The structural deformations caused by environmental changes in temperature, vibration, and other factors are harmful to the stability of high precision measurement equipment. The stability and optimal design method of a 2D optoelectronic angle sensor have been investigated in this study. The drift caused by structural deformations of the angle sensor has been studied and a drift error model has been achieved. Key components sensitive to thermal and vibrational effects were identified by error sensitivity analysis and simulation. The mounts of key components were analyzed using finite element analysis software and optimized based on the concept of symmetric structures. Stability experiments for the original and optimized angle sensors have been carried out for contrast. As a result, the stability of the optimized angle sensor has been improved by more than 63%. It is verified that the modeling and optimal design method is effective and low-cost, which can also be applied to improve the stability of other sensors with much more complex principles and structures.

A sensitivity- and resolution-improving method for a low-frequency micro-vibration accelerometer is presented in this paper. A sensitivity model of the measurement system is derived and established. The key parameters that limit the sensitivity and the resolution of the accelerometer were identified through the sensitivity coefficient analysis method. The structural parameters and the signal process method were then optimized. Experimental results show that the sensitivity of the accelerometer has improved from 1.10 V/(m/s²) to 19.21 V/(m/s²), and the resolution has improved from 1.47 mm/s² to 0.21 mm/s². The lowest working frequency range has expanded from 1 Hz to 0.7 Hz. The presented method is effective and cheap and can be applied to other sensors.

Drift exhibits time-varying, cumulative, and stochastic characteristics, which degrade the accuracy of high-precision measuring instruments, especially in long-term measurements. This paper presents a drift error compensation method for laser displacement measurement systems by integrating a Bayesian lag regression model with new information integration. The primary factors influencing the drift error were analyzed, and characteristic analyses were conducted on the drift error data and key influencing factor data collected during non-measurement intervals. A Bayesian lag regression model was subsequently established. Model parameters were estimated using a recursive Bayesian tracking and prediction algorithm initialized with the non-informative prior distributions. The drift error values predicted by the model have been used to compensate for drift errors during operational periods, while outputs from idle periods have been utilized to update the model parameters. Experimental validation has been performed on a homemade laser Doppler displacement measurement system, demonstrating an average reduction of 75% in variation and 92% in root mean square error (RMSE), across six repeated experiments. Furthermore, the proposed method achieves average reductions in RMSE of 72% and 71% compared to conventional multiple regression and support vector machine methods, respectively. These results confirm the effectiveness and robustness of the proposed compensation methodology.

Drift issues are commonly encountered in precision instruments operating in standard measurement environments due to temperature fluctuations, material property variations, and environmental disturbances, which represent a significant bottleneck to achieving high measurement accuracy. To address this limitation, a drift error compensation method based on ensemble empirical mode decomposition (EEMD) and multivariate lag regression has been proposed in this paper. The structure, principles, and working environment of a high-precision two-dimensional angle sensor have been analyzed, and the primary influencing factors and mechanisms contributing to drift errors have been systematically investigated. Drift and error source signals have been decomposed and denoised using EEMD, and effective intrinsic mode function (IMF) components have been extracted. The lag characteristics of these components have been analyzed and incorporated into a multivariate regression model for drift error compensation. Partial regression analysis and significance testing have been employed to optimize the model, reducing complexity and enhancing generalization. Experimental results show that drift errors in the yaw and pitch directions have been reduced by more than 60.01% and 67.51%, respectively, after compensation. When compared with classical multivariate regression, LSTM, and SVM methods, the proposed approach demonstrates certain advantages in error compensation performance, robustness, and complexity. Additionally, the method is also suitable for broader applications to other high-precision measurement instruments.

A novel design method based on topology optimization is proposed and demonstrated to enhance thermal stability in laser four-degree-of-freedom (4-DOF) measurement systems against environmental temperature fluctuations. The overall thermal deformation of the measurement systems is calculated by finite element analysis. The thermal errors caused by thermal deformation of workpieces are analyzed and modeled. The workpieces of the 4-DOF measurement systems are designed using topology optimization, resulting in a 50% reduction in thermal deformation. Furthermore, the temperature field of the measurement system is optimized by incorporating thermal insulation materials, and stability experiments are performed on the system both before and after optimization. The stability of the laser beam is improved by 53.9%, 49.0%, 58.0%, and 52.5% in two angular and two straightness directions, respectively. Experimental results demonstrate that the proposed method effectively enhances the stability of the 4-DOF measurement systems and can be applied to improve the thermal stability of other precision instruments.

Uncertainty evaluation for unknown distribution data is a key problem to be solved in uncertainty evaluation theory. To evaluate the measurement uncertainty of data with unknown distributions, a novel uncertainty evaluation method based on the particle filter (PF) and beta distribution is proposed in this paper. A beta distribution with wide adaptability was adopted as the distribution type of measurement results, the parameters of the beta distribution were taken as the parameters to be estimated, and a state-space model was established. The PF method, suitable for non-Gaussian data, was utilized to obtain the estimates of the parameters of the beta distribution according to the measurement results. Finally, the best estimates of the measurement results and their uncertainty were calculated using the beta distribution parameters. Simulation results show that the proposed method is adaptive to accurately evaluate the measurement uncertainties of data, especially for non-Gaussian distribution data or asymmetrically distributed data. Multiple evaluation results show that the method has good robustness. The experimental results for the drift errors of a laser interferometer show that the uncertainty result of the proposed method is consistent with the Monte Carlo method. This method is suitable for a variety of distribution types that can be characterized through beta distribution and can solve the optimal estimation and uncertainty evaluation of most measurement results with unknown distribution types.