When I am trying to fit my data with the prony series equation (using SOLVER), the value of g_i comes to be greater than 1. Can any one give a rough idea of the values of g_i and t_i for bitumen (VG 10/VG 30)?
you can refer to a PhD thesis by M.F. Woldekidan from TUDelft. In his dissertation he detailed how to calculate prony series parameters by using master curve data in frequency domain.
you can refer to a PhD thesis by M.F. Woldekidan from TUDelft. In his dissertation he detailed how to calculate prony series parameters by using master curve data in frequency domain.
you can refer to a PhD thesis by M.F. Woldekidan from TUDelft. In his dissertation he detailed how to calculate prony series parameters by using master curve data in frequency domain.
Hi Nikhil,
For adequate Prony series fitting, you may want to read more about the importance of presmoothing of raw data before fitting.
Also instead of just trying to use solver to fit the data based on sum square error minimization, you may need also to read about collocation method, Schapery (1961) used the collocation method Prony series model to experimental data.
Some details can be found in the following book: Kim, Y. R. (2008). "Modeling of asphalt concrete", Chapter 6.
Please let me know if you need more details or references.
Best regards,
Michael
Hi Pramod,
You can see the following link.
https://polymerfem.com/polymer_files/Prony_Series_Conversion.pdf
This requires optimization, for minimizing the error between measured and modeled data. Now, it is important that the initial seeding values be chosen appropriately.
I hope this will help. Let me now if you find any difficulty.
Hello Dear,
First, you have to determine your shifting method, and build your Excel sheet with an appropriate manner. Then, using the solver add in in Excel software you must minimize the Sum of Errors by changing the constant of your shifting method and the Prony series coefficients simultaneously.You must repeat the optimization process by running the solver function until there is no other decrease in the Sum of Errors value.Now, your shift factors as well as the Prony series coefficients have been solved and finalized for the selected reference temperature/frequency.
For more details you can refer to my article https://www.researchgate.net/publication/316362425_Hot_mix_asphalt_time-temperature_shifting_and_fitting_techniques_A_comparative_study?_iepl%5BviewId%5D=nREOFPl9lWaWVbKk3tX8du7gZ0xcy0I7adOH&_iepl%5Bcontexts%5D%5B0%5D=prfhpi&_iepl%5Bdata%5D%5BstandardItemCount%5D=2&_iepl%5Bdata%5D%5BuserSelectedItemCount%5D=0&_iepl%5Bdata%5D%5BtopHighlightCount%5D=1&_iepl%5Bdata%5D%5BstandardItemIndex%5D=1&_iepl%5Bdata%5D%5BstandardItem1of2%5D=1&_iepl%5BtargetEntityId%5D=PB%3A316362425&_iepl%5BinteractionType%5D=publicationTitle.
You can also refer to an article which i highly recommended
https://www.researchgate.net/publication/277174248_An_investigation_of_different_fitting_functions_to_accurately_model_the_compressive_relaxation_modulus_master_curve_of_asphalt_mixes?_iepl%5BviewId%5D=JZrqujpgmAweZH9keMqgO3jqDFv1xqUQfCa3&_iepl%5Bcontexts%5D%5B0%5D=prfhpi&_iepl%5Bdata%5D%5BstandardItemCount%5D=3&_iepl%5Bdata%5D%5BuserSelectedItemCount%5D=0&_iepl%5Bdata%5D%5BtopHighlightCount%5D=1&_iepl%5Bdata%5D%5BstandardItemIndex%5D=3&_iepl%5Bdata%5D%5BstandardItem3of3%5D=1&_iepl%5BtargetEntityId%5D=PB%3A277174248&_iepl%5BinteractionType%5D=publicationTitle
Article An investigation of different fitting functions to accuratel...
Article Hot mix asphalt time-temperature shifting and fitting techni...
- Badges
- Science topic