金屬材料專業(yè)外文翻譯2

1、<p><b>　　翻譯原文</b></p><p>　　Delta ferrite prediction in stainless steel welds using neural network analysis and comparison with other prediction methods</p><p>　　M. Vasudevan a,?

2、, A.K. Bhaduri a, Baldev Raj a, K. Prasad Raob</p><p>　　a Metallurgy and Materials Group, Indira Gandhi Centre for Atomic Research, Kalpakkam, India</p><p>　　b Department of Metallurgy, Indian I

3、nstitute of Technology, Chennai, India</p><p>　　Received 2 May 2002; received in revised form 11 December 2002; accepted 17 February 2003</p><p><b>　　Abstract</b></p><p>

4、;　　The ability to predict the delta ferrite content in stainless steel welds is important for many reasons. Depending on the service requirement,manufacturers and consumers often specify delta ferrite content as an alloy

5、 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 co

6、ntrolling delta ferrite content by modifying the weld metal com</p><p>　　1. Introduction</p><p>　　The ability to estimate the delta ferrite content accurately has proven very useful in predictin

7、g the various properties of austenitic SS welds. A minimum delta ferrite content is necessary to ensure hot cracking resistance in these welds [1,2], while an upper limit on the delta ferrite content determines the prope

8、nsity to embrittlement due to secondary phases, e.g. sigma phase, etc., formed during elevated temperature service [3]. At cryogenic temperatures, the toughness of the austenitic SS we</p><p>　　FN = A[1 + ex

9、p(B + C_G)]?1 (1)</p><p>　　where A, 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

10、extrapolation to higher Creq and Nieq values. This Function Fit method can be used for a wide range of weld metal compositions and owing to the analytical form of this model, the FN can be quantified easily. However, the

11、 accuracy of this method is not greater than the WRC-1992 diagram. Vitek et al. [8,9] sought to over</p><p>　　A potential risk associated with neural network analysis is over-fitting of the training data. To

12、 avoid over-fitting, Mackay [10] developed a Bayesian framework to control the complexity of the neural network, with its main advantages being that it provides meaningful error-bars for predictions and also enables iden

13、tifying the input variables that are important in the non-linear regression. Hence, in the present study, Bayesian neural network (BNN) analysis was applied to develop a generalized m</p><p>　　2. Database<

14、;/p><p>　　As the aim of the present work was to model for the FN as a function of chemical composition, the database of 924 datasets for shielded metal arc (SMA) weld compositions and delta ferrite contents, re

15、presenting the common 300-series SS weld compositions (viz., 308, 308L, 309,309L, 316, 316L, etc.) and duplex stainless steels used for generating the WRC-1992 diagram was used [11]. For the datasets in which the composi

16、tion values for elements such as Nb, Ti, V, Cu and Co were not available, their </p><p>　　and cannot be used to define the range of applicability of the neural network model as the input variables are expect

17、ed to interact in neural network analysis. In BNN analysis, size of the error-bars define the range of useful applicability of the trained network.</p><p>　　Table 1 Range, mean and standard deviations of th

18、e composition variables (input) and the FN (output)</p><p>　　3. BNN analysis</p><p>　　The networks employed consist of 13 input nodes xi representing the 13 composition variables, a number of hi

19、dden nodes hi and one output y. The schematic structure of the network is shown in Fig. 1. The single output represents the FN. Both the input and output variables were normalized within the range ±0.5 as follows:&l

20、t;/p><p>　　where xN is the normalized value of x, which has maximum and minimum values given by xmax and xmin. Eighty different neural network models were created using the datasets, with the number of the hidd

21、en units varying from 1 to 16 and with five different sets of random seeds used to initiate the network for a given number of hidden units. All these models were trained on a training dataset that consisted of a random s

22、election of half the datasets (i.e. 462 datasets), while the remaining half forme</p><p>　　Here the bias is designated as θ and is analogous to the constant in linear regression. The transfer from the hidden

23、 units to the output is linear, and is given by:</p><p>　　The output y is therefore a non-linear function of xj, with the function usually selected for flexibility being the hyperbolic tangent. Thus, the net

24、work is completely described if the number of input nodes, output nodes and the hidden units are known along with all the weights wij and biases θi.</p><p>　　These weights wij are determined by training the

25、network and involves minimization of a regularized sum of squared errors.The BNN analysis of Mackay [10] allows the calculation of error-bars with two components—one representing the perceived level of noise (σv) in the

26、output and the other indicating the uncertainty in the data fitting. This latter component of the error-bars emanating from the Bayesian framework allows the relative probabilities of the models with different complexity

27、 to be asse</p><p>　　where t is the target for the set of inputs x, while y the corresponding network output. σy is related to the uncertainty of fitting for the set of inputs x. By using LPE, the penalty fo

28、r making a wild prediction is reduced if that prediction is accompanied by an appropriately large error-bar, with a larger value of the LPE implying a better model. Further, by this method it is also possible to automati

29、cally identify the input variables that are significant in influencing the output variable, as</p><p>　　3.1. Over-fitting problem</p><p>　　In BNN analysis, two solutions are implemented which co

30、ntribute to avoid over-fitting. The first is contained in the algorithm due to MacKay [12]: the complexity parameters α and β are inferred from the data, therefore allowing automatic control of the model complexity. The

31、second resides in the training method. The database is equally divided into a training set and a testing set. To build a model, about 80 networks are trained with different number of hidden units and seeds, using the tra

32、ining</p><p>　　3.2. Committee model</p><p>　　The networks with different number of hidden units will give different predictions. But predictions will also depend on the initial guess made for th

33、e probability distribution of the weights (the prior). Optimum predictions are often made using more than one model, by building a committee. The prediction .y of a committee of networks is the average prediction of its

34、members, and the associated error-bar is calculated according to Eq. (6): </p><p>　　where L is the number of networks in a committee. Note that we now consider the predictions for a given single set of input

35、s and that exponent l refers to the model used to produce the corresponding prediction y(l ). In practice, an increasing number of networks are included in a committee and their performances are compared on the testing s

36、et. Most often,the error is minimum when the committee contains more than one model. The selected models are then retrained on the full database.</p><p>　　4. Results and discussions</p><p>　　The

37、 characteristics of the BNN model on FN is discussed in detail elsewhere [13]. The comparison between the predicted and measured FN values for the committee of models (38 models in the committee) is shown in Fig. 2 for t

38、he complete dataset. There was excellent agreement between the measured and the predicted FN values. The correlation coefficient was determined to be 0.98025.</p><p>　　4.1. Significance of the individual ele

39、ments on the FN</p><p>　　Fig. 3 indicates the significance σw of each of the input variables as perceived by the first five neural network models in the committee. The σw value represents the extent to which

40、 a particular input explains the variation in the output, as for a partial correlation coefficient in linear regres-sion analysis. It is observed from Fig. 3 that the elements Mn and Nb are not significant in influencing

41、 the FN. The observation of Mn not having a significant influence on the FN for the 300-series aus</p><p>　　Fig. 2. Comparison between the predicted and measured FN values for the entire dataset using the co

42、mmittee of models</p><p>　　Fig. 3. Perceived significance σw values of the first five FN models for each input.</p><p>　　4.2. Comparison of accuracy of present model with other existing methods&

43、lt;/p><p>　　Analysis of the error distributions (measured FN–predicted FN) for the present BNN model shows that the absolute error was <2.5 for most of the datasets used in the training, while for the FNN-19

44、99 model the absolute error was <3 for about 80% of the dataset used in training. It is important to note here that in the present BNN model, the entire datasets were used for retraining the committee of models, while

45、 in the FNN-1999 model only 90% of the datasets were used for training. Further, the err</p><p>　　error between the measured and predicted FN values for the present BNN model and the other three methods were

46、 compared and it was found that the present BNN model has the lowest error among the four methods, BNN model showing an improvement of 43%</p><p>　　over the FNN-1999 model and about 65% over the WRC-1992 di

47、agram and Function Fit model. Table 3 shows the RMS error values for all the four methods. As the RMS error values represent the quan- titative measure of the degree of fit of the various models to the datasets on which

48、they were trained, this comparison clearly establishes that among the available methods the present BNN model is the most accurate model for prediction of FN in austenitic SS welds.</p><p>　　Fig. 5. Predicte

49、d FN vs concentration of the elements for 309 austenitic stainless steels weld. The plot shows the variation in the FN when one of the element is varied and all other concentration are held constant at the 309 SS composi

50、tion except Fe, which is adjusted to compensate for the varying element concentration.</p><p>　　4.3. Effect of compositional variations on the FN</p><p>　　The severe limitation of the WRC-1992 d

51、iagram is that the coefficients in the terms for Creg and Nieg formulas are constant and hence the influence of an individual element on FN is same irrespective of the change in the base composition. As neural networks c

52、an take into account the interaction between the input variables on their influence over the output variable, the interaction between the different elements on their influence over the FN is quantified for stainless stee

53、l welds using the BNN</p><p>　　4.3.1. The 309 stainless steel weld</p><p>　　The variation in the predicted FN as a function of the variation in the concentration of the elements is found to be n

54、on-linear (Fig. 5). The FN is found to decrease with increasing concentration of the elements C, N and Ni. These elements acts as austenite stabilizers. The FN is found to increase with increasing concentration of the el

55、ements Cr, Si and V and these elements are called ferrite stabilizers. The above observations are in agreement with the literature. The elements Mn, Mo, Nb, Ti, C</p><p>　　the WRC-1992 diagram will always be

56、 less accurate. The BNN model generated by us is more accurate compared to the WRC-1992 diagram which was generated based on the linear regression analysis. Hence, the trends of the influence of concentration of the elem

57、ents on FN predicted by the model is more useful in controlling FN through compositional modifications in this type of steel (Fig. 5).</p><p>　　Fig. 6. Predicted FN vs concentration of the elements for duple

58、x stainless steel weld. The plot shows the variation in the FN when one of the element is varied and all other concentration are held constant at the duplex stainless steel composition except Fe, which is adjusted to com

59、pensate for the varying element concentration.</p><p>　　4.3.2. Duplex stainless steel (alloy 2205) weld</p><p>　　The variation in the FN with variation in the concentration of the elements is fo

60、und to be non-linear (Fig. 6). The increase in the concentration of the elements C, N, Mn and Ni is found to decrease the FN. However, the effect of Mn is not as significant as the other austenite stabilizers. The increa

61、se in the concentration of the elements Cr, Si, Mo, V and Co is found to increase the FN for the duplex stainlesssteel welds. The effect of vanadium is not as significant as the other ferrite stabili</p><p>

62、　　5. Conclusions</p><p>　　1. The generalized model for predicting the FN in stainless steel welds using BNN analysis has been developed. The accuracy of the BNN model in predicting FN is superior compared to

63、 the existing FN prediction methods.</p><p>　　2. Significance of the individual elements on FN has been quantified. Neural network analysis has shown that elements like manganese and niobium are insignifican

64、t in influencing the FN in stainless steel welds.</p><p>　　3. The effect of variation in the concentration of the elements on the FN have been quantified for 309 and duplex stainless steel welds. Neural netw

65、ork analysis has shown that there is a change in the role of elements when the base composition is changed.</p><p>　　4. Cobalt is found to be ferrite stabilizer for the duplex stainless steel welds and is fo

66、und not to influence the FN for the austenitic stainless steel welds.</p><p>　　References</p><p>　　[1] C.D. Lundin, C.P.D. Chou, Hot cracking susceptibility of austenitic stainless steel weld me

67、tals, WRC Bull. 289 (1983) 1–80.</p><p>　　[2] C.D. Lundin, W.T. Delong, D.F. Spond, Ferrite-fissuring relationships in austenitic stainless steel, Weld Met. 54 (8) (1975) 241s–246s.</p><p>　　[3]

68、 J.M. Vitek, S.A. David, The sigma phase transformation in austenitic stainless steels, Weld. J. 65 (4) (1986) 106s–111s.</p><p>　　[4] E.R. Szumachowski, H.F. Reid, Cryogenic toughness of SMA austenitic stai

69、nless steel weld metals, Weld. J. 57 (11) (1978) 325s–333s.</p><p>　　[5] D.J. Kotecki, Ferrite control in duplex stainless steel weld metal, Weld. J. 65 (10) (1986) 273s–278s.</p><p>　　[6] D.J.

70、Kotecki, D.T.A. Siewert, WRC-92 constitution diagram for stainless steel weld metals: a modification of the WRC-1988 diagram, Weld. J. 71 (5) (1992) 171s–178s.</p><p>　　[7] S.S. Babu, J.M. Vitek, Y.S. Iskand

71、er, S.A. David, New model for prediction of ferrite number in stainless steel welds, Sci. Technol.Weld. 2 (6) (1997) 279–285.</p><p>　　[8] J.M. Vitek, Y.S. Iskander, E.M. Oblow, Improved ferrite number predi

72、ction in stainless steel arc welds using artificial neural networks.Part 1. Neural network development, Weld. J. 79 (2) (2000) 33–40.</p><p>　　[9] J.M. Vitek, Y.S. Iskander, E.M. Oblow, Improved ferrite numb

73、er prediction in stainless steel arc welds using artificial neural networks.Part 2. Neural network development, Weld. J. 79 (2) (2000) 41–50.</p><p>　　[10] D.J.C. Mackay, Bayesian non-linear modeling with ne

74、ural networks,in: H. Cerjack (Ed.), Mathematical Modeling of Weld Phenomena,vol. 3, The Institute of Materials, London, 1997, pp. 359–389.</p><p>　　[11] C.N. McCowan, T.A. Siewert, D.L. Olson, Stainless stee

75、l weld metal:prediction of ferrite content, WRC Bull. 342 (1989) 1–36.</p><p>　　[12] D.J.C. MacKay, A practical Bayesian framework for backpropagation networks, Neural Comput. 3 (1992) 448–472.</p>&l

76、t;p>　　[13] M. Vasudevan, M. Murugananth, A.K. Bhaduri, Application of Bayesian neural network for modeling and prediction of FN in austenitic stainless steel welds, in: H. Cerjak, H.K.D.H. Bhadeshia (Eds.), Mathematic

77、al Modelling of Weld Phenomena—VI, Institute of Materials, 2002, pp. 1079–1099.</p><p>　　[14] E.R. Szumachowski, D.J. Kotechi, Effect of manganese on stainless steel weld metal ferrite, Weld. J. 63 (5) (1984

78、) 156s–161s.</p><p>　　[15] M. Vasudevan, A.K. Bhaduri, B. Raj, K. Prasad Rao, Bayesian neural network analysis of the compositional variations on the ferrite number in 316LN austenitic stainless steel welds,

79、 Trans. Ind. Ins.Met. 55 (5) (2002) 389–396.</p><p><b>　　中文翻譯</b></p><p>　　利用神經(jīng)網(wǎng)絡(luò)預(yù)測與其他預(yù)測方法對δ鐵素體不銹</p><p><b>　　焊縫的分析和比較</b></p><p><b>　　摘要&

80、lt;/b></p><p>　　能夠預(yù)測不銹鋼焊縫中δ鐵素體含量的重要性有很多原因。根據(jù)服務(wù)的需求,制造商和消費(fèi)者常常指定δ鐵素體含量作為合金規(guī)格,以確保焊接所需的最低或包含最大的鐵素體的水平。最近的研究活動(dòng)都集中在研究各種合金元素對δ鐵素體含量的影響和通過改變焊縫金屬的成分來控制鐵素體的含量。多年以來,大量的研究包括金相圖、功能合適的模型，倒傳遞類神經(jīng)網(wǎng)絡(luò)模型前饋提出了預(yù)測不銹鋼焊縫中δ鐵素體含量的方法

81、。在所有的方法中，據(jù)報(bào)道神經(jīng)網(wǎng)絡(luò)方法相比其他方法更為準(zhǔn)確。一個(gè)與神經(jīng)網(wǎng)絡(luò)分析相關(guān)的潛在風(fēng)險(xiǎn)是訓(xùn)練資料的過擬合。為了避免過擬合,麥凱已經(jīng)發(fā)展出一種貝葉斯框架來控制復(fù)雜的神經(jīng)網(wǎng)絡(luò)。</p><p>　　該方法的主要優(yōu)點(diǎn)是它提供了有意義的error-bars模型的預(yù)測,它也有可能識別非線性回歸中自動(dòng)輸入變量具有的重要意義。目前的研究工作、貝葉斯神經(jīng)網(wǎng)絡(luò)模型(BNN)對不銹鋼焊接點(diǎn)δ鐵素體含量的預(yù)測已經(jīng)提高。不同濃度的影

82、響的元素對鐵素體內(nèi)容被量化三角洲對于類型309奧氏體不銹鋼和雙相不銹鋼合金2205，不同濃度的元素對δ鐵素體含量的影響被量化。BNN的模型被發(fā)現(xiàn)相比其他預(yù)測不銹鋼焊縫中δ鐵素體含量的方法更加準(zhǔn)確。</p><p><b>　　1．介紹</b></p><p>　　經(jīng)證明能夠精確地判斷δ鐵素體含量對預(yù)測奧氏體不銹鋼焊縫的各種性質(zhì)非常重要。為了確保這些焊縫中的熱裂紋阻力，

83、δ鐵素體含量最低是必要的[1,2]，由于二次相，σ相等等，形成于高溫條件下，δ鐵素體含量的上限就決定了脆裂的傾向[3]。在低溫環(huán)境下，奧氏體不銹鋼焊縫的韌性受δ鐵素體含量強(qiáng)烈影響[4]。對于雙相不銹鋼焊縫金屬,指定一個(gè)較低的鐵素體限制是因?yàn)閼?yīng)力腐蝕開裂阻力而指定上限是為了確保足夠的延性和韌性[5]。因此,根據(jù)服務(wù)的需求較低的限制和/或一個(gè)上限鐵素體含量通常被指定。在金屬填料組成的選擇期間、確定了WRC-1992最準(zhǔn)確的被普遍使用估算鐵素

84、體含量的圖[6]。通過Creq = Cr +Mo+ 0.7Nb、Nieq =Ni+ 35 C + 20 N + 0.25Cu公式的運(yùn)用生成了WRC- 1992金相圖。這些方程的局限性是不考慮焊縫堿基組成方面的變化不同元素保持不變的價(jià)值觀系數(shù)。然而,Creq和Nieq表達(dá)式中,每個(gè)合金被添加的元素系數(shù)的相對影響可能改變整個(gè)組成范圍。此外，這些表達(dá)式忽視了元素之間的相互作用。同時(shí)，WRC- 1992金相圖中沒有考慮相對數(shù)量的合金元素。雖然硅

85、、鈦、鎢是已知</p><p>　　FN = A[1 + exp(B + C_G)]?1 (1)</p><p>　　其中A，B和C是常數(shù)。由于WRC-1992圖的半經(jīng)驗(yàn)?zāi)Ｐ偷膬?yōu)勢，包括考慮其他合金元素的效果和易用性外推到更高的Creq和Nieq值。此函數(shù)擬合方法，可以為焊縫金屬組成，由于該模型的解析形式的廣泛使用，F(xiàn)N可能容易量化。然而，這種方法的精度不大于在WRC-1

86、992圖。維特克等人。 [8,9]尋求克服憲法圖和函數(shù)擬合的方法，不考慮使用鐵素體不銹鋼焊縫預(yù)測的神經(jīng)網(wǎng)絡(luò)元素的相互作用，主要限制。在精度δ鐵素體含量，利用神經(jīng)網(wǎng)絡(luò)預(yù)測與反向傳播的優(yōu)化方案，涉及前饋網(wǎng)絡(luò)的改善，已經(jīng)清楚地帶來了他們的研究。 幾個(gè)堿基組成的各種元素上的δ鐵素體含量的影響進(jìn)行了檢查計(jì)算作為一個(gè)功能組成的新生力量。然而，正是他們的分析，可以直接解釋最終新生力量元素的貢獻(xiàn)。預(yù)測和鐵素體不銹鋼焊縫測量仍然對科學(xué)的興趣，在目前所有的

87、方法，由于限制，新的方法和憲法圖不斷被提出來預(yù)測一個(gè)SS的類型更廣泛的δ鐵素體含量。正是在這種背景下，在這項(xiàng)工作中，采取了更精確的神經(jīng)網(wǎng)絡(luò)的發(fā)展為基礎(chǔ)的預(yù)測工具，估計(jì)不同的不銹鋼焊縫的δ鐵素體含量的各種合金元素的作用。訓(xùn)練數(shù)據(jù)擬合與神經(jīng)網(wǎng)絡(luò)分析是一個(gè)潛在的風(fēng)險(xiǎn)。為了避免過擬合，麥凱[10]開發(fā)了貝葉斯框</p><p><b>　　2. 數(shù)據(jù)庫</b></p><p>

88、;　　由于目前的工作的目的是為FN功能的化學(xué)成分做模型，924集適合于（SMA）屏蔽金屬電弧焊接組成和δ鐵素體含量較常見的300系列不銹鋼焊接組成（即數(shù)據(jù)庫[11]，308，308L，309,309L，316，316L等）和用雙相不銹鋼產(chǎn)生WRC-1992圖的運(yùn)用。</p><p>　　表1范圍，組成變量的平均值和標(biāo)準(zhǔn)偏差（輸入）和檔案號（輸出）</p><p>　　鈮，鈦，V，銅，鈷等元

89、素成分值不為數(shù)據(jù)集，其值被假定為零。表1顯示的范圍內(nèi)，每個(gè)組成的變量的均值和標(biāo)準(zhǔn)差（輸入）和檔案號（輸出）。這只是一種覆蓋范圍的想法，并不能用來作為預(yù)計(jì)到互動(dòng)的神經(jīng)網(wǎng)絡(luò)分析的輸入變量定義神經(jīng)網(wǎng)絡(luò)模型的適用范圍。在貝萊爾分析中， 錯(cuò)誤條大小定義了訓(xùn)練有素的網(wǎng)絡(luò)有益的適用性范圍。</p><p><b>　　3、貝萊爾分析</b></p><p>　　網(wǎng)絡(luò)包括由13個(gè)輸入

90、節(jié)點(diǎn)xi代表的13變量、許多hi隱藏節(jié)點(diǎn)和一個(gè)輸出y組成，網(wǎng)絡(luò)結(jié)構(gòu)示意圖如圖1。單個(gè)輸出代表的檔案號。輸入和輸出變量進(jìn)行標(biāo)準(zhǔn)化±0.5范圍內(nèi)的如下：</p><p>　　其中，xn是X，其中有由XMAX和XMIN給出的最高和最低值的標(biāo)準(zhǔn)化值。八十個(gè)不同的神經(jīng)網(wǎng)絡(luò)模型創(chuàng)建了使用的數(shù)據(jù)集，許多隱藏的單位數(shù)從1到16變動(dòng)，5套不同的隨機(jī)種子用于啟動(dòng)一個(gè)給定數(shù)量隱藏的單位的網(wǎng)絡(luò)。所有這些模型在一個(gè)由隨機(jī)選擇一半

91、組成的數(shù)據(jù)集（即462集）中進(jìn)行了培訓(xùn)，而剩下的一半形成測試數(shù)據(jù)集，被用來檢驗(yàn)如何用看不見的數(shù)據(jù)形成模型的。</p><p>　　圖1.輸入節(jié)點(diǎn)、隱單位和輸出節(jié)點(diǎn)的網(wǎng)絡(luò)結(jié)構(gòu)示意圖</p><p>　　從投入產(chǎn)出的計(jì)算，通過以下的雙曲正切傳遞函數(shù)操作輸入XJ的線性函數(shù)乘以權(quán)重wij，使輸入每一個(gè)隱患的單位，其中N是輸入變量的總數(shù)：</p><p>　　這里的斜紋被指定

92、為θ，類似于線性回歸的常數(shù)。從隱藏的單位轉(zhuǎn)移到輸出是線性的，和由下式給出：</p><p>　　輸出y是一個(gè)XJ的非線性函數(shù)，通常選擇的靈活性是雙曲正切函數(shù)。因此，網(wǎng)絡(luò)是完全描述如果輸入節(jié)點(diǎn)，輸出節(jié)點(diǎn)和隱藏的單位數(shù)是已知的所有的權(quán)重wij和斜紋θi。這些權(quán)重wij通過培訓(xùn)網(wǎng)絡(luò)，并且涉及到一個(gè)正規(guī)化平方誤差總和最小化被確定。</p><p>　　馬偕的的貝萊爾分析[10]計(jì)算錯(cuò)誤酒吧允許兩部

93、分組成一個(gè)代表知覺的噪音水平（σV）輸出和其他指示的數(shù)據(jù)擬合的不確定性。這后者的貝葉斯框架產(chǎn)生的錯(cuò)誤酒吧組成部分，允許不同復(fù)雜程度的相對概率模型進(jìn)行評估。這使得定量錯(cuò)誤的酒吧，這取決于在裝修，空間功能的不確定性在輸入空間的位置不同的估計(jì)。因此，而不是一套獨(dú)特的重量計(jì)算，權(quán)重的概率分布是用來定義在裝修的不確定性。因此，這些錯(cuò)誤酒吧變大，當(dāng)數(shù)據(jù)稀疏或局部嘈雜。在這種情況下，錯(cuò)誤的一個(gè)非常有用的措施，是由以下的預(yù)測誤差（液相）的對數(shù)：<

94、/p><p>　　其中t是為輸入x集合的目標(biāo)，而y對應(yīng)輸出的網(wǎng)絡(luò)。 ΣY與擬合輸入x集合的不確定性相關(guān)。用液相外延，使野生預(yù)測的刑罰減少，如果這一預(yù)測是一個(gè)較大的值，這意味著一個(gè)更好的模型的液相外延，伴隨著一個(gè)適當(dāng)大的錯(cuò)誤吧。此外，用這種方法還可以自動(dòng)識別輸入變量，對影響輸出變量有著重要的作用，在回歸分析中不太重要的輸入變量可以降低加權(quán)。</p><p>　　3.1、過度擬合問題</p&

95、gt;<p>　　在貝萊爾的分析，兩種方案的實(shí)施，有助于避免過擬合。首先由于麥凱在算法中被容納[12]：從數(shù)據(jù)推斷出復(fù)雜性參數(shù)α和β，因此允許模型的復(fù)雜的自動(dòng)化控制。第二駐存在于訓(xùn)練方法中。該數(shù)據(jù)庫同樣分為訓(xùn)練集和測試集。要建立一個(gè)模型，約80網(wǎng)絡(luò)隱患的單位和種子使用的訓(xùn)練集，不同數(shù)量的訓(xùn)練，然后他們通過液相排名使用看不見的測試集預(yù)測。</p><p><b>　　3.2、委員會(huì)模式<

96、;/b></p><p>　　隱患單位的不同數(shù)量的網(wǎng)絡(luò)，將給予不同的預(yù)測。但預(yù)測也將取決于初始猜測的概率分布的權(quán)重（前）。最佳的預(yù)測往往使用多個(gè)模型，建立了一個(gè)委員會(huì)。網(wǎng)絡(luò)的一個(gè)委員會(huì)預(yù)測¯y是其成員的平均預(yù)測，并根據(jù)公式計(jì)算相關(guān)的錯(cuò)誤。（6）：</p><p>　　其中L是網(wǎng)絡(luò)中的一個(gè)委員會(huì)。請注意，我們現(xiàn)在考慮一個(gè)給定的單組輸入和指數(shù)L用于生產(chǎn)相應(yīng)的Y（L）模型的預(yù)測。

97、在實(shí)踐中，越來越多的網(wǎng)絡(luò)，包括在委員會(huì)和測試集相比，他們的表演。大多數(shù)情況下當(dāng)該委員會(huì)包含多個(gè)模型，錯(cuò)誤是最低的。選定了模型，然后再培訓(xùn)完整的數(shù)據(jù)庫。</p><p><b>　　4、結(jié)果與討論</b></p><p>　　FN貝萊爾模型的特點(diǎn)關(guān)于細(xì)節(jié)進(jìn)行了討論[13]。 FN委員會(huì)（該委員會(huì)在38模型）模型預(yù)測值與實(shí)測值之間的比較如圖2所示為完整的數(shù)據(jù)集。測量和預(yù)測

98、FN值之間有很好的協(xié)議。相關(guān)系數(shù)確定為0.98025。</p><p>　　4.1、FN圖3中的各個(gè)元素的意義表明委員會(huì)的第一個(gè)五年的神經(jīng)網(wǎng)絡(luò)模型的每個(gè)輸入變量的意義σW。σW值代表一個(gè)特定的輸入在何種程度上解釋為輸出的變化,如同一個(gè)線性回歸中的錫安分析偏相關(guān)系數(shù)。</p><p>　　圖2使用模型委員會(huì)比較了預(yù)測和實(shí)測的FN值之間的整個(gè)數(shù)據(jù)集

99、 </p><p>　　圖3認(rèn)為每個(gè)輸入值第一個(gè)五年FN模型的意義σW</p><p>　　從圖3可以觀察到，Mn和Nb元素對FN沒有有效的影響。對300系列奧氏體不銹鋼錳的觀察報(bào)告在FN上不具有重大影響，，它與報(bào)告的結(jié)果錳的變化從1到12 WT％幾乎沒有影響一致沉積的FN[14]。然而目前的研究發(fā)現(xiàn)，有一個(gè)對FN影響不大的元素Nb，包括在WRC-1992圖所