Improved C-optimal design method for ice load identification by determining sensor locations

Abstract

The ice load exerted on structures will be affected by many factors and difficult to estimate. Ice load identification is an effective way to obtain the ice loads. The identification of loads has always been problematic owing to the ill-condition in the corresponding mechanical model. Although an ill-conditioned mechanical model can be solved using conventional and improved regularisation methods, these methods cannot always provide stable and accurate identification results. In contrast, reducing or eliminating the ill-condition in the mechanical model is more effective and less difficult than solving it. In this paper, an improved C-optimal design method that reduces or eliminates the ill-condition in a mechanical model for the indirect monitoring of ice loads by determining sensor locations is presented. An engineering structure in a cold region was selected for a case study to describe in detail the improved C-optimal design and its usage. Six different original mechanical models were established based on the 8 × 8, 10 × 8, 12 × 8, 10 × 10, 12 × 10, and 12 × 12 two-dimensional Chebyshev orthogonal polynomials and were expressed as linear system of equations. Each mechanical model was reduced to its final form using a conventional C-optimal design, a Block C-optimal design, and an improved C-optimal design to reduce the problem's ill-condition. The condition number of the coefficient matrix of the final mechanical model and the running time corresponding to the conventional C-optimal design, the Block C-optimal design, and the improved C-optimal design were recorded and used to demonstrate the effectiveness and advantages of the improved C-optimal design compared with the conventional C-optimal and Block C-optimal designs. The comparison results demonstrate that the improved C-optimal design has no clear advantage over the conventional C-optimal and Block C-optimal designs in terms of the problem's ill-condition, but it has a significant advantage in terms of computational cost. Thereafter, a numerical example of distributed static load identification was used to show the effectiveness of the improved C-optimal design; the example shows that the final mechanical model corresponding to the sensor locations determined by the improved C-optimal design can produce stable and accurate fittings. Finally, an experiment was conducted to further demonstrate the effectiveness of the improved C-optimal design.