Non-destructive detection method for nonlinear anchorage state of prestressed anchor cables based on the MSVAR model

With the growing application of prestressed anchor cables in engineering, accurately assessing their anchoring status has become essential. This study proposes a novel vibration-based non-destructive method using the Markov-Switching Vector Autoregressive (MSVAR) model to characterize anchorage conditions. By analyzing vibration signals, the method identifies nonlinear behavior associated with anchoring force and grout defects. Three scaled specimens replicating typical anchoring states were tested. The MSVAR model revealed hidden state transitions, and information entropy was introduced to quantify the degree of nonlinearity. Nonlinear coefficients, determined via density peak clustering (DPC), were found to correspond with anchorage force. A rapid detection approach was established by analyzing the slope of nonlinear coefficients in the over-tension stage, enabling efficient tension estimation. Field validation showed that the nonlinear coefficients increased with tension but with diminishing growth rates. During loading and unloading, coefficients remained nearly constant at the same tension levels, indicating stability. Compared to the Hilbert transform method, the MSVAR-DPC approach achieved a 53 % improvement in prediction accuracy and reduced processing time by 63 %. This confirms its robustness and adaptability under complex field conditions. As the first approach to introduce an entropy-based nonlinear coefficient for evaluating anchorage force, this method enhances detection sensitivity and reliability while addressing limitations of traditional techniques. It provides a new paradigm for real-time health monitoring of anchor cables in practical engineering applications.