2.2.2. Displacements

Generally, the methods that can be applied on accelerations can also be applied to displacement [117]. However, the displacement is usually not directly measured during monitoring [118]. In principle, acceleration measurement can be doubly integrated to give displacement, but this process is notoriously error-prone due to unknown initial conditions such as integration constants and low frequency noise of measurement that is amplified in an inverse square manner. In reality, the displacement at the measured location can only be recovered from field measured acceleration in an approximate sense, depending on the frequency characteristics of the contributing activities.

In the SHM system, one strategy to resolve the issue of unknown initial conditions makes use of the basic fact in structural dynamics that initial condition effects decay exponentially with time. Thus, one can start the numerical integration process before the main event to be captured, so as to allow a 'burn-in' time for the (unknown) initial condition effect to die down to negligible level during the main event that matters. On the other hand, the presence of noise especially in the low frequency regime presents a major difficulty. In addition to amplification of low frequency noise during numerical integration, data acquisition hardware typically has 'pink' noise in the low frequencies, i.e., with PSD inversely proportional to frequency. Integrating the 'raw' measured acceleration will often lead to significant systematic over-estimation of displacement, in many cases a 'flying off' trace of time history. In particular, a constant error in the acceleration gives a linear trend in the velocity and a quadratic trend in the displacement. One basic strategy is to suppress the noise by a causal filter with parameters designed to significantly attenuate the frequency

components in the data below and above specified cut-off frequencies. Acceleration data is filtered before numerically integrated to give velocity data, which is filtered again and then integrated to give displacement data. Filtering produces distortion in the acceleration data and hence the integrated displacement. This will need to be controlled and verified in the development of SHM system.

### *2.3. Time-Frequency Domain Methods for Vibration-Based SHM*

In addition to time domain and frequency domain dynamic properties, the properties in both time domain and frequency domain can also be used for SHM due to the development of advanced time-frequency analysis. Compared to time domain and frequency domain methods, the amount of time-frequency domain methods is much fewer. The time-frequency domain methods are more powerful because it contains the information of stable frequency domain properties and can further show the change with time. However, it is admitted that they require a lot of calculation resources and space for data storage.

Short time Fourier Transform, Wavelet Transform [119], and Hilbert-Huang Transform [120] including empirical mode decomposition are the most widely used timefrequency analysis methods. Usually, only the measured accelerations or dynamic strains are required for these methods, and the high frequency components may change significantly once the local damage occurs. Therefore, it is not necessary for these methods to construct the undamaged model for the monitored structure. This is a very attractive advantage of these methods; however, it is noteworthy that the time-frequency methods can only locate the local damages but cannot evaluate the severity of local damages. Further investigations of applying time-frequency domain methods on real structures are expected in the near future.

### **3. Current Technical Codes Related to Vibration-Based Structural Health Monitoring**

In this section, the current technical standards and codes related to vibration-based structural health monitoring are reviewed, including both ISO standards and national codes.

ISO has four technical committees related to building and construction: TC 59 (Committee on Architecture and Civil Engineering), TC 98 (Committee on Fundamentals of Structural Design), TC135 (Committee on Nondestructive Testing), and TC268 (Committee on Urban and Community Sustainable Development). TC 59 including its SCs has published 124 ISO standards of which 33 under the direct responsibility of ISO/TC 59 (Table 1), TC 98 including its SCs has published 23 ISO standards (Table 2), TC 135 including its SCs has published 97 ISO standards of which 1 under the direct responsibility of ISO/TC 135 (Table 3), and TC 268 (including its SCs) has published 26 ISO standards of which 10 under the direct responsibility of ISO/TC 268 (Table 4). The ISO standards published by ISO/TC135 are all about non-destructive testing, including detailed procedures of different non-destructive testing methods. They are not reviewed herein since they are more relevant to damage detection rather than SHM system.

In fact, the codes published by ISO TC 59 do not only specify the general principles to determine requirements of structural performance, but also provides a general approach to assess the structural safety based on structural performance. They are a very important framework of a SHM system, but they lack details on how to implement in real engineering projects. The standards published by ISO TC 98 focus more on reliability and show the requirements and procedures to assess structure health condition based on structural reliability. They also provide approaches and procedures to prepare national and organization codes. However, structural reliability is more abstract, and it contains more complicated mathematical models, which is difficult to be applied in real SHM projects. The regulations published by ISO TC 268 focus on smart building and sustainable development. They provide the foundation on how to construct smart community infrastructures. Of course, the SHM system is helpful to construct smart community infrastructures and maintain sustainable development. Therefore, they provide the future work scope for current SHM systems, but they lack more details on how to construct a SHM system for an existing building.


### **Table 1.** Published ISO standards by TC 59's SCs.

### **Table 2.** Published ISO standards by TC 98's SCs.


### **Table 3.** Published ISO standards by TC 135's SCs.


