This SERDP Exploratory Development (SEED) Project focused on extending the applicability of a developed structural fault monitoring technique (laser-measured surface vibration) to the structural elements and systems of historic buildings. The Department of Defense (DoD) controls an estimated 90,000 buildings and structures that are eligible for National Register of Historic Places (NRHP) evaluation. Rehabilitation of buildings and structures is one approach federal agencies can take, when appropriate, to mitigate those federal historic properties that are found to be historically significant, as defined by the NRHP evaluation process. Prior to initiating a rehabilitation project, project managers undertake a study to determine the conditions of the various buildings, features, and systems, including heating, plumbing, and structural elements. Developing a toolkit of nondestructive methods to “look behind the walls” of historic and under-documented structures can provide necessary data to make real-time decisions for cost effective management options related to DoD evaluation of historic buildings and structures.

The objectives of this project were to:

1. Extend the structural acoustic/scanning laser Doppler vibrometer (SLDV)/inversion technique to historic buildings and structures by developing advanced inversion algorithms.
2. Assess the efficacy of applying these new techniques to various parts of a building fabric or structure (including those fabricated from concrete, brick, masonry, iron, steel, wood, etc.).
3. Demonstrate proof of concept in the laboratory.

In this vibration monitoring/structural acoustics-based approach, the dynamic surface displacements of a structure caused by weak externally produced forces (acoustic speakers or shakers) are spatially and spectrally mapped with an SLDV.  A number of inversion algorithms invert these spatial vibration scans into various material parameter maps that serve to locate subsurface faults.

In determining the feasibility for extending the SLDV/inversion approach augmented with new developments to various parts of a building fabric and structure, researchers conducted a study using a numerically generated vibration database in conjunction with finite element-based structural acoustic codes. The finite element-based structural acoustic codes were previously developed in other programs. The isotropic structures for which numerical data were generated included: (1) thin plates of plaster, steel, and concrete; (2) thick plates of plaster and steel wherein flaws at three depths could be studied; and (3) a slab of wood with internal flaws. The first two case studies were successfully handled using the isotropic flexural wave inversion algorithms. The third case study involving wood was inherently more complex given that the material was orthotropic in nature.

Current algorithms that invert measured vibration maps into internal elastic parameters require knowledge of the equations of motion appropriate for the structure under study, thereby restricting their areas of application. Using extensive experience in the development of inversion algorithms, this project addressed the development of novel training algorithms for fault detection that do not depend on a-priori knowledge of the structural equations of motion or the related parameters.

In one such adaptive approach, this project explored the idea of cascading various algorithms. One promising approach applied to thick plate structures used the flexural inversion operator appropriate to thin plates. The effective stiffness parameters so obtained were then inserted into the generalized force equation method that locates regions with non-zero forces and identifies those as faults. This adaptive approach was shown to be successful.

In a second approach, this study defined a set of differential equations that have arbitrary coefficients that multiply sets of spatial and temporal derivatives of the measured displacements. In this formulation, the equations appear as homogeneous sets of partial differential equations whose coefficients are generally unknown, yet which can be trained for any particular structure. Therefore, given a sufficient number of measurements on a control section, the coefficients can be determined, thereby training the algorithm to detect fluctuations due to material parameter or structural differences. As with previous inversion techniques, the trained algorithm also provided local properties thus providing locations of any faults. Furthermore, validation criteria were explored for this adaptive coefficient approach based on a reading of the minimum variance normalized by the mean square value demonstrated by the associated coefficients.

This research improved the toolkit of non-invasive, non-destructive methods for effectively and efficiently assessing the structural condition and integrity of the fabric of historic buildings and structures, resulting in enhanced DoD cultural resources management capacities and a more streamlined approach to account for National Historic Preservation Act requirements. The developed fault monitoring technique is able to “look behind the walls” by converting readily obtained surface vibration maps into detailed descriptions concerning the underlying structure.