This paper presents a method to reconstruct symmetric geometric models from point cloud with inherent symmetric structure. Symmetry types commonly found in engineering parts, i.e., translational, reflectional and rota...This paper presents a method to reconstruct symmetric geometric models from point cloud with inherent symmetric structure. Symmetry types commonly found in engineering parts, i.e., translational, reflectional and rotational symmetries are considered. The reconstruction problem is formulated as a constrained optimization, where the objective function is the sum of squared distances of points to the model, and constraints are enforced to keep geometric relationships in the model. First, the explicit representations of symmetric models are presented. Then, by using the concept of parameterized points (where the coor-dinate components are represented as functions rather than constants), the distances of points to symmetric models are deduced. With these distance functions, symmetry information, for both 2D and 3D models, is uniformly represented in the process of reconstruction. The constrained optimization problem is solved by a standard nonlinear optimization method. Owing to the explicit representation of symmetry information, the computational complexity of our method is reduced greatly. Finally, examples are given to demonstrate the application of the proposed method.展开更多
The high-frequency electromagnetic waves of ground-penetrating radar(GPR)attenuate severely when propagated in an underground attenuating medium owing to the influence of resistivity,which remarkably decreases the res...The high-frequency electromagnetic waves of ground-penetrating radar(GPR)attenuate severely when propagated in an underground attenuating medium owing to the influence of resistivity,which remarkably decreases the resolution of reverse time migration(RTM).As an effective high-resolution imaging method,attenuation-compensated RTM(ACRTM)can eff ectively compensate for the energy loss caused by the attenuation related to media absorption under the influence of resistivity.Therefore,constructing an accurate resistivity-media model to compensate for the attenuation of electromagnetic wave energy is crucial for realizing the ACRTM imaging of GPR data.This study proposes a resistivity-constrained ACRTM imaging method for the imaging of GPR data by adding high-density resistivity detection along the GPR survey line and combining it with its resistivity inversion profile.The proposed method uses the inversion result of apparent resistivity data as the GPR RTM-resistivity model for imposing resistivity constraints.Moreover,the hybrid method involving image minimum entropy and RTM is used to estimate the medium velocity at the diff raction position,and combined with the distribution characteristics of the reflection in the GPR profile,a highly accurate velocity model is built to improve the imaging resolution of the ACRTM.The accuracy and eff ectiveness of the proposed method are verified using the ACRTM test of the GPR simulated data of a typical attenuating media model.On this basis,the GPR and apparent resistivity data were observed on a field survey line,and use the GPR resistivity-constrained ACRTM method to image the observed data.A comparison of the proposed method with the conventional ACRTM method shows that the proposed method has better imaging depth,stronger energy,and higher resolution,and the obtained results are more conducive for subsequent data analysis and interpretation.展开更多
Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameters in the search directions. In this note, by combining the nice numerical performance of PR and HS met...Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameters in the search directions. In this note, by combining the nice numerical performance of PR and HS methods with the global convergence property of the class of conjugate gradient methods presented by HU and STOREY(1991), a class of new restarting conjugate gradient methods is presented. Global convergences of the new method with two kinds of common line searches, are proved. Firstly, it is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continously dif ferentiable function with Curry-Altman's step size rule and a bounded level set. Secondly, by using comparing technique, some general convergence properties of the new method with other kind of step size rule are established. Numerical experiments show that the new method is efficient by comparing with FR conjugate gradient method.展开更多
基金the National Natural Science Foundation of China (No. 50575098)China Postdoctoral Science Foundation (No. 20070421176)
文摘This paper presents a method to reconstruct symmetric geometric models from point cloud with inherent symmetric structure. Symmetry types commonly found in engineering parts, i.e., translational, reflectional and rotational symmetries are considered. The reconstruction problem is formulated as a constrained optimization, where the objective function is the sum of squared distances of points to the model, and constraints are enforced to keep geometric relationships in the model. First, the explicit representations of symmetric models are presented. Then, by using the concept of parameterized points (where the coor-dinate components are represented as functions rather than constants), the distances of points to symmetric models are deduced. With these distance functions, symmetry information, for both 2D and 3D models, is uniformly represented in the process of reconstruction. The constrained optimization problem is solved by a standard nonlinear optimization method. Owing to the explicit representation of symmetry information, the computational complexity of our method is reduced greatly. Finally, examples are given to demonstrate the application of the proposed method.
基金supported by the National Natural Science Foundation of China (No.41604102)the Guangxi Natural Science Foundation project (No.2020GXNSFAA159121).
文摘The high-frequency electromagnetic waves of ground-penetrating radar(GPR)attenuate severely when propagated in an underground attenuating medium owing to the influence of resistivity,which remarkably decreases the resolution of reverse time migration(RTM).As an effective high-resolution imaging method,attenuation-compensated RTM(ACRTM)can eff ectively compensate for the energy loss caused by the attenuation related to media absorption under the influence of resistivity.Therefore,constructing an accurate resistivity-media model to compensate for the attenuation of electromagnetic wave energy is crucial for realizing the ACRTM imaging of GPR data.This study proposes a resistivity-constrained ACRTM imaging method for the imaging of GPR data by adding high-density resistivity detection along the GPR survey line and combining it with its resistivity inversion profile.The proposed method uses the inversion result of apparent resistivity data as the GPR RTM-resistivity model for imposing resistivity constraints.Moreover,the hybrid method involving image minimum entropy and RTM is used to estimate the medium velocity at the diff raction position,and combined with the distribution characteristics of the reflection in the GPR profile,a highly accurate velocity model is built to improve the imaging resolution of the ACRTM.The accuracy and eff ectiveness of the proposed method are verified using the ACRTM test of the GPR simulated data of a typical attenuating media model.On this basis,the GPR and apparent resistivity data were observed on a field survey line,and use the GPR resistivity-constrained ACRTM method to image the observed data.A comparison of the proposed method with the conventional ACRTM method shows that the proposed method has better imaging depth,stronger energy,and higher resolution,and the obtained results are more conducive for subsequent data analysis and interpretation.
文摘Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameters in the search directions. In this note, by combining the nice numerical performance of PR and HS methods with the global convergence property of the class of conjugate gradient methods presented by HU and STOREY(1991), a class of new restarting conjugate gradient methods is presented. Global convergences of the new method with two kinds of common line searches, are proved. Firstly, it is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continously dif ferentiable function with Curry-Altman's step size rule and a bounded level set. Secondly, by using comparing technique, some general convergence properties of the new method with other kind of step size rule are established. Numerical experiments show that the new method is efficient by comparing with FR conjugate gradient method.
