Dissolved gas analysis (DGA) method is an essential and efficient method for incipient fault detection of an oil-immersed power transformer. Condition assessment is often conducted by using DGA fault interpretation methods, but, little consideration has been given to the measurement uncertainty of dissolved gases. This paper is focused on the analysis of current DGA interpretation methods under a condition of reasonable measurement error. The measurement error is obtained by analysis of the accuracy of IEC/CIGRE laboratories. New variants of DGA gas records are generated by using ±10% as the measurement error rate. Duval Triangle, IEC, Roger and Doemenburg methods are re-examined with the DGA original gas records and their variants for error redundancy investigation. Three specific zones of Duval Triangle are concluded for improving its reliability performance. Shortcomings of interpretation codes in IEC, Roger and Doemenburg methods, which affect the fault detection performance, are discussed.

The inverse-free extreme learning machine (ELM) algorithm proposed in [4] was based on an inverse-free algorithm to compute the regularized pseudo-inverse, which was deduced from an inverse-free recursive algorithm to update the inverse of a Hermitian matrix. Before that recursive algorithm was applied in [4], its improved version had been utilized in previous literatures [9], [10]. Accordingly from the improved recursive algorithm [9], [10], we deduce a more efficient inverse-free algorithm to update the regularized pseudo-inverse, from which we develop the proposed inverse-free ELM algorithm 1. Moreover, the proposed ELM algorithm 2 further reduces the computational complexity, which computes the output weights directly from the updated inverse, and avoids computing the regularized pseudoinverse. Lastly, instead of updating the inverse, the proposed ELM algorithm 3 updates the LDLT factor of the inverse by the inverse LDLT factorization [11], to avoid numerical instabilities after a very large number of iterations [12]. With respect to the existing ELM algorithm, the proposed ELM algorithms 1, 2 and 3 are expected to require only (8+3)/M , (8+1)/M and (8+1)/M of complexities, respectively, where M is the output node number. In the numerical experiments, the standard ELM, the existing inverse-free ELM algorithm and the proposed ELM algorithms 1, 2 and 3 achieve the same performance in regression and classification, while all the 3 proposed algorithms significantly accelerate the existing inverse-free ELM algorithm