Metrological calibration and uncertainty evaluation of MEMS accelerometers for structural health monitoring in seismic regions

2.1. Sensors under test

Three MEMS accelerometers were selected: the Analog Devices ADXL355 (±2 g, 25 μg/√Hz noise density), the InvenSense MPU-6050 (±2-±16 g, 400 μg/√Hz), and the STMicroelectronics LIS3DHH (±2.5 g, 45 μg/√Hz) [10, 11]. Each was interfaced with a Raspberry Pi 4B at 500 Hz sampling rate.

2.2. Calibration setup

Calibration followed the comparison method of ISO 16063-21 [9] using an electrodynamic shaker (B&K Type 4808), a reference accelerometer (B&K Type 8305, $U_{ref}=$ 0.5 %, $k=$ 2), a signal generator, and dual-channel dynamic signal analyzer. Sinusoidal excitation was applied at 20 frequencies from 1 to 200 Hz at 0.1, 0.5, and 1.0 g, averaged over 10 cycles per point. The setup is shown in Fig. 1.

Fig. 1Schematic diagram of the calibration system based on ISO 16063-21

2.3. Uncertainty evaluation

Uncertainty was evaluated per JCGM 100 (GUM) [12]. The combined standard uncertainty $u_c$ includes: reference accelerometer ($u_{ref}$), repeatability ($u_{rep}$), temperature ($u_T$), table stability ($u_{tab}$), signal processing ($u_{sig}$), and ADC digitization ($u_{ADC}$). The temperature uncertainty $u_T=$ 0.26 % was derived from the manufacturer datasheet thermal sensitivity coefficient (0.02 %/°C) and the ±1 °C laboratory variation (rectangular distribution). The signal processing uncertainty $u_{sig}=$ 0.17 % accounts for windowing effects (Hanning window leakage), FFT frequency resolution (0.5 Hz bin width at 500 Hz sampling rate), and amplitude averaging over 10 cycles. Expanded uncertainty U was obtained with $k=$ 2 (95 % confidence).

2.4. Field validation

The ADXL355 was deployed on a five-story reinforced concrete building in Tashkent (seismic zone VIII) [1]. Ambient vibration over 72 hours was compared with a Kinemetrics EpiSensor ES-T using operational modal analysis via frequency domain decomposition.

3.1. Calibration results

Fig. 2 presents sensitivity deviation versus frequency at 0.5 g. The ADXL355 maintained deviations below ±1.5 %, while the LIS3DHH reached ±2.8 % at low frequencies and the MPU-6050 showed deviations up to 4.7 %. The MPU-6050 was tested at ±2 g range; its higher deviations stem from the elevated noise floor (400 μg/√Hz versus 25 μg/√Hz for ADXL355) and limited on-chip temperature compensation. Sensitivity deviations at 0.1 g and 1.0 g remained within ±0.3 % of the 0.5 g values, confirming adequate linearity. Cross-axis sensitivity was not separately quantified in this study; however, the comparison method of ISO 16063-21 inherently captures combined on-axis and off-axis effects within the reported uncertainty budget. Dedicated cross-axis characterization is planned for future work. Numerical data are given in Table 1.

Fig. 2Sensitivity deviation versus frequency for three MEMS accelerometers at 0.5 g. Shaded region: ±2 % tolerance

3.2. Uncertainty budget

Table 2 and Fig. 3 present the uncertainty budget for the ADXL355 at 50 Hz. The reference accelerometer was the dominant contributor (~55 %), consistent with prior findings [13].

The expanded uncertainty was 2.3 % for the ADXL355, 3.1 % for the LIS3DHH, and 5.8 % for the MPU-6050 (Fig. 4). The ADXL355 satisfies laboratory-grade requirements (≤ 3 %) per ISO 16063-21 [9].

Fig. 3Uncertainty contribution breakdown for ADXL355 at 50 Hz

Fig. 4Expanded uncertainty U (k= 2) versus frequency with ISO 16063-21 grade thresholds

3.3. Field validation

Fig. 5 presents the field validation. The first three natural frequencies showed differences of 1.0 %, 0.9 %, and 1.2 % between EpiSensor and ADXL355 ($R^2=$ 0.999). Since frequency shifts exceeding 5-10 % indicate structural damage [4], the ~1 % discrepancy confirms MEMS adequacy for SHM. The ADXL355 node cost (~50-100 USD) is two orders of magnitude below conventional accelerometers, supporting cost-effective seismic monitoring [3]. The 72-hour validation period does not capture long-term drift; periodic recalibration is recommended for permanent installations.

Fig. 5Field validation: a) natural frequencies from reference and MEMS sensors; b) correlation (R2= 0.999)

a) Modal frequencies

b) Correlation