This multi-disciplinary research project, which builds upon the findings of a previous NCPTT-funded project on Structural Health Monitoring (SHM) to determine the health of the nation’s historic structures, develops Life-Cycle Assessment charts for the Preservation and Rehabilitation (LCA-PR) of historic structures. Quantifiable parameters will be developed through LCA-PR charts to evaluate not only the structural state of the heritage building, but also the effect of rehabilitation campaigns. Quantitative information about the structural degradation can aid in the development of the most cost-effective, long-term infrastructure management plans that reduce both energy and material consumption, thusly yielding sustainable maintenance schemes for the nation’s cultural heritage.

**Main Contributions**

As part of this project, *Structural Life Cycle Analysis* graphs which indicate the sustainability of a structure in regards to its actual versus designed performance are introduced. Figure 1 shows a conceptual view of the proposal. The rate at which the decrease in structural functionality occurs depends upon the structural sustainability of the built system. Structural Sustainability is a measure of the degradation rate and inversely relates to the slope of the curve. Figure 1 represents the lifespan for a structure that has been recently constructed. For an existing structure, a reference point of structural functionality must be determined according to the current structural condition.

Based on the approach presented in Figure 1, with the goal of preservation to ensure that historic structures survive for posterity, a LCA-PR framework is proposed. This framework addresses and incorporates three scenarios: (1) gradual structural degradation from environmental and operational conditions, (2) rapid structural damage from disasters and (3) rapid structural improvement due to preservation or rehabilitation campaigns. While rapid degradation or improvement in structural integrity can only be evaluated after the occurrence of an event, the gradual structural degradation naturally allows for prognosis of future behavior. In this project, to predict the long term, gradual degradation of a structural system, prognostic methodologies are implemented into the LCA-PR framework. Such prognosis is accomplished by training Support Vector Regression (SVR) models with the data collected through sensors placed on the structure. In this prognostic approach, as more data is collected, the trained SVR model is refined and prediction accuracy is improved. Figure 2 schematically outlines the LCA-PR framework.

**Project Progress Update**

** **A Review on Prognostic Evaluation of Historic Masonry Structures

This project presents a review of not only the established literature on prognostic evaluation but also the available inspection techniques for masonry construction with an objective to relate these two disassociated areas of knowledge, thus laying the foundation for prognostic evaluation of historic masonry.

Prognostic evaluation consists of four main stages: monitoring, diagnostics, prediction, and maintenance. The first step entails monitoring user selected, damage-sensitive features of a system (e.g. vibration modes frequencies, modal parameters, peak values, etc.) obtained from the system through a series of sensors or onsite inspections beginning at time t0. In the diagnostic phase, these features, monitored continuously or intermittently, are then pre-processed to assess the current health state or performance of the system. When repeated successively, diagnosis supplies information that can be used to train statistical models that can forecast the system’s future health state. The remaining time prior to the point at which the predicted health state intersects the corresponding user-defined failure threshold at the system’s end of life, *t _{EoL}*, defines the remaining useful life (RUL) of the system (see Figure 3). This failure threshold is a conservative limit on damage level, beyond which the system is inadequate for its intended use. Therefore,

*t*does not necessarily signify complete system failure. In the final step, based upon the estimated RUL, maintenance actions are scheduled for time tm to extend the RUL of the system (see Figure 3).

_{EoL}

Adaptively Weighted Support Vector Regression

Among the available techniques for prognostic evaluation, SVR shows particular potential for applicability to historic masonry structures as it is capable of handling the nonlinear responses of masonry assemblies due to the complexity of their materials and geometry. As a part of this project the proposed adaptively weighted SVR approach is presented. Besides, the theoretical background for SVR as well as the algorithmic development for adaptive weighting is both presented.

The basic steps of this adaptively weighted prognostic approach can be demonstrated on an initial dataset of *n* points. In Figure 4, the dataset is divided into three parts: the *preliminary training set* consisting of the first *m* points, the *hold-out set* consisting of the following *h* points, and the *forecasting set* consisting of the next *f* points. During the preliminary stage, optimal λ is selected. For this, multiple candidate λ values (ten λ values for each multiple of 10 from 10^{-15} to 10^{5}) are tested in their ability to predict the hold-out set of *h* points from *m* to *n*, where *n *= *m *+ *h*. The resulting L1 norm prediction error of the hold-out set is summed for each model trained by a different candidate λ, and, by comparison, the candidate λ producing the model with the least prediction error over the hold-out set is chosen as the optimal λ. During the forecasting stage, this optimal λ is then used to train a refined model using the total dataset that was used in the preliminary stage (i.e. up to *n*) to predict the forecasting set (i.e. from *n* to* p*). The adaptively weighted approach then repeats this process as additional measurements become available by adding these *new* data points to the training set and updating λ accordingly. The detailed steps of this process are shown in Algorithm 1.

**An Empirical Assessment of Load Carrying Capacity of a Scaled Masonry Dome**

The project also focuses on the establishment of a semi-empirical relationship to estimate the reduction in the load carrying capacity due to damage by exploiting the experimentally detected deviations in the natural frequencies for a tile dome. Finite element model developed to analyze the dome is calibrated against both non-destructive vibration measurements and destructive load-displacement measurements up to failure. Once a FE model that can accurately represent both linear (natural frequencies) and nonlinear (load carrying capacity) behavior of the domes is obtained, the model is then executed to simulate incremental development of cracks. The first natural frequency and remaining load carrying capacity of the dome are monitored to define the desired empirical relationship, which is ultimately generalized for spherical domes with varying span-to-rise ratios.

MATLAB’s *fminsearch *function was used for the optimization problem. For the dome studied herein, the coefficients are obtained to be α_{1}=3.78, α_{2}=18.98, α_{3}=6.45, α_{4}=1.47 and α_{5}=3.46. The power function obtained with these coefficients supply a conservative, upper bound as depicted in Figure 5 (left).

Figure 6 demonstrates the three-dimensional plots of the functional relationship of same thickness but with height-to-span rations varying from 0.15 to 0.50. This functional form demonstrated in Figure 6 can be improved by increasing the number of simulation runs and can be made more generally applicable by considering the different thicknesses, boundary conditions and materials that can be used for masonry domes. Therefore, the semi-empirical relationship presented herein should be considered to be for demonstration purposes only.

Click to enter the monitoring website

In order to achieve the objective of real-time, long-term monitoring and easy to be accessed by infrastructure managers, it becomes impractical to conduct on-site monitoring. On the other hand, Remote Monitoring technology solves these problems perfectly. In this project, the proposed remote monitoring system is able to retrieve sensor data generated from ambient excitations. This data will be processed and then be visualized on a website. Also, when outliers are detected by this system, it is capable of sending email alert related to the structural health state of the testing structure. This technique can be divided into three stages: 1. Data acquisition stage; 2. Data processing stage; 3 data communication stage.