1、翻译原文 Delta ferrite prediction in stainless steel welds using neural network analysis and comparison with other prediction methods M. Vasudevan a, A.K. Bhaduri a, Baldev Raj a, K. Prasad Raob aMetallurgy and Materials Group, Indira Gandhi Centre for Atomic Research, Kalpakkam, India bDepartment of Me
2、tallurgy, Indian Institute of Technology, Chennai, India Received 2 May 2002； received in revised form 11 December 2002； accepted 17 February 2003 Abstract The ability to predict the delta ferrite content in stainless steel welds is important for many reasons. Depending on the service requirement,ma
3、nufacturers and consumers often specify delta ferrite content as an alloy specification to ensure that weld contains a desired minimum or maximum ferrite level. Recent research activities have been focused on studying the effect of various alloying elements on the delta ferrite content and controlli
4、ng delta ferrite content by modifying the weld metal compositions. Over the years, a number of methods including constitution diagrams, Function Fit model, Feed-forward Back-propagation neural network model have been put forward for predicting the delta ferrite content in stainless steel welds. Amon
5、g all the methods, neural network method was reported to be more accurate compared to other methods. A potential risk associated with neural network analysis is over-fitting of the training data. To avoid over-fitting, Mackay has developed a Bayesian framework to control the complexity of the neural
6、 network. Main advantages of this method are that it provides meaningful error-bars for the model predictions and also it is possible to identify automatically the input variables which are important in the non-linear regression. In the present work, Bayesian neural network (BNN) model for predictio
7、n of delta ferrite content in stainless steel weld has been developed. The effect of varying concentration of the elements on the delta ferrite content has been quantified for Type 309 austenitic stainless steel and the duplex stainless steel alloy 2205. The BNN model is found to be more accurate co
8、mpared to that of the other methods for predicting delta ferrite content in stainless steel welds. 1. Introduction The ability to estimate the delta ferrite content accurately has proven very useful in predicting the various properties of austenitic SS welds. A minimum delta ferrite content is neces
9、sary to ensure hot cracking resistance in these welds 1,2, while an upper limit on the delta ferrite content determines the propensity to embrittlement due to secondary phases, e.g. sigma phase, etc., formed during elevated temperature service 3. At cryogenic temperatures, the toughness of the auste
10、nitic SS welds is strongly influenced by the delta ferrite content 4. In duplex stainless steel weld metals,a lower ferrite limit is specified for stress corrosion cracking resistance while the upper limit is specified to ensure adequate ductility and toughness 5. Hence, depending on the service req
11、uirement a lower limit and/or an upper limit on delta ferrite content is generally specified. During the selec-tion of filler metal composition, the most accurate diagram to date WRC-1992 is used generally to estimate the _-ferrite content 6. The Creq and Nieq formulae used for generating the WRC-19
12、92 constitution diagram is given by Creq=Cr+Mo+0.7Nb and Nieq= Ni+35C+20N+0.25Cu. The limitation of these equations is that values of the coefficients for the different elements remain unchanged irrespective of the change in the base composition of the weld. However, the relative influence of each a
13、lloying addition given by the elemental coefficients in the Creq and Nieq expressions is likely to change over the full composition range. Furthermore,these expressions ignore the interaction between the elements. Also, there are a number of alloying elements that have not been considered in the WRC
14、-1992 diagram. Elements like Si, Ti, W have not been given due to considerations, though they are known to influence the delta ferrite content. Hence, the delta ferrite content estimated using the WRC-1992 diagram would always be less accurate and may never be close to the actual measured value. In
15、the Function Fit model 7 for estimating ferrite, the difference in free energy between the ferrite and the austenite was calculated as a function of composition and this was related to ferrite number (FN). The equation used in this model to determine FN is given below: FN = A1 + exp(B + C_G)1 (1) wh
16、ereA, B and C are the constants. The advantages of this semi-empirical model over the WRC-1992 diagram include its considering effect of other alloying elements and the ease of extrapolation to higher Creq and Nieq values. This Function Fit method can be used for a wide range of weld metal compositi
17、ons and owing to the analytical form of this model, the FN can be quantified easily. However, the accuracy of this method is not greater than the WRC-1992 diagram. Vitek et al. 8,9 sought to overcome the major limitation of the constitution diagram and the Function Fit method of not taking into acco
18、unt the elemental interactions, by using neural networks for predicting ferrite in SS welds.The improvement in accuracy in predicting the delta ferrite content by using neural networks, involving a feed-forward network with a back-propagation optimization scheme, has been clearly brought in their st
19、udy. The effect of various elements on the delta ferrite content for a few base compositions was examined by calculating the FN as a function of composition. However, it was not possible in their analysis to directly interpret the elemental contributions to the final FN. The prediction and measureme
20、nt of ferrite in SS welds remains of scientific interest due to limitations in all the current methods, and newer methods and constitution diagrams are continuously being proposed to predict the delta ferrite content for a wider range of SS types. It was in this context that the development of a mor
21、e accurate neural network based predictive tool for estimating the effect of various alloying elements on the delta ferrite content for different SS welds was taken up in this work. A potential risk associated with neural network analysis is over-fitting of the training data. To avoid over-fitting, Mackay 10 developed a Bayesian framework to control the complexity of the neural network, with its main advantages being that it
