Performance Prediction for Steel Bridges Using SHM Data and Bayesian Dynamic Regression Linear Model: A Novel Approach

Data Availability Statement

Acknowledgments

Notation

A_t

gain coefficient;

B_t

dynamic early warning threshold;

C_t

process error variance of θ_t;

D_t

information set before and at time t;

d_t/2

scale parameter;

e_t

prediction error at time t;

f_t

prediction value at time t;

m_t

point estimation of θ_t;

N(·)

normal probability density function;

n_t/2

shape parameter;

p(·)

probability density function;

Q_t

prediction error variance;

R

steel yield strength;

R_t

prior estimation of state error variance;

R(X)

structure reactance function;

S_M

extreme stresses monitored or predicted with time;

S_t

estimation of monitoring error variance;

S(X)

monitoring load effect function;

T(·)

probability distribution function of T-distribution;

V_t

monitored error variance;

v_t

monitored noise;

W_t

state vector variance;

w_t

state error;

X

various random variables that affect the structure reactance;

Y_t = [y_t−1, y_t−2, …, y_t−n]

monitoring vector at time t;

${\overline{Y}}_t$

mean value of Y_t;

y_t

monitoring data at time t;

Z(X)

function of structural performance;

α_t

state transition coefficient;

β

reliability;

${\epsilon }_t$

estimation error;

∂

partial derivative;

$\sum$

summation;

θ_t

state variable;

ϕ_t

monitoring precision;

δ

discount factor;

Γ(·)

gamma distribution function;

μ_t

mean value derived from the monitored data up to time t−1 and the latest predicted data at time t;

σ_t

standard deviation derived from the monitored data up to time t−1 and the latest predicted data at time t;

μ_R

mean resistance;

σ_R

resistance standard deviation;

μ_S

mean load effect;

σ_S

load effect standard deviation;

γ_M

sensor error coefficient;

μ_M

mean of S_M; and

σ_M

standard deviation of S_M.

References