A data-centric approach to generative modelling for 3D-printed steel

The emergence of additive manufacture (AM) for metallic material enables components of near arbitrary complexity to be produced. This has potential to disrupt traditional engineering approaches. However, metallic AM components exhibit greater levels of variation in their geometric and mechanical properties compared to standard components, which is not yet well understood. This uncertainty poses a fundamental barrier to potential users of the material, since extensive post-manufacture testing is currently required to ensure safety standards are met. Taking an interdisciplinary approach that combines probabilistic mechanics and uncertainty quantification, we demonstrate that intrinsic variation in AM steel can be well described by a generative statistical model that enables the quality of a design to be predicted before manufacture. Specifically, the geometric variation in the material can be described by an anisotropic spatial random field with oscillatory covariance structure, and the mechanical behaviour by a stochastic anisotropic elasto-plastic material model. The fitted generative model is validated on a held-out experimental dataset and our results underscore the need to combine both statistical and physics-based modelling in the characterization of new AM steel products.

However it is done, the authors need to show that their model generates a physically meaningful value of G for steel. I'm certain that this will prove trivial to do -but it would be very helpful as the data here are sure to be cited and used.

Review form: Referee 3
Is the manuscript an original and important contribution to its field? Excellent

Is the paper of sufficient general interest? Excellent
Is the overall quality of the paper suitable? Excellent Can the paper be shortened without overall detriment to the main message? Yes Do you think some of the material would be more appropriate as an electronic appendix? Yes

Recommendation?
Accept with minor revision (please list in comments)

Comments to the Author(s)
This paper presents a generative statistical model that enables the quality of a design to be predicted before being manufactured. The paper is interesting and well written. It is of interest to 3D printing engineers. The paper can be accepted as it is. But some of the font sizes in the figures are too small to read. I suggest the readers increase them.

20-Jul-2021
Dear Dr Dodwell The Editor of Proceedings A has now received comments from referees on the above paper and would like you to revise it in accordance with their suggestions which can be found below (not including confidential reports to the Editor).
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Yours sincerely Raminder Shergill proceedingsa@royalsociety.org on behalf of Professor Yihui Zhang Board Member Proceedings A Reviewer(s)' Comments to Author: Referee: 1 Comments to the Author(s) This study is of interest to researchers in additive manfuacturing. The anisotropic Gaussian process used in the study is robust, and has decent accuracy. The following comments are to be considered to improve the manuscript: 1) the title is too broad, and should be specified on mechanical property. 2) In Page 3 line 42, the authors claim "the geometry of WAAM steel depends on factors that are not easily measured or controlled". Please specify what factors.
3) The Design of Experiment should be described. The manufacturing parameters are not specified either. Otherwise, the quality of the training dataset is qustionable. 4) Model Cross Validation: Test set performance was not included. 5) Why was the "natural gradient ascent" optimization metric chosen? Justification is required. 6) In table 1, parameters have not been normalised. The differing dimensionality might affect final results obtained? 7) In page 11 line 40-41, what sampling method was used? 8) Cross-validation was not discussed in the paper. The accuracy of the prediction should be specified by discussing the results of the model's application on the test data.
Referee: 2 Comments to the Author(s) This is an excellent paper that, through taking into account the geometric variation that AM inevitably generates and accounting for anisotropy, should prove to be very helpful in driving forward understanding and quantification of uncertainty wrt. mechanical properties of AM produced components. In my opinion one very minor revision is needed however -and this related to G12. page 8 Line 24: E1 and E2 are entirely as would be expected for a steel as is Poisson ratio (154 and 148 GPa and 0.3 respectively) G12 however is far higher than would be expected -the Shear modulus of steel being, typically, 60-80 GPa.
However it is done, the authors need to show that their model generates a physically meaningful value of G for steel. I'm certain that this will prove trivial to do -but it would be very helpful as the data here are sure to be cited and used.
Referee: 3 Comments to the Author(s) This paper presents a generative statistical model that enables the quality of a design to be predicted before being manufactured. The paper is interesting and well written. It is of interest to 3D printing engineers. The paper can be accepted as it is. But some of the font sizes in the figures are too small to read. I suggest the readers increase them.

6
Is the paper of sufficient general interest? Acceptable Is the overall quality of the paper suitable? Acceptable Can the paper be shortened without overall detriment to the main message? Yes Do you think some of the material would be more appropriate as an electronic appendix? No

Recommendation?
Accept as is

Comments to the Author(s) No other comments
Review form: Referee 2

Is the paper of sufficient general interest? Excellent
Is the overall quality of the paper suitable? Excellent Can the paper be shortened without overall detriment to the main message? Yes Do you think some of the material would be more appropriate as an electronic appendix? No

Recommendation? Accept as is
Comments to the Author(s) I am happy with the changes made -and somewhat relieved i didn't send you on a wild goose chase. Those figures all look reasonable now.

Review form: Referee 3
Is the manuscript an original and important contribution to its field? Good

Is the overall quality of the paper suitable? Excellent
Can the paper be shortened without overall detriment to the main message? Yes Do you think some of the material would be more appropriate as an electronic appendix? No

Comments to the Author(s)
The authors have addressed all the comments.

08-Oct-2021
Dear Dr Dodwell I am pleased to inform you that your manuscript entitled "A Data-Centric Approach to Generative Modelling for 3D-Printed Steel" has been accepted in its final form for publication in Proceedings A.
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Reviewer 1
Q1. The title is too broad, and should be specified on mechanical property. Reply to Reviewers. We believe the paper presents a general study of generative modelling of 3D printed steel. Whilst we do not include all aspects of 3D-Printed steel, we include more than just the mechanical properties. For example uncertain manufacturing defects (geometric), material properties and the resulting structural behaviour. We therefore request to keep the title more general as 'A Data-Centric Approach to Generative Modelling of 3D-Printed Steel'.
Q2 On Page 3 line 42, the authors claim "the geometry of WAAM steel depends on factors that are not easily measured or controlled". Please specify what factors. Reply to Reviewers. Thank you for this comment; we have improved the text to make these factors clearer. The original paragraph 'The geometry of WAAM steel depends on factors that are not easily measured or controlled, motivating the treatment of material geometry as a random variable whose statistical properties can in principle be described.' now reads as follows: 'The final geometry of WAAM steel is treated as a random variable, whose statistical properties can in principle be described, due to the complex interaction between the process input parameters, including the welding voltage and current, robot arm speed and position, layer temperature, ability to cool between welding passes and part thickness.' Q3. The Design of Experiment should be described. The manufacturing parameters are not specified either. Otherwise, the quality of the training dataset is questionable. Reply to Reviewers. The experimental protocol has now been included, in the new Appendix (a), and referenced from the main text: 'For building the components that comprise the training dataset, wire of 1.0 mm diameter was used while the employed welding speed and wire feed rate were 15-30 mm/s and 4-8 m/min respectively. The employed shield gas was 98% AR and 2% CO 2 at a flow rate of 10-20 L/min, the current and arc voltage of the deposition process were 100-140 A and 18-21 V respectively, while the deposition rate was between 0.5-2.0 kg/h.' Q4. & Q8. Here we address two comments from the same reviewer together, these are (4) Model Cross Validation: Test set performance was not included. (8) Cross-validation was not discussed in the paper. The accuracy of the prediction should be specified by discussing the results of the model's application on the test data. Reply to Reviewers. There appears to be some confusion on this point, for which we apologise and will seek to avoid in the manuscript: In settings where one is attempting to predict a dependent variable (y) given one or more independent variables (x), cross-validation can be used to test how well y is predicted using knowledge of x and a statistical model. This is not our setting; there is no analogue of x in our generative statistical model (except perhaps, in an abstract sense, where x represents the notional geometry of the component -but then we have only two different instances of x in our dataset). Our statistical generative model is validated in Section 4(b), where predictions of the mechanical performance of a circular hollow section (CHS) are tested in detail. It may be that confusion has arisen because cross-validation is also widely used to train statistical models, and our generative statistical model also needs to be trained. However, several equally valid approaches to training exist, and in this paper we employed maximum (marginal) likelihood. Maximum (marginal) likelihood was used for this work because it facilitates straight-forward model selection via the Akaike information criterion (AIC). Note that the (marginal) likelihood is formally equivalent to training by exhaustive leave-p-out cross-validation averaged over all values of p and all held-out test sets when using the log posterior predictive probability as the scoring rule; see Fong E, Holmes CC. On the marginal likelihood and cross-validation. Biometrika. 2020 Jun 1;107(2):489-96. The text in Section 2(b) of the manuscript has been clarified as follows: