# 基于层次分析法的城市沉降监测方案优选An Optimal Selection Method of Urban Subsidence Monitoring Based on AHP

DOI: 10.12677/GSER.2021.101005, PDF, HTML, XML, 下载: 49  浏览: 94

Abstract: Subsidence monitoring can effectively reflect the changes of ground elevation in time and provide important technical support and decision-making suggestions for the rapid development of cities. However, the selection of urban subsidence monitoring is often affected by factors such as budget, region, etc., the traditional method is arbitrary and subjective, and difficult to balance the observa-tion accuracy and economic cost. To solve the above problems, this paper proposes an optimal se-lection method of urban subsidence monitoring based on AHP. Through the construction of judg-ment matrix, consistency test and weight calculation of influence factors, the qualitative and quan-titative decision analysis method is used to comprehensively evaluate the land subsidence observa-tion scheme in a specific city. The experimental results show that the scheme of using GPS to moni-tor the land subsidence in this city is better than the traditional leveling. The GPS observation can meet the accuracy and effectively save manpower, time and economic costs. The relevant results can provide reference for the selection of other surveying and mapping projects.

1. 引言

2. 方法

2.1. 城市地面沉降监测层次结构模型

Figure 1. Urban settlement monitoring scheme structure hierarchy diagram

2.2. 基于专家经验构建判断矩阵

Table 1. Meaning of scale 1~9

$A=\left[\begin{array}{cc}\begin{array}{cc}{a}_{11}& {a}_{12}\\ {a}_{21}& {a}_{22}\end{array}& \begin{array}{cc}\cdots & {a}_{1n}\\ \cdots & {a}_{2n}\end{array}\\ \begin{array}{cc}⋮& ⋮\\ {a}_{n1}& {a}_{n1}\end{array}& \begin{array}{cc}\ddots & ⋮\\ \cdots & {a}_{nn}\end{array}\end{array}\right]$

2.3. 层次单排序及一致性检验

${a}_{ij}=\frac{{a}_{ij}}{{\sum }_{i=1}^{n}{a}_{ij}}$ (1)

${w}_{i}={\sum }_{j=1}^{n}{a}_{ij}$ (2)

${w}_{i}=\frac{{w}_{i}}{{\sum }_{j=1}^{n}{w}_{i}}$ (3)

${\lambda }_{\mathrm{max}}={\sum }_{i=1}^{n}\frac{{\left[Aw\right]}_{i}}{n{w}_{i}}$ (4)

$CI=\frac{{\lambda }_{\mathrm{max}}-n}{n-1}$ (5)

Table 2. RI values

$CR=\frac{CI}{RI}$ (6)

2.4. 层次总排序及一致性检验

${P}_{i}={\sum }_{j=1}^{m}{a}_{j}{b}_{ij}$ (7)

$\begin{array}{l}{B}_{1}:{a}_{1}{b}_{11}+{a}_{2}{b}_{12}+\cdots +{a}_{m}{b}_{1m}\\ {B}_{2}:{a}_{1}{b}_{21}+{a}_{2}{b}_{22}+\cdots +{a}_{m}{b}_{2m}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}⋮\\ {B}_{n}:{a}_{1}{b}_{n1}+{a}_{2}{b}_{n2}+\cdots +{a}_{m}{b}_{nm}\end{array}$ (8)

$CR=\frac{{a}_{1}C{I}_{1}+{a}_{2}C{I}_{2}+\cdots +{a}_{m}C{I}_{m}}{{a}_{1}R{I}_{1}+{a}_{2}R{I}_{2}+\cdots +{a}_{m}R{I}_{m}}$ (9)

3. 案例分析

Figure 2. The monitoring scheme selects the judgment matrix of each level

Figure 3. Matlab calculation results

4. 结束语

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