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Structural health monitoring of complex structures is often limited by restricted accessibility to locations of interest within the structure and availability of operational loads. In this work, a novel output-only virtual sensing scheme is proposed. This scheme involves the implementation of the modal expansion in an augmented Kalman filter. Performance of the proposed scheme is compared with two existing methods. Method 1 relies on a finite element model updating, batch data processing, and modal expansion (MUME) procedure. Method 2 employs a recursive sequential estimation algorithm, which feeds a substructure model of the instrumented system into an Augmented Kalman Filter (AKF). The new scheme referred to as Method 3 (ME-AKF), implements strain estimates generated via Modal Expansion into an AKF as virtual measurements. To demonstrate the applicability of the aforementioned methods, a rollercoaster connection was instrumented with accelerometers, strain rosettes, and an optical sensor. A comparison of estimated dynamic strain response at unmeasured locations using three alternative schemes is presented. Although acceleration measurements are used indirectly for model updating, the response-only methods presented in this research use only measurements from strain rosettes for strain history predictions and require no prior knowledge of input forces. Predicted strains using all methods are shown to sufficiently predict the measured strain time histories from a control location and lie within a 95% confidence interval calculated based on modal expansion equations. In addition, the proposed ME-AKF method shows improvement in strain predictions at unmeasured locations without the necessity of batch data processing. The proposed scheme shows high potential for real-time dynamic estimation of the strain and stress state of complex structures at unmeasured locations. 

Rollercoasters are challenging structures. Although the ever-changing geometry can guarantee a thrilling ride, the complexity of loading patterns due to the intricate geometry make testing and analysis of these structures challenging. Fatigue-induced damage is one of the most common types of damage experienced by civil engineering structures subjected to cyclic loading such as bridges and rollercoasters. Fatigue cracking eventually occurs when structures undergo a certain number of loading and unloading recurrences. This cyclic loading under stresses above a certain limit induces microcracking that can eventually propagate into failure of a member or connection. Because of the geometric and structural similarities between rollercoasters and bridge connections, similar techniques can be used for structural health monitoring and estimation of remaining fatigue life. Uniaxial fatigue analysis methods are widely used for the analysis of bridge connections. However, there is little guidance for the analysis of complex connections. They can experience variable amplitude, multiaxial, and non-proportional loading. In such cases uniaxial fatigue methods are insufficient and can lead to underestimates. A framework for the understanding and analysis of multiaxial fatigue damage using strain data collected from strain rosettes is presented. Uniaxial and multiaxial fatigue analysis methods proposed for non-proportional loading are compared. Methods proposed are applicable to both rollercoaster and bridge connections. The critical plane method is used for the estimation of multiaxial fatigue life. Results show that non-proportional loading and the accuracy of the critical plane estimation can cause a significant decrease in the estimates of remaining fatigue life. This methodology is anticipated to be used for real-time fatigue prognosis and evaluation tools for bridge networks. 

High cycle fatigue is a major cause of cracking in steel structures subjected to cyclic loading. It can result in substantial financial losses and structural failures compromising the safety of users. Uniaxial methods are in many cases insufficient for large in-service structures with complex geometry and connections subjected to multiaxial non-proportional loadings. A new method for fatigue life prediction for complex structures is presented using the critical plane method and the Kalman filter. The applicability of the methodology proposed is demonstrated and evaluated in a roller coaster support structure. Strain rosettes and accelerometers were installed on a support bracket near weld lines to measure responses. A substructure model is defined and used to estimate response prediction in the weld of the support bracket. The estimation of the input and the state estimation is performed using the augmented Kalman filter method, based on the response measurements and the substructured model. This new methodology is anticipated to be used for real-time fatigue prognosis of highway bridges.