# High-Fidelity Modeling of Laser Levels via Pulse-Window Software Lock-In PSD Sensing

## TL;DR

This paper introduces a new method to accurately measure laser level dynamics using a non-contact sensor and software algorithm, improving model predictions for better instrument design.

## Contribution

A novel Pulse-Window Software Lock-in (PWSL) sensing framework combined with data-driven model updating to enhance laser level self-leveling mechanism accuracy.

## Key findings

- The PWSL algorithm achieved high-fidelity displacement signal extraction with 10 kHz carrier suppression of broadband noise.
- Model updating reduced damping prediction error from 14.34% to 0.97% by introducing an equivalent friction coefficient.
- The non-contact PSD system provided authentic responses with 4.22% frequency prediction error.

## Abstract

Accurate identification of dynamic parameters, specifically natural frequency and damping ratio, is critical for optimizing the disturbance rejection performance of laser level self-leveling mechanisms. However, traditional Finite Element Analysis (FEA) often struggles to quantify micro-friction damping, while contact measurement methods introduce added mass interference. To address these challenges, this paper proposes an integrated framework combining Pulse-Window Software Lock-in (PWSL) sensing with a data-driven model updating strategy. Initially, a rigid-body dynamic model theoretically predicted a natural frequency (fsim) of 2.987 Hz and a damping ratio (ζsim) of 0.1255. To acquire authentic responses, a non-contact Position Sensitive Detector (PSD) system was developed. The custom PWSL algorithm leverages the laser’s 10 kHz carrier to extract high-fidelity displacement signals, effectively suppressing broadband noise despite embedded hardware limitations. Experimental results demonstrated that the measured frequency (fexp = 2.861 Hz) aligned well with predictions (4.22% error). In contrast, the measured damping ratio (ζexp = 0.1435) exceeded the simulation value by 14.34%, quantitatively revealing the energy dissipation caused by unmodeled bearing friction. Based on this disparity, the FEA model was inversely updated by introducing an equivalent friction coefficient, successfully reducing the damping prediction error to 0.97%. This study establishes a high-fidelity updated model, providing a reliable basis for the refined design of precision pendulum instruments.