What is model free Numerical Optimization method?
Numerical optimization method is the model free method using non-linear least square optimization. It is created by Kinetics Neo Team in NETZSCH and implemented only in Kinetics Neo software.
Numerical method searches optimal functions Ea(alpha) and logA(alpha) in order to get best fit for the conversion (T,t). Numerical method is based on the results of the analytical Friedman method. The results of Friedman Method (curves E(α) and A(α) ) then optimized numerically in order to achieve the better fit between experimental and simulated curves. Calculation of LogA is done for the first order reaction f(alpha)=1-alpha.
The function for optimization is the sum of squares of deviations between measured value Conversion_experimental(T,t) and simulated value Conversion_simulated(T,t). This sum is calculated over all curves and over all points in each curve.
Our numerical method searches numerically values Ea(alpha) and LogA(alpha) which minimize the optimization function. Internally each point of curves E(α) and A(α) is a subject of small changes, and for each change the sum of the squares of residuals is checked: is it better or worse than before. If better then new point in E(α) or A(α) is saved. The iterations are repeated until no any numerical improvements happens.