow expansion effect variable; the output comprehensive evaluation index of the j-th decision unit , comprehensive evaluation index of the input of the j-th decision-making unit ; The jth decision-making unit effect evaluation index parameter .

[0026] Furthermore, the efficiency scoring of the decision-making unit in step S3) includes determining inputs and outputs, building a linear programming model, setting constraints and solving the linear programming problem, and analyzing and evaluating the results, specifically including:

[0027] Step 31) Determine input and output: select input for decision-making unit j and effect evaluation index parameters, where decision-making unit j selects As input, effect evaluation index parameter selection As input;

[0028] Step 32) Construct a linear programming model: Construct the objective function for decision-making unit j, with the goal of achieving the effect evaluation index parameter of decision-making unit j under specific weight conditions Maximize, that is ;

[0029] Step 33) Set constraints and solve the linear programming problem: the efficiency index parameter K of decision-making unit j j If it does not exceed 1, it will not appear to be more than 100% efficient;

[0030] Establishing constraints , , ; The weight coefficient 、 Is an unknown number, and finally solve the effect evaluation index parameter of decision unit j A specific weighted combination of inputs and outputs to achieve the maximization goal;

[0031] Step 34) Result analysis and evaluation: Based on the specific weight combination in the linear programming solution, the evaluation index parameters are evaluated by maximizing the effect of decision unit j. Evaluate the effectiveness of decision-making unit j;

[0032] Step 35) Based on the effectiveness evaluation results of each group of decision-making units, the non-strong effectiveness (maximization efficiency index parameter K jmax ≠1) The unit adjusts the dosage configuration of its input variables (thickener and water reducer), conducts effectiveness analysis, production effect analysis, input redundancy analysis and effect deficiency analysis through boundary constraints and dual values ​​of planning models, adjusts the mixing ratio of thickener and water reducer in each group of decision units, and guides the inefficient decision units to gradually optimize to the effect frontier (that is, maximize the efficiency index parameter K jmax =1).

[0033] Furthermore, step 35) includes:

[0034] Convert the constraint programming model in step 33) into a dual model, introduce the non-Archimedean infinitesimal ε, and input the variable S - , effect slack variable S +， , , , , , , where λ j is the weight combination coefficient of the jth group of decision units, and the optimal value θ obtained in the dual model j0 is the efficiency value, when θ j0 <1 indicates that this group of decision-making units is inefficient. j0 =1 indicates that the efficiency of the phrase decision unit is relatively optimal.

[0035] Furthermore, step 35) further includes: optimizing to the calibrated efficiency frontier (i.e., maximizing the efficiency index parameter K) through input effect L, effect benefit M, comprehensive benefit N, and quantitative guidance of slack variable S. jmax =1), and finally the optimization of the co-addition scheme of thickener and water reducer in PVA fiber reinforced concrete was achieved.

[0036] Beneficial effects of the present invention:

[0037] 1. A reliable, scientific, and feasible method for optimizing the co-addition of thickeners and water reducers in polyvinyl alcohol fiber concrete is provided. This method overcomes the defects of the existing technology in the design of co-addition of thickeners and water reducers in polyvinyl alcohol fiber concrete, such as "non-standard methods", "inaccurate data", and "limited application", and improves the systematicness and accuracy of the co-addition scheme of thickeners and water reducers in polyvinyl alcohol fiber concrete.

[0038] 2. By optimizing the ratio of thickener and water reducer, the fluidity and stability of polyvinyl alcohol fiber concrete can be effectively regulated to avoid poor concrete performance caused by improper proportion, which in turn leads to insufficient strength, cracking and other quality problems, thereby improving the workability, mechanical properties and durability of polyvinyl alcohol fiber concrete;

[0039] 3. By optimizing the use of thickeners and water reducers in polyvinyl alcohol fiber concrete, the cost problems caused by unreasonable excessive use can be reduced, and cost control and resource conservation can be achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0041] Figure 1 is a flow chart of the method provided by this application;

[0042] Figure 2 It is the logic block diagram of this application. DETAILED DESCRIPTION

[0043] In order to make the purpose, features, and advantages of this application more obvious and easy to understand, the technical solutions in the embodiments of this application will be clearly and completely described below in conjunction with the drawings in the embodiments of this application. Obviously, the embodiments described below are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0044] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments.

[0045] In the description of this application, it should be understood that the terms "upper", "lower", "top", "bottom", "inside", "outside", etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on this application.

[0046] The present application is described below with reference to specific embodiments:

[0047] In this embodiment, polyvinyl alcohol fiber concrete is prepared by cementitious materials, water, fine aggregate, polyvinyl alcohol fiber, and external admixtures, wherein the cementitious materials are cement and fly ash, the fine aggregate is quartz sand, the polyvinyl alcohol fiber is Japanese Kuraray PVA fiber, and the external admixtures are thickener and water reducer.

[0048] The raw material details and technical indicators of each component in polyvinyl alcohol fiber concrete are shown in Table 1.

[0049]

[0050] Table 1 Details of raw materials for each component of polyvinyl alcohol fiber concrete

[0051] The combined addition scheme of thickener and water reducer is the ultimate research goal of this example. Except for the mixing ratio of admixtures, the mixing ratios of other components are shown in Table 2 below.

[0052]

[0053] Table 2 Proportions of various components of polyvinyl alcohol fiber concrete

[0054] Note: The PVA fiber ratio is by volume, and the ratios of other components are by mass; water and quartz sand are the ratios relative to the cementitious material.

[0055] The design of the composite mixing ratio of thickener and water reducer is shown in Table 3.

[0056]

[0057] Table 3 Thickener and water reducer compounding ratio scheme

[0058] Note: The mixing ratio of thickener and water reducer is the proportion of cementitious materials.

[0059] According to Tables 2 and 3, cement, fly ash, quartz sand, water, PVA fiber, thickener, and water reducer were mixed and stirred, and the flow expansion of the polyvinyl alcohol fiber concrete composite material was measured in the laboratory to provide basic data for the case demonstrated in the present invention.

[0060] As stated in this application:

[0061] Step 1) The design optimization problem of the co-addition of thickener and water reducer in polyvinyl alcohol fiber concrete is divided into categories according to the overall goal, decision-making unit, input index (input) and effect index (output). Based on the interaction form between each category, a multi-level pre-analysis framework model for evaluation and decision-making is constructed. The model includes the overall goal unit, decision-making unit, input index unit and effect index unit.

[0062] The overall target unit is the ultimate goal of optimizing the composite ratio of thickener and water reducer in polyvinyl alcohol fiber concrete.

[0063] The decision-making unit contains several groups (in this example, the decision-making unit is a set of different composite mixing ratio schemes of thickeners and water reducers in polyvinyl alcohol fiber concrete, with a total of 20 decision-making units), including different composite mixing ratio schemes of thickeners and water reducers in polyvinyl alcohol fiber concrete. Each decision-making unit corresponds to a composite mixing ratio scheme of thickeners and water reducers.

[0064] The input indicator unit is the mass mixing ratio set of thickener and water reducer in each group of decision units.

[0065] The effect index unit is the flow expansion degree set of the corresponding polyvinyl alcohol fiber concrete in each group of decision units.

[0066] In this example, the input index is the mass ratio set of the specific thickener and water reducer in each decision unit, and the effect index is defined as the flow expansion set of the corresponding polyvinyl alcohol fiber concrete in each decision unit, with a total of 20 effect index variables.

[0067] The pre-analysis framework model in this example is a multi-level model guided by the overall goal and constructed based on the interaction mechanism relationship between decision-making units, input indicators, and effect indicators, such as Figure 2 shown.

[0068] Step 2) Based on the multi-level pre-analysis framework model, considering the input and output data of all decision-making units, the optimal effect site and effect frontier are obtained through boundary constraints and planning solution, and the relative efficiency of homogeneous decision-making units under various input indicators and effect indicators is evaluated.

[0069] As in step 22), the data for all DMU-specific input indicators and effect indicators in this example are derived from laboratory flowability tests, and the test results are shown in Table 4 below;

[0070]

[0071] Table 4 Laboratory fluidity test results

[0072] In this example, the dosage of thickener and water reducer specific to each decision-making unit is used as input elements to construct the input vector X=(X1, X2) in the decision-making unit production process;

[0073] X1=(0.1, 0.2, 0.3, 0.4), X2= (0.1, 0.2, 0.4, 0.6, 0.8)

[0074] In this example, the specific flow expansion degree of each group of decision-making units is used as the effect element to construct the effect vector Y= (Y1) in the production process of the decision-making unit;

[0075] Y1=(0.1, 0.2, 0.4, 0.6, 0.8)

[0076] In this example, (X, Y) is defined as the possible set of all possible decisions;

[0077] (X1, Y1) = (0.1, 0.1, 140)

[0078] (X2, Y2) = (0.2, 0.1, 123)

[0079] (X3, Y3) = (0.3, 0.1, 116)

[0080] (X4, Y4) = (0.4, 0.1, 106)

[0081] …

[0082] (X 20 , Y 20 ) = (0.4, 0.8, 186)

[0083] In this example, the optimal effect site and effect frontier of each group of decision-making units are obtained through boundary constraints and planning solution.

[0084] As shown in step 23), in this example, the effect evaluation index parameter K of each group of decision-making units is obtained by inputting the comprehensive evaluation index P and outputting the comprehensive evaluation index P. ' get;

[0085] The input comprehensive evaluation index is obtained by performing algebraic operations on the input vector X = (X1, X2) and the corresponding weight vector:

[0086] In this example, there are 20 mixed solutions for thickener and water reducer. Each decision solution has two input variables, thickener and water reducer, and one effect variable, flow expansion. The comprehensive evaluation index P of the 20 decision units is: ' And input comprehensive evaluation index P:

[0087] ,

[0088] ,

[0089] …

[0090] ,

[0091] The j-th decision-making unit effect evaluation index parameter .

[0092] In this example, efficiency is evaluated using the effect evaluation index parameter K for each decision-making unit. A larger K indicates that the combined dosage of thickener and water reducer in this solution has a better effect on the fluidity of polyvinyl alcohol fiber concrete. A decision-making unit with a K score of 1 is located on the effect frontier, indicating that it has the highest efficiency. A decision-making unit with a score less than 1 is below the effect frontier, indicating that there is room for efficiency improvement.

[0093] Step 3) According to the efficiency scores of all decision-making units, the effective / ineffective decision-making units are judged. For the ineffective decision-making units, the dosage configuration of the thickener and water reducer is precisely adjusted to gradually optimize them to the calibrated efficiency frontier (maximizing the efficiency index parameter K jmax =1) to optimize the co-addition scheme of thickener and water reducer in PVA fiber reinforced concrete. Specifically, it can be divided into the following steps:

[0094] Step 31) Determine input and output: select input for decision-making unit j and effect evaluation index parameters, where decision-making unit j selects As input, effect evaluation index parameter selection As input;

[0095] Step 32) Construct a linear programming model: Construct the objective function for decision-making unit j, with the goal of achieving the effect evaluation index parameter of decision-making unit j under specific weight conditions Maximize, that is ;

[0096] Step 33) Set constraints and solve the linear programming problem: the efficiency index parameter K of decision-making unit j j If it does not exceed 1, it will not appear to be more than 100% efficient;

[0097] Establishing constraints , , ; The weight coefficient 、 Is an unknown number, and finally solve the effect evaluation index parameter of decision unit j A specific weighted combination of inputs and outputs to achieve the maximization goal;

[0098] Step 34) Result analysis and evaluation: Based on the specific weight combination in the linear programming solution, the evaluation index parameters are evaluated by maximizing the effect of decision unit j. Evaluate the effectiveness of decision-making unit j;

[0099] Step 35) Based on the effectiveness evaluation results of each group of decision-making units, the non-strong effectiveness (maximization efficiency index parameter K jmax ≠1) The unit adjusts the dosage configuration of its input variables (thickener and water reducer), conducts effectiveness analysis, production effect analysis, input redundancy analysis and effect deficiency analysis through boundary constraints and dual values ​​of planning models, adjusts the mixing ratio of thickener and water reducer in each group of decision units, and guides the inefficient decision units to gradually optimize to the effect frontier (that is, maximize the efficiency index parameter K jmax =1).

[0100] Here, the dual value of the constraint programming model is to transform the original constraint programming model into a dual model, introduce the non-Archimedean infinitesimal ε, and input the variable S - , effect slack variable S + . , , , , , , where λ j is the weight combination coefficient of the jth group of decision units, and the optimal value θ obtained in the dual model j0 is the efficiency value, when θ j0 <1 indicates that this group of decision-making units is inefficient. j0 =1 indicates that the efficiency of the phrase decision unit is relatively optimal.

[0101] In this example, the input effect L, effect benefit M, comprehensive benefit N, and slack variable S are used for quantitative guidance until the calibrated efficiency frontier is optimized, ultimately achieving the optimization of the co-addition scheme of thickener and water reducer in polyvinyl alcohol fiber reinforced concrete.

[0102] In this example, the input effect L and effect benefit M of the 20 decision-making units are shown in Table 5. Comprehensive benefit N, input / effect slack variable S - / S + As shown in Table 6 below.

[0103]

[0104] Table 5 Input, effect, and comprehensive benefit indicators

[0105]

[0106] Table 6 Input / Effect Slack Variables

[0107] In this example, the comprehensive benefit indicators N, S and - and S + There are three indicators in total to judge the effectiveness of each decision-making plan:

[0108] If the comprehensive benefit is 1 and the input / effect slack variables are both 0, the decision plan is strongly effective;

[0109] If the comprehensive benefit is 1, but the input or effect slack variable is greater than 0, the decision plan is weakly effective;

[0110] If the comprehensive benefit is less than 1, the decision plan is not effective.

[0111] The results show that decision-making units 1, 13, and 17 are strongly effective, indicating that the proportions of these three thickeners and water reducers achieve a relatively optimal fluidity for PVA fiber-reinforced concrete. The remaining decision-making units are ineffective and require adjustments to their thickener and water reducer dosages.

[0112] In this example, the ratio between the input of thickener and water reducer and the flow expansion effect of polyvinyl alcohol fiber concrete is analyzed through scale returns, and the input configuration of thickener and water reducer in each decision-making unit is optimized.

[0113]

[0114] Table 7 Input / Effect Slack Variables

[0115] In this example, the scale returns coefficients of 20 decision-making units are used as indicator parameters to perform scale returns analysis:

[0116] When the scale return coefficient is less than 1, the production scale output is small, and the ratio of the input of thickener and water reducer to the output of fluid expansion will increase rapidly with the increase of scale, which is increasing scale returns (if the scale is too small, the scale can be expanded to increase benefits);

[0117] When the scale return coefficient = 1, production reaches its peak, the ratio of the input of thickener and water reducer to the output of fluid expansion is proportional to the optimal production scale, which is called fixed scale return;

[0118] When the coefficient of returns to scale is greater than 1, the production scale is too large, resulting in slower output, which is called diminishing returns to scale. That is, when input increases, the proportion of output increase will be less than the proportion of input increase (excessive scale can reduce the benefits of scale increase).

[0119] The results show that the strong and effective decision-making units 1, 13, and 17 have fixed returns to scale, and the current input resource allocation of thickeners and water reducers should be maintained; decision-making units 2, 3, 4, 5, 6, 7, 8, and 9 have increasing returns to scale, and the input of thickeners and water reducers should be increased to use the scale effect to improve the efficiency of the flow expansion of polyvinyl alcohol fiber concrete; decision-making units 10, 11, 12, 14, 15, 16, 18, 19, and 20 have decreasing returns to scale, and the input of thickeners and water reducers should be reduced to optimize resource allocation and avoid efficiency decline.

[0120] In this example, the specific dosage configurations of thickeners and water reducers that need to be adjusted are quantitatively analyzed through input redundancy analysis (difference variable analysis) in order to achieve the target efficiency of optimal fluidity of polyvinyl alcohol fiber concrete.

[0121] In this example, the input redundancy analysis of 20 groups of decision-making units is shown in Table 8 below.

[0122]

[0123] Table 8 Input / Effect Slack Variables

[0124] In this example, the slack variables S of 20 decision-making units are - (Difference variable) is used as an indicator parameter for input redundancy analysis:

[0125] (1) Relaxation variable S - Refers to the amount of input that needs to be reduced to achieve the target efficiency;

[0126] (2) Input redundancy rate refers to the ratio of “excessive input” to “already invested”. The larger the value, the more “excessive input” there is.

[0127] The results show that the thickener dosage in decision units 2, 3, 4, 7, and 8 is redundant by 0.087, 0.165, 0.227, 0.042, and 0.076 units, respectively, accounting for 0.439, 0.552, 0.567, 0.142, and 0.191 of the total investment, respectively. In groups 2, 3, 4, 7, and 8, the thickener dosage needs to be reduced by the corresponding redundant amount to achieve optimal fluidity efficiency of polyvinyl alcohol fiber concrete, while the water reducer dosage can be left unchanged.

[0128] Combined with the above-mentioned scale returns analysis, except for 2, 3, 4, 7, and 8, non-effective decision-making units 5, 6, and 9 have increasing scale returns, and non-effective decision-making units 10, 11, 12, 14, 15, 16, 18, 19, and 20 have decreasing scale returns. Their slack variables are all 0. After proportional adjustment (radial adjustment), they can reach the optimal effect frontier without the need for additional non-radial adjustment (slack adjustment).

[0129] Based on a comprehensive assessment of laboratory fluidity testing, the optimal design scheme for the co-blending of thickeners and water-reducing agents for PVA fiber-reinforced concrete in this example is selected. Although decision units 1, 13, and 17 are strongly effective, group 1 exhibits poor workability and difficulty in forming, while groups 13 and 17 both exhibit bleeding. Although decision unit 14 is deemed ineffective, the laboratory test results for this group demonstrate excellent workability and no bleeding. By adjusting the proportions (radially) of this thickener and water-reducing agent configuration, the PVA fiber-reinforced concrete can achieve optimal fluidity. The following design scheme for the co-blending of thickeners and water-reducing agents suitable for PVA fiber-reinforced concrete in this example is presented.

[0130] Table 9 Optimization scheme of thickener and water reducer for polyvinyl alcohol fiber reinforced concrete in this example

[0131]

[0132] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0133] The preferred embodiments of the present invention are described in detail above, but the present invention is not limited to the specific details in the above embodiments. Within the technical concept of the present invention, various equivalent transformations (such as quantity, shape, position, etc.) can be made to the technical solution of the present invention, and these equivalent transformations are all protected by the present invention.

Claims

1. A method for optimizing the compounding of a thickener and a water reducer based on polyvinyl alcohol fiber concrete, characterized in that: The steps include: Step S1) Construct a multi-level pre-analysis framework model, which includes an overall goal unit, a decision unit, an input indicator unit, and an effect indicator unit. The overall target unit is to optimize the composite ratio of thickener and water reducer in polyvinyl alcohol fiber concrete to ensure the excellent working performance of fiber concrete; The decision-making unit includes several groups, including different composite mixing ratio schemes of thickener and water reducer in polyvinyl alcohol fiber concrete; each decision-making unit corresponds to a composite mixing design ratio of thickener and water reducer; The input index unit is a mass mixing ratio set of thickener and water reducer in each group of decision units; The effect index unit is a set of flow expansion degrees of the corresponding polyvinyl alcohol fiber concrete in each group of decision units; Step S2) Based on the pre-analysis framework model, the input and output data of all decision-making units are considered, and the maximum efficiency index parameters of each group of decision-making units are obtained through the planning model and boundary constraints, and the effectiveness of homogeneous decision-making units is evaluated under various input index and effect index conditions; Step S3) Based on the efficiency scores of all decision-making units, valid / invalid decision-making units are identified, and the dosage configuration of the thickener and water reducer of the invalid decision-making units is precisely adjusted, and the optimization is gradually carried out to the efficiency frontier, thereby achieving the optimization of the thickener and water reducer co-addition scheme in the polyvinyl alcohol fiber reinforced concrete; The step 2) includes the following steps: Step S21) establishing the mixing ratios of various thickeners and water reducers for polyvinyl alcohol fiber reinforced concrete; Step S22) Constructing n groups of decision making units by combining different compounding ratios of thickener and water reducer; The dosage of thickener and water reducer corresponding to each decision-making unit is used as input elements to construct the input vector X of the production process represented by the decision-making unit; The flow expansion degree corresponding to each group of decision-making units is used as the effect element to construct the effect vector Y in the production process of the decision-making units; Define (X, Y) as the possible set of all possible decisions; Step S23) Obtain the input comprehensive evaluation index P and the output comprehensive evaluation index P' of each group of decision-making units to obtain the effect evaluation index parameter K; perform efficiency evaluation based on the effect evaluation index parameter K of each group of decision-making units.

2. The method for optimizing the compounding of thickener and water reducer based on polyvinyl alcohol fiber concrete according to claim 1, characterized in that: The step S23) specifically includes: Each decision-making unit contains two input variables, thickener and water reducer, and one effect variable, flow expansion. Let: , , , , ; Among them, i represents the i-th scheme of co-adding thickener and water reducer, with a total of n groups of decision units; represents the dosage of thickener in the jth decision plan, represents the dosage of water reducer in the jth decision plan; represents the flow expansion of PVA fiber reinforced concrete in the jth decision scheme; Represents the corresponding weight coefficient of thickener input variable, Represents the corresponding weight coefficient of the water reducer input variable; Represents the weight coefficient of the flow expansion effect variable; the output comprehensive evaluation index of the j-th decision unit ; Comprehensive evaluation index of input of the jth decision-making unit ; Effect evaluation index parameter of the jth decision unit .

3. The method for optimizing the compounding of a thickener and a water reducer based on polyvinyl alcohol fiber concrete according to claim 2, characterized in that: The step S3) specifically includes: Step 31) Determine input and output: select input for decision-making unit j and effect evaluation index parameters, where decision-making unit j selects As input, effect evaluation index parameter selection As input; Step 32) Construct a linear programming model: Construct the objective function for decision-making unit j, with the goal of achieving the effect evaluation index parameter of decision-making unit j under specific weight conditions Maximize, that is ; Step 33) Set constraints and solve the linear programming problem: Set constraints , , ; The weight coefficient 、 Is an unknown number, and finally solve the effect evaluation index parameter of decision unit j A specific weighted combination of inputs and outputs to achieve the maximization goal; Step 34) Result analysis and evaluation: Based on the specific weight combination in the linear programming solution, the evaluation index parameters are evaluated by maximizing the effect of decision unit j. Evaluate the effectiveness of decision-making unit j; Step 35) Based on the effectiveness evaluation results of each group of decision-making units, adjust the dosage configuration of the input variables for the non-strongly effective units. Through analysis of the dual value of the boundary constraints and the planning model, adjust the mixing ratio of the thickener and water reducer in each group of decision-making units to guide the non-efficient decision-making units to be gradually optimized to the effect frontier.

4. The method for optimizing the compounding of a thickener and a water reducer based on polyvinyl alcohol fiber concrete according to claim 3, characterized in that: The step 35) includes: Convert the constraint programming model in step 33) into a dual model, introduce the non-Archimedean infinitesimal ε, and input the variable , effect slack variable , , ; Solution , Constraints: , , ; Among them, E m is the vector matrix of m-dimensional space, E s is the vector matrix of s-dimensional space, e is the unit vector, λ j is the weight combination coefficient of the jth group of decision units, and the optimal value θ obtained in the dual model j0 As the efficiency value of the decision-making unit, when θ j0 <1 indicates that this group of decision-making units is inefficient. j0 =1 indicates that the efficiency of the phrase decision unit is relatively optimal; By introducing input variables , effect slack variable Each group of decision-making units is analyzed and the input of each group of decision-making units is adjusted to optimize the co-addition scheme of thickener and water reducer in polyvinyl alcohol fiber reinforced concrete.

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