A Physics-Based Tweedie Exponential Dispersion Process Model for Metal Fatigue Crack Propagation and Prognostics

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

First of all, I would like to express my sincere thanks for selecting our journal for your submission. The article is very well-written and meticulously prepared. Should you address the questions I have posed, I would be keen to review the article again.

- How does the Tweedie exponential-dispersion model outperform existing degradation path analysis models in engineering, and can you provide examples of its superior performance?

- Are there scenarios where the Tweedie exponential-dispersion model is inappropriate or underperforms due to its assumptions about positive response variables, excessive dispersion, and asymmetry?

- How does the performance of the Tweedie exponential-dispersion model compare with specific stochastic processes like WP, GP, IGP, and compound Poisson process in practical scenarios?

- How do the parameters in the physics-based Tweedie exponential-dispersion model relate to the physical properties of the materials or systems under study, and can these relationships provide physical insights?

- Image processing techniques are also used in order to get a solution about fatigue crack propagation without a bigger problem for the material. Please mention a little bit about this in the introduction section, it adds depth to your article.

State-of-the-art review of applications of image processing techniques for tool condition monitoring on conventional machining processes. Int J Adv Manuf Technol 130, 57–85 (2024). https://doi.org/10.1007/s00170-023-12679-1

Review of tool condition monitoring in machining and opportunities for deep learning. Int J Adv Manuf Technol 109, 953–974 (2020). https://doi.org/10.1007/s00170-020-05449-w

- How was the model validated against real-world datasets or case studies, and what were the criteria for its validation?

- What implications does the model have for materials science and engineering, especially in designing materials with improved fatigue resistance?

- What software or tools were used in the analysis, and what recommendations are there for researchers looking to apply this model in their work?

- How do you define the failure threshold in the context of degradation failure, and how is it determined for different materials or products?

- How do the estimated p-percentile lifetimes calculated using the proposed model compare with actual observed lifetimes in practice, especially in the context of the materials tested?

- The model's validity seems to be supported by comparing with other models like WP, GP, and IGP based on AIC criteria; can you elaborate on why the TEDP model shows better suitability for the data?

- Can you discuss any potential biases or uncertainties in the parameter estimation process, especially concerning the maximum likelihood estimation method used?

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The reviewer has gone through the contents of this research paper rigorously. This research work deals with numerical analysis using a physics-based TED model for predicting metal fatigue crack propagation and prognostics.  The beneficial features of the TED model developed by the authors need to be clarified and justified regarding the limitation of the application in industrial engineering.  Therefore, the outcomes of the present works have not yet technically given a significant contribution to be used in any engineering field for predicting cracks or defects in material engineering during application.

Abstract: The authors need to revise the last sentence with a specific and brief description of the significant findings of the present work.  

Introduction: the authors need to rewrite this section of the paper and improve it in terms of literature review and obtain justification from the gaps of literature for carrying out the present research. In addition, the literature also needs to elaborate on the objectives of the present research in this section vis-a-vis its application in industry or any other application. The novelty of the work should be mentioned at the end of the introduction section.

Results and discussion: The authors should clarify the comment about the magnitude of C depending on m. in fatigue crack growth of engineering materials (p.4#line 138-139), both C and m values are obtained from linear regression of da/dN vs. delta K constructed in the double log curve of x-y axes: the C value is the independent variable, whereas m is the slope of the curve. Therefore, the authors should provide the literature support at least.

The authors need to add a comprehensive discussion specifically and deeply by comparing the present work with the previous research available in many literatures.

Conclusion: Please balance the objectives so that the claimed conclusion is achieved. In addition, the conclusion should draw any specific findings obtained from the numerical analysis in discussion of the outcomes of the present work. 

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The authors integrated the Tweedie exponential dispersion process (TEDP) with Paris Law to develop a physics-based crack length prediction model. 

My comments:

1. Line 138-139. The authors wrote, 'the magnitude of C depends on m. In fact, C and m have a strong negative correlation'. Please provide justification or add the reference.

2. Eq.(6), dN/da or da/dN?

3. Equation numbering after (23) is wrong. Many in-text cross-reference equation numbers are confused. (e.g. Line 290: Eq.(4), Line 262: F(a/b), Line 264: Eq.(27)).

4. How to define the lifetime in the case study？

5. Writing mistakes. Line 247-248. photovoltaic modules in Line 253?

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have revised the previous manuscript appropiately. Therefore, the reviewer supports the revision manuscript to being published in the Journal.