A parametric study of adhesive bonded joints with composite material using black-box and grey-box machine learning methods: Deep neuron networks and genetic programming
Graphical abstract
Introduction
The long-term financial and environmental viability has pushed aviation and transportation industries to engage in the application of a lightweight multi-material design strategy for primary structures [1]. This has stimulated the application of structural adhesives due to their compatibility with a wide range of material types and the possibility of combining multi-material structures. Adhesive joining also exhibits high strength-to-weight ratio, uniform stress transfer, design flexibility, damage tolerance, and crash/fatigue resistance over conventional joining methods [2].
The performance of adhesive bonded joints depends on several effective design variables such as surface treatment, material parameters (properties of adhesive and adherend), and geometrical configuration (adhesive thickness, overlap length, stacking sequence, fillet etc.), which have been studied intensively by using conventional analysis methods, such as analytical model, numerical model and experiment. For instance, da Silva et al. [3] investigated the importance of geometric parameters on the lap shear strength respectively. Similar works have also been done by many other researchers [[4], [5], [6], [7]], either by adjusting the geometric dimensions or the combination of materials within the joints. Their works contribute to the science of adhesive bonded joints to understand the effects of individual key design factors.
However, most of the existing studies use “one-factor-at-a-time” (OFAT) technique, which only investigates the effects of one design variable on responses of the interests rather than assessing the mutual effect of all effective variables on the overall performances. Actually, the mutual effect of design variables of an adhesive bonded joint is very complicated and erratic. Therefore, the latest studies start to use evidence-based machine learning techniques to replace the conventional numerical and experimental methods to investigate the mutual effects of design variables of the adhesive joint. Artificial neuron network (ANN) is one of these promising machine learning techniques. ANN tends to find the relationships between parameters and outputs based on a specific form of activation function. The first interest on artificial neurons was emerged after McCulloch and Pitts published their work in 1943 [8]. Inspired by networks of biological neurons, artificial neurons were modelled by these biological neurons. At present, there are a few studies using the technique in analysis of structural joints. Mashrei [9] predicted the bond strength of fibre reinforced polymers to concrete joints using a back-propagation neuron networks. The method was then applied to predict the strength of a single lap joint by considering the effects of width and length of adherends [10], to predict the adhesive bonded pultruded composites by considering different bonding angles [11] and to predict the strength of adhesive bonded single lap composite joints with varying overlap length and adhesive thickness [12]. The results of these studies show that the efficiency of ANN method is very high in comparison with the results of analytical and multiple linear regression models. However, only continuous and basic geometry parameters were considered in these studies.
Another machine learning technique, which was used in analysis of adhesive joints, is Genetic Programming (GP). The technique is a variant of genetic algorithm, which attracted many attentions of researchers after its first application by Forsyth [13] in pattern recognition. Initially, researchers used genetic programming in formulating capacities of different types of steel beams [[14], [15], [16]], the distortional buckling stress of steels [17] and mechanical properties of rock [18]. Then, genetic programming also demonstrated its potential in tackling complex nonlinear structural engineering problems [19,20] and effects of microstructure on overall mechanical performance of composite materials [21]. Recently, genetic programming technique started to be used to develop meta-models for design optimization of composite lattice materials [22] and functional structures [23,24]. However, there are not many studies using GP in analysis of the performance of lap joints. According to the author's knowledge, the only work has been done by Al-Mosawe et al. [25] and Liu et al. [26]. In Ref. [25], GP was used to predict the bond strength of a double strap joint under various loading rates, which is made of carbon fibre reinforced polymers and steel adherends. However, the work only considered limited linear continuous variables in the analysis, such as bond length, loading rate and Young's modulus of adherends. In Ref. [26], GP was used to analyse the mode I vs. mode II strain energy release rate ratio at the crack tip in a single lap joint and an equation was proposed related with the material properties and thickness of the adherends and adhesive.
Although some efforts have been made to use machine learning techniques in analysis of adhesive lap joints, the existing studies are generally based on very simple cases, which only consider limited continuous variables. So far, there is no well received systematic study in this field that involves all possible design variables of a joint in a machine learning model, especially the discrete variables such as the type of adherends and adhesive. Hence, this study aims to develop two machine learning models for predicting the performance of single lap joints based on both deeper ANN (DNN) and genetic programming techniques, which could consider the effects of mixed continuous and discrete design variables of the joints. The training and testing data of the machine learning models are sampled by Latin Hypercube method and generated by Finite Element (FE) models. Based on the results, the performances of the two machine learning models are analysed, and their potential applications are also discussed.
Section snippets
Parametric FE model and validation
To generate the data set for training and testing machine learning models, a parametric FE model is developed based on surface-based Cohesive Zone Method (CZM) in Ansys Workbench to calculate the failure load of a single lap joint under a static tensile loading. In the model, the geometry parameters and material parameters of the constituents (adherends and adhesive) of the joint are defined as variables. The schematic of the parametric geometry model is shown in Fig. 1, which illustrates the
Data points sampling
The principle of data-based approaches requires an appropriate data set from a specific problem domain for the purpose of accurate training and testing. It is expected that the selected data set can well represent the properties of the problem domain. In another words, it is better to have more averagely distributed data points in the problem domain. Therefore, sampling techniques are usually employed. Latin Hypercube Sampling (LHS) technique was used in this study, which has been widely
Results of machine learning models
To avoid “over-fitting”, three groups of data which were pre-processed by 3-fold cross validation method, are used in developing both two machine learning models. Each group of data is randomly divided by the ratio of 0.2. The validation of the training results of the DNN model on the 3 different groups of data are shown in Fig. 9(a–c) respectively. The points in all the three charts are close to the validation lines. It illustrates that the training accuracy of the developed DNN model remains
Conclusion
Two machine learning models (GP and DNN) are developed in this study to predict the ultimate failure load of single lap joints by considering four continuous geometry variables and three discrete material variables. The data sets for training and testing the machine learning models are selected by employing the DoE method Latin Hypercube Sampling (LHS). To generate the data set for the machine learning models, a parametric FE model is developed in Ansys Workbench and validated by two different
Credit author statement
Zewen Gu: Writing – Original Draft, Methodology, Software, Formal analysis. Yiding Liu: Writing – Original Draft, Software, Validation, Investigation. Jianqiao Ye: Writing - Review & Editing, Supervision. Darren J. Hughes: Visualization, Investigation. Xiaonan Hou: Conceptualization, Writing - Review & Editing, Supervision.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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