Back propagation genetic and recurrent neural network applications in modelling and analysis of squeeze casting process

Highlights

• Experimental work at research center of NIT, Suratkal, India.

• Research work useful for the foundry industries.

• Reverse mapping useful to automate squeeze casting process.

• Research work finds its application in reducing waste, energy and materials consumption in foundries.

Abstract

Today, in competitive manufacturing environment reducing casting defects with improved mechanical properties is of industrial relevance. This led the present work to deal with developing the input-output relationship in squeeze casting process utilizing the neural network based forward and reverse mapping. Forward mapping is aimed to predict the casting quality (such as density, hardness and secondary dendrite arm spacing) for the known combination of casting variables (that is, squeeze pressure, pressure duration, die and pouring temperature). Conversely, attempt is also made to determine the appropriate set of casting variables for the required casting quality (that is, reverse mapping). Forward and reverse mapping tasks are carried out utilizing back propagation, recurrent and genetic algorithm tuned neural networks. Parameter study has been conducted to adjust and optimize the neural network parameters utilizing the batch mode of training. Since, batch mode of training requires huge data, the training data is generated artificially using response equations. Furthermore, neural network prediction performances are compared among themselves (reverse mapping) and with those of statistical regression models (forward mapping) with the help of test cases. The results shown all developed neural network models in both forward and reverse mappings are capable of making effective predictions. The results obtained will help the foundry personnel to automate and précised control of squeeze casting process.

Introduction

The ever-increasing demand for the squeeze cast products from past few decades might be due to the desirable properties, like high strength to weight ratio, minimum porosity and refined microstructure. These properties depend mainly on the hybrid processing method adopted in squeeze casting by combining the desirable features of conventional casting and forging processes. The process developed with the idea of solidification under pressure introduced early in 1878 by D. K. Chernov. The first experiment on squeeze casting was conducted for production of brass and bronze cylinders during 1973 [1]. Later with the growing demand for light weight materials in automobile and aerospace applications, drawn the attention of researchers towards achieving high strength to weight ratio. In this regard, a great deal of research work is carried out during the early 1990s and 2000s. Major research work reported during those periods was on improving the microstructure characteristics and mechanical properties, using well known analytical, numerical and classical engineering experimental approaches.

The authors [2] used the theoretical approach, namely derivative based differential thermal analysis to determine the influence of squeeze pressure on solidification time, under cooling and phase transition point. It was observed that, the applied squeeze pressure had drastically reduced the solidification time as compared to that of gravity castings. Numerical simulation using Navier stokes equation coupled with energy equations were used to determine the solidification time under different squeeze pressures [3]. The solidification time effects on mechanical properties were investigated by using analytical and classical engineering experimental approaches [4]. The results obtained by Gracia’s virtual and steady state heat flow models had showed more than 20% deviations.

Classical engineering experimental approach was used to study the influence of casting temperatures on the properties of zinc and aluminium alloys [5]. It was observed that experiments were conducted for the fixed die temperature, squeeze pressure and pressure duration. The extensive research work was conducted to examine the effects of applied pressure variations on mechanical and microstructure characteristics for the fixed values of casting and die temperatures [6], [7], [8]. The casting temperature and squeeze pressure effects on microstructure features and mechanical properties were investigated for the constant pressure duration and die temperatures [9], [10]. Squeeze pressure, pouring and die temperature influence on microstructure characteristics and mechanical properties were studied by varying one factor at a time and keeping rest of the process variables at their respective mid-values [11], [12]. Time delay or waiting time, pressure duration, inoculants, degassing, die and pouring temperature variations were studied to prevent the macro defects in squeeze casting [13].The major research work reported in the above literatures was based on classical engineering experimental, numerical and analytical approaches. The above methods estimate the combined (interaction) effects, but require many experiments and huge computational time with the increase in the number of process variables. Thus analysis and conclusions drawn from the above methods does not reveal complete insight of the process and suggested optimal parameter setting are not considered to be global in nature. Further, practical guidelines suggested by distinguished researchers may not provide complete information on process optimization.

In the recent past, squeeze casting research was directed towards studying the process variables under conventional modelling tools. Statistical Taguchi method is the conventional modelling tool, wherein the process variables are varied simultaneously and appropriate set of data is collected and analyzed. Further the significant parameters can be identified and linear/non-linear input-output relationship can be developed for a process. Taguchi method applied successfully to study effectively the process variables on mechanical properties of aluminium based alloys [14], [15]. However, major limitations are addressed form the above literatures is listed as shown below,

• Taguchi method is limited to test all interaction factors.

• A separate model for each output restricts the model to capture dependency among the outputs.

• Limited research is carried out in developing and testing the input-output relations in squeeze casting process. Not much of the work, especially on reverse mapping of the squeeze casting process is reported in the literature.

The shortcomings of statistical methods, listed above can be addressed by using the soft computing tools namely genetic algorithms (GA), particle swarm optimization (PSO), artificial bee colony optimization (ABC), neural networks (NN), fuzzy logic (FL), ant colony optimization (ACO) and their diverse combinations. Selection of appropriate method is often difficult task for the researchers due to different learning mechanisms, tuning parameters, computational efficiency, and solution accuracy for the problem domain. Industry relevance and foundry personnel requirements focussed to gain better solution and accuracy due to offline monitoring of squeeze casting process. NNs were applied successfully in the past to predict multiple outputs (that is, density and secondary dendrite arm spacing) and casting variables (namely, waiting time, holding time, pouring temperature, squeeze pressure, and die temperature) [16]. Interesting to note that, increase in time delay after 4 s, showed decreased values of density and increase in secondary dendrite arm spacing. Five input variables operating at wide range were used to develop squeeze casting process models. The training data was collected using the regression equations, where the interaction terms were neglected completely, resulted in high percent deviation [16]. Solidification time and temperature gradient of the squeeze cast parts were predicted successfully using NNs [17], [18]. NNs trained with soft computing tools as auxiliary hybrid systems had shown better prediction performances in ground coupled heat pump systems [19], [20], [21], [22], [23]. The back propagation neural network was adopted to develop such hybrid computational tools in their research applications. PSO had outperformed ABC and differential evolution (DE), in determining the optimal input parameters for glass fibre reinforced plastic (GFRP) composites [24]. GA had performed better than PSO and DE in tube spinning process [25]. It was interesting to note that, PSO had yielded better results in terms of computational efficiency for unconstrained non-linear problems, whereas GA outperformed for constrained non-linear problems with continuous or discrete design variables [26]. GA, PSO, and ACO tools had shown approximately similar results to solve construction site layout problems [27]. ABC, GA and PSO tools were used to tune the neural network that could approximate the gene expressions [28]. GA-NN outperformed PSO-NN and ABC-NN, to yield low deviation (that is, maximum deviation and minimum deviation) value from the reference zero line [28]. PSO, BP and GA were used to optimize the neural network parameters for accurate prediction of cutting zone temperature [29]. It is to be noted that, GA tuned NN outperformed both BP and PSO tuned NN with regard to mean absolute deviation. NN based expert systems (i.e. PSO, GA, BP tuned NN) were used to model the welding process of reactive material in both forward and reverse directions [30]. The steepest descent method based BPNN had predicted better results than GANN and PSONN in modelling the welding process. From the above literatures, it may be concluded that, back propagation and GA tuned NNs are widely used. However, it is difficult to arrive at a decision best method among soft computing based approaches for the given situation [31], [32], [33], [34], [35].

The multi-layer neural network applications in modelling the process are well known. The discussed literature in earlier section is focussed on modelling and prediction of a static system (that is, the neural networks are trained for particular input-output data patterns) with a single hidden layer. NNs with two hidden layers were employed successfully to map the input-output relationships of pressure die casting process [36]. It had been observed that, the prediction performances were found better when the network was trained with multiple hidden layers. In the recent past, the complex input-output relationship was mapped by introducing the dynamic elements, as a feedback connection to the network, referred as recurrent neural network (RNN) [37]. In RNN, output of each layer is fed back to itself as well as other layers. Feedback to the neurons resulted in improved prediction and faster computation [38]. In the recent past, RNN was applied successfully to predict the grain size, hardness, tensile strength and wear properties of Al-4.5Cu-5TiB₂composites [38]. Material removal rate in electric discharge machining was predicted successfully by utilizing RNN [39]. There exists wide scope to develop suitable expert systems (that is, recurrent neural network) to capture the dynamics of manufacturing processes [35].

The practical requirement of any metal casting industries is to develop the system that predicts multiple inputs-outputs in forward and reverse directions, specifically for online monitoring process. DOE will model and analyze only single output at a time thus fails to predict multiple outputs and to capture complete insight of dependencies among outputs [40]. Reverse prediction, utilizing the response equation, require transformation matrix to be square one. Therefore, reverse prediction can be determined only for response equation having linear terms, whereas transformation matrix might not be invertible always. Important to note that, regression equations without the interaction terms does not fit close to their respective true input/output relationships. Hence, a significant scope exists to conduct successfully both forward and reverse mapping by utilizing artificial neural networks to achieve the practical requirements.

Back propagation algorithm trained NN (BPNN) works with steepest descent principle. This algorithm finds a major limitation in the solutions getting trapped at local minima. However, evolutionary GA searches global minima at many distinct locations simultaneously in huge space. Thus heuristic search technique (that is, GA), restrict getting trapped at local minima solutions. GA is used to replace the back propagation algorithm, to search global fitness solutions in the integrated GA tuned NN (GA-NN) approach. In GA-NN, error is determined as the difference between neural network prediction and their respective target value, and the same is fed back to GA as fitness function to optimize the synaptic weights of NN to minimize the error. Further, dynamic elements introduced as feedback to the outputs, which minimize the error in recurrent neural network. Not much of the work has been reported on the forward and reverse modelling of squeeze casting process in the literature. The schematic representation of methodology employed to develop neural network is shown in Fig. 1.

Four neural network models (BPNN-1H, BPNN-2H, RNN and GA-NN) have been developed in the present work and their performances have been compared prediction in terms of their prediction accuracy. The following key objectives are defined in this regard,

• Forward Mapping: GA, Recurrent and BP algorithm trained NN are used as forward mapping tool to predict the outputs for the known combination of squeeze cast process variables. Further, prediction accuracies of NN models are compared among themselves and with those of statistical models with the help of test cases.

• Reverse Mapping: Neural network models are used as reverse mapping tools in which a set of process variables combination is determined for the desired output. In addition, prediction performances are compared among different NN models with the help of test cases.