Logarithmic decay functions describe a logarithmic decay in weights over time. The decayed weight sequence is denoted Wg_i.

wg_j=log(j,k’+1)/s

s=sum(log(j,k’+1))

Where Wg_i represents the weight sequence of Rg[-(k’+1)]_i+1, and wg_j is the j-th element of Wg_i.

The alarm intensity wn_i is obtained by summing the element-wise products of the weight sequence Wg_i and the anomaly score sequence Rg[-(k’+1)]_i+1.

wn_i=sum(Wg_i** Rg[-(k’+1)]_i+1)

SPL routine:

Cell A3 represents the logarithmic decay process;

Cell A5 calculates the weights wg_j.