Low-cost raindrop sizing with piezoelectric sensor: A mechanical approach
Authors: Wei Chi-Ling , Wang Li-Pen 
Published: March 2024

Raindrop size distribution (DSD) is a key factor to derive reliable rainfall estimates. It is highly related to a number of integral rainfall variables, such as rain intensity (R), rain water content (W) and radar echo (Z) and thus can contribute to a range of hydrological and meteorological applications, such as rainfall-induced landslide warnings and radar rainfall calibration. Disdrometers are commonly used to measure DSDc. Well-known disdrometer sensors include JWD, Parsivel and 2DVD . These sensors may have their own strengths and weaknesses, but their costs are all much higher than that of widely-deployed catching gauges (e.g. tipping bucket and weighing gauges). This makes it infeasible to have a widespread, or dense, DSD monitoring network. To address this issue, our ultimate goal is to develop a lightweight and low-cost disdrometer with descent accuracy.In this work, we have prototyped a disdrometer with a piezoelectric cantilever. It is not new to use piezoelectric materials as rain sensors because of its low cost and low maintenance. It is however not trivial to &#8216;calibrate&#8217; this type of sensors, and various calibration methods have been proposed in the literature. However, whereas most of these sensors associate received signal with rainfall properties directly (via statistical or machine learning approaches), we propose to formulate the drop sensing process as a &#8216;mechanical&#8217; problem. More specifically, we first form a physical model that can well simulate the signal response of continuous excitation force on a piezoelectric cantilever based on an existing theoretical model. We then analytically derive the inverse function of the model which can obtain the excitation force directly from the measured signals. The derived force-time signal is found to linearly associate with DSD and can also be used for other purposes including kinetic energy analysis.In spite of the sound underlying theory, the real-world signal is far from perfect, containing a considerable amount of noise. Additionally, as our physical model requires conducting differentiation and second-order differentiation, to which the impact of noise is even destructive. Although we have made efforts to improve the quality of signal from the source, it does not fully solve the problem because the physical model is highly sensitive to signal gradients. To effectively deduce the impact of noise, we then introduced various signal &#8216;noise&#8217; models, which were reported to well resemble the behavior of real-world signal noises, to train a machine learning (ML) model, such that the actual excitation force function can be derived from various weather conditions.To verify the proposed sensor and signal processing model, we have set up lab experiments using an in-house device with micropumps and high-voltage raindrop detachment devices to control the required size, drop location, and timing of the drops. Preliminary results from a given range of drop sizes have shown the potential of the proposed sensor and ML-based signal processing model to well derive drop sizes from our experimental device. We plan on further testing our sensor outdoor and compare the measurements with those collected from a co-located Parseval2 disdrometer.