Keywords: bridge condition, damage detection, condition assessment, state representation methodology, structural health monitoring, support vector machines.

This paper introduces a newly proposed "state representation methodology" (SRM) and its application to bridge condition assessment based on the bridge monitoring data. The SRM is a novel tool that can provide some ideas and algorithms for data mining in a bridge monitoring system. The state of a system such as bridge structure can be obtained by a state variable that is calculated using a state representation equation (SRE). A kernel function method which plays an important role in the support vector machines (SVM) is applied to obtain solutions for the SRE. In the computation the SRE needs to be changed into a large-scale linear constraint problem (LSLCP). A new compatible algorithm is therefore proposed for solving the LSLCP. Before using the SRM, it is necessary that the system features need to be extracted from the data of complex responses observed in the system. Consequently, a new time-frequency analysis tool, called the frequency slice wavelet transform (FSWT), will be able to powerfully reveal a change in the characteristics in vibration signal. The FSWT produces five new properties in contrast with the traditional wavelet transform. Therefore, the paper will show the new method that can be used widely in signal processing. Finally, an application example in the laboratory bridge monitoring system (LBMS) will demonstrate how to apply the SRM, LSLCP, and FSWT methods to practical problems. Several algorithms mainly explained in the paper will provide a useful implementation for the current bridge monitoring system development.

First the time domain data needs to be changed into the transformation domain features in the SRM. Then we are able to derive a system state variable in the feature space. Furthermore, we need to make a statistic state probability distribution of the derived variable. Finally, the question of "condition assessment" of the present system becomes a problem of "state assessment". The main conclusions in this study are summarized as follows:

1. SRM provides a new general idea for a non-parametric description of the system state. The system state can be described as a state variable expressed by the SRE. The SRE can be improved by the kernel-based function learning method, which has been successfully used in SVM. Therefore, the SVM method is very helpful in the SRM.
2. An improved linear programming algorithm is designed to solve the large-scale linear constraint problem in the SRE. This algorithm exhibits strong global convergence properties and high-performance computation in polynomial time under a non strict condition. It has significant effectiveness even if the linear problem is extremely ill conditioned, such as the Hilbert ill-conditioned matrix.
3. A new time-frequency analysis tool is developed. The FSWT can be used for signal processing in many fields. The FSWT has five new properties compared with the traditional wavelet. The center of the time-frequency window is the observing center in contrast with the wavelet transform (WT). The FSWT can be adaptively controlled by the frequency resolution ratio of the measured signal. The original signal can be decomposed on a frequency slice function (FSF); theoretically, it can also be rebuilt using an infinite correlation function with the FSF. Moreover, the FSWT has many reconstructive procedures that are not directly related to the FSF. Furthermore, the FSWT has many useful transmutations. The FSF can be designed freely and has perfect symmetry in the time and frequency domains. The FSWT has higher performance against noise than the WT, and is available to many signals, especially for transient vibration signals.
4. It is successful in that a stable time-frequency transient damping parameter is the system feature in the SRM analysis is computed via a statistical method and the FSWT analysis.

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