Abstract Inverse estimation of moving heat source is a common issue in many fields. A real-time method based on Kalman filter is proposed and further developed to identify the moving heat source in a three-dimensional heat transfer system. Firstly, a step-renewed state space model considering the source position is established according to principle of source contribution. Using this model, a technique coupling fuzzy adaptive Kalman filter with weight recursive least squares algorithm is implemented to realize the simultaneous estimation of moving heat source and temperature field. Different spatiotemporal changes of heat source and measurement noises are assumed to validate the feasibility and test its performances of this technique. Results illustrates that this method can be used to inversely estimate moving heat source with different changes rates and directions. When the moving velocity varies as 0.25, 0.50, 1.00 mm/s and the time period is employed as 100, 200, 400, 800 s, the estimated heat source can accurately agree with exact one while the reconstructed temperature field is of low deviation. The mean relative errors of estimated heat source are no more than 3.25% and mean relative errors of temperature are smaller than 1.37% while standard deviation of measurement noises increases from 0.01 to 5.00, which demonstrates that this method is of high robustness and can be used under a deteriorated condition.

中文翻译：

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基于阶跃更新卡尔曼滤波器的瞬时三维传热系统运动热源估计

摘要 运动热源的逆估计是许多领域的普遍问题。提出并进一步发展了一种基于卡尔曼滤波器的实时方法来识别三维传热系统中的移动热源。首先，根据源贡献原理，建立考虑源位置的步进更新状态空间模型。利用该模型，实现了模糊自适应卡尔曼滤波器与权重递推最小二乘算法的耦合技术，实现了移动热源和温度场的同时估计。假设热源和测量噪声的不同时空变化来验证该技术的可行性并测试其性能。结果表明，该方法可用于反估计具有不同变化速率和方向的移动热源。当移动速度变化为0.25、0.50、1.00 mm/s，时间段为100、200、400、800 s时，估计的热源与精确的热源吻合，而重建的温度场偏差小。估计热源平均相对误差不超过3.25%，温度平均相对误差小于1.37%，测量噪声标准偏差从0.01增加到5.00，表明该方法鲁棒性高，可以使用在恶化的情况下。估计的热源与精确的热源吻合，而重建的温度场偏差小。估计热源平均相对误差不超过3.25%，温度平均相对误差小于1.37%，测量噪声标准偏差从0.01增加到5.00，表明该方法鲁棒性高，可以使用在恶化的情况下。估计的热源与精确的热源吻合，而重建的温度场偏差小。估计热源平均相对误差不超过3.25%，温度平均相对误差小于1.37%，测量噪声标准偏差从0.01增加到5.00，表明该方法鲁棒性高，可以使用在恶化的情况下。