## ABSTRACT

Structural Health Monitoring (SHM) using wireless sensor networks involves deployment of various sensors like accelerometers in the area to be monitored. This project deals with various methods used for monitoring health of civil structures and detection and localization of damage using frequency and modal analysis techniques. We have primarily focused on processing of accelerometer data using time-frequency analysis tools. One of the most effective methods for time-frequency analysis of low frequency, non-stationary signals, as is the case with SHM, is discrete wavelet transform. In this project we have implemented the mallat algorithm of DWT by writing a program in C, furthermore, we have also developed a GUI for the above mentioned algorithm in Python and implemented it with results in both numerical and graphical form for better understanding.

Key Words: Smart wireless sensor, wireless sensor network, structural health monitoring, modal identification, damage detection, wavelet transform, discrete wavelet transform, Mallat algorithm

## 1. INTRODUCTION

Structural health monitoring is estimating the state of structural health, or detecting the changes in structure that affect its performance. Two major factors are time-scale of change and severity of change. Time-scale is how quickly the change occurs, and severity is the degree of change. Two major categories of SHM are disaster response (earthquake, explosion, etc.) and continuous health monitoring (ambient vibrations, wind, etc.).

Using traditionally wired sensors to implement such a SHM system with a dense array of sensors is quite challenging because of the difficulties in deploying and maintaining the associated wiring. Recent development of smart sensors has created the possibility of dense array of sensors in SHM. Damage detection algorithms which can take advantage of the distributed computing environment offered by smart sensor technology are highly desired but currently limited. Dense arrays of low-cost smart wireless sensor networks (WSNs) have the potential to improve the quality of the SHM dramatically using their on-board

Computational and wireless communication capabilities. These WSNs provide rich information which SHM algorithms can utilize to detect, locate and assess structural damage caused by severe loading events and by progressive environmental deterioration as well as economical realization of the SHM system. Information from densely instrumented structures is expected to result in deeper insight into the physical state of the structural system.

## 2. SHM using WSN

- Monitoring systems have the potential to facilitate the more economical management and maintenance of modern infrastructure.
- Main steps in SHM:Damage detection and localisation

Quantification of severity of damage

Prediction of remaining life of structure - Vibration based condition monitoring of structures contains several techniques :

### 2.1 Natural frequency based method

The basic idea behind this approach is that modal parameters i.e. natural frequency, mode shape and modal dampings are functions of physical properties of structures namely mass, damping and stiffness. Therefore, any change in the physical properties will cause detectable changes in the modal parameters. Since the measuring of natural frequency is easier than that of change in structural damping, change can be detected from dynamic analysis using natural frequency and mode shapes. However, there is some debate on whether the use of modal parameters is significant enough to be a good indicator of damage or deterioration. From previous studies, it is observed that the effect on natural frequency when damage occurs in a structure is often of relatively low sensitivity. The low sensitivity of frequency shifts to damage requires either very precise measurements or large levels of damage. The alternative to using natural frequency as damage identification is by using mode shape, with the use of Modal Assurance Criteria MAC to determine the level of correlation between modes from the control beam and those from the damaged beam. Only one accelerometer sensor is required here. The measurement of one pair of frequencies will yield a locus of possible damage sites. The loci for several pairs of modes may be superimposed, the actual damage site being given by the intersection of the curves. But only accurate for laboratory scale beam like structures.

### 2.2 Mode Shape based method

This method requires either a single excitation point and many sensors or a roving exciter with one or more fixed sensors. Two commonly used methods to compare two sets of mode shapes are the Modal Assurance Criterion, MAC and the Coordinate Modal Assurance Criterion, COMAC

The different kinds of sensors being used these days for SHM are: Accelerometers, GPS (accurate to millimeters), Pressure sensors. For vibration based SHM we will be using accelerometers.

## 3. Use of Combined Parameter Index (CPI)

Combined Parameters Index (or CPI), is the stiffness percentage ratio of the damaged case to the control case. CPI eliminates all the positive values of this ratio and will average out the negative values for each mode. Damage severity and localization is a function of natural frequency and modal shape.

**Combined Parameter Index (CPI)**

CPI index is a parameter used for detecting damage severity and localization of the same.

Frequency reduction index (FRI) and Mode shape reduction index (MSRI) are also used to do the same job as CPI.

But CPI shows more sensitivity to damage severity and localization than FRI and MSRI.

CPI sensitivity increases when the damage is located elsewhere than mid-span.

For the CPI the fourth mode has the highest sensitivity.

MSRI is the least sensitive at all damage levels

## 4. Objectives of Structural Health Monitoring

1) Detecting the existence of the damage on the infrastructure and Locating the damage

2) Identifying the types of damage

3) Quantifying the severity of the damage .

## 5. Methods involved

### Time-Frequency Feature Extraction Methods

#### 5.1 Short Time Fourier Transform

Short-Time Fourier transform (STFT) is the method that represents the signal in both time and frequency domains. This property facilitates detection of anomalies by tracking the phase changes over time.

Time-frequency representation by STFT is performed by a discrete Fast Fourier Transform (FFT) algorithm in a sliding window. Each new sliding window overlaps with a previous window in order to reduce the boundary effects. STFT coefficients have a time delay at each frequency.

Limitations:

Many signals require a more flexible approach – vary the window size to determine more accurately either time or frequency. Use of narrower windows at high frequencies for better time resolution and use of wider windows at low frequencies for better frequency resolution is required. But STFT uses windows of fixed size.

#### 5.2 Wavelet Analysis

The present resolution problem of the STFT is eliminated by using a variable length window in Wavelet transform. Wavelet analysis is capable of utilizing long time intervals (large window) where precise low frequency information is needed, and short time intervals (small window) where high frequency information is considered.

### 5.3 Maximum Overlap Discrete Wavelet Transform (MODWT)

MODWT is a computationally efficient method for time-frequency representation of time series. The MODWT transform is similar to the discrete wavelet transform (DWT), but it does not produce a down sampling of wavelet coefficients, which allows it to overcome the lack of translation- invariance present in DWT and does not require the length of the signal to be a power of two. In contrast to CWT, MODWT calculates coefficients at scales 2j (where j is a level of transform) without the loss of information. This property provides faster computation of MODWT coefficients than CWT computation.

## 6. Real time analysis of signals from sensor

### 6.1 Introduction

- Continuous-time periodic signal can be represented by a Fourier series corresponding to a sum of harmonically related complex exponential signal.
- As the time period of a periodic signal is increased infinitely so that signal becomes aperiodic, the coefficient function is known as Continuous time Fourier transforms.
- In practical application, signals processed by computer has two main characteristics :- Discrete nature and finite lengthSo the idea is to expand finite-length sequence to periodic sequence, compute its Discrete Fourier Series, so that we can get the discrete spectrum in frequency domain.

This is known as Discrete Fourier transform. We cannot localize time with help of this so we use some other methods such as STFT, CTWT and DWT so that we can have time as well as frequency resolution.

### Limitations of Fourier Analysis

(1) Cannot not provide simultaneous time and frequency localization, (2) Not useful for analyzing time-variant, non-stationary signals (time-varying spectra). (3) Not efficient for representing discontinuities or sharp corners (i.e.,requires a large number of Fourier components to represent discontinuities).

### Drawbacks of STFT

Time/Frequency localization depends on window size.

Once you choose a particular window size, it will be the same for all frequencies.

Many signals require a more flexible approach – vary the window size

to determine more accurately either time or frequency.

### Properties of Wavelets

- Simultaneous localization in time and scale

– The location of the wavelet allowsto explicitly representing the location of events in time.

– The shape of the wavelet allows representing different detail or resolution - Sparsity: for functions typically found in practice, many of the coefficients in a wavelet representation are either zero or very small.
- Linear-time complexity: many wavelet transformations can be accomplished in O(N) time.
- Adaptability: wavelets can be adapted to represent a wide variety of functions (e.g., functions with discontinuities, functions defined on bounded domains etc.). Well suited to problems involving images, open or closed curves, and surfaces of just about any variety. Can represent functions with discontinuities or corners more efficiently (i.e., some have sharp corners themselves).

### Discrete wavelet transform (DWT)

- DWT is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: it captures both frequency and location information (location in time).
- Applications: -The discrete wavelet transform has a huge number of applications in science, engineering, mathematics and computer science. Most notably, it is used for signal coding, to represent a discrete signal in a more redundant form, often as a preconditioning for data compression. Practical applications can also be found in signal processing of accelerations for gait analysis, in digital communications and many others.

One level of the transform

The DWT of a signal x is calculated by passing it through a series of filters. First the samples are passed through a low pass filter with impulse response g resulting in a convolution of the two:

[]=[]∗[]= ∑ [][−]

The signal is also decomposed simultaneously using a high-pass filter h. The outputs giving the detail coefficients (from the high-pass filter) and approximation coefficients (from the low-pass). It is important that the two filters are related to each other and they are known as a quadrature mirror filter.

However, since half the frequencies of the signal have now been removed, half the samples can be discarded according to Nyquist’s rule. The filter outputs are then sub sampled by 2 (Mallat’s and the common notation is the opposite, g- high pass and h- low pass)

This decomposition has halved the time resolution since only half of each filter output characterizes the signal. However, each output has half the frequency band of the input so the frequency resolution has been doubled.

### Cascading and Filter banks

This decomposition is repeated to further increase the frequency resolution and the approximation coefficients decomposed with high and low pass filters and then down-sampled. This is represented as a binary tree with nodes representing a sub-space with different time-frequency localization. The tree is known as a filter bank.

At each level the signal is decomposed into low and high frequencies. Due to the decomposition process the input signal must be a multiple of where is the number of levels.

### DWT Procedure

- An appropriate mother wavelet function and corresponding scaling is first chosen.
- The original signal x[n] is windowed and 2j samples of the same are passed through a half band high pass filter g[n] and a low pass filter h[n] derived from the chosen scaling function.
- Low pass filters are associated with the scaling function and provide approximation.
- High pass filters are associated with the wavelet function and provide detail coefficients.
- Convolve the input with the low pass filter and down sample by 2 to get the approx. vector.
- Convolve the input with the high pass and down sample by 2 to get the detail vector.
- High pass filter provides coefficients of discrete wavelet transform at the corresponding level.
- Larger the number of levels used greater is the frequency resolution and lesser is the time resolution.
- Set the input = approx, and repeat for number of times to get desired decomposition level.

10. Using DWT we get higher frequency resolution for lower frequencies and higher time resolution for higher frequencies.

11. The maximum frequency that can be detected by DWT algorithm is equal to half of the sampling frequency.

## Conclusion

The entire project was focused on signal processing of typical sensors like accelerometers so that exact frequency content of the signal could be known. Once the frequency composition and corresponding time information is extracted from the signal, different analysis techniques available in civil engineering literature can then be applied so that the damage intensity and location could be accurately detected, which is in fact, the main objective of structural health monitoring(SHM).

## References

[1] Combined modal parameters-based indexfor damage identification in a beamlike structure: theoretical development and verification M.M. Fayyadh, H. A. Razak, Z. Ismail

[2]Wireless sensors for structural health monitoring and damage detection techniques B. Arun Sundaram, K. Ravisankar, R. Senthil and S. Parivallal

[3]Detection of damage location using mode shape deviation: Numerical study Moatasem M. Fayyadh and H. Abdul.

[4]Time-Frequency Analysis-Concepts and Methods by Franz Hlawatsch François Auger

[5]Wavelet Transform for Structural Health Monitoring: A Compendium of Uses and Features M. M. Reda Taha, A. Noureldin, J. L. Lucero and T. J. Baca4