CN113688458B - Foundation scheme optimization method based on analytic hierarchy process - Google Patents
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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 3, 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 root of the result obtained in the step (1); (3) carrying out normalization processing on the result obtained in the step (2); (4) solving the maximum characteristic value of the comparison judgment matrix; and 4, step 4: checking 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
Technical Field
The invention relates to the technical field of foundation design, in particular to a foundation 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 insufficient 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 methods such as delphire method, target prediction method, 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;
and 2, step: 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 more important |
| 5 | By comparison of two factors, one of which is clearly important |
| 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, B 1 ，B 2 Respectively, if B is one of the influencing factors 1 And B 2 Of equal importance, then the scale B 1 /B 2 =1; if B is 1 Ratio B 2 Clearly important, then the scale B 1 /B 2 =5 or scale B 2 /B 1 ＝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 i N times of square root m i
(3)m i Normalization 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＝[W 1 W 2 ... W n ] T that is, feature vectors, W, of the decision matrix are compared 1 ,W 2 ,...,W n Is B1, B 2 ,...,B n Corresponding 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) i Is 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 evaluation of 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 deviation consistency index CI, there is complete consistency when CI =0, satisfactory consistency when CI is close to 0, and conversely, the larger CI, the higher the inconsistency.
And 5: fuzzy comprehensive evaluation:
(1) Establishing a factor set of an evaluation object: u = { U = 1 ,u 2 ,u 3 ,...,u n }
(2) Establishing an evaluation grade set: v = { V = 1 ,v 2 ,v 3 ,...,v n }
V is a set of overall evaluation results for the study subjects.
(3) Evaluating each factor to establish fuzzy matrix R
(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 base 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 according to an embodiment of the present invention.
Detailed Description
The invention is further described with reference to the following specific examples and figures:
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 B 1 High safety adaptability B 2 Convenient for construction B 3 Small influence of B 4 (ii) a The index layer comprises an artificial C 1 Of material C 2 Machinery C 3 Of other C 4 Bearing capacity C 5 Sedimentation and plucking resistance function C 6 Construction period C 7 Difficulty and ease degree C 8 Quality control C 9 Ambient environment C 10 Secondary influence of C 11 ；
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 = { good, medium, bad };
(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 BiA layer B as criterion i A weight for the target layer a; w is a group of CiB Is an index layer C i Weight for criterion layer B; w CiA Is an index layer C i A weight for A;
W CiA ＝W CiB W BiA
R i is a B i Under-guideline scheme S i The evaluation level weight matrix of (2) is directly read from the table, for example:
TABLE 4B 1 Fuzzy comprehensive evaluation table
Scheme S i The evaluation grade weight value is given after expert discussion;
R i ’＝W CiA R i
scheme S i And (3) comprehensive evaluation score:
S＝WV T
and finally, the scheme with the maximum score value is the preferred scheme.
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 base model selection in a design stage.
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 (2)
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: calculating the weight of the current 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 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;
(6) And carrying out comprehensive evaluation, and evaluating by adopting a maximum membership principle.
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, the more intuitive 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 selected, and the purposes of reasonable design and cost reduction are achieved.
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| CN109242316A (en) * | 2018-09-13 | 2019-01-18 | 北京航空航天大学 | Hydraulic system energy efficiency evaluating method based on Fuzzy AHP |
| CN109377024A (en) * | 2018-09-30 | 2019-02-22 | 北京航空航天大学 | A kind of recovery capability appraisal procedure comprehensive based on step analysis and grey fuzzy |
| CN110580580A (en) * | 2019-09-02 | 2019-12-17 | 长沙理工大学 | Bridge hanging basket construction risk assessment method based on fuzzy analytic hierarchy process |
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| CN109242316A (en) * | 2018-09-13 | 2019-01-18 | 北京航空航天大学 | Hydraulic system energy efficiency evaluating method based on Fuzzy AHP |
| CN109377024A (en) * | 2018-09-30 | 2019-02-22 | 北京航空航天大学 | A kind of recovery capability appraisal procedure comprehensive based on step analysis and grey fuzzy |
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