We propose a strategy for optimizing a sensor trajectory in order to estimate the time dependence of a localized scalar source in turbulent channel flow. The approach leverages the view of the adjoint scalar field as the sensitivity of measurement to a possible source. A cost functional is constructed so that the optimal sensor trajectory maintains a high sensitivity and low temporal variation in the measured signal, for a given source location. This naturally leads to the adjoint-of-adjoint equation based on which the sensor trajectory is iteratively optimized. It is shown that the estimation performance based on the measurement obtained by a sensor moving along the optimal trajectory is drastically improved from that achieved with a stationary sensor. It is also shown that the ratio of the fluctuation and the mean of the sensitivity for a given sensor trajectory can be used as a diagnostic tool to evaluate the resultant performance. Based on this finding, we propose a new cost functional which only includes the ratio without any adjustable parameters, and demonstrate its effectiveness in predicting the time dependence of scalar release from the source.
翻译:我们提出了一个优化传感器轨迹的战略,以估计局部的卡路里源在扰动通道流中的时间依赖性。 这种方法将连接的卡路里场的观点作为测量可能的源的敏感度。 成本功能的构建是为了使最佳传感器轨迹在测量的信号中保持高灵敏度和低时间差异, 以给定源位置。 这自然导致连接的连接方程式, 传感器轨迹是迭代优化的基础。 显示根据传感器在最佳轨迹上的测量得出的估计性能, 与固定传感器相比, 大大改进了。 还表明, 波动比率和特定传感器轨迹敏感度的平均值可以用作评估结果性能的诊断工具。 基于这一发现, 我们提议一个新的成本功能, 仅包括没有可调整参数的比, 并显示其在预测源释放卡路里的时间依赖性方面的有效性 。