The distributed configuration is an effective approach for implementing Hotellingâs T² test to detect faults in large-scale systems. Multiple T² tests are employed in the distributed configuration in which each test uses measurements from a different set of sensors. A decomposition (i.e. an allocation of the sensors among different sets called subsystems) must first be selected to implement the multiple T² tests. The detection performance of the multiple T² tests and their ability to satisfy certain operational constraints depend on the decomposition. We propose two methods that find a feasible decomposition of a large-scale system for which the detection performance of the multiple T² tests is near optimal. The methods first use greedy algorithms to generate many feasible candidate subsystems and decompositions. The methods then quickly evaluate the detection performance of these feasible candidates using easy to compute analytic expressions and finally select a feasible decomposition with the best performance.

分布式配置是实施Hotelling的T ²测试以检测大型系统中的故障的有效方法。在分布式配置中采用了多个T ²测试，其中每个测试都使用来自不同传感器组的测量值。必须首先选择分解（即在称为子系统的不同集合之间分配传感器）来实施多个T ²测试。T ²的检测性能测试及其满足某些操作约束的能力取决于分解。我们提出了两种方法，可以找到大型系统的可行分解，对于该系统，多个T ²测试的检测性能接近最佳。该方法首先使用贪婪算法来生成许多可行的候选子系统和分解。然后，该方法使用易于计算的解析表达式快速评估这些可行候选对象的检测性能，并最终选择性能最佳的可行分解方法。