Optimal parameters identification and sensitivity study for abrasive waterjet milling model.

*(English)*Zbl 1444.35161Summary: In this paper we present the work related to the parameters identification for abrasive waterjet milling (AWJM) model that appears as an ill-posed inverse problem. The necessity of studying this problem comes from the industrial milling applications where the possibility to predict and model the final surface with high accuracy is one of the primary tasks in the absence of any knowledge of the model parameters that should be used. The adjoint approach based on corresponding Lagrangian gives the opportunity to find out the unknowns of the AWJM model and their optimal values that could be used to reproduce the required trench profile. Due to the complexity of the nonlinear problem and the large number of the model parameters, we use an automatic differentiation software tool. This approach also gives us the ability to distribute the research on more complex cases and consider different types of model errors and 3D time dependent model with variations of the jet feed speed. This approach gives us a good opportunity to identify the optimal model parameters and predict the surface profile both with self-generated data and measurements obtained from the real production. Considering different types of model errors allows us to receive the results acceptable in manufacturing and to expect the proper identification of unknowns.

##### MSC:

35R30 | Inverse problems for PDEs |

35R25 | Ill-posed problems for PDEs |

35B30 | Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs |

65K10 | Numerical optimization and variational techniques |

35Q93 | PDEs in connection with control and optimization |

49K99 | Optimality conditions |

##### Keywords:

inverse problems; abrasive waterjet; PDE constrained optimization; Tikhonov regularization; automatic differentiation; numerical analysis; parameters estimation
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\textit{D. Auroux} and \textit{V. Groza}, Inverse Probl. Sci. Eng. 25, No. 11, 1560--1576 (2017; Zbl 1444.35161)

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