Elastic properties of the Tjoint components
1. Introduction
Sensitive engineering structures are designed to be safe such that catastrophic failures can be avoided. Traditionally, this has been achieved by introducing safety factors to compensate for the lack of considering a structure’s fullscale behavior beyond the expected loads. Safety factors create a margin between realtime operational loading and residual strength remaining in the structure. Historically, although failsafe and safelife methodologies were among design strategies for many years, the increasing impact of economical considerations and emerging inspection technologies led to a new design strategy called damage tolerance strategy [1]. Damage tolerant designed structures have an added cost which is related to the frequency and duration of inspections. For such structures, inspection intervals and damage thresholds are estimated and at every inspection the structure’s health is investigated by looking for a maximum flaw, crack length and orientation. If necessary, modified investigation times are proposed, especially at vulnerable locations of the structure. Other limitations of the damage tolerant strategy include a lack of continuous assessment of the structure’s health status and the need to pause the regular operation of the structure during offline inspections. Over time, beside some historical catastrophic failures, the advancement of nondestructive technologies and economical benefits have directed designers to the introduction of the concept of Structural Health Monitoring (SHM). It may be hard to find a comprehensive and consistent definition for SHM, but as Boller suggested in [1], “SHM is the integration of sensing and possibly actuation devices to allow the loading and damage state of the structure to be monitored, recorded, analyzed, localized, quantified and predicted in a way that nondestructive testing becomes an integral part of the structure”. This definition contains two major elements: load monitoring and damage diagnosis as the consequence of operational loading (which is often subject to a stochastic nature).
The review of literature shows an increasing number of research programs devoted to the development of damage identification systems to address problems such as assuming costeffective methods for optimal numbering and positioning of sensors; identification of features of structures that are sensitive to small damage levels; the ability to discriminate changes caused by damage from those due to the change of environmental and testing conditions; clustering and classification algorithms for discrimination of damaged and undamaged states; and comparative studies on different damage identification methods applied to common datasets [2]. These topics are currently the focus of various groups in major industries including aeronautical [3, 4], civil infrastructure [5], oil [6, 7], railways [8], condition monitoring of machinery [9, 10], automotive and semiconductor manufacturing [2]. In particular, new multidisciplinary approaches are increasingly developed and used to advance the capabilities of current SHM techniques.
2. Motivation of this study
A standard SHM technique for a given structure compares its damaged and healthy behaviors (by contrasting signals extracted from sensors embedded at specific points of the structure) to the database pretrained from simulating/testing the behavior of the structure under different damage scenarios. Ideally, the change in the vibration spectra/stressstrain patterns an be related to damage induced in the structure, but it is possible at the same time that these deviations from a healthy pattern are caused by imperfect manufacturing processes including uncertainty in material properties or misalignment of fibers inside the matrix (in the case of composite structures), an offset of an external loading applied to the structure during testing, etc. Based on a strainedbased SHM, this article addresses the important effect of manufacturing/testing uncertainties on the reliability of damage predictions. To this end, as a case study a benchmark problem from the literature is used along with a finite element analysis and design of experiments (DOE) method. Among several existing DOE experimental designs (e.g., [1116]) here we use the wellknown full factorial design (FFD).
3. Case study description
The structure under investigation is a composite Tjoint introduced in [17], where a strainbased structural health monitoring program, GNAISPIN (Global Neural network Algorithm for Sequential Processing of Internal sub Networks), was developed using MATLAB and NASTRANPATRAN. The Tjoint structure, shown in Figure 1, consists of four major segments including the bulkhead, hull, overlaminates and the filler section. The finite element model of the structure is assumed to be twodimensional (2D) and strain patterns are considered to be identical in the thickness direction of the structure. The geometrical constraints and applied load are also shown in Figure 1. The lefthand side constraint only permits rotation about the zaxis and prevents all other rotational and translational degrees of freedom. The righthand side constraint permits translation along the xaxis (horizontal direction) and rotation about the zaxis. The displacement constraints are positioned 120mm away from the corresponding edges of the hull. The structure is subjected to a pulloff force of 5 kN. In [17], several delaminations were embedded in different locations of the structure, but in this study only a single delamination case is considered between hull and the left overlaminate. The strain distribution is then obtained for nodes along the bondline (the top line of the hull between the right and lefthand constraints), which are the nodes most affected by the presence of embedded delamination.
Using ABAQUS software, two dimensional orthotropic elements were used to mesh surfaces of the bulkhead, hull, and overlaminates, whereas isotropic elements were used to model the filler section. The elastic properties of the hull, bulkhead, and the overlaminates [17] correspond to 800 gramspersquare of plain weave Eglass fabric in a vinylester resin matrix (Dow Derakane 411350). The properties of the filler corresponded to chopped glass fibers in the same vinylester resin matrix as summarized in Table 1.




E1 (GPa)  26.1  23.5  2.0 
E2 (GPa)  3.0  3.0  
E3 (GPa)  24.1  19.5  
v12=v23  0.17  0.17  0.3 
v13  0.10  0.14  
G12=G23 (GPa)  1.5  1.5  0.8 
G13 (GPa)  3.3  2.9 
In order to verify the developed base ABAQUS model, strain distributions along the bondline for the two cases of healthy structure and that with an embedded delamination are compared to the corresponding distributions presented in [17]. Figures 2.a and 2.b show a good accordance between the current simulation model and the one presented in [17] using NASTRANPATRAN. The only significant difference between the two models is found at the middle of the Tjoint where results in [17] show a significant strain drop compared to the ABAQUS simulation. Figure 3 also illustrates the 2D strain distribution obtained by the ABAQUS model for the healthy structure case.
Next, using the ABAQUS model for the DOE study, fiber orientations in the bulkhead, hull and overlaminate as well as the pulloff loading offset were considered as four main factors via a full factorial design, which resulted in sixteen runs for each of the health states (healthy and damaged structure). Two levels for each factor were considered: 0 or +5 degrees counterclockwise with respect to the xaxis (Figure 4). Table 2 shows the assignment of considered factors and their corresponding levels. Table 3 represents the full factorial design for the two structural health cases.




Regions of fiber angle error (misalignment) 
Overlaminate  A  0 or 5 
Bulkhead  B  0 or 5  
Hull  C  0 or 5  
Loading offset  Loading angle  D  0 or 5 


run  A  B  C  D  Case 
1  0  0  0  0  No Delamination 
2  5  0  0  0  
3  0  0  5  0  
4  5  0  5  0  
5  0  5  5  0  
6  5  5  5  0  
7  0  5  0  5  
8  5  5  0  5  
9  0  0  0  5  
10  5  0  0  5  
11  0  0  5  5  
12  5  0  5  5  
13  0  5  5  5  
14  5  5  5  5  
15  0  5  0  0  
16  5  5  0  0  
17  0  0  0  0  Delamination of 50mm long at 200mm from left edge 
18  5  0  0  0  
19  0  0  5  0  
20  5  0  5  0  
21  0  5  5  0  
22  5  5  5  0  
23  0  5  0  0  
24  5  5  0  0  
25  0  0  0  5  
26  5  0  0  5  
27  0  0  5  5  
28  5  0  5  5  
29  0  5  5  5  
30  5  5  5  5  
31  0  5  0  5  
32  5  5  0  5 
In order to illustrate the importance of the effect of uncertainty in fiber misalignment (e.g., during manufacturing of the structure’s components), one can readily compare the difference between the strain distributions obtained for a case containing, e.g., 5^{o} misalignment in the overlaminate (i.e., run # 2 in Table 3) and that for the perfectly manufactured healthy case (run # 1). A similar difference can be plotted between the case without any misalignment but in the presence of delamination (damage) which corresponds to run # 17 – and the perfectly manufactured healthy case (run # 1). These differences are shown in Figure 5.
By comparing the strain distributions in Figures 5.a and 5.b one can conclude that 5 degrees misalignment of fibers in the overlaminate (run # 2) has resulted in a significant deviation from the base model (run # 1) compared to the same deviations caused by the presence of delamination (run # 17); and hence, emphasizing the importance of considering fiber misalignment in real SHM applications and database developments. The next section is dedicated to perform a more detailed factorial analysis of results and obtain relative effects of the four alignment factors A, B, C, and D as samples of uncertainty sources in practice.
4. DOE effects analysis
Two different approaches are considered in the effects analysis; a pointtopoint and an integral analysis. In the pointtopoint approach, the difference between the horizontal strain values at three locations along the bondline (first, middle and the last node in Figure 4) and those of the ideal case are considered as three output variables. On the other hand, the integral approach continuously evaluates the strain along the bond line where the number of considered points (sensors) tends to infinity. In fact the strain values obtained from the FE analysis would correspond to the strain data extracted from sensors embedded in the Tjoint. The integral analysis for each given run, calculates the area under the strain distribution along the bond line, minus the similar area in the ideal case. The comparison of the two approaches, hence, provides an opportunity to assess the impact of increasing the number of sensors on the performance of SHM in the presence of manufacturing errors (here misalignments). For each approach, the most dominant factors are identified via comparing their relative percentage contributions on the output variables as well as the corresponding halfnormal probability plots (see [16] for more theoretical details). Subsequently, ANOVA analysis was performed to statistically determine the significance (Fvalue) of key factors.
4.1. Pointtopoint analysis results
Figure 4 shows the position of nodes assigned for the pointtopoint analysis strategy. The first and last sensor points are considered to be 50mm away from the nearest constraint on the contact surface of hull and overlaminate. The middle point is located below the pulloff load point. Table 4 shows the results of FE runs based on the factor combinations introduced in Table 3. As addressed before, the presented data for the first group of runs (i.e., for healthy structures – runs 1 to 16) are the difference between strain values of each run and run 1; while the corresponding data for the second group (damaged Tjoint – runs 17 to 32) represent the difference between strain values for each run and run 17. Table 5 represents the ensuing percentage contributions of factors and their interactions at each node for the two cases of healthy and delaminated Tjoint. For the first node, which is close to the most rigid constraint on the left hand side of the structure, the only important factors are the misalignment of fibers in the hull (factor C) and its interaction with the loading angle offset (CD). This would be explained by the type of constraints imposed on the structure which is free horizontal translation of the opposite constraint on the right side. Figure 6 shows the half normal probability plot of the factor effects for the 1^{st} node, confirming that factors C and CD are distinctly dominant parameters affecting the strain response at this node.
Logically, one would expect that the mid node response would be strongly influenced by any loading angle offset as it can produce a horizontal force component and magnify the effect of the free translation boundary condition on the neighboring constraint; therefore, for the middle point response, the misalignment of fibers in the hull (C) and the loading angle error (D) and their interactions (CD) are the most significant factors, as also shown from the corresponding half normal probability plot in Figure 7. Finally, due to the short distance of the last (3^{rd}) measuring node to the right constraint point and the strong influence of the large hull section beneath this measuring node, the parameter C was found to be the most dominant factor, followed by D, CD, AC, AD, and ACD (Figure 8).













1  0  0  0  0  0  0  0  No Delamination (Healthy) 
2  5  0  0  0  1.0979E06  2.273E06  0.000013536  
3  0  0  5  0  4.23422E05  3.0625E05  4.04549E05  
4  5  0  5  0  4.4637E05  0.000029522  5.78129E05  
5  0  5  5  0  4.23426E05  0.000032361  4.04549E05  
6  5  5  5  0  4.46377E05  3.1389E05  5.78129E05  
7  0  5  0  5  2.58877E05  0.000040385  1.21364E05  
8  5  5  0  5  2.71377E05  0.000038519  5.23E07  
9  0  0  0  5  2.58911E05  0.000036949  0.000012135  
10  5  0  0  5  2.71419E05  0.000034988  5.219E07  
11  0  0  5  5  2.17078E05  0.000111352  2.26219E05  
12  5  0  5  5  2.16311E05  0.000105259  3.74989E05  
13  0  5  5  5  2.17102E05  0.000115452  2.26229E05  
14  5  5  5  5  0.000021634  0.000109486  3.74999E05  
15  0  5  0  0  5E10  1.445E06  0  
16  5  5  0  0  1.0987E06  3.83E06  1.35358E05  








17  0  0  0  0  0  0  0  Delamination of size 50mm at 210mm from left 
18  5  0  0  0  8.428E07  1.744E06  1.35359E05  
19  0  0  5  0  4.22965E05  0.000030471  4.04562E05  
20  5  0  5  0  4.43366E05  0.000028817  5.78142E05  
21  0  5  5  0  4.22971E05  0.000032214  4.04562E05  
22  5  5  5  0  4.43376E05  0.00003069  5.78142E05  
23  0  5  0  0  8E10  1.416E06  1E10  
24  5  5  0  0  8.44E07  3.272E06  1.35357E05  
25  0  0  0  5  2.61841E05  0.000035177  1.21353E05  
26  5  0  0  5  0.000027744  3.2725E05  5.221E07  
27  0  0  5  5  2.61841E05  0.000035177  1.21353E05  
28  5  0  5  5  2.09678E05  0.000103816  3.75002E05  
29  0  5  5  5  2.13567E05  0.000114459  2.26242E05  
30  5  5  5  5  2.09723E05  0.000107997  3.75012E05  
31  0  5  0  5  2.61794E05  0.000038553  1.21366E05  
32  5  5  0  5  0.000027738  0.000036197  5.233E07 





Healthy  Damaged  Healthy  Damaged  Healthy  Damaged  
A  0.13868  0.017835  0.043177  1.01244  4.91255  6.414703 
B  8.15E12  0.03857  0.117004  2.8447  1.95E08  0.113719 







AB  8.79E11  0.038593  5.28E05  1.694425  2.63E10  0.113632 
AC  0.000112  0.066135  0.054639  1.098861  3.868746  5.223829 
AD  0.032741  0.112498  0.083222  0.983084  3.214382  2.070652 
BC  2.67E07  0.038292  0.000938  1.810764  9.47E11  0.113615 
BD  3.63E08  0.038687  0.01842  2.126322  2.33E08  0.113723 







ABC  2.51E09  0.038622  6.35E07  1.713334  2.63E10  0.113615 
ABD  1.15E09  0.038568  1.08E07  1.716435  1.05E11  0.113619 
ACD  0.04235  0.204216  0.000548  1.6494  2.163531  3.219085 
BCD  2.87E07  0.038282  0.000141  1.748334  5.16E10  0.113611 
ABCD  3.12E09  0.038622  4.12E08  1.714975  1.05E11  0.113628 







A  1  291.69  291.69  291.69  20.44  0.002 
C  1  4368.92  4368.92  4368.92  306.09  0.000 
D  1  380.71  380.71  380.71  26.67  0.001 
A*C  1  229.71  229.71  229.71  16.09  0.003 
A*D  1  190.86  190.86  190.86  13.37  0.005 
C*D  1  347.23  347.23  347.23  24.33  0.001 
Error  9  128.46  128.46  14.27  
Total  15  5937  .57 
Next, based on the identified significant factors from the above results for the 3^{rd} node, an ANOVA analysis (Table 6) was performed considering the rest of insignificant effects embedded in the error term. As expected, the pvalue for the factor C is zero and the corresponding values for factors D and CD are 0.001. The pvalue for all other factors is greater than 0.001. Therefore, assuming a significance level of 1%, for the 3^{rd} node response, much like the 1^{st} and middle nodes, factors C, D and their interaction CD can be reliably considered as most significant. Table 7 shows the ANOVA results for all the three nodes when only these three factors were included.
One interesting observation during the above analysis was that we found no significant deviation of main results when we repeated the analysis for the block of runs with delamination (compare the corresponding values under each node in Table 5 for the two healthy and damage cases). This indicated that
Source  DF  Seq SS  Adj SS  Adj MS  F 

C  1  1451.4  1451.4  1451.4  2165.69 

D  1  17.2  17.2  17.2  25.65 

C*D  1  2283.4  2283.4  2283.4  3407.16 

Error  12  8.0  8.0  0.7  
Total  15  3759.9  
Source  DF  Seq SS  Adj SS  Adj MS  F 

C  1  10356.0  10356.0  10356.0  1524.83 

D  1  13279.4  13279.4  13279.4  1955.28 

C*D  1  1900.1  1900.1  1900.1  279.77 

Error  12  81.5  81.5  6.8  
Total  15  25616.9  
Source  DF  Seq SS  Adj SS  Adj MS  F 

C  1  4368.9  4368.9  4368.9  62.36 

D  1  380.7  380.7  380.7  5.43 

C*D  1  347.2  347.2  347.2  4.96 

Error  12  840.7  840.7  70.1  
Total  15  5937.6 
Figures 9.a – 96.f represent the main factor and interaction plots for the pointtopoint analysis. For the first and last points, the lines for interaction of hull fiber misalignment and the loading angle offset are crossed, which indicates a high interaction between those parameters at the corresponding node. This interaction indication agrees well with the high Fvalue provided by the ANOVA analysis for CD in Table 7 for the first node. For the middle node, the individual lines for C and D in the main plots are in the same direction but with a small difference in their slopes. For the last (3^{rd}) node, the main factor plots for parameters C and D have slopes with opposing signs, suggesting that for this node, the fiber misalignment angle and loading angle offset have opposite influences on the strain response. This again could be explained by the imposed type of constraint on the right side of the Tjoint.
4.2. Integral analysis results
In this approach the objective function for each run was considered as the area between the curve representing the strain distribution of the nodes lying on the bond line and that of the base case. For the first group of runs (healthy structure, run#116), the first run is the base curve, whereas for the second group (embedded delamination case, run # 17 – 32) the 17^{th} run (i.e., only delamination and no other fiber misalignment or loading angle error) is considered as the base. Table 8 lists the objective values for each run during this analysis. Table 9 represents the obtained percentage contribution of each factor. The parameters C and CD again play the main role on the strain distribution, but to be more accurate one may also consider other factors such as A, D, AD, and AC.












0  No Delamination 





1.79422E05  





4.33694E05  





5.6027E05  





4.33843E05  





5.60299E05  





3.73717E05  





3.14578E05  





3.72118E05  





3.14519E05  





3.0095E05  





3.77188E05  





3.04696E05  





3.80525E05  





1.31538E07  





1.79444E05  





0  Delamination of size 50mm at 210mm from left 





1.79696E05  





4.35521E05  





5.66002E05  





4.35663E05  





5.66009E05  





1.32937E07  





1.79724E05  





3.7407E05  





3.15725E05  





3.7407E05  





3.9519E05  





3.28869E05  





3.98452E05  





3.7563E05  





3.15788E05 
In order to show the dominant factors graphically, the corresponding half normal probability plot (Figure 10) was constructed; Figure 10 recommends considering AC as the last dominant factor. Next, a standard ANOVA analysis was performed (Table 10) and results suggested ignoring the effect of factors AC and D with a statistical significance level of α=0.01. Nevertheless, recalling the percentage contributions in Table 9 it is clear that the top two main factors are C and CD, as it was the case for the pointtopoint analysis. However in the pointtopoint analysis, D was also highly significant at the selected nodes, whereas in the integral method it shows much less overall contribution. This would mean that









B  0.001652565  0.02290527 






AB  0.000177577  0.031520485 
AC  0.423871764  0.189479205 



BC  0.000285795  0.030478626 
BD  0.000820031  0.026597215 



ABC  8.33724E05  0.039747913 
ABD  4.48647E06  0.035628966 
ACD  2.188823941  1.425288598 
BCD  0.000680545  0.027279407 
ABCD  2.77746E08  0.036203388 







A  1  260.75  260.75  260.75  26.90  0.001 
C  1  1632.87  1632.87  1632.87  168.43  0.000 
D  1  95.06  95.06  95.06  9.81  0.012 
A*C  1  16.87  16.87  16.87  1.74  0.220 
A*D  1  206.82  206.82  206.82  21.33  0.001 
C*D  1  1679.97  1679.97  1679.97  173.28  0.000 
Error  9  87.25  87.25  9.69  
Total  15  3979.60 
Finally, similar to the pointtopoint analysis, comparing the contribution percentage values for the two blocks of runs in Table 9 (healthy vs. damaged structure), the delamination seems to have no major interaction with the other four uncertainty factors. In order to statistically prove this conclusion, a 2^{5} full factorial was performed, considering delamination as a new fifth factor E. Ignoring the 3^{rd} order interactions and embedding them inside the body of error term, ANOVA results were obtained in Table 11. It is clear that the E (damage) factor itself has a significant contribution but not any of its interaction terms with noise factors.







A  1  626.54  626.54  626.54  48.33  0.000 
B  1  17.71  17.71  17.71  1.37  0.260 
C  1  2817.34  2817.34  2817.34  217.30  0.000 
D  1  274.12  274.12  274.12  21.14  0.000 







A*B  1  12.82  12.82  12.82  0.99  0.335 
A*C  1  28.51  28.51  28.51  2.20  0.158 
A*D  1  1.49  1.49  1.49  0.12  0.739 
A*E  1  13.53  13.53  13.53  1.04  0.322 
B*C  1  13.22  13.22  13.22  1.02  0.328 
B*D  1  16.58  16.58  16.58  1.28  0.275 
B*E  1  13.06  13.06  13.06  1.01  0.331 
C*D  1  1.02  1.02  1.02  0.08  0.782 
C*E  1  12.65  12.65  12.65  0.98  0.338 
D*E  1  13.08  13.08  13.08  1.01  0.330 
Error  16  207.44  207.44  12.97  
Total  31  4081.34 
5. Conclusions
Two different approaches, a pointtopoint analysis and an integral analysis, were considered in a case study on the potential effect of uncertainty factors on SHM predictability in composite structures. The point–topoint (discrete) analysis is more similar to real applications where the number of sensors is normally limited and the SHM investigators can only rely on the data extracted at specific sensor locations. The integral approach, on the other hand, calculates the area of a continuous strain distribution and, hence, simulates an ideal situation where there are a very large number of sensors embedded inside the structure. The comparison of the two approaches showed the impact of increasing the number of strain measurement points on the behavior of the prediction model and the associated statistical results. Namely, for all sensor positions considered in the pointtopoint (discrete) analysis, the main factors were the misalignment of fibers in the hull and the loading angle offset, but for the integral (continuous) approach, the aggregation of smaller factors over the bond line resulted in increasing significance of other parameters such as overlaminate misalignment angle and its interaction with other factors. However the top contributing factors remained the same between the two analyses, indicating that increasing the number of sensors does not eliminate the noise effects from fabrication such as misalignment of fibers and loading angle offset. Another conclusion from this case study was that, statistically, there was no sign of significant deviation in contribution patterns of factors between the healthy and damaged structure. This suggests that different sensor positioning scenarios may change the sensitivity of the response to noise factors but the deviation would be regardless of the absence or presence of delamination. In other words the relative importance of studied noise factors would be nearly identical in the healthy and damaged structure. Finally, results suggested that that the absolute effect of individual manufacturing uncertainty factors in deviating the structure’s response can be as high as that caused by the presence of delamination itself when compared to the response of the healthy case, even in the absence of misalignment errors. Hence, a basic SHM damage prediction system under the presence of preexisting manufacturing/testing errors may lead to wrong decisions or false alarms. A remedy to this problem is the use of new stochastic SHM tools.
Acknowledgments
Authors are grateful to Dr. J. Loeppky from Irving K. Barber School of Arts and Sciences at UBC Okanagan for his useful suggestions and discussions. Financial support from the Natural Sciences and Engineering Research Council (NSERC) of Canada is also greatly acknowledged.
References
 1.
Christian BOLLER, Norbert MEYENDORF. “StateoftheArt in Structural Health Monitoring for Aeronautics” Proc. of Internat. Symposium on NDT in Aerospace, Fürth/Bavaria, Germany, December 35, 2008.  2.
Charles R. FARRAR, Keith WORDEN. “An Introduction to Structural Health Monitoring” Phil. Trans. R. Soc. A 365, 303–315, 2007.  3.
C. Boller, M. Buderath. “Fatigue in aerostructures – where structural health monitoring can contribute to a complex subject” Phil. Trans. R. Soc. A 365, 561–587, 2007.  4.
R. Ikegami. “Structural Health Monitoring: assessment of aircraft customer needs” Structural Health Monitoring 2000, Proceedings of the Second International Workshop on Structural Health Monitoring, Stanford, CA, September 810, Lancaster – Basel, Technomic Publishing Co, Inc, pp. 1223, 1999.  5.
J.M.W. BROWNJOHN. “Structural Health Monitoring of Civil Infrastructure” Phil. Trans. R. Soc. A 365, 589622, 2007.  6.
Light Structures AS. “Exploration & Production: The Oil & Gas Review, Volume 2” 2003.  7.
Ved Prakash SHARMA, J.J. Roger CHENG. “Structural Health Monitoring of Syncrude’s Aurora II Oil Sand Crusher” University of Alberta, Department of Civil & Enviromental Engineering, Structural Engineering Report No 272, 2007.  8.
D. BARKE, W.K. CHIU. “Structural Health Monitoring in Railway Industry: A Review” Structural Health Monitoring 4, 8193, 2005.  9.
B.R. RANDALL. “State of the Art in Monitoring Rotating Machinery – Part I” J. Sound and Vibrations 38, March, 1421, 2004.  10.
B.R. RANDALL. “State of the Art in Monitoring Rotating Machinery – Part II” J. Sound and Vibrations 38, May, 1017, 2004.  11.
B. Tang, “Orthogonal arraybased Latin hypercubes” Journal of the American Statistical Association, 88(424):1392–1397, 1993.  12.
J.S. Park, “Optimal Latinhypercube designs for computer experiments” Journal of Statistical Planning and Inference, 39:95–111, 1994.  13.
X. Qu, G. Venter, R.T. Haftka, “New formulation of minimumbias central composite experimental design and Gauss quadrature” Structural and Multidisciplinary Optimization, 28:231–242, 2004.  14.
R. Jin, W. Chen, A. Sudjianto, “An efficient algorithm for constructing optimal design of computer experiments” Journal of Statistical Planning and Inference, 134:268–287, 2005.  15.
T.W. Simpson, D.K.J. Lin, W. Chen, “Sampling strategies for computer experiments: Design and analysis” International Journal of Reliability and Applications, 2(3):209–240, 2001.  16.
R.H. Myers, D.C. Montgomery, “Response Surface Methodology—Process and Product Optimization Using Designed Experiments” New York: Wiley, 1995.  17.
A. Kesavan, S. John, I. Herszberg, “Strainbased structural health monitoring of complex composite structures” Structural Health Monitoring, 7:203213, 2008.