A Deflection-Based Bridge Diagnosis Method

Algorithm 1

BUILD_DC.

INPUT: 𝑉: the set of all deflection checkpoints on a bridge;

𝐻: a set of deflection data acquired in the infancy of the bridge;

     𝛼,𝛽∶0≤𝛼,𝛽<1,

OUTPUT: 𝐺=(𝑉,𝐸,label): an (𝛼,𝛽)-DC graph of the bridge.

   {

( 1) initially, 𝐸 is empty;

( 2) choose a real number 𝜀, 0<𝜀<1;

   /^∗ the meaning of 𝜀 is clear according to statement 8; ∗

( 3) choose two integers 𝑟 and 𝑙;

   /^∗ the meanings of 𝑟 and 𝑙 are clear according to statements 5-6; ∗

(4) for every pair of checkpoints, 𝑃 and 𝑄,

   {

/^∗ sentences 5-6 calculate 𝑟 sample correlated coefficients between 𝑃 and 𝑄; ∗

(5) randomly select 𝑟 pairs of length-𝑙 sequences from 𝐻, one for 𝑃, and the other for 𝑄;

(6) for each pair of selected sequences, calculate a sample correlated coefficient;

   /^∗ sentence 7 gets an initial estimate of 𝐼_𝐻,𝛼(𝑃,𝑄); ∗

(7) find the smallest interval [𝑎,𝑏] so that the 𝑟 sample correlated coefficients obtained

     previously fall in it with frequency ≥𝛼;

   /^∗ sentence 8 gets a final estimate of 𝐼_𝐻,𝛼(𝑃,𝑄) by eliminating the randomness of the

     initial estimate; ∗

(8)  𝑎←𝑎−𝜀; 𝑏←𝑏+𝜀;

     /^∗ sentence 9 adds a legal edge in 𝐸; ∗

(9) if 1−(1/2)(𝑏−𝑎)≥1−𝛽, then add in 𝐸 the edge {𝑃,𝑄} with label [𝑎,𝑏];

   }

}