CHAPTER 1 INTRODUCTION
1.4 Dissertation Outlines
Chapter 2 reviews that the Taguchi method, neural networks, combined Taguchi method with a neural network, the GTA welding for type 304
stainless steels, the pulsed Nd:YAG laser micro-weld for the lithium-ion secondary batteries, and RSW process for high strength steel sheets in automotive industry. Chapter 3 presents that the proposed approach was used to determine optimal conditions for improving process quality of the GTA welding, the pulsed Nd:YAG laser micro-weld and RSW process. In addition, this chapter presents the initial optimization via Taguchi method, and a neural network with the Levenberg-Marquardt back-propagation (LMBP) algorithm to search for the optimal parameter combination for these welding processes. Chapter 4 provides the discussion comparison with previous works and the proposed procedures. Finally, Chapter 5 concludes the main results of the presented work.
CHAPTER 2
LITERATURE REVIEW
2.1 Taguchi method
The philosophy of Taguchi is broadly applicable. It considers tree stages in process development: system design, parameter design and tolerance design [2,7]. In system design, the engineer uses scientific and engineering principles to determine the basic configuration. The main objective of system design is to determine the manufacturing process that can produce the product within the specified limits and tolerance at the lowest cost. In the parameter design stage, specific values for the system parameters are determined. Parameter design in production process design determines the operating levels of the manufacturing processes so that variation in product parameters is minimized. Tolerance design is used to specify the best tolerances for the parameters. The objective of tolerance design is to find optimal ranges of the operating conditions that minimize the sum of variation cost and cost of the product.
In addition, traditional experimental design is primarily used to improve the average level of a process (e.g., arithmetic mean of a sample). In modern quality engineering, experimental design work is used to develop robust designs to improve the quality of the product. Taguchi’s parameter design is to achieve robust quality by reducing effects of environmental conditions and variations caused by deterioration of certain components [7,8]. This is achieved by the selection of various design alternatives or by varying the levels of the design parameters for component parts or system elements. It can optimize the performance characteristics through the settings of design parameters and reduce
The tools for executing the parameter design oh Taguchi method are shown as below [7-10]:
Orthogonal array
Orthogonal array (OA) based matrix experiments are used for a variety of purposes in Robust Design. They are used to study the effects of control factors and noise factors, and determine the best quality characteristic for particular applications. Taguchi has tabulated 18 basic orthogonal arrays that are called standard OAs. Note that the orthogonality was preserved even when the dummy level technique was applied to one or more factors. In addition, the noise factor could be assigned to the outer array to find some level of a control factor that does not have much variation in the results, even though a noise factor is definitely present.
Evaluation by S/N ratios
Taguchi has created a transformation of the repetition data to another value, which is to say a measure of the variation present. The transformation is the signal-to-noise ratio (S/N ratio, SNR). There are several S/N ratios available depending on the type characteristic being present, such as lower-is-better (LB), nominal-is-best (NB), or higher-is-better (HB).
For a static problem, Taguchi classified them into three different S/N ratio types, as shown in equation 2-1, 2-2 and 2-3.
2
⎟⎠ were n denote the number of repetition, y represents the response mean, and
s is the standard deviation of response.
Analysis of variance
The Analysis of Variance (ANOVA) was developed by Sir Ronald Fisher in the 1930’s as a way to interpret the results from agricultural experiments.
ANOVA is not a complicated method and has a large amount of mathematical uniqueness associated with it. The purpose of the ANOVA is to investigate welding process parameters, which can significantly affect the quality characteristics. The percent contribution in the total sum of the squared deviations can be used to evaluate the importance of the welding process parameter change on these quality characteristics. In addition, the F-Test named after Fisher can also be used to determine which welding process parameters have a significant effect on the quality characteristics. Usually, when the value of F-Test is greater than 4, it means that a change in the process parameter has a significant effect on the quality characteristics. When the contribution of a factor is small, the sum of squares for that factor is combined with the error. This process of disregarding the contribution of a selected factor and subsequently adjusting the contributions of the other factors is known as “Pooling”.
Confirmation tests
Using the Taguchi method for parameter design, the predicted optimum setting need not correspond to one of the rows of the matrix experiment.
Therefore, the final step is to compare the estimated value with the confirmative experimental value using the optimal level of the control factors to confirm with
the experimental reproducibility. The estimated S/N ratio ηopt using the optimal level of the control factors can be calculated as:
( )
the mean S/N ratio at the optimal level, and q is the number of the control factors that significantly affect the quality characteristic.The confidence interval is a maximum and minimum value between which the true average should fall at some stated percentage of confidence. The confidence limits of the above estimation can be calculated taking into account the following equation: degrees of freedom for pooled error, Vep is the pooled error variance, r the sample size for the confirmation experiment, and neff is the effective sample size: associated with items used in the ηopt estimate.
Apply Taguchi method to welding processes
Juang et al. [11] presented a study that application of Taguchi method to select parameters for obtaining an optimal weld pool geometry in the GTA welding of stainless steel. In this study, a weighting method is used to integrate the loss functions into the overall loss function (the higher-is-better of S/N ratio);
the weighting factors for the front height and back height of the weld pool were selected as 0.4, the weighting factors for the front width and back width of the weld pool were selected as 0.1.
Li et al. [12] using the RSW process as an example, this paper presents a new robust design and analysis framework for products and processes with parameter interdependency. The experiment was designed using a two-stage, sliding-level factor approach. Welding current was chosen as a “slide factor”
whose settings are determined based on those of others including both control and noise factors. By proper coding, a stepwise regression procedure was used to develop a response model, with which the response modeling approach for robust design is applied.
Tarng et al. [13] used grey-based Taguchi method for the optimization of the submerged arc welding (SAW) process parameters in hardfacing with considerations of multiple weld qualities. In this approach, the grey relational analysis was used as the performance characteristic in the Taguchi method. Then, optimal process parameters were determined by using the parameter design proposed by the Taguchi method.
2.2 Neural networks
Neural networks are used for modeling of complex manufacturing processes, usually with regard to process and quality control [14,15]. Several
well known supervised learning networks use a back propagation (BP) neural network. Funahashi [16] proved that the BP neural network may approximately realize any continuous mapping. Back propagation learning employs a gradient descent algorithm to minimize the mean square error between the target data and the predictions of a neural network. However, one of the major problems with basic BP algorithm (gradient descent algorithm) has been the extended training time required. The techniques for accelerating convergence have fallen into two main categories: heuristic methods and standard numerical optimization methods such as the Levenberg-Marquardt back-propagation (LMBP) algorithm [17].
Levenberg-Marquardt back-propagation algorithm
The LMBP algorithm is similar to the quasi-Newton method, in which a simplified form of the Hessian matrix (second derivatives) is used. Starting from the Taylor series approach of second order, for a generic function F(x), the following can be written [17-19].
k
This equation can be re-written in the following form.
The updating rule for the Newton algorithm is then obtained.
)
Considering a generic quadratic function as the objective function, as represented in equation 2-11 for a multi-input multi-output system (here the iteration index is omitted and i is the index of the outputs)
∑
= Jacobian, the Hessian matrix can be approximated by the following.≈ 2-15
This approach can update equation 2-10 and gives the Gauss-Newton algorithm.
[
J (x)J(x)]
1J (x)e(x)xk = T − T
Δ 2-16
One limitation that can happen with this algorithm is that the simplified Hessian matrix might not be invertible. To overcome this problem, a modified Hessian matrix can be used.
I positive definite, and therefore can be invertible. This last change in the Hessian matrix corresponds to the Levenberg-Marquardt algorithm.
[
J (x)J(x) I]
1J (x)e(x)xk = T + − T
Δ μ 2-18
When the scalar μ is zero, this is just Gauss-Newton, using the approximate Hessian matrix. When μ is large, this becomes gradient descent with a small step size. The algorithm begins with μ set to some small value (e.g. μ=0.01). If a step does not yield a smaller value for e, then the step is repeated with μ multiplied by some factor θ＞1 (e.g. θ=10). Eventually e
should be decreased, since we would be taking a small step in the direction of steepest descent. If a step does produce a smaller value for e, then μ is divided by θ for the next step, ensuring that the algorithm will approach Gauss-Newton, which should provide faster convergence [17].
The LMBP algorithm is the fastest algorithm that has been tested for
training multiplayer networks of moderate size, even though it requires a matrix inversion at each iteration. It requires two parameters, but the algorithm does not appear to be sensitive to this selection. In addition, Kumar et al. proved [20] that the LMBP algorithm and Gauss-Newton were found to perform best for least square problems. In particular, the LMBP algorithm performs better with a poor initial estimate compared to the Gauss-Newton method. Summary, the LMBP algorithm provides a nice compromise between the speed of Newton’s method and the guaranteed convergence of steepest descent.
Training of back propagation Network
A neural network, which can capture and represent the relationship between the process variables and process outputs, was developed in this stage.
Multi-layer perceptions are feed-forward neural networks are commonly used for solving difficult predictive modeling problems [21]. They usually consist of an input layer, one or more hidden layers, and one output layer. The neurons in the hidden layers are computational units that perform non-linear mapping between inputs and outputs. A feed-forward neural network was used in this study. The transfer functions for all hidden neurons are a tangent sigmoid function as shown in equation 2-19. The transfer functions for the output neurons are a linear function as shown in equation 2-20 [22].
)
Determining the number of hidden neurons is critical in the design of
that usually leads to over-fitting. On the other hand, too few hidden neurons restrict the learning capability of a network and degrade its approximation performance [21].
Apply neural networks to welding processes
Kim et al. [23] develop an intelligent system in gas metal arc (GMA) welding process using MATLAB/SIMULINK software. Based on multiple regressions and a neural network, the mathematical models were derived from extensive experiments with different welding and complex geometrical features.
In this study, using a generalized least mean square (LMS) algorithm, the BP algorithm minimizes the mean square difference between the real and the desired output. The developed neural network model can proposed for real-time quality control based on observation of bead geometry and for on-line welding process control. However, it was trained for 200,000 iterations.
Wu et al. [24] present a study that introduces a Kohonen network (self-organising feature map) system for process monitoring and quality evaluation in GMA welding. The Kohonen network is an unsupervised learning neural network. It can be used to solve classification tasks and to find structures in data. In the present study the evaluation gives a rather high recognition rate.
Nagesh et al. [25] used a neural network with basic BP algorithm (gradient descent algorithm) to model the shielded metal-arc welding process. The trained neural network model had achieved good achieved good agreement with the training data and had yielded satisfactory generalization. It was trained for 11,000 iterations.
Ridings et al. [26] present a study that describes the application of neural network techniques to the prediction of the outer diameter weld bead shape for
three wire, single pass per side, submerged arc, linepipe seam welds, using the weld process parameters as inputs. This study show that the use of neural network models for the prediction of weld bead geometry has the potential for a detailed shape to be input into through process models, rather than having to assume a shape from a limited number of defining parameters.
Jeng et al. [27] adopted two back-propagation (BP) and one learning vector quantization (LVQ) neural network models to predict the laser welding parameters and the associated welding quality individually, because some of the parameters are strongly interconnected and must be determined by sequence.
LVQ is a supervised learning technique that uses class information to move the classification set slightly, so as to improve the quality of the classifier decision region.
Lee et al. [28] employed multiple regression analysis and neural network to predict the back-bead of geometry in the GMA welding process. The neural network showed superior results to the multiple regression analysis in terms of field of prediction error rate.
Vitek et al. [29] present a welding process that combined plasma arc welding with laser welding was used to make autogenous bead on plate welds on a sheet stock of a carbon steel. The predictions of the neural network model showed excellent agreement with experiment results, indicating that a neural network model is a viable means for predicting weld pool shape. Thirty-three different experimental welds were made. These welds provide a total data set of 33 weld conditions and the corresponding weld pool shape. It was subdivided into 11 train/test pairs consisting of 30 and 3 data points respectively.
Tarng et al. [30] used a neural network to construct the relationships between welding process parameters and weld pool geometry in GTA welding.
An optimization algorithm called simulated annealing was then applied to the network for searching the process parameters with an optimal weld pool geometry. The quality aluminum welds based on the weld pool geometry was classified and verified by a fuzzy clustering technique. In this study, cleanliness of specimens was selected as the input of BP network model.
Han [31] used a neural network to obtain the knowledge about the fatigue lives of weldments with welding defects under fatigue load. A total data set of 15 conditions and the corresponding fatigue life. It was divided into train and test pairs consisting of 10 and 5 data points respectively.
2.3 Integrated the Taguchi method and a neural network
Rowlands et al. [32] present a study that illustrate how optimal parameter design can be achieved by using design of experiments in conjunction with neural network. Applying the method, the neural network was trained by the results of a fractional factorial design, and was then used to estimate the response values for the full factorial design.
Chiu et al. [33] used the neural network model and the Taguchi method to determine the optimal parameter setting in a gas-assisted injection molding. The results showed that the integrated method is capable of treating continuous parameter values.
Khaw et al. [6] proved that benefits could be obtained by using the Taguchi concept for neural network design. First, this methodology is the only known method for neural network design that considers robustness. It enhances the quality of the neural network designed. Second, the Taguchi method uses orthogonal arrays (OAs) to systematically design a neural network. With the effective use of the Taguchi method, several important design factors of a neural
network can be considered simultaneously. The design and development time for neural networks can be reduced tremendously. The Taguchi method is not strictly confined to the design of BP neural networks. It can be used to evaluate neural networks of different types such as counter-propagation, Boltzmann machine, and self-organizing map.
2.4 The gas tungsten arc (GTA) welding
The GTA welding is an arc welding process that uses an arc between a tungsten electrode (non-consumable) and the weld pool. The process is used with shielding gas and without the application of pressure for pieces to be welded. GTA welding was originally developed for aluminum and stainless steel that are difficult to be welded. The GTA welding process is now widely used with other alloys. The aircraft industry is one principal users of GTA welding [1].
There are many parameters that affect the GTA welding quality, such as electrode type, shielding gas type, welding current, travel speed of the welding torch and so forth.
GTA welding and related processes are capable of producing very high-quality welds but for consistent results the influence of the welding parameters on weld geometry and quality must be identified and controlled [34].
In conventional DC GTA welding, the main control parameters are shown in Table 2-1. The desired welding parameters are usually determined based on experience or handbook values. However, it does not insure that the selected welding parameters result in optimal or near optimal welding quality characteristics for that particular welding system and environmental conditions.
Table 2-1 Parameters for GTA welding
Primary Secondary
Current Travel speed
Arc length Polarity Shielding gas
Electrode vertex angle Filler addition
Quality characteristic of the GTA welding process
Basically, the GTA welding quality is strongly characterized by the weld pool geometry. The weld pool geometry plays an important role in determining the mechanical properties of the weld [25,35-36]. The measurements of the weld pool geometry were performed for evaluating the quality of GTA welds. The width of weld bead and the depth of penetration are used to describe the weld pool geometry, as shown in Fig.2-1.
Fig.2-1 Schematic of measurement for weld pool geometry
Parameters of the GTA welding process
Several methods are useful in determining which factors to include in the initial experiments such as brainstorming, flowcharting, and cause-effect diagram [7]. Fig.2-2 is the cause-effect diagram of this process.
Fig.2-2 Cause and effect diagram of the GTA welding process
2.5 Nd:YAG laser micro-weld
In the mass production process of lithium-ion secondary batteries, the lap-weld process of safety vent and cathode lead is the major factor to affect product quality and production efficiency. The laser spot welding is the micro-joining technique most frequently used in the electron related industry.
Spot welding was the first welding operation to be carried out with lasers. The higher-pulse repetition rates and pulse-tailoring capabilities attainable with Nd:YAG and CO2 lasers have meant that spot welding is a standard application for these devices [37,38]. However, one of the prime advantages of the Nd:YAG