Design Methods and Strategies for Forward and Inverse Problems of Turbine Blades Based on Machine Learning

To study the feasibility of using machine learning technology to solve the forward problem(prediction of aerodynamic parameters)and the inverse problem(prediction of geometric parameters)of turbine blades,this paper built a forward problem model based on backpropagation artificial neural networks(BP-ANNs)and an inverse problem model based on radial basis function artificial neural networks(RBF-ANNs).The S2(a stream surface obtained by extending a radial curve in turbo blades)calculation program was used to generate the dataset for single-stage turbo blades,and the back propagation algorithm was used to train the model.The parameters of five blade sections in a single-stage turbine were selected as inputs of the forward problem model,including stagger angle,inlet geometric angle,outlet geometric angle,wedge angle of leading edge pressure side,wedge angle of leading edge suction side,wedge angle of trailing edge,rear bending angle,and leading edge diameter.The outputs are efficiency,power,mass flow,relative exit Mach number,absolute exit Mach number,relative exit flow angle,absolute exit flow angle and reaction degree,which are eight aerodynamic parameters.The inputs and outputs of the inverse problem model are the opposite of that of the forward problem model.The models can accurately predict the aerodynamic parameters and geometric parameters,and the mean square errors(MSEs)of the forward problem test set and the inverse problem test set are 0.001 and 0.00035,respectively.This study shows that machine learning technology based on neural networks can be flexibly applied to the design of forward and inverse problems of turbine blades,and the models built by this method have practical application value in regression prediction problems.

Uniqueness, scale, and resolution issues in groundwater model parameter identification

This paper first visits uniqueness, scale, and resolution issues in groundwater flow forward modeling problems. It then makes the point that non-unique solutions to groundwater flow inverse problems arise from a lack of information necessary to make the problems well defined. Subsequently, it presents the necessary conditions for a well-defined inverse problem. They are full specifications of （1） flux boundaries and sources/sinks, and （2） heads everywhere in the domain at at least three times （one of which is t = 0）, with head change everywhere at those times being nonzero for transient flow. Numerical experiments are presented to corroborate the fact that, once the necessary conditions are met, the inverse problem has a unique solution. We also demonstrate that measurement noise, instability, and sensitivity are issues related to solution techniques rather than the inverse problems themselves. In addition, we show that a mathematically well-defined inverse problem, based on an equivalent homogeneous or a layered conceptual model, may yield physically incorrect and scenario-dependent parameter values. These issues are attributed to inconsistency between the scale of the head observed and that implied by these models. Such issues can be reduced only if a sufficiently large number of observation wells are used in the equivalent homogeneous domain or each layer. With a large number of wells, we then show that increase in parameterization can lead to a higher-resolution depiction of heterogeneity if an appropriate inverse methodology is used. Furthermore, we illustrate that, using the same number of wells, a highly parameterized model in conjunction with hydraulic tomography can yield better characterization of the aquifer and minimize the scale and scenario-dependent problems. Lastly, benefits of the highly parameterized model and hydraulic tomography are tested according to their ability to improve predictions of aquifer responses induced by independent stresses not used in the inverse modeling efforts.