MEMS Anemometry Sensing Tower (MAST)

• MAST is a MEMS-based anemometry platform using pentagonally arranged hot-wire sensors to measure 360° wind vectors for UAV applications.
• It integrates embedded signal conditioning and neural network inversion to achieve precise wind speed and angle estimations with sub-0.2 m/s and 1.6° RMSE accuracy.
• The compact system operates at high bandwidth (570 Hz) and low power (<1 W), enabling real-time gust analysis and advanced flight control on UAVs.

The MEMS Anemometry Sensing Tower (MAST) is a fast-response, solid-state, microelectromechanical system (MEMS) anemometry platform optimized for real-time, high-bandwidth wind vector estimation on unmanned aerial vehicles (UAVs). The core innovation of the MAST is the integration of pentagonally arranged MEMS hot-wire flow sensors with embedded signal conditioning and neural-network-driven signal inversion, enabling robust and accurate measurement of wind speed and direction across a 360° azimuth. Designed to address the limitations of legacy anemometry in dynamic UAV environments—specifically constraints of form factor, bandwidth, robustness, and two-dimensional sensitivity—MAST achieves sub-0.2 m/s speed accuracy and sub-2° angular error at bandwidths up to 570 Hz, with a total system mass near 40 g and power draw below 1 W (Simon et al., 2022).

1. Physical Architecture and Geometry

At the core of the MAST is a MEMS hot-wire sensor fabricated on a $4.2 \times 3.3 \times 0.66$ mm silicon die. Each die features four platinum ribbon resistances configured as the legs of a Wheatstone bridge. The individual “wire” constitutes eleven parallel 10 μm × 0.1 μm platinum strips on a silicon nitride membrane; three legs remain substrate-anchored while the fourth (designated $R_x$) is freestanding via silicon etch. Steady Joule heating in constant-voltage mode ($V_T \approx 10$ V) elevates all legs above ambient, with $R_x$ differentially cooled by incident airflow through a sub-die orifice.

System-level wind sensing is realized by mounting five such MEMS sensors (each with an AD623 instrumentation amplifier) on separate pole-PCBs, arranged in a regular pentagon atop a central chassis-PCB. The five axes provide angular coverage labeled $A_0$ through $A_4$ counterclockwise; the arrival angle $\theta$ is measured CCW from the $A_0$–$A_3$ bisector. This geometry provides sufficient overlap of individual sensor “sensitivity windows” (approximately ±30° per axis) across the full 360°.

2. Sensing Principle and Governing Equations

The core principle is analogous to classical hot-wire anemometry: velocity is transduced into convective cooling, altering the thermal—and thus electrical—properties of the ribbon. The energy balance for each leg is

$$\dot{Q}_{Joule} = \dot{Q}_{conduction} + \dot{Q}_{convection}$$

with the convective term parameterized as $$\dot{Q}_{convection} \propto (T_{wire}-T_{air}) f(U)$$, typically modeled via modified King’s Law; for microscale ribbons, $f(U) \approx A + B U^n$, $n \approx 0.5-0.6$.

Under constant-voltage bridge bias, the output voltage imbalance is:

$$V_L - V_R = \left[ \frac{R_x}{R_x+R_1} - \frac{R_3}{R_2+R_3} \right] V_T$$

Given $R_1 = R_2 = R_3 \approx$ constant (chip ambient), $V_L - V_R$ is a monotonic, though not closed-form, function of local velocity $U$ and angle of incidence. The nuances of angular sensitivity are governed by the spatial orientation of each hot-wire relative to the incoming flow vector.

3. Calibration and Signal Acquisition

MAST calibration is conducted in a precision wind tunnel (1.2 × 0.6 m cross-section), spanning steady freestream velocities $U_\infty$ from 1.3 to 5.0 m/s, and azimuthal angles $\theta$ stepped 0°–358° in 2° increments. At each $(U_\infty, \theta)$ coordinate, 30 s of 1 kHz data are acquired after amplifier gain adjustment and zero-flow offset compensation.

The resultant calibration dataset comprises five voltage traces $V_i(U_\infty, \theta), i=0..4$. Both $U_\infty$ and $\theta$ are unknown in operational use; thus, explicit inversion is impractical. Instead, a data-driven multivariate model learns the mapping $(V_0...V_4)\mapsto(\hat{U}, \hat{\theta})$. Sensor angular sensitivity is maximal when the wire is at near-perpendicular orientation to the flow; with five axes, the pentagonal setup provides nearly complete (with slight overlap) coverage of the unit circle due to the roughly 70° wide “sensitive windows.”

4. Neural Network-Based Signal Inversion

Signal interpretation in MAST leverages two feed-forward neural networks, calibrated directly on wind tunnel data:

• Angle Network: Input $n_s=5$ (all voltage channels), with two hidden layers sized $8n_s$ and $4n_s+5$ (ReLU activations), and scalar output $\hat{\theta}$.
• Speed Network: Input dimension 3 (the three largest $V_i$ per timepoint), with one hidden layer of size 6 (ReLU), outputting scalar $\hat{U}$.

Networks are trained using the Adam optimizer, with the following loss structure:

• Angle: $$L_{angle} = \mathrm{mean}(|\mathrm{wrap}(\hat{\theta}-\theta)|)$$ (where $\mathrm{wrap}$ preserves continuity at 0°/360°).
• Speed: $L_{speed} = \mathrm{mean}(|\hat{U} - U_\infty|)$.

Randomized sampling every 15 ms mitigates temporal correlation. Convergence occurs in approximately 20 epochs. The resulting model performance, as validated in static wind tunnel conditions, achieves mean $|\hat{\theta}-\theta| = 1.6^{\circ}$ and mean $|\hat{U}-U_\infty| = 0.14$ m/s, with 95% of predictions within 5.0° and 0.36 m/s, respectively.

5. Static and Dynamic Performance Evaluation

MAST exhibits the following quantitative metrics in wind tunnel tests and dynamic characterization:

Metric	Value	Test Condition
Speed RMSE	0.14 m/s	Static calibration
Speed error (95th pct.)	≤0.36 m/s	Static calibration
Direction RMSE	1.6°	Static calibration
Direction error (95th pct.)	≤5.0°	Static calibration
–3 dB Bandwidth	≈570 Hz	Square-wave response
Temporal Rise Time	≈0.64 ms	Phase-averaged square-wave
Transfer Function	$$\frac{2.724\times10^4s + 1.412\times10^8}{s^2 + 7.276\times10^4s + 1.80\times10^8}$$	Frequency response

A –3 dB bandwidth near 570 Hz corresponds to the ability to resolve aerodynamic fluctuations on $\mathcal{O}$(1 ms) timescales, i.e., within the relevant range for UAV gust, turbulence, and rotor-wake phenomena.

6. Integrated UAV Implementation and Applications

The pentagonal MAST, comprising five MEMS dies and PCB assembly, weighs approximately 40 g and consumes around 0.8 W at 16 V. Embedded neural network inference on a Raspberry Pi single-board computer executes in approximately 1.56 ms, compatible with real-time 250–500 Hz UAV flight controller loops. Initial on-board tests on a custom quadrotor (the “FlowDrone”) confirm operation with negligible impact on vehicle payload, power budget, or control execution.

This sensing capability enables the real-time measurement of high-frequency wind phenomena critical to flight stability, turbulence modeling, gust estimation, and advanced closed-loop flight control. The system’s architecture allows for the capture of unsteady flow structures—an essential requirement for advanced UAV performance in complex atmospheric or turbulent environments (Simon et al., 2022).