| Summary: | Sensor placement plays an important role in terrain deformation monitoring systems and has an essential effect on data collection. The difficulty of sensor placement entails obtaining the most adequate and reliable information with the fewest number of sensors. Most sensor placement schemes are currently based on randomized non-uniform sampling and probability statistics, such as structural modality and optimization methods, which are difficult to directly apply due to the randomness and spatial heterogeneity of terrain deformation. In this study, the placement conditions of two-dimensional non-uniform sampling with equal arc length were deduced for underwater terrain deformation monitoring based on the MEMS accelerometer network. In order to completely reconstruct the underwater terrain, the arc length interval of the sensors should be less than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfrac><mn>1</mn><mrow><mn>2</mn><mi mathvariant="sans-serif">Ω</mi></mrow></mfrac></mrow></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Ω</mi></semantics></math></inline-formula> is the maximum frequency of the detected terrain). The maximum MRE and maximum RMSE were both less than seven percent in a terrain deformation monitoring experiment and a water tank test. The research results help technicians apply contact sensor arrays for underwater terrain monitoring.
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