CN113688458A

CN113688458A - Foundation scheme optimization method based on analytic hierarchy process

Info

Publication number: CN113688458A
Application number: CN202111001216.6A
Authority: CN
Inventors: 陈乐�; 刘宝堂
Original assignee: China MCC17 Group Co Ltd
Current assignee: China MCC17 Group Co Ltd
Priority date: 2021-08-30
Filing date: 2021-08-30
Publication date: 2021-11-23
Anticipated expiration: 2041-08-30
Also published as: CN113688458B

Abstract

The invention discloses a foundation basic scheme optimization method based on an analytic hierarchy process, and belongs to the technical field of foundation basic design. The method comprises the following steps: step 1: establishing a hierarchical model: the hierarchical model, the target layer, is the final result of the need; step 2: establishing a comparison judgment matrix: in order to highlight the weight of each layer on the previous layer, the method is usually embodied in a manner of constructing a judgment matrix; and step 3: calculating the weight of the current layer to the previous layer, and calculating by adopting a root method: (1) calculating the product of each row of elements of the comparison judgment matrix; (2) calculating the n-th square root of the result obtained in the step (1); (3) normalizing the result obtained in the step (2); (4) solving the maximum eigenvalue of the comparison judgment matrix; and 4, step 4: checking the consistency; and 5: and (5) fuzzy comprehensive evaluation. The invention is based on an analytic hierarchy process and combines fuzzy comprehensive evaluation to achieve the purposes of reasonable design and cost reduction.

Description

Foundation scheme optimization method based on analytic hierarchy process

Technical Field

The invention relates to the technical field of foundation design, in particular to a foundation basic scheme optimization method based on an analytic hierarchy process.

Background

The process of basic model selection is a process with strong comprehensiveness and individuality, influence factors such as engineering cost, structural reliability, structural functions and the like need to be comprehensively considered in the process of model selection, and foundations of different types have different advantages and different application ranges. Similar engineering experience can be adopted for some simple projects, but the engineering experience is far from sufficient for processing some complex projects, and some means are required for solving the problems. There may be multiple alternative base solutions for the same building, which requires some means to select the best solution. There are two general categories of methods that are preferred: one is qualitative, such as delphi, target prediction, etc.; another class is quantitative methods, such as neural network methods and the like. The analytic hierarchy process is widely applied in various fields in recent years, and compared with other optimal schemes, the analytic hierarchy process realizes the combination of qualitative analysis and quantitative analysis, so that the analysis result is more accurate.

The fuzzy comprehensive evaluation is to convert qualitative evaluation into quantitative evaluation, and the theory is based on a membership theory. Fuzzy mathematics is used to make a general evaluation on things or objects which are limited by various factors, and the result is expressed in a vector form. In the processes of selecting a basic scheme and analyzing basic reliability, a plurality of determined and uncertain influence factors exist, the uncertain influence factors are difficult to be subjected to formulaization and functionalization processing by using classical mathematics, fuzzy comprehensive evaluation is based on fuzzy mathematics, the variability and the randomness of the influence factors are considered, and the influence factors can be known more visually.

The analytic hierarchy process and the fuzzy comprehensive evaluation are combined, a model for optimizing and selecting the foundation base is established, the advantages of the analytic hierarchy process and the fuzzy comprehensive evaluation can be fully utilized, a more reasonable scheme is selected, and the purposes of reasonable design and cost reduction are achieved.

Disclosure of Invention

1. Problems to be solved

Aiming at the defects and shortcomings in the prior art, the invention provides a foundation basic scheme optimization method based on an analytic hierarchy process, which is based on the analytic hierarchy process and combined with fuzzy comprehensive evaluation to establish a foundation basic scheme optimization model, fully utilizes the advantages of the two, optimizes a more reasonable scheme, achieves the purposes of reasonable design and cost reduction, and solves the problem that optimal selection is difficult to realize during foundation basic model selection in the design stage.

2. Technical scheme

In order to achieve the purpose, the technical scheme provided by the invention is as follows:

a foundation basic scheme optimization method based on an analytic hierarchy process comprises the following steps:

step 1: establishing a hierarchical model:

the hierarchical model is shown in fig. 1, a target layer is a required final result, such as an optimal basic scheme, a criterion layer is an influence factor influencing the final result, and an index layer is an influence factor influencing the criterion layer;

step 2: establishing a comparison judgment matrix:

in order to highlight the influence weight of each layer on the previous layer, the influence weight is usually embodied in a manner of constructing a judgment matrix, and generally, a 1-9 scaling method is adopted:

TABLE 1 Scale of "1-9

Scale	Means of
		1	Compared with the two factors, the importance degree is the same
3	Two factors are compared, one of which is slightly important
		5	Two factorsIn contrast, one of the factors is of significant importance
7	Two factors are compared, one of which is strongly important
		9	Two factors are compared, one of which is extremely important
2、4、6、8	Intermediate values of two adjacent judgments

Note: for the previous layer A, B₁，B₂Respectively, if B is one of the influencing factors₁And B₂Of equal importance, then the scale B₁/B₂1 is ═ 1; if B is₁Ratio B₂Clearly important, then the scale B₁/B₂5 or scale B₂/B₁＝1/5。

Comparing and judging the matrix:

wherein:

1≤i≤n,1≤j≤n；

and step 3: calculating the weight of the current layer to the previous layer:

the weight is calculated by adopting a root method, and the method comprises the following specific steps:

(1) calculating the product Mi of each row of elements of the comparison judgment matrix

(2) Calculating M_iN times of square root m_i

(3)m_iNormalization process

Wherein i is the ith row of the comparison and judgment matrix, and n is the order of the comparison and judgment matrix;

W＝[W₁ W₂ ... W_n]^Tthat is, feature vectors, W, of the decision matrix are compared₁,W₂,...,W_nIs B1, B₂,...,B_nCorresponding relative importance weights.

(4) Calculating and comparing the maximum eigenvalue lambda of the judgment matrix_max

In the formula, i is the ith row of the comparison and judgment matrix; n is the order of the comparison judgment matrix; a is a comparison judgment matrix; (AW)_iIs the ith element of AW.

And 4, step 4: and (3) checking consistency:

in the formula, n is the order of the comparison judgment matrix, and CR is a consistency index; CI is deviation consistency index; RI is a random consistency index, and its values are given in the following table:

TABLE 2 values of the random consistency index RI

Number n of matrix orders	1	2	3	4	5	6	7	8	9	10
											Random consistency index RI	0	0	0.58	0.90	1.12	1.24	1.32	1.41	1.45	1.49

When CR is less than 0.1, the consistency meets the requirement, otherwise, the constructed comparison judgment matrix needs to be modified and then verified; for the off-conformity index CI, there is complete conformity when CI is 0, satisfactory conformity when CI is close to 0, and conversely, the greater CI, the higher nonconformity.

And 5: fuzzy comprehensive evaluation:

(1) establishing a factor set of an evaluation object: u ═ U₁,u₂,u₃,...,u_n}

(2) Establishing an evaluation grade set: v ═ V₁,v₂,v₃,...,v_n}

V is the set of overall evaluation results for the study subjects.

(3) Evaluating each factor to establish fuzzy matrix R

(i＝1,2,3,...,n；j＝1,2,3,...,m)

(4) Determining the weight of each single factor;

(5) selecting a fuzzy operator to carry out fuzzy synthesis;

(6) and carrying out comprehensive evaluation, and evaluating by adopting a maximum membership principle.

3. Advantageous effects

Compared with the prior art, the invention has the beneficial effects that:

the invention discloses a foundation basic scheme optimization method based on an analytic hierarchy process, which can solve the problem that optimal selection is difficult to realize during foundation model selection in a design stage.

Drawings

FIG. 1 is a hierarchical model diagram of the present invention;

FIG. 2 is a hierarchical model diagram of an embodiment of the invention.

Detailed Description

The invention will be further described with reference to specific embodiments and the accompanying drawings in which:

example 1

Referring to fig. 1-2, a method for optimizing a foundation basic solution based on an analytic hierarchy process of the present embodiment includes the steps of:

1. the best solution A is the target layer; the criterion layer comprises a low cost B₁High safety adaptability B₂Convenient for construction B₃Small influence of B₄(ii) a The index layer comprises an artificial C₁Material C₂Machine C₃And others C₄Bearing capacity C₅Sedimentation and resistance to plucking function C₆Construction period C₇Difficulty and ease degree C₈Quality control C₉Ambient environment C₁₀Secondary influence of C₁₁；

2. Establishing a comparison and judgment matrix of a quasi-lateral layer relative to a target layer, calculating the weight of the standard layer relative to the target layer, and carrying out consistency check, wherein if the consistency is not met, the comparison and judgment matrix needs to be reconstructed;

(2) establishing an index layer corresponding to each criterion layer, calculating a weight comparison judgment matrix of the index layer to the criterion layer, and carrying out consistency check, wherein if the consistency is not met, the comparison judgment matrix needs to be reconstructed;

3. fuzzy comprehensive evaluation

(1) Establishing a factor set of an evaluation object;

(2) establishing a comment set; u ═ fine, good, medium, poor, very poor };

(3) constructing an evaluation grade matrix V ═ {5, 4, 3, 2, 1 }; the good correspondence is 5 points, the poor correspondence is 1 point, and the rest correspond in sequence;

the following evaluation tables were established:

TABLE 3 fuzzy comprehensive evaluation table

(4) Calculating each scheme score

For scheme Sn:

W_BiAlayer B as criterion_iA weight for target layer A; w_CiBIs an index layer C_iWeight for criterion layer B; w_CiAIs an index layer C_iA weight for A;

W_CiA＝W_CiBW_BiA

R_iis B_iUnder-guideline scheme S_iThe evaluation level weight matrix of (2) is directly read from the table, for example:

TABLE 4B₁Fuzzy comprehensive evaluation table

Scheme S_iThe evaluation grade weight value is given after expert discussion;

R_i’＝W_CiAR_i

scheme S_iAnd (3) comprehensive evaluation score:

S＝WV^T

and finally, the scheme with the maximum score value is the preferred scheme.

The present invention and its embodiments have been described above schematically, without limitation, and what is shown in the drawings is only one of the embodiments of the present invention, to which the actual method is not limited. Therefore, if the person skilled in the art receives the teaching, without departing from the spirit of the invention, the person skilled in the art shall not inventively design the similar structural modes and embodiments to the technical solution, but shall fall within the scope of the invention.

Claims

1. A foundation basic scheme optimization method based on an analytic hierarchy process is characterized in that: the method comprises the following steps:

step 1: establishing a hierarchical model:

the hierarchical model, the target layer, is the required final result, such as the optimal basic scheme, the criterion layer is the influencing factor influencing the final result, and the index layer is the influencing factor influencing the criterion layer;

step 2: establishing a comparison judgment matrix:

in order to highlight the influence weight of each layer on the previous layer, the influence weight is usually embodied in a manner of constructing a judgment matrix, and generally a scale method of '1-9' is adopted;

and step 3: and calculating the weight of the layer to the previous layer by adopting a root method:

(1) calculating the product of each row of elements of the comparison judgment matrix;

(2) calculating the n-th square root of the result obtained in the step (1);

(3) normalizing the result obtained in the step (2);

(4) solving the maximum eigenvalue of the comparison judgment matrix;

and 4, step 4: checking the consistency;

and 5: fuzzy comprehensive evaluation:

(1) establishing a factor set of an evaluation object;

(2) establishing an evaluation grade set;

(3) performing single factor evaluation on each factor, and establishing a fuzzy matrix;

(4) determining the weight of each single factor;

(5) selecting a fuzzy operator to carry out fuzzy synthesis;

2. The method of claim 1, wherein the method comprises the following steps: the analytic hierarchy process realizes the combination of qualitative analysis and quantitative analysis, the analysis result is more accurate, the fuzzy comprehensive evaluation is based on fuzzy mathematics, the variability and the randomness of influencing factors are considered, more visual understanding can be given to people, the analytic hierarchy process is combined with the fuzzy comprehensive evaluation, the advantages of the analytic hierarchy process and the fuzzy comprehensive evaluation can be fully utilized, a more reasonable scheme is optimized, and the purposes of reasonable design and cost reduction are achieved.