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journa l homepage: www.e lsev ier .com/ locate / jmatprotec

eural network modeling of arc spot welding

bdulkadir Cevika,∗, M. Akif Kutukb, Ahmet Erkligb, Ibrahim H. Guzelbeyb

Department of Civil Engineering, University of Gaziantep, TurkeyDepartment of Mechanical Engineering, University of Gaziantep, Turkey

r t i c l e i n f o

rticle history:

eceived 14 August 2006

eceived in revised form 6 June 2007

ccepted 12 September 2007

a b s t r a c t

This study presents neural network (NN) for the prediction of ultimate capacity of arc spot

welding. The proposed NN model is based on experimental results. The ultimate capacity

of arc spot welding is modeled in terms of weld strength, average welding thickness and

diameter. The results of the proposed NN model are later compared with results of existing

codes and are found to more accurate. Moreover, the proposed NN model is presented in

eywords:

rc spot welding

eural networks

explicit form as a mathematical function. Parametric studies are also carried out to ana-

lyze the effect of each variable. The proposed NN model is a unified formulation valid for

governing shear failures.

© 2007 Elsevier B.V. All rights reserved.

part is 0.18 in. (4.57 mm) or less. Otherwise, when the thick-ness of connected parts are thicker than 0.18 in. (4.57 mm), the

ltimate capacity

. Introduction

elding is a very effective means to connect two or moreieces of material together. The four most commonly usedelding processes are shielded metal arc welding (SMAW),

ubmerged arc welding (SAW), gas metal arc welding (GMAW),nd flux core arc welding (FCAW) (Chen, 1999).

Among these processes arc spot welding (Fig. 1) has becomeopular recently due to its ability to spot weld from one sidef the work as a fast method of producing multiple spot weldsith a high degree of reproducibility. Arc spot welding is aIG/MAG method intended to produce spot welds. The weld-

ng torch has a gas nozzle with support legs, and the weldingime is controlled by a timer. The resulting welds are oftenverlap joints, as produced by conventional resistance spotelding. However, in this case, the workpiece needs to beccessible from both sides (Merritt and Ricketts, 2001; Weman,003).

In comparison with continuous welding, the process has

he following advantages (Merritt and Ricketts, 2001; Weman,003):

∗ Corresponding author. Tel.: +90 342 3172409; fax: +90 342 3601107.E-mail address: akcevik@gantep.edu.tr (A. Cevik).

924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.jmatprotec.2007.09.025

• Less heating and distortion.• Very simple to operate: simply position and press.• Lower, better-shaped convexity, particularly when welding

thin sheet.

2. Nominal strength of arc spot welds

Welds used for cold-formed steel construction may be clas-sified as arc welds (or fusion welds) and resistance welds.Arc welding is usually used for connecting cold-formed steelmembers to each other as well as connecting such thin mem-bers to heavy, hot-rolled steel framing members. It is used forgroove welds, arc spot welds, arc seam welds, fillet welds, andflare groove welds. The AISI design provisions for welded con-nections are applicable only for cold-formed steel structuralmembers, in which the thickness of the thinnest connected

welded connection should be designed according to the AISCSpecifications (AISC, 1989, 1993). Additional design informa-

138 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 137–144

Fig. 1 – Arc spot weld—single thickness of sheet (Chen,

4. Optimal NN model selection

1999).

tion on structural welding of sheet steels can also be found inthe AWS Code (Chen, 1999; AWS, 1989).

In AISI (1996) arc spot welds are divided into two types, i.e.,Section E2.2.1 shear and Section E2.2.2 tension. The experi-mental database used in this article (obtained from referenceMcGuire and Pekoz, 1979), only dealt with arc spot welds sub-jected to shear. According to Section E2.2.1 of AISI (1996) thegoverning equations are as follows (CCFSWC, 2001).

The nominal shear strength, �n, of each arc spot weldbetween sheet or sheets and supporting member shall bedetermined by using the smaller of either:

(a)�n = 0.589(de)2Fxx (1)

(b)For(

da

t

)≤ 0.815

(E

Fu

)0.5, �n = 2.20(t)(da)(Fu) (2)

For 0.815(

E

Fu

)0.5<

(da

t

)≤ 1.397

(E

Fu

)0.5,

�n = 0.280

[1 + 5.59

(E/Fu)0.5

(da/t)

](t)(da)(Fu) (3)

For(

da

t

)≥ 1.397

(E

Fu

)0.5, �n = 1.40(t)(da)(Fu) (4)

where �n is the nominal shear strength of an arc spot weld, dthe visible diameter of outer surface of arc spot weld, da theaverage diameter of the arc spot weld at mid-thickness of twhere da the (d − t) for a single sheet and (d − 2t) for multiplesheets (not more than four lapped sheets over a supportingmember), and de is the effective diameter of fused area atplane of maximum shear transfer.

de = 0.7d − 1.5t but ≤ 0.55d (5)

t is the total combined base steel thickness (exclusive of coat-ings) of sheets involved in shear transfer above the plane ofmaximum shear transfer, Fxx the filler metal strength desig-

nation in AWS electrode classification, and Fu is the tensilestrength as specified in Section A3.1 or A3.2 or as reduced forlow ductility steel (CCFSWC, 2001).

Fig. 2 – Basic elements of an artificial neuron.

3. Neural networks

A neural network is a ‘machine’ that is designed to model theway in which the brain performs a particular task or func-tion of interest, the network is usually implemented usingelectronic components or simulated in software on a digi-tal computer. Neural networks are an information processingtechnique built on processing elements, called neurons thatare connected to each other (Hecht-Nielsen, 1990).

Artificial neuron (Fig. 2) is the basic element of a neuralnetwork which consists of three main components namely asweights, bias, and an activation function. Each neuron receivesinputs x1, x2,. . ., xn, attached with a weight wi which showsthe connection strength for that input for each connection.Each input is then multiplied by the corresponding weight ofthe neuron connection. A bias bi can be defined as a type ofconnection weight with a constant nonzero value added tothe summation of inputs and corresponding weights u, givenin the following equation:

ui =H∑

j=1

wijxj + bi (6)

The summation ui is transformed as the output using a scalar-to-scalar function called an “activation or transfer function”,F(ui) yielding a value called the unit’s “activation”, as follows:

O = f (ui) (7)

Neural networks are commonly classified by their networktopology (i.e. feedback, feed forward) and learning or train-ing algorithms (i.e. supervised, unsupervised). For example amultilayer feed forward neural network with back propagationindicates the architecture and learning algorithm of the neu-ral network. Back propagation algorithm is used in this study,which is the most widely used supervised training method fortraining multilayer neural networks due to its simplicity andapplicability. It is based on the generalized delta rule and waspopularized by Rumelhart et al. (1986).

The performance of a NN model mainly depends on the net-work architecture and parameter settings. One of the most

j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 137–144 139

Table 1 – Back propagation Training Algorithms used inNN training

Matlab functionname

Algorithm

trainbfg BFGS quasi-Newton back propagationtraincgf Fletcher–Powell conjugate gradient back

propagationtraincgp Polak–Ribiere conjugate gradient back

propagationtraingd Gradient descent back propagationtraingda Gradient descent with adaptive lr back

propagationtraingdx Gradient descent w/momentum and

adaptive linear back propagationtrainlm Levenberg–Marquardt back propagationtrainoss One step secant back propagationtrainrp Resilient back propagation (Rprop)trainscg Scaled conjugate gradient back

daoertrpv

Viwtaiedanlb%aNtniaNfiitg“pfiai

propagation

ifficult tasks in NN studies is to find this optimal networkrchitecture, which is based on determination of numbers ofptimal layers and neurons in the hidden layers by trial andrror approach. The assignment of initial weights and otherelated parameters might also influence the performance ofhe NN in a great extent. However there is no well-definedule or procedure to have optimal network architecture andarameter settings where trial and error method still remainsalid. This process is very time consuming.

In this study Matlab NN toolbox is used for NN applications.arious Back propagation Training Algorithms used are given

n Table 1. Matlab NN toolbox randomly assigns the initialeights for each run each time, which considerably changes

he performance of the trained NN even all parameters and NNrchitecture are kept constant. This leads to extra difficultiesn the selection of optimal network architecture and param-ter settings. To overcome this difficulty a program has beeneveloped in Matlab, which handles the trial and error processutomatically. The program tries various number of layers andeurons in the hidden layers both for first and second hidden

ayers for a constant epoch for several times and selects theest NN architecture with the minimum MAPE (mean absoluteerror) or RMSE (root mean squared error) of the testing set,

s the training of the testing set is more critical. For instance aN architecture with 1 hidden layer with 7 nodes is tested 10

imes and the best NN is stored where in the second cycle theumber of hidden nodes is increased up to 8 and the process

s repeated. The best NN for cycle 8 is compared with cycle 7nd the best one is stored as best NN. This process is repeatedtimes where N denotes the number of hidden nodes for the

rst hidden layer. This whole process is repeated for chang-ng number of nodes in the second hidden layer. More overhis selection process is performed for different back propa-ation training algorithms such as “trainlm”, “trainscg” andtrainbfg” given in Table 1. The program begins with sim-

lest NN architecture, i.e. NN with 1 hidden node for therst and second hidden layers and ends up with optimal NNrchitecture. The flowchart is of the whole process is shownn Fig. 3.

Fig. 3 – Flowchart of optimal NN selection.

5. Numerical application

The main focus of this study is nominal strength predictionof arc spot welds using NNs based on experimental values.Therefore an extensive literature survey has been performedfor available experimental results. Experimental results (120tests) in Table A1 taken from reference AISI, 1996 given withrelated material parameters were used as training and testsets for NN training. The datasets for test and training arerandomly selected among experimental results where 97 setsare training set and 23 sets are test set. The data collectedwere divided according to the governing failure equation pre-sented in Section E2.2.1-1 of AISI (AWS, 1989). Failure of 37specimens was governed by Eq. (1), while 55 specimens byEq. (2), 12 specimens by Eq. (3), and 11 specimens by Eq.(4). Detailed comparisons (CCFSWC, 2001) can be found inTable A1.

5.1. Results of NN model

The optimal NN architecture in this part was found to be3–7–1 NN architecture with logistic sigmoid transfer function(logsig). The training algorithm was quasi-Newton back prop-

140 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t

Table 2 – Statistical parameters of train and test sets

R MAPE MSE

Train set 0.984 0.09221 2.748628Test set 0.969 0.138573 3.174732

Fig. 4 – Correlation of NN and experimental results fortraining set.

agation (BFGS). Statistical parameters of test and training setsof NN model are presented in Table 2. The prediction of theproposed NN model versus actual experimental values andtheir comparison with previously proposed formulations isgiven in Table A1. The correlation for NN model and exper-imental results of learning and testing sets are given inFigs. 4 and 5. The results of proposed NN model are more

accurate compared to existing design equations as given inTable A1.

Fig. 5 – Correlation of NN and experimental results for testset.

e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 137–144

6. Explicit formulation of NN model

The main objective is to obtain the explicit formulationof nominal shear strength as a function of geometric andmechanical properties of spot welding (the parameters, Fu, d,tav, were defined in Section 2):

�n = f (Fu, d, tav)

�n = 100(

11 + e−W

)

where

W = −5.22(

11 + e−U1

)+ 1.29

(1

1 + e−U2

)+ 615

(1

1 + e−U3

)

+0.19(

11 + e−U4

)+ (−0.12)

(1

1 + e−U5

)

+(−0.18)(

11 + e−U6

)+ (−0.13)

(1

1 + e−U7

)+ 4.185

U1 = (0.009Fu) + (13.1d) + (−24.5tav) + 74.3U2 = (0.24Fu) + (−18.3d) + (34.6tav) + 8.1U3 = (−1.01Fu) + (−85.5d) + (16.5tav) − 452.1U4 = (0.127Fu) + (16.6d) + (−103.75tav) − 7U5 = (0.122Fu) + (−66.07d) + (−107.6tav) + 64.2U6 = (0.184Fu) + (−52d) + (−53.1tav) + 57.3U7 = (−0.005Fu) + (−4.47d) + (−74.02tav) + 6.1

The proposed equation above is obtained from NN tool-box of Matlab using a developed macro. It should be notedthat the proposed explicit formulation of the NN models pre-sented above are valid for the ranges of training set given inTable A1. Further details on explicit formulations of NN mod-els can be found in Guzelbey et al. (2006a,b) and Cevik andGuzelbey (2007).

7. Parametric study

It is obvious from statistical results (R = 0.985 for training andR = 0.969 for testing) above that the proposed ANN model

Fig. 6 – Trend of �n vs. Fu (tav = 0.02 in.).

j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 137–144 141

Fig. 7 – Trend of �n vs. Fu (tav = 0.04 in.).

a(aitstoppTp

8

Tpffis

Fig. 9 – Performance of experimental shear strength vs. NNshear strength.

Fig. 10 – Performance of experimental shear strength vs.shear strength computed according to AISI (1996).

Fig. 8 – Trend of �n vs. tav (d = 0.6 in.).

ccurately learned to map the relationship between the �n

nominal shear strength of arc spot weld) and its geometricnd mechanical properties. Thus the trained ANN proposedn this study was used to conduct a parametric study to inves-igate the effect of changing geometric parameters and yieldtrength on the nominal shear strength of arc spot welds. Therend for various parameters is shown in Figs. 6–8. Observedutcomes may be given as: The relationship of geometricarameters with yield strength (FY) is found to be directly pro-ortional and linearly dependent on which was as expected.he trend of geometric parameters with each other shows aarabolic relationship in general.

. Conclusion

his study proposes an approach for nominal shear strengthrediction of arc spot welding based on NNs. Mainly 4 different

ailure types are observed for arc spot welding regarding shearailure. Thus the nominal shear strength of arc spot weldings calculated according to the governing failure equation pre-ented in Section E2.2.1-1 of AISI (1996). This study presents

a unified formulation based on NNs being valid for all shearfailure types at the same time. The results of the proposedNN model are compared with results of existing design equa-tion of AISI and are found to be more accurate (Figs. 9 and 10).The proposed NN model is further derived in explicit form asa mathematical function. The outcomes of the study are verypromising in general.

Acknowledgement

This study is supported by Gaziantep University ScientificResearch Projects Unit.

Appendix A

Results of proposed NN model compared with codes is givenin Table A1.

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137–144

Table A1 – Results of proposed NN model compared with existing codes (bold sets are test sets)

Specimendesignation

Fu (ksi) d (in.) tav (in.) �uoa (kips) de da da/t Eq. (1) �n

b �n�uo

Eq. (2) �n�n�uo

Eq. (3) �n�n�uo

Eq. (4) �n�n�uo

�nnc �nn

�uo

AA/B18/7D1 67 0.79 0.049 13.5 0.435 0.0491 15.1 NA NA 10.7 0.79 NA NA NA NA 11.63 0.86AA/B18/7D2 67 0.8 15 12.4 0.75 0.75 15 NA NA 11.1 0.90 NA NA NA NA 11.87 0.96AA/B18/7D3 67 0.81 0.049 13.1 0.446 0.761 15.5 NA NA 11 0.84 NA NA NA NA 11.82 0.90AA/B18/7D4 67 0.85 0.05 14.4 0.468 0.8 16 NA NA 11.8 0.82 NA NA NA NA 12.29 0.85A A/B 28/7 C1 109.8 0.64 0.016 2.76 0.352 0.624 39 NA NA NA NA NA NA 3.07 1.11 3.32 1.20A A/B 28/7 C2 109.8 0.64 0.016 1.94 0.352 0.624 39 NA NA NA NA NA NA 3.07 1.58 3.32 1.71A A/B 28/7 C3 109.8 0.57 0.016 2.6 0.314 0.554 34.6 NA NA NA NA NA NA 2.73 1.05 2.76 1.06A A/B 28/7 C4 109.8 0.59 0.016 2.54 0.325 0.574 35.9 NA NA NA NA NA NA 2.82 1.11 2.91 1.15A A/B 28/7 C5 109.8 0.56 0.016 2.72 0.308 0.544 34 NA NA NA NA NA NA 2.68 0.99 2.69 0.99A A/B 18/7 D1 64.7 0.78 0.044 7.68 0.429 0.736 16.7 NA NA 9.22 1.20 NA NA NA NA 10.6 1.38A A/B 18/7 D2 64.7 0.74 0.044 9.04 0.407 0.696 15.8 NA NA 8.72 0.96 NA NA NA NA 10.1 1.12A A/B 18/7 D3 64.7 0.73 0.044 8.02 0.402 0.686 15.6 NA NA 8.59 1.07 NA NA NA NA 9.97 1.24A A/B 18/7 D4 64.7 0.73 0.044 10 0.402 0.686 15.6 NA NA 8.59 0.86 NA NA NA NA 9.97 1.00A A/B 18/7 D5 64.7 0.74 0.044 10 0.407 0.696 15.8 NA NA 8.72 0.87 NA NA NA NA 10.1 1.01A E/B 28/7 C1 98 0.43 0.018 1.9 0.237 0.412 22.9 NA NA NA NA 2.13 1.12 NA NA 2.05 1.08A E/B 28/7 C2 98 0.44 0.018 2.2 0.4222 0.422 23.4 NA NA NA NA 2.14 0.97 NA NA 2.09 0.95A E/B 28/7 C3 98 0.46 0.018 1.4 0.253 0.442 24.6 NA NA NA NA NA NA 2.18 1.56 2.2 1.57A E/B 28/7 C4 98 0.52 0.018 3 0.286 0.502 27.9 NA NA NA NA NA NA 2.48 0.83 2.55 0.85A A/B 12/7 D1 51.1 0.79 0.108 13.5 0.391 0.682 6.31 10.8 0.80 NA NA NA NA NA NA 10.52 0.78A A/B 12/7 D2 51.1 0.78 0.108 8.84 0.384 0.672 6.22 10.4 1.18 NA NA NA NA NA NA 9.99 1.13A A/B 12/7 D3 51.1 0.78 0.108 8.11 0.384 0.672 6.22 10.4 1.28 NA NA NA NA NA NA 9.99 1.23A A/B 12/7 D4 51.1 0.8 0.108 8.22 0.398 0.692 6.41 11.2 1.36 NA NA NA NA NA NA 11.01 1.34A A/B 12/7 D5 51.1 0.82 0.108 11.3 0.412 0.712 6.59 12 1.06 NA NA NA NA NA NA 11.9 1.05AE/C28/16C1 98 0.39 0.018 2.55 0.215 0.372 20.7 NA NA NA NA 2.1 0.82 NA NA 1.87 0.73AE/C28/16C2 98 0.4 0.018 1.36 0.22 0.382 21.2 NA NA NA NA 2.1 1.54 NA NA 1.91 1.40AE/C28/16C3 98 0.41 0.018 2 0.226 0.392 21.8 NA NA NA NA 2.1 1.05 NA NA 1.95 0.98AE/C28/16C4 98 0.41 0.018 2.3 0.226 0.392 21.8 NA NA NA NA 2.1 0.91 NA NA 1.95 0.85AE/C28/16C5 98 0.44 0.018 2.7 0.242 0.422 23.4 NA NA NA NA 2.1 0.78 NA NA 2.09 0.77A E/B 14/7 D1 56.4 1 0.081 28.3 0.55 0.919 11.3 NA NA 18.5 0.65 NA NA NA NA 25.8 0.91A E/B 14/7 D2 56.4 1.01 0.081 27.6 0.556 0.929 11.4 NA NA 18.8 0.68 NA NA NA NA 25.9 0.94A E/B 14/7 D3 56.4 1.03 0.081 27.8 0.567 0.95 11.8 NA NA 19 0.68 NA NA NA NA 25.88 0.93A E/B 14/7 D4 56.4 1 0.081 28.9 0.55 0.919 11.4 NA NA 18.4 0.64 NA NA NA NA 25.8 0.89A E/B 14/7 D5 56.4 1.1 0.082 27.9 0.605 1.018 12.5 NA NA 20.6 0.74 NA NA NA NA 24.8 0.89A E/B 18/7 D1 56.4 0.87 0.054 13.9 0.479 0.817 15.3 NA NA 10.8 0.78 NA NA NA NA 12.73 0.92A E/B 18/7 D2 56 4 0 810 0 054 15 0 446 0 756 14 NA NA 10.1 0.67 NA NA NA NA 12.37 0.82AE/B18/7D3 56.4 0.83 0.055 14.5 0.457 0.775 14.2 NA NA 10.5 0.72 NA NA NA NA 12.62 0.87AE/B18/7D4 56.4 0.87 0.054 14.5 0.479 0.816 15.1 NA NA 10.9 0.75 NA NA NA NA 12.73 0.88AE/B18/7D5 56.4 0.88 0.054 14 0.484 0.826 15.3 NA NA 11.1 0.79 NA NA NA NA 12.78 0.91AE/B18/16D1 56.4 0.79 0.055 12.9 0.435 0.735 13.4 NA NA 10 0.78 NA NA NA NA 12.35 0.96AE/B18/16D2 56.4 0.8 0.056 10.8 0.44 0.744 13.2 NA NA 10.4 0.96 NA NA NA NA 12.54 1.16AE/B18/16D3 56.4 0.81 0.056 12.4 0.446 0.755 13.6 NA NA 10.4 0.84 NA NA NA NA 12.6 1.02AE/B18/16D4 56.4 0.83 0.054 10.9 0.457 0.776 14.4 NA NA 10.4 0.95 NA NA NA NA 12.5 1.15AE/B18/16D5 56.4 0.85 0.054 13.2 0.468 0.796 14.7 NA NA 10.7 0.81 NA NA NA NA 12.62 0.96AA/B12/7D(B-C)1 54.9 0.9 0.101 20.6 0.479 0.799 7.91 16.2 0.79 NA NA NA NA NA NA 18.31 0.89AA/B12/7D(B-C)2 54.9 0.92 0.101 24.8 0.493 0.819 8.11 17.1 0.69 NA NA NA NA NA NA 22.25 0.90AA/B12/7D(B-C)3 54.9 0.92 0.102 20.3 0.491 0.818 8.02 17 0.84 NA NA NA NA NA NA 22.53 1.11AA/B12/7D(F-C)1 54.9 0.92 0.101 24.1 0.493 0.819 8.11 17.1 0.71 NA NA NA NA NA NA 22.25 0.92

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)137–144

143

AA/B12/7D(F-C)2 54.9 0.95 0.101 24.9 0.10124 0.849 8.41 18.6 0.75 NA NA NA NA NA NA 25.53 1.03AA/B12/7D(E-C)1 54.9 0.95 0.101 24.1 0.84 0.849 8.41 18.6 0.77 NA NA NA NA NA NA 25.53 1.06AA/B12/7D(E-C)2 54.9 0.98 0.102 24.1 0.533 0.878 8.61 20.1 0.83 NA NA NA NA NA NA 26.19 1.09AA/B18/7D(B-C)1 59 0.8 0.047 11.7 0.44 0.753 16 NA NA 9.2 0.79 NA NA NA NA 11.3 0.97AA/B18/7D(B-C)2 59 0.85 0.047 10 0.468 0.803 17.1 NA NA 9.8 0.98 NA NA NA NA 11.77 1.18AA/B18/7D(B-C)3 59 0.79 0.047 10 0.435 0.743 15.8 NA NA 9.1 0.91 NA NA NA NA 11.19 1.12AA/B18/7D(F-C)1 59 0.82 0.047 11.1 0.451 0.773 16.4 NA NA 9.4 0.85 NA NA NA NA 11.49 1.04AA/B18/7D(F-C)2 59 0.84 0.047 12.7 0.462 0.793 16.9 NA NA 9.7 0.76 NA NA NA NA 11.68 0.92AA/B18/7D(F-C)3 59 0.85 0.047 11.8 0.468 0.803 17.1 NA NA 9.8 0.83 NA NA NA NA 11.77 1.00AA/B18/7D(E-C)1 59 0.87 0.047 9.74 0.479 0.823 17.5 NA NA 10 1.03 NA NA NA NA 11.93 1.22AA/B18/7D(E-C)2 59 0.83 0.047 11.5 0.457 0.783 16.7 NA NA 9.6 0.83 NA NA NA NA 11.59 1.01AA/B18/7D(E-C)3 59 0.86 0.047 10.8 0.473 0.813 17.3 NA NA 9.9 0.92 NA NA NA NA 11.85 1.10AA/B12/7D(AA-C)1 54.9 1.04 0.101 24.5 0.572 0.939 9.3 NA NA 22.9 0.93 NA NA NA NA 26.06 1.06AA/B12/7D(AA-C)2 54.9 0.96 0.101 22.5 0.521 0.859 8.5 19.2 0.85 NA NA NA NA NA NA 25.89 1.15AA/B12/7D(AA-C)3 54.9 0.9 0.101 14 0.479 0.799 7.91 16.2 1.16 NA NA NA NA NA NA 18.31 1.31AA/B18/7D(BB-C)1 59 0.85 0.048 12.6 0.468 0.802 16.8 NA NA 10 0.79 NA NA NA NA 11.91 0.95AA/B18/7D(BB-C)2 59 0.78 0.048 11.1 0.429 0.732 15.3 NA NA 9.1 0.82 NA NA NA NA 11.26 1.01AA/B12/7C(E-AA)2 54.9 0.85 0.101 10.7 0.444 0.749 7.42 13.9 1.30 NA NA NA NA NA NA 13.98 1.31AA/B12/7C(E-D)1 54.9 1 0.101 28.7 0.549 0.899 8.9 21.3 0.74 NA NA NA NA NA NA 26.22 0.91AA/B12/7C(E-D)2 54.9 0.97 0.101 26.5 0.528 0.869 8.6 19.7 0.74 NA NA NA NA NA NA 26.08 0.98AA/B12/7C(E-D)3 54.9 0.99 0.101 29.1 0.542 0.889 8.8 20.7 0.71 NA NA NA NA NA NA 26.21 0.90AA/B18/7C(E-AA)1 59 0.64 0.047 10 0.352 0.593 12.5 NA NA 7.3 0.73 NA NA NA NA 9.3 0.93AA/B18/7C(E-AA)2 59 0.62 0.047 7.46 0.341 0.574 12.3 NA NA 6.9 0.92 NA NA NA NA 9 1.21AA/B18/7C(E-AA)3 59 0.65 0.047 10.5 0.358 0.603 12.9 NA NA 7.3 0.70 NA NA NA NA 9.44 0.90A A/B 24/7 C(E-AA)1 107.6 0.54 0.024 3.8 0.297 0.516 21.5 NA NA NA NA 4 1.05 NA NA 3.6 0.95A A/B 24/7 C(E-AA)2 107.6 0.6 0.024 4.48 0.33 0.576 24 NA NA NA NA NA NA 4.16 0.93 4.23 0.94AA/B24/7C(E-AA)3 107.6 0.56 0.024 4.9 0.308 0.536 22.3 NA NA NA NA 4 0.82 NA NA 3.8 0.78A E/B 24/7 D(E-C)1 107.6 0.72 0.024 6 0.396 0.696 29 NA NA NA NA NA NA 5.03 0.84 5.74 0.96A E/B 24/7 D(E-C)2 107.6 0.71 0.024 6.3 0.391 0.686 28.5 NA NA NA NA NA NA 4.98 0.79 5.6 0.89A E/B 24/7 D(E-C)3 107.6 0.73 0.024 6.16 0.402 0.706 29.4 NA NA NA NA NA NA 5.1 0.83 5.88 0.95AA/B10/7D(E-CC)1 48.8 1.04 0.139 26.1 0.52 0.901 6.49 19.1 0.73 NA NA NA NA NA NA 24 0.92AA/B10/7D(E-CC)2 48.8 1.05 0.139 20.9 0.526 0.911 6.55 19.6 0.94 NA NA NA NA NA NA 24.31 1.16AA/B10/7D(E-E)1 48.8 1.14 0.139 34.5 0.589 1.001 7.19 24.5 0.71 NA NA NA NA NA NA 34.11 0.99AA/B10/7D(E-E)2 48.8 1.24 1.24 28.3 0.659 1.101 7.89 30.7 1.08 NA NA NA NA NA NA 26.08 0.92BA/B18/7D1 67 1.39 0.095 28.6 0.765 1.2 12.6 NA NA 33.6 1.17 NA NA NA NA 29.62 1.04BA/B18/7D2 67 1.35 0.095 37.3 0.743 1.16 12.2 NA NA 32.5 0.87 NA NA NA NA 36.99 0.99BA/B18/7D3 67 1.37 0.095 32.4 0.754 1.18 12.4 NA NA 33 1.02 NA NA NA NA 33.87 1.05BA/B18/7D4 67 1.41 0.097 26.3 0.776 1.216 12.5 NA NA 34.8 1.32 NA NA NA NA 25.17 0.96BA/B18/7D1S 64.7 0.77 0.088 12.7 0.407 0.594 6.8 11.7 0.92 NA NA NA NA NA NA 13.96 1.10BA/B18/7D2S 64.7 0.82 0.088 16.2 0.442 0.644 7.3 13.8 0.85 NA NA NA NA NA NA 14.09 0.87BA/B18/7D3S 64.7 0.82 0.088 15.4 0.442 0.644 7.3 13.8 0.90 NA NA NA NA NA NA 14.09 0.91BA/B18/7D4S 64.7 0.72 0.088 11.7 0.372 0.544 6.2 9.8 0.84 NA NA NA NA NA NA 13.73 1.17BA/B18/7D5S 64.7 0.82 0.088 8.6 0.442 0.644 7.3 13.8 1.60 NA NA NA NA NA NA 14.09 1.64BA/B12/7D2 51.1 0.83 0.216 6 0.257 0.398 1.8 4.7 0.78 NA NA NA NA NA NA 5.73 0.96BA/B12/7D3 51.1 0.84 0.216 5 0.264 0.408 1.9 4.9 0.98 NA NA NA NA NA NA 5.74 1.15BA/B14/7D(A-C)1 47.6 1.01 0.154 17.2 0.476 0.702 4.6 16 0.93 NA NA NA NA NA NA 16.17 0.94BA/B14/7D(A-C)2 47.6 1.08 0.155 20.9 0.524 0.77 5 19.4 0.93 NA NA NA NA NA NA 23.23 1.11BA/B14/7D(D-C)1 47.6 1.04 0.154 16.1 0.497 0.732 4.8 17.5 1.09 NA NA NA NA NA NA 18.65 1.16BA/B14/7D(D-C)2 47.6 0.95 0.154 11.8 0.434 0.642 4.2 13.3 1.13 NA NA NA NA NA NA 12.11 1.03

n g t

r

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