Four Design-Parameter Requirements of a Deformation-Monitoring Scheme: 18-Geom-B3 Networks and Precise Engineering Surveys, December 2018, Q12

Question 12 (Part C): Four Design-Parameter Requirements of a Deformation-Monitoring Scheme (8 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

The design of a deformation-monitoring network is governed by four quality requirements — the same criteria that drive network pre-analysis (Q1), specialised to deformation work:

Precision (accuracy). The network must resolve movements at least a specified fraction (commonly one-quarter to one-fifth) of the smallest deformation of interest, so a real movement stands out above the measurement noise. This sets the required standard deviations of the coordinates (target error-ellipse sizes) and hence the instruments and observation plan.
Sensitivity. The scheme must be geometrically able to detect the expected deformation in the direction it is expected to occur. Sensitivity is the smallest displacement (in a given direction) that the network can identify as significant; the configuration must be oriented so that its strongest-determined directions align with the anticipated movement (e.g. across a dam, along a slope).
Reliability. There must be enough redundancy that gross errors (blunders) are detectable (internal reliability) and that any undetected blunder has only a limited effect on the results (external reliability). High, uniform redundancy numbers make the scheme self-checking — essential when decisions about public safety rest on it.
Economy (cost-effectiveness). Among all designs meeting the precision, sensitivity and reliability criteria, the chosen one should minimise cost — number of stations, instruments, observation time and travel. Economy is the constraint that turns the other three from “as good as possible” into “just good enough, at least cost.”

In practice these four are traded off in the pre-analysis/simulation loop: the design is iterated (moving points, adding observations, choosing instruments) until precision, sensitivity and reliability targets are all met at minimum cost.

Concept & Theory

Topic. Quality criteria for optimal design of deformation-monitoring networks.

Key relations. Precision (error-ellipse size from $\mathbf{Q}_{xx}$); sensitivity (minimum detectable displacement in a direction); reliability (redundancy numbers $r_i$, internal/external reliability); economy (cost).

Why this works. A monitoring net exists to decide whether movement has occurred; that decision needs enough precision to see it, geometry aligned to detect it, redundancy to trust it, and it must be affordable — the four criteria formalise exactly these needs.

Common pitfall. Optimising precision alone while ignoring sensitivity (a very precise net still fails if its strong axis is perpendicular to the expected motion) or reliability (no redundancy ⇒ an undetected blunder is read as deformation).

Source. Kuang, Geodetic Network Analysis and Optimal Design; Chrzanowski et al.; Mikhail & Gracie §11.

Question 12 of 12: Four Design-Parameter Requirements of a Deformation-Monitoring Scheme

Question 12 (Part C): Four Design-Parameter Requirements of a Deformation-Monitoring Scheme (8 marks)