Research On Complex Optical Surface Reconstruction And Multi-Sensor Data Fusion Method Based On Gaussian Process

With a rapid development of ultra precision machining technology,complex optical surfaces integrated with multiple features have been widely applied in many fields,such as optics,electronics and biomedicine,to realize the miniaturisation and versatile functionalities.And precision measurement technologies are required to measure the multi-featured complex surfaces at each scale and comprehensively evaluate the machining accuracy to guarantee the products quality.Various instruments have been developed in the past decades,such as multi-sensor systems,and applied in the multi-featured complex surfaces measurement.It's a pity that most sensors are simply integrated into the same machine and it's still lack of a systematic study on some basic theory of surface reconstruction models,measurement planning,multi-sensor data registration and fusion.This results in poor cooperation and complementarity between sensors and fails to fully demonstrate the advantages of multi-sensor measurement technology.Meanwhile,the data from those machined surfaces generally has statistical characteristics such as Gaussian distribution or approximate Gaussian distribution.While most of the methods haven't taken into account the relationship between the surface model and data distribution,and also neglect the correlations among the points.Gaussian Process(GP)is a Bayesian model combined with the kernel method,which has an excellent adaptive and nonlinear processing ability.It can deal with both Gaussian and non-Gaussian distribution data and can also provide a probability distribution with prediction value and uncertainty,so it is suitable for the processing of surface measurement data.Therefore,this thesis starts from the research on the surface model and presents a complex surface reconstruction and data fusion method based on GP.It's aimed to realize the surface statistical characterization,adaptive sampling and multi-sensor data fusion by constructing the corresponding relationship between the geometric characteristics and kernel properties,and then improve the measurement efficiency and reconstruction accuracy.The main works and achievements of this thesis are concluded as follows:Firstly,a complex surface reconstruction method based on the composite kernel functions is proposed.The method not only takes into account the data distribution and the correlations among the points,but also combines the properties of surface geometric features and kernel functions together,and then integrates the surface prior knowledge into the selection of the kernel functions.Finally,better surface reconstruction accuracy will be achieved with the same points.In addition,this method can also learn the noise from the measurement data,and provide the mean value and its uncertainty at the same time.Secondly,to further improve the measurement efficient of complex surfaces with a contact probe,an adaptive surface sampling method is proposed based on GP with a specific kernel function.The method makes use of GP as a mathematical foundation to model the complex surfaces by designing composite covariance kernel functions for learning different topographies,and the estimated error and uncertainty of the model will be used as a critical criterion to perform on-line sampling of the measured surface.The self-optimization algorithm in the model can satisfy the surface reconstruction accuracy with less points.Thirdly,a multi-sensor data fusion method based on GP model with a specific kernel function is proposed.The multi-sensor measurement systems are applied in the measurement of complex surfaces to improve the efficiency and accuracy.If there is no obvious systematic deviation between two datasets after calibration,a heteroscedastic GP data fusion will be used to reconstruct the surface and reduce the surface uncertainty.If the systematic deviation of a sensor is difficult to be compensated,then a dependent GP regression model is adopted to deal with the systematic and random measurement errors and obtain fusion results with high accuracy and low uncertainty.An integrated data fusion method based on the weighted least square method and the GP model is applied if there is a large amount of data or high registration errors,to improve the computational efficiency and reduce the registration errors.Fourthly,an in-situ multi-sensor measurement system has been designed for the optical grinding machine and some measurement experiments on the machined workpieces have also been done.According to the cooperative and complementary requirement of the measurement system,a contact sensor and a non-contact sensor are combined,and both sensors are calibrated.To improve the system accuracy,some key parts of the system are optimized,and the geometric errors are also calibrated.The measurement data obtained from different sensors is compensated based on these calibration models.Finally,algorithms based GP are integrated into the in-situ measurement system and applied in the reconstruction,sampling,fusion of the machined complex surfaces,improving the measurement efficiency and reconstruction accuracy.In conclusion,surface reconstruction,adaptive sampling and data fusion methods based on GP make full use of the data distribution and the correlation information,which will overcome the shortcomings of the traditional methods and provide a better surface characterization on multi-featured surfaces.With the development of computer technology and artificial intelligence,these machine learning methods based on statistical models will make a breakthrough in the multi-featured complex surface measurement field and promote the development and application of the next generation of advanced optical surfaces in a number of areas.