A Numerical Comparison between Preisach, J-A and D-D-D Hysteresis Models in Computational Electromagnetics
Round 1
Reviewer 1 Report
This work presents a numerical analysis of 3 magnetic models. The introduction is interesting, and the paper is well-written. The description of the three modeling approach is quite short and poorly connects the modeling parameter to the physical aspects. In addition, the presentation of the modeling is reduced to B(H) approach. It doesn’t detail the capacity of these modeling to describe magnetostriction as well as the effects induced by stress or plastic strain.
The results are strongly dependent on the identification procedure. The curve fitting method used to identify model parameters has to be detailed and improved. For example, the parameter Ms of JA model is the saturation parameter that is physically understood. Figures 1c and 1d clearly show that the identification of this parameter is unsuitable because the saturation level of B is overestimated (about two times the correct value). In the same manner, Ms is a material parameter that doesn’t change when considering minor or major loops. Its value cannot change between fig1a and figb for curve-fitting reasons. The physic behind the modeling approach seems to be not understood. This way, the numerical results presented seem to be reduced to a fitting curve problem that is poorly resolved for the JA and the CPM.
A discussion about the meaning of each constant and the procedure used to determine them inside the various model has to be added. In addition, an identification time of these constants will help to compare the three modeling approaches.
Author Response
R: This work presents a numerical analysis of 3 magnetic models. The introduction is interesting, and the paper is well-written. The description of the three modeling approach is quite short and poorly connects the modeling parameter to the physical aspects. In addition, the presentation of the modeling is reduced to B(H) approach. It doesn’t detail the capacity of these modeling to describe magnetostriction as well as the effects induced by stress or plastic strain.
A: Since this manuscript (ms) is a short communication, we decided to show only the main equations with a brief explanation of the 3 models, as detailed descriptions of these models can be found in the mentioned references. However, a connection of the modelling parameters to the physical aspects has been now included also for the CPM and J-A models. The only B(H) approach has been adopted because the focus of the ms is only to magnetic materials.
R: The results are strongly dependent on the identification procedure. The curve fitting method used to identify model parameters has to be detailed and improved. For example, the parameter Ms of JA model is the saturation parameter that is physically understood. Figures 1c and 1d clearly show that the identification of this parameter is unsuitable because the saturation level of B is overestimated (about two times the correct value). In the same manner, Ms is a material parameter that doesn’t change when considering minor or major loops. Its value cannot change between fig1a and figb for curve-fitting reasons. The physic behind the modeling approach seems to be not understood. This way, the numerical results presented seem to be reduced to a fitting curve problem that is poorly resolved for the JA and the CPM.
A: The authors are grateful to the Reviewer for his comment. Indeed, we exchanged M with B for the J-A of the Neodymium material and Figs. 1c and 1d and Tables 1 and 2 have been updated. Regarding Figs. 1a and 1b, we considered the Fe-Si minor loops 2 and 6 as major loops, since our goal was to find challenging hysteresis shapes rather than physical meaning for testing the 3 models. This point has been added in Sec. 2.1.
R: A discussion about the meaning of each constant and the procedure used to determine them inside the various model has to be added. In addition, an identification time of these constants will help to compare the three modeling approaches.
A: As stated in the previous comments, we have included now the meaning of each constant and the procedure used to determine them inside the various models. However, we preferred to keep them out from the computational time comparison, as the specific identification method could affect the results (accuracy and time) and we did not optimize them, but rather used open sources codes. Our goal was indeed to point out the simplicity and efficiency of the proposed D-D-D method, not provide an exercise of curve fitting optimization. For these reasons, we didn’t even implement an identification procedure for our method. This aspect has been remarked in the revised discussions.
Reviewer 2 Report
Title: A Numerical Comparison between Preisach, J-A and D-D-D Hysteresis Models in Computational Electromagnetics
Journal: Applied Sciences
ID: applsci-2219281-peer-review-v1
Suggestions for Revision:
The authors have compared three models of hysteresis for magnetic materials including soft as well as hard magnetic phases. The authors have provided the sufficient background and well explained the models that they have selected for comparison in this work. The manuscript is well written. However, there are few minor suggestions that may be considered to improve the quality of the manuscript:
1. The authors should explain the changes that they have made in equation (4) with respect to the equation (1) of ref [34].
2. Line 143: “As can be observed, the CPM and D-D-D models can fit well all the shapes of hysteresis loops, whereas the J-A model is not able to fit semi-hard and hard materials”. It will be better if the authors can provide a possible reason for this.
3. In Table 1, huge difference in the values of parameters of FeSi loop2 and loop6, fitted with D-D-D model are observed, although D-D-D model fits all the loops well. Authors should explain possible reason for this.
4. In Table 1, “1.2131e6” format should be same as other values. (1.2131∙106)
5. Line 172: “On overall, the proposed D-D-D model shows good accuracy for all materials with the best Pearson correlation coefficients (except NdFeB at 80 °C)”. On the contrary, from Table 2, the value of Pearson correlation coefficients seems best for NdFeB at 80 °C. So, as per the Line 167: “The value range of r2 is [0, 1], and the closer to 1, the more accurate the fitting is.”, NdFeB at 80 °C should also be with good accuracy.
Comments for author File: 
Comments.docx
Author Response
The authors have compared three models of hysteresis for magnetic materials including soft as well as hard magnetic phases. The authors have provided the sufficient background and well explained the models that they have selected for comparison in this work. The manuscript is well written. However, there are few minor suggestions that may be considered to improve the quality of the manuscript:
- The authors should explain the changes that they have made in equation (4) with respect to the equation (1) of ref [34].
We made no substantial changes respect to eq. (1) of ref. [34] of the previously submitted ms (the only delta symbol was replaced by the function sign() to minimize the text explanation). However, since we caught a mistake in such equation (i.e., the vacuum permeability not to be there), we preferred to update ref. [34] with the paper we referred to for the mathematical and numerical implementation (matlab code) of the J-A model.
- Line 143: “As can be observed, the CPM and D-D-D models can fit well all the shapes of hysteresis loops, whereas the J-A model is not able to fit semi-hard and hard materials”. It will be better if the authors can provide a possible reason for this.
A possible reason for this point has been provided in the revised ms.
- In Table 1, huge difference in the values of parameters of FeSi loop2 and loop6, fitted with D-D-D model are observed, although D-D-D model fits all the loops well. Authors should explain possible reason for this.
Loops 2 and 6 have been treated as individual major loops, as explained in the revised ms (Sec 2.1). Since the shape and the values of H and B are quite different for these two loops, it is obvious that D-D-D parameters are quite different among each other.
- In Table 1, “1.2131e6” format should be same as other values. (1.2131∙106)
The authors are grateful to the Reviewer for catching this typo.
- Line 172: “On overall, the proposed D-D-D model shows good accuracy for all materials with the best Pearson correlation coefficients (except NdFeB at 80 °C)”. On the contrary, from Table 2, the value of Pearson correlation coefficients seems best for NdFeB at 80 °C. So, as per the Line 167: “The value range of r2is [0, 1], and the closer to 1, the more accurate the fitting is.”, NdFeB at 80 °C should also be with good accuracy.
The Reviewer is right if thinking in terms of absolute values. However, we were comparing the r^2 of our D-D-D model (0.99921) with those of the other 2 methods and for CPM we get 0.99927, which is slightly higher. Though comparable, this is the only case where the r^2 of our model is not the highest.
Reviewer 3 Report
The manuscript entitled “A Numerical Comparison between Preisach, J-A and D-D-D 2 Hysteresis Models in Computational Electromagnetics” written by De Santis et al. is well-presented and the methodology is clearly stayed, hence I recommend the manuscript for acceptance after considering some minor comments listed as follows:
1) Please, do not use abbreviations in the title. It must be corrected.
2) Update your introduction with references from 2022 to 2023.
3) Please, modify your discussion with references found in the literature. Compared with other works is recommendable.
Author Response
The manuscript entitled “A Numerical Comparison between Preisach, J-A and D-D-D Hysteresis Models in Computational Electromagnetics” written by De Santis et al. is well-presented and the methodology is clearly stayed, hence I recommend the manuscript for acceptance after considering some minor comments listed as follows:
- Please, do not use abbreviations in the title. It must be corrected.
This is an editorial issue that we prefer to leave to the Editorial board. In any case, we agree with the Reviewer that using acronyms in the title is not professional. However, while the Jiles-Atherton model is well-known, our model is novel and not-known. Therefore, using D’Aloia-Di Francesco-De Santis in the title, besides being too long, would give no information to the readers.
- Update your introduction with references from 2022 to 2023.
References from 2022 to 2023 have been updated in the revised ms.
- Please, modify your discussion with references found in the literature. Compared with other works is recommendable.
References, when possible, have been included in the discussion and conclusions of the revised ms.
Round 2
Reviewer 1 Report
This new article version represents a significant improvement from the previous version. However, the results obtained are still very sensitive to fitting procedures. I recommend comparing D-D-D model to results obtained in the literature for the two other models. In this way, the value of the new modeling tool should represent its real quality, and the discussion will be meaningful.
Author Response
We are thankful to the Reviewer for his comment, which has contributed to improve the overall quality of the manuscript. Indeed a better selection of ferromagnetic materials and a more "fair" comparison is provided in the revised version. As said in the previous revision, the chosen CPM and J-A models have been selected because open-source matlab codes and identification procedures are available online, so they have been tested and verified. In order to compare our D-D-D model with these two models, a smart selection of materials should be done, based also on available measurements, in order to be representative of soft and hard materials. For soft materials, we found out that Szewczyk made also available with his code the measurements of a ZnMn ferrite. Morevoer, in the new ref. [29] are reported also the 5 identified J-A parameters (that we verified with our optimization procedure). So this was a good benchmark to test the CPM and D-D-D against the available results of J-A. Another well-known benchmark for soft materials is the TEAM 32 with the challenging loops of Fe-Si along the rolling direction (when no anistropy is considered). In this case measurements are also available and Szabò et al. provided fitting results for the CPM in [32]. It was already pointed out in [32] that, to obtain a good Preisach distribution function, a 3rd order polynomial function is needed bringing the number of a,b,c parameters to 9 (plus the reversibility coefficient d and 2 more). Since we opted for a fair comparison (limiting the number of parameters up to 5) the results for the 1st order polynomial is provided, which is nor performant as the J-A results. For this material and major loop (11), also the D-D-D is suffering because with such a slope and width of the loop, the saturation is meet earlier than the measurements. To improve the accuracy in these cases, a reversible term as for the CPM could also be added for the D-D-D model with a very limited effort in terms of computational cost. This comment has been added in the revised discussions. Finally, we kept the same hard materials, first because we have measurements only for them, and secondly because after fixing the J-A fitting from the previous revision, we showed that it is still suffering hard materials. So on overall, our D-D-D model remain the best trade-off in terms of accuracy for the tested ferromagnetic materials and the faster one.
