A point cloud obtained by stereo matching algorithm or three-dimensional (3D) scanner generally contains much complex noise, which will affect the accuracy of subsequent surface reconstruction or visualization processing. To eliminate the complex noise, a new regularization algorithm for denoising was proposed. In view of the fact that 3D point clouds have low-dimensional structures, a statistical low-dimensional manifold (SLDM) model was established. By regularizing its dimensions, the denoising problem of the point cloud was expressed as an optimization problem based on the geometric constraints of the regularization term of the manifold. A low-dimensional smooth manifold model was constructed by discrete sampling, and solved by means of a statistical method and an alternating iterative method. The performance of the denoising algorithm was quantitatively evaluated from three aspects, i.e., the signal-to-noise ratio (SNR), mean square error (MSE) and structural similarity (SSIM). Analysis and comparison of performance showed that compared with the algebraic point-set surface (APSS), non-local denoising (NLD) and feature graph learning (FGL) algorithms, the mean SNR of the point cloud denoised using the proposed method increased by 1.22 DB, 1.81 DB and 1.20 DB, respectively, its mean MSE decreased by 0.096, 0.086 and 0.076, respectively, and its mean SSIM decreased by 0.023, 0.022 and 0.020, respectively, which shows that the proposed method is more effective in eliminating Gaussian noise and Laplace noise in common point clouds. The application cases showed that the proposed algorithm can retain the geometric feature information of point clouds while eliminating complex noise.

The operating point of a propeller hydropower station will deviate from the effective workspace while the discharge reduces excessively during dry seasons. It usually leads to a decrease in efficiency and even to being unable to work. To solve the above problem, a scheme named decreasing capacity to increase efficiency was presented in this article. A low-specific-speed propeller runner with fixed blades that has the same installing dimensions as the original one was redesigned and equipped in dry seasons. A positive circulation at the outlet of the blades bigger than in conventional runners is allowed. Some key technologies about hydraulic design for runner blades were researched, which include distribution of velocity circulation at the inlet and outlet of the runner, thickening of the epiphyseal line of an aerofoil, unfolding aerofoil being converted to a cylindrical section, etc. In the section on digital modeling for runner blades, aerofoils on the cylindrical sections at the rim and at the hub were constructed employing the trend extrapolation method. Moreover, a blade digital model was built at one time according to the aerofoils on all cylindrical sections by means of a successful redevelopment to UniGraphics, and it has perfect symmetry. A case presented indicates that the method of decreasing capacity to increase efficiency is feasible. Using the method, the turbine efficiency increased from less than 28.6% to 83.4% while the discharge decreased from 3.20 m³s⁻¹ to 1.00 m³s⁻¹, and then the hydropower unit was able to work properly.