*2.2. Proposed Feedforward Artificial Neural Network*

Two computational schemes based on FFANN were designed to estimate the residual lifespan of oil-submerged transformers. The first model was based on predicting the DP when only the 2-furaldehyde (2FAL) concentration measured from the oil samples is available for new and existing transformers. The second FFANN model proposed was based on predicting the transformer LOL when the 2FAL and DP are available to the utility owner, typically for the transformer operating at a site where un-tanking the unit will be a daunting and unfeasible task.

The choice of inputs, outputs, and network structure in the FFANN prototype is dependent on the efficiency of the FFANN models. The measurements for the gas concentrations concerning the emerging transformer faults were gathered from the real data of a power transformer. In this work, the development of an FFANN was split into four phases: data gathering and processing, FFANN modeling, training, and testing.

#### 2.2.1. Data Gathering and Processing

In the data gathering and processing stage, various transformers from 315 kVA to about 40 MVA 132 kV were considered in the study. These units had been removed from service and were processed in a workshop to diagnose their conditions. The oil sample of individual units was analyzed in the laboratory to attain the 2FAL concentration existing in the oil sample. Concurrently, the sample of the solid insulation material was extracted and analyzed in the laboratory to attain the degree of polymerization. For the respective unit, the lifetime of the unit in-service was collected from the original equipment manufacturer. It follows that the data were divided into two datasets: one contained the measured DP and the measured 2FAL, and in the other dataset, a dataset with column vectors comprising the DP, 2FAL and LOL of the unit was assembled. It should be noted that the LOL is essentially the remnant life of the unit (i.e., the designed services life of the unit minus the lifetime in operation). In processing the datasets, the inputs as well as target data are determined and fed into the ANN matrix for training and validation. In the first model, the 2FAL was specified to be the input, whereas the corresponding DP was specified as the target. In the second proposed model, the transformer remnant life was defined as the target response whereas the available DP and 2FAL dataset were utilized as the inputs. These datasets were classified into three categories: learning, verification, and evaluation. The learning sample comprised 70% of the entire dataset, with the remaining 30% used for verification and evaluation.

#### 2.2.2. ANN Models

In this work, the MATLAB/SIMULINK tool was utilized to execute two ANN models. To identify the optimal ANN model, the learning or training rate (LR) and momentum cost (MC) was changed between 0 to 0.9. However, since all variables were altered iteratively, underfitting as well as overfitting systems remained possible. Overfitting happens whenever a system is proficient in memorizing the system but is unable to extrapolate new input for the system. The early halting approach has been used to achieve an optimized performance to address the overfitting challenge. The termination criteria were obtained by evaluating the mean square error of the learning data during training using data that are limited in size.
