A Two-Time-Scale Approach for Discrete-Time Kalman Filter Design and Application to AHWR Flux Mapping
A Two-Time-Scale Approach for Discrete-Time Kalman Filter Design and Application to AHWR Flux Mapping
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DOI：
10.1109/tns.2015.2500917
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发表时间：
2016-02-01
影响因子：
1.8
通讯作者：
Belur, Madhu N.
中科院分区：
文献类型：
--
作者：
Ananthoju, Rajasekhar;Tiwari, A. P.;Belur, Madhu N.
在大型核反应堆中，如先进重水反应堆（AHWR），堆芯中子通量分布需要连续监测并显示给操作员。这一任务是由在线通量映射系统完成的，该系统采用合适的算法从大量堆芯探测器的读数来估计堆芯通量分布。目前，大部分的算法采用通量合成法，内边界条件法，和基于同时最小二乘解的中子扩散和探测器响应方程的方法。这些方法的一个共同特点是假设反应堆中的中子通量分布与时间无关。卡尔曼滤波为基础的方法的应用也被发现，虽然在非常有限的程度。在本文中，我们制定了在AHWR通量映射问题的任务，作为一个问题的最佳估计的时间依赖的中子通量在大量的网格点的核心。该解决方案是使用著名的卡尔曼滤波技术，其工程沿着与反应器的时空动力学模型。然而，试图解决卡尔曼滤波问题，在一个简单的方式是不成功的，由于严重的数值病态所造成的同时存在的缓慢和快速的现象，通常存在于核反应堆。因此，一组状态变量已被建议，从而原来的高阶模型的反应堆被解耦成一个慢子系统和一个快速子系统。现在，根据慢子系统和快子系统的顺序，原始的时间更新和卡尔曼增益方程也被解耦成慢子系统和快子系统的单独的方程组。解耦后的方程组可以很容易地求解。所提出的方法已在一些典型的瞬态情况下进行了验证。使用所提出的方法估计的整体精度已经非常好的网格通量，通道通量，象限通量，和核心平均通量。
In large nuclear reactors such as the Advanced Heavy Water Reactor (AHWR), the core neutron flux distribution needs to be continuously monitored and displayed to the operator. This task is accomplished by an online Flux Mapping System, which employs a suitable algorithm to estimate the core flux distribution from the readings of a large number of in-core detectors. Most of the algorithms available today employ the Flux Synthesis method, Internal Boundary Condition method, and the method based on simultaneous least squares solutions of neutron diffusion and detector response equations. A common feature of these methods is the assumption that the neutron flux profile in the reactor is independent of time. Application of Kalman filtering-based approaches are also found though to a very limited extent. In this paper, we have formulated the task of flux-mapping problem in AHWR as a problem of optimally estimating the time-dependent neutron flux at a large number of mesh points in the core. The solution is obtained using the well-known Kalman filtering technique which works along with a space-time kinetics model of the reactor. However, the attempt to solve the Kalman filtering problem in a straightforward manner is not successful due to severe numerical ill-conditioning caused by the simultaneous presence of slow and fast phenomena typically present in a nuclear reactor. Hence, a grouping of state variables has been suggested whereby the original high-order model of the reactor is decoupled into a slow subsystem and a fast subsystem. Now according to the order of the slow and fast subsystems, the original time update and Kalman gain equations have also been decoupled into separate sets of equations for the slow and fast subsystems. The decoupled sets of equations could be solved easily. The proposed method has been validated in a number of typical transient situations. Overall accuracy in the estimation using the proposed methodology has been very good for mesh fluxes, channel fluxes, quadrant fluxes, and the core average flux.