Sensitivity and Convergence Behavior of Maximum Likelihood Estimation with Gamma Process Model

I have developed a MATLAB code that employs the Maximum Likelihood Estimation (MLE) technique and a Gamma process model to predict IGBT's Vce curves over time using a specific dataset (it predicts within the early cycles of the device, then repredicts with adding the data of the following cycles to emitate Online prognosis). The provided code involves data preprocessing, parameter estimation, and voltage prediction steps. However, there are two aspects that I would like to understand better in relation to this model's behavior.

1. Sensitivity to Initial Parameter Values:I'm interested in comprehending how the model's sensitivity to the initial values of parameters influences the accuracy and reliability of the voltage predictions. Specifically, I would like to explore whether variations in the initial parameter values significantly impact the predictions and if there are certain parameter combinations that lead to divergent results.
2. Convergence and Divergence Behavior:During the prediction process, I have observed a peculiar behavior where the voltage predictions tend to converge initially, then suddenly diverge, and eventually converge again. I suspect that this behavior might be influenced by specific characteristics of the dataset or the underlying gamma process model. I am seeking insights into the underlying factors causing this behavior and how it relates to the parameter optimization process.

The model leverages Maximum Likelihood Estimation to estimate the parameters of a Gamma process, which, in turn, is utilized for voltage prediction. If you have expertise in the area of Gamma processes, MLE, or IGBT's Vce prediction models, your guidance will greatly assist me in comprehending and improving the behavior of my model.

Answer 1

[arushi]

Hi Al-mu'tez billah

The behaviour of the model in the aspects can be attributed to the following factors:

1. Sensitivity to Initial Parameter Values: The maximum likelihood estimation (MLE) process often uses an iterative optimization approach. The accuracy of the predictions depends on the initial parameter values chosen. If the initial values are poorly chosen, it can cause the algorithm to converge at a local minimum or maximum instead of the desired global one. In some cases, it may even lead to completely divergent results. As a result, the model's predictions are highly influenced by the initial parameter values.
2. Convergence and Divergence Behaviour: This behaviour is commonly observed when the learning rate is set to be excessively high. A high learning rate causes a significant change in the parameter value, which can result in missing the local maximum or minimum value. Therefore, reducing the learning rate would lead to either continuous divergence or convergence, depending on the initial parameter value.

There could be other factors contributing to the model's behaviour, such as the data structure.

Could you please provide the dataset you are using for estimation and the methodology you are employing to determine the initial parameter values?