Physics-informed machine learning assisted uncertainty quantification for the corrosion of dissimilar material joints
Introduction
Self-Piercing Riveting (SPR), Resistance Spot Welding (RSW) and Rivet-Weld (RW) are some of the extensively used joining techniques in the automotive and other industrial fields [1], [2], [3]. These joints can be used for a variety of applications involving the joining of similar or dissimilar materials. The SPR joining technique is a mechanical joining process which is used to join two or more sheets of materials by creating a metallic interlock between them [4]. RSW process uses the resistance heat between sheet interfaces to create a localized fusion zone which upon cooling, forms a weld joint. The RW joining technique is a hybrid joining method which combines the strengths of both the SPR and RSW joining techniques while by-passing the weaknesses of both these methods.
During the applications of these joining methods for dissimilar metals such as steel and aluminum, the joints can be susceptible to galvanic corrosion in the presence of an electrolyte [5]. When the two dissimilar metals are being joined, crevices and gaps form among the metal sheets and the rivets, which can sometimes act as the nucleation sites for the galvanic corrosion [6]. As a result, the corrosion induced material loss and geometry change of the joints can cause performance degradation, which plays an important role in the failure and fatigue of the joints and therefore reduces their useful life. Other corrosion related phenomena such as the formation of the corrosion products can also lead to problems by covering the surface of the metals. This can change the geometry of the joint and therefore impact the internal loading of the joint, leading to unexpected stress concentrations in the joint and other damages [7,8]. Experimental studies on other kinds of dissimilar material joints such as magnetic pulse welding (MPW) joints have also been conducted [9]. A difference is found in the failure mechanism of the two pairs of joints that are tested due to the presence of zinc in one of the tested specimens. It is seen that the existence of zinc layer can lead to the reduction in the total electrochemical corrosion rate of aluminum/steel joints, but it also resulted in the reduction in the strength of the weld, thus leading to different failure mechanisms. Various studies have been performed to study the nucleation, initiation and propagation of localized corrosion and the corrosion protection of such joints [10], [11], [12]. Kotadia et al. [13] conducted experimental studies on the performance of dissimilar metal SPR joints and coatings. They found that corrosion had significantly influenced the lap shear performance and the failure mechanism of the joints and these results were dependent upon the type of coating on the joints. The microstructure evolution of corroded SPR and RSW Al-Fe joints were studied by Wen et al. [14] and they found that there is a difference in the corrosion process in these joints due to the formation of secondary phase precipitate because of the heat generated during welding. Additionally, the corrosion behavior in Aluminum alloy and galvanized steel RSW and SPR joints were investigated in salt spray environment [15], and it was reported that the crevice generated by different joining methods has an important impact on corrosion behavior. The significant impact of the uncertainties associated with the geometric and environmental factors as well as the joining methods on the corrosion behaviors, as reported in the literature, necessitates the uncertainty quantification (UQ) studies for the corrosion of dissimilar material joints.
Numerical methods, e.g., finite element (FE) modeling, are powerful tools which are used to investigate the effect of different geometrical and environmental factors on the corrosion initiation and evolution, which can be challenging to study using experimental testing, and quantitatively characterize the corrosion phenomena. Dependences of corrosion on various variables, e.g., the geometry of the metals, pH value of the electrolyte bath, etc., have been studied using the numerical methods [16,17]. For example, Chang et al. [18] investigated the effect of initial pit size, corrosion pitting current, and material properties on the fatigue life of corrosion aircraft materials by creating a probabilistic model based on a quantitative evaluation of the nucleation and growth of pits and crack propagation processes. Stochastic models, which incorporate the influence of stresses, relative humidity, pH and temperature, and can be used to characterize both corrosion volume and depth growth have also been developed [19]. Xie et al. [20] conducted multi-state Markov modeling of pitting corrosion in stainless steel which was exposed to chloride-containing environment. Numerical simulation work studying the dependence on pH on galvanic corrosion has been studied by Kamble et al. [21]. They used COMSOL models to conduct this study and found that increasing the pH causes a reduction in the corrosion rate. Shariati et al. [22] developed a novel approach to tackle the challenges seen in corrosion simulations by proposing a toolchain which is flexible, efficient and extensible. They use an algebraic flux correction method to solve the Poisson-Nernst-Planck model using parallel implementation that results in reduction of the simulation time by a factor of 4. A hybrid physics-based finite element model was developed to simulate the corrosion process of Fe-Al joints [23], where experimental results were used in the form of stochastic nucleation input information along with a physics-based FE model to simulate the corrosion in the SPR joints. These studies advance our knowledge regarding the corrosion phenomena and critical determining factors but lack the capability to quantitatively demonstrate the impact of corrosion on the overall performance of structures.
While employing physics-based FE simulations for UQ could result in prohibitively high computational costs, studies associated with the analysis of failure behaviors using data-driven machine learning as surrogate models have also been reported in the literature to improve the efficiency for UQ [24,25]. Similarly, Stern et al. [26] used a machine learning based surrogate model to conduct accelerated Monte Carlo (MC) system reliability analysis with a good balance on the accuracy and computational efficiency. Similar machine learning based UQ studies have also been reported for other applications [27], [28], [29]. While the surrogate modeling approaches have been used for UQ studies, the performance of a surrogate model also depends on the dataset available for the model development. More data points in general lead to better model accuracy, they could however induce higher sampling costs since more function evaluations are required to acquire those data points. Consequently, adaptive sampling strategies [30], [31], [32], [33], [34], [35] have been developed to improve the fidelity of the surrogate model using a minimum number of data points. By using adaptive sampling, an initial low fidelity surrogate model is often constructed firstly based on a small set of training samples, and additional sample points are identified iteratively, following a certain sampling criterion, and added to the training data set to improve the performance of the surrogate model. Jones et al. developed an active learning method using an expected improvement measure based upon the response surface approach [30]. An efficient global reliability analysis (EGRA) method was developed by Bichon et al. [31] for structural systems design where an adaptive sampling criterion was created to balance the effort between a regional search near the response surface and a global search in the parametric space for reliability analysis. Lee and Jung [32] developed a constraint boundary sampling (CBS) method for constraint optimization problems, which focused on the approximation of constraint boundaries in the global design region using surrogate models. Echard et al. [33] developed an adaptive sampling strategy for reliability analysis where an active learning reliability method was combined with the adaptive Kriging and Monte Carlo simulation, namely the AK-MCS method. The AK-MCS method appears to be efficient for reliability analysis, since it is a local sampling approach and focuses only on a set of Monte Carlo samples generated from a given design point instead of approximating the performance function in the entire sample space. Wang and Wang [34] introduced a maximum confidence enhancement (MCE) based sequential sampling approach that can be employed simultaneously with the design optimization process, which uses the cumulative confidence level (CCL) as a sampling criterion to select sample points with the maximum value of the estimated CCL improvement successively. To address the issues related to sampling from data pools with different level of information fidelity levels, adaptive sampling strategies have been developed recently to considering adaptive surrogate modeling with partially observed information [35].
The machine learning based techniques have also been used for reliability assessment which focusses on corrosion effects. Dong et al. [36] studied the reliability of wind turbines considering the effect of corrosion and inspection. They quantified the effect of inspection, based on its quality for a given inspection strategy with and without the consideration of corrosion using probabilistic methods. An evidence theory-based kriging model was developed by Xie et al. [37] which used adaptive sampling to perform quantification of margins and uncertainties for the assessment of structural reliability for pressure vessels with corrosion damage. A time-dependent reliability-based redundancy assessment of corrosion effected deteriorated reinforced concrete structures against progressive collapse was presented by Feng et al. [38], where the modelling uncertainty was empirically specified. Ma et al. [39] developed a systematic framework to quantify hybrid uncertainties for the probabilistic prediction of corrosion damage in aging RC bridges which can concurrently tackle empirical information, sparse data and probability distribution with parameter uncertainty. A novel population-based pitting corrosion degradation model for piggable oil and gas pipelines is developed by Heidary and Groth [40]. They developed a hierarchical Bayesian model based on a non-homogeneous gamma process to combine the uncertain in-line inspection data and physics of failure knowledge of pitting corrosion process, which shows a good agreement with commonly used degradation models. Sarkar et al. [41] present a stochastic reduced order model approach for quantifying uncertainty in systems undergoing corrosion. While considering the randomness in anode-cathode sizes, they use this model to estimate the statistics of corrosion current density and also compare the performance of this model against the more common Monte-Carlo approach. UQ is crucial role in reduction of uncertainties in the design and operation of structures under the influence of corrosion. However, a lot of the performed studies use Monte Carlo simulations to conduct uncertainty analysis, which can be computationally expensive, where our model integrates adaptive surrogate modeling with physics-based FE simulation platform which balance the conflict of computational expense and analysis fidelity in UQ.
In this study, a physics-informed machine learning approach has been developed to conduct UQ study on the galvanic corrosion process in the Fe-Al joints. A physics-based FE model is firstly developed and validated with the experimental results, which is used to simulate the galvanic corrosion process. This physics-based computational model forms the basis of the following parametric study wherein the influences of various geometric and environmental factors on the corrosion process and material loss are investigated. These factors include the gap between the electrodes, roughness of the anode and the temperature and conductivity of the electrolyte. Based on the material loss estimation, sensitivity analysis on the couplings of these factors is carried out to identify the main sources of uncertainty. To improve the computational efficiency, a probabilistic confidence-based adaptive sampling technique is integrated with the physics-based simulation to study the impact of the synergetic effects between different uncertainty parameters. The adaptive sampling technique, which enables the cost-effective identification of multiple disjointed parametric regions with a minimum number of sample tests and verification efforts, helps in reducing the burden on running expensive corrosion simulations therefore improving the efficiency. Material loss is found for these synergistically coupled models, which then acts as the training data for the machine learning based surrogate model. The trained machine learning model can then be used to quantify the sources of uncertainty in the whole process and also to perform statistical corrosion analysis for Fe-Al joints, which will help the design and manufacturing of the Fe-Al joints with better corrosion performance.
Section snippets
Physics-informed machine learning method for uncertainty quantification
In this section, the physics-informed machine learning method for uncertainty quantification is introduced. Section 2.1 explains the multiphysics-based corrosion modeling, and Section 2.2 then details the physics-informed adaptive surrogate modeling technique employing the multiphysics-based simulation and Gaussian process adaptive sampling.
Corrosion propagation and parametric study
To demonstrate the proposed platform for statistical corrosion analysis, corrosion is simulated based on the developed FE model for a period of 3600 s. Fig. 5 shows the electrolytical potential in the electrolyte with the anode (light grey), the cathode (dark grey) and the electrolyte (rainbow colored part). Comparing Fig. 5 with Fig. 2 shows how the corrosion process results in the material loss and how this corrosion front propagates. The material loss for the FE model is then calculated
Summary and conclusion
In this study, uncertainty quantification was conducted on the galvanic corrosion of the dissimilar material joints between an aluminum anode and a steel cathode, using a physics-informed machine learning framework and the probabilistic confidence based adaptive sampling technique. An FE model was developed to simulate the corrosion evolution in the dissimilar material joints and estimate the resulted material loss. The sensitivity analysis were carried out based on the parametric study for
CRediT authorship contribution statement
Parth Bansal: Writing – review & editing, Writing – original draft, Formal analysis, Data curation. Zhuoyuan Zheng: Writing – original draft, Methodology, Conceptualization. Chenhui Shao: Formal analysis, Data curation, Conceptualization, Visualization, Methodology. Jingjing Li: Data curation, Conceptualization, Visualization, Methodology. Mihaela Banu: Project administration, Data curation, Conceptualization, Visualization, Methodology. Blair E Carlson: Data curation. Yumeng Li: Writing –
Declaration of Competing Interest
The authors have no conflict of interest.
Acknowledgment
This work was financially supported by the U. S. Department of Energy via Award No. DE-EE0008456.
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