Active aliasing technique and risk versus error mechanism in blade tip timing

Rotating blades are functional and weak components with a high failure risk, which affects the working ability and operation safety of turbomachinery. Therefore, it is significant to monitor the blades. Blade tip timing (BTT) is a potential measurement technique for rotating blades' health monitoring owing to its noncontact and efficiency. However, severe undersampling and excessive probes hinder the application of BTT. Thus, identifying the parameters for blade condition monitoring from severely undersampled BTT signals is a hotspot in current research. In this work, we reviewed and summarized a novel bi-probe-based BTT method proposed in our previous work for frequency identification in the non-resonant region. On this basis, we considered the amplitude identification and mathematically derived the maximum frequency that can be identified (supremum frequency) and the maximum error that can be permissible (error tolerance) by the proposed method, which provided theoretical guidance for selecting appropriate layouts and delay schemes. Finally, we revealed the dialectical relationship between the risk of successful reconstruction and the upper bounding of error termed risk versus error mechanism, which facilitated further error reduction.