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.

中文翻译：

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通过确定传感器位置来改进冰载荷识别的 C 最优设计方法

摘要 作用在结构上的冰荷载受多种因素影响，难以估计。冰载荷识别是获取冰载荷的有效方法。由于相应机械模型中的病态，载荷的识别一直存在问题。尽管可以使用传统的和改进的正则化方法来解决病态力学模型，但这些方法不能始终提供稳定和准确的识别结果。相比之下，减少或消除力学模型中的病态比解决它更有效且难度更低。在本文中，提出了一种改进的 C 优化设计方法，该方法通过确定传感器位置来减少或消除用于间接监测冰载荷的机械模型中的病态。选择寒冷地区的工程结构进行案例研究，详细描述改进的C优化设计及其用法。基于 8 × 8、10 × 8、12 × 8、10 × 10、12 × 10 和 12 × 12 二维切比雪夫正交多项式建立了六个不同的原始力学模型，并表示为线性方程组。每个机械模型都使用传统的 C 优化设计、块 C 优化设计和改进的 C 优化设计简化为最终形式，以减少问题的病态。最终力学模型的系数矩阵的条件数和常规C优化设计、Block C优化设计对应的运行时间，改进的 C 最优设计被记录并用于证明改进的 C 最优设计与传统的 C 最优和块 C 最优设计相比的有效性和优势。对比结果表明，改进的C-最优设计在问题的病态方面与传统的C-最优和Block C-最优设计相比没有明显优势，但在计算成本方面具有显着优势。此后，通过分布式静载荷识别的数值例子来证明改进的C优化设计的有效性；该示例表明，与由改进的 C 优化设计确定的传感器位置相对应的最终机械模型可以产生稳定和准确的拟合。最后，