WIRELESS HEALTH MONITORING SYSTEM FOR SMART STRUCTURES USING

calculated and those in the database. Essentially a

nearest-neighbor approach, small distances between

coefficient vectors suggest very strong agreement

between two time-series models:

𝐷 = 𝑏𝑖𝐷𝐵 − 𝑏𝑖

𝑥 2𝑝

𝑖=1 (2)

The residual error of the AF model is a damage

sensitive feature, but it is also influenced by the

operational variability of the structure. To separate

changes in the residual error resulting from structural

damage and operational variability, an auto-feedback

with exogenous input (AFX) time-series model is

used to model the relationship between the AF model

residual error, 𝑟𝑘𝑥 , and the measured response, 𝑥𝑘 :

𝑥𝑘 = 𝛼𝑖𝑥𝑘−𝑖 +𝑎𝑖=1 𝛽𝑗 𝑟𝑘−𝑗

𝑥𝑏𝑗=0 + 𝜀𝑘

𝑥 (3)

Coefficients on past measurements and the residual

error of the AF model are 𝛼𝑖 and 𝛽𝑗 , respectively.

The residual of the AFX model, 𝜀𝑘𝑥 , is the damage

sensitive feature used to identify the existence of

damage regardless of the structure’s operational state.

Determination of the AF and AFX model orders (p, a,

and b) are done by exploring the autocorrelation

function of the model residual errors. The model

orders selected correspond to the autocorrelation lag

where the autocorrelation function is nearly zero.

3.2 The Two-Tiered Time-Series Damage

detection and identification Algorithm

To implement the statistical pattern recognition

approach, the structure is observed in its undamaged

state under a variety of environmental and

operational conditions in order to populate a database

of AF models of dimension p (denoted as AF (p))

paired with AFX models of dimension a and b

(denoted as AFX (a, b)). The standard deviation of

the residual error of the database AFX model 𝜎 𝜀𝐷𝐵 , is also stored. Prior to using the raw time-

history records, the mean and variance of the records

are normalized to zero and one respectively. After

measuring the response of the structure, 𝑥𝑘 , in an

unknown state (damage or undamaged), an AF(p)

model is fitted. The coefficients of the fitted AF

model are compared to the database of AF-AFX

model pairs previously calculated for the undamaged

structure. A match is determined by minimizing the

Euclidian distance, D, of the newly derived AF

model and the database AF model coefficients, 𝑏𝑖𝑥

and 𝑏𝑖𝐷𝐵 , respectively. If no structural damage is

experienced and the operational conditions of the two

models are close to one another, the selected AF

model from the database will closely approximate the

measured response. If damage has been sustained by

the structure, even the closest AF model of the

database will not approximate the measured structural

response well.

The measured response of the structure in the

unknown state, 𝑥𝑘 , and the residual error of the fitted

AF model, 𝑟𝑘𝑥 , are substituted into the database AFX

model to determine the residual error, 𝜀𝑘𝑥 , of the AFX

model:

𝑥𝑘 = 𝛼𝑖

𝐷𝐵𝑥𝑘−𝑖 +𝑎𝑖=1 𝛽𝑗

𝐷𝐵𝑟𝑘−𝑗𝑥𝑏

𝑗=0 + 𝜀𝑘𝑥 (4)

Since the residual of the AFX (a, b) model is the

damage sensitive feature in the analysis, if the

structure is in a state of damage, the statistics of the

AFX model residual, 𝜀𝑘𝑥

will vary from that of the

AFX model corresponding to the undamaged

structure. It has been shown that damage can be

identified when the ratio of the standard deviation, 𝜎,

of the model residuals exceeds a threshold value

established from good engineering judgment [2] as

shown in Eq. (5).

𝜎 𝜀𝑥

𝜎 𝜀𝐷𝐵 ≥ ℎ. (5)

Establishing a threshold, h , that minimizes the

number of false-positive and false-negative

identifications of damage is necessary for robust

damage detection and identification.

3.3 Implementation of Auto-feedback Time Series

Modeling

The wireless sensing units can individually perform

most of the computations associated with the

statistical pattern recognition algorithms. The role of

the unit is well defined with the responsibility of

recording the structural response, normalizing the

response, and fitting AF models to the measurements.

After the AF model is fit, the model’s coefficients

would be wirelessly communicated to a centralized

data server housing a database populated by AF-AFX

model pairs. Once a model match is made, the

coefficients of the AFX model are transmitted to the

wireless sensing unit where the standard deviation of

the AFX model is calculated. The ratio of standard

deviations of AFX model errors shown in Equation

(5) is calculated and compared to a previously

established threshold. A software module is written

for the wireless sensing units embedded application

layer that determines the coefficients of an AF(p)

model based on a segment of the recorded data.

Multiplying both sides of Eq. (1) by the current

A Nagaraju et al,Int.J.Comp.Tech.Appl,Vol 2 (6), 4021-4027

IJCTA | NOV-DEC 2011 Available [email protected]

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ISSN:2229-6093