In the first scenario, multiple engines with different overhaul times are analysed using the developed framework in chapter 6. The framework can be applied to the two aero engines (a two-shaft and a three-shaft). Both aero engines are subject to same problem. The following technical configurations for a three-shaft High Bypass Ratio engine are Fan Diameter - 97.4 inches, Eight-stage intermediate pressure (IP) compressor, Six-stage high pressure (HP) compressor, Single Combustor with 24 fuel injectors, Single-stage HP turbine, Single-stage IP turbine and Four-stage low pressure (LP) turbine. A two-shaft technical configuration includes low-bypass turbofan engine with a mixed exhaust, low-pressure and high-pressure spools. The fan and booster stages are powered by low-pressure turbine, high-pressure compressor is driven by high- pressure turbine.
This scenario of the case study focuses on a single-stage turbine nozzle guide vanes (NGV) of a gas turbine. The data presented in Table 7-3 were developed in conjunction with industry partners and presented as a representative of real data.
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Table 7-3 Data with multiple engines and overhaul state used for the analysis (validation data)
Engine No Time (hrs) Time (Cycles) Scrapped Quantity
10010 6000 1000 2 10010 12000 2000 4 10010 18000 3000 9 10011 6000 1000 2 10011 15000 2500 4 10011 19800 3300 9 10012 6000 1000 2 10012 19200 3200 4 10012 36000 6000 9 10012 48000 8000 11 10012 66000 11000 14 10013 12000 2000 2 10013 21000 3500 4 10013 36000 6000 9 10013 60600 10100 11 10014 6000 1000 2 10014 15000 2500 4 10014 36000 6000 9 10014 48000 8000 11 10015 6000 1000 2 10015 15000 2500 4 10015 19200 3200 9 10015 36000 6000 11 10015 48000 8000 14 10015 66000 11000 20 10016 5880 980 2 10016 13200 2200 4 10016 21600 3600 9 10016 36000 6000 11 10017 5520 920 2 10017 8400 1400 4 10017 15000 2500 9 10017 33000 5500 11 10017 48000 8000 14 10019 6000 1000 2 10019 12000 2000 4 10019 18000 3000 9 10019 24000 4000 11 10019 30000 5000 14
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The OS represents an overhaul state described in chapter 6, this case analyses a single engine (10015) from the multiple engines data in Table 7-3 using same η and β parameters. In Table 7-4, comparison of results from the historical failure data are analysed using LSM and MLE methods. The outcomes of data analysis using the two methods varied slightly. While LSM gives high β, MLE produces less β. The MLE method has a high η value, and LSM outputs a low η value.
Table 7-4 The rejected components, η and β outcomes for LSM and MLE methods
Methods η β OS1 OS2 OS3 OS4 OS5 OS6 Total
LSM 4353.8 1.6 3 9 5 21 13 23 74
MLE 4523.5 1.5 4 9 5 19 14 19 70
The η value suggests 63.2% of components reflect performance loss. The values show difference between the LSM and MLE. The difference is due to the median rank discussed in chapter 6. The Weibull β of ‘1.0’ indicates an exponential distribution of the data, ‘2.0’ is a Rayleigh distribution and ‘3.0’ is a normal distribution of the data. The β values tend to unity describing the effect of the failure mode, therefore, β range between 1.5 and 1.6 with a difference of 0.1 indicating deviation away from the degradation observed data. As indicated in Table 7-1, this outcome is significant because initially the β of 1.5 will produce high number of rejections, while β of 1.6 give a less number of rejections in the model. However, as replacement continues, high numbers of rejections are observed between OS4 and OS6. As an engine's β increases, estimated rejections decrease. There is bigger variation and sensitivity to variation in each individual component β. The optimised zoom-in capability estimates the most realistic 𝜂 and β with error values. Hence, if the β value is greater than 2, indicates a small variation in the degradation data.
The results presented in Figure 7-8 show the number of data points and trajectory of non-linearity. The points illustrate a cumulative distribution for a through-life predictive model of a single-stage assembly.
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Figure 7-8 Single system (A) LSM β = 1.6 and (B) MLE β = 1.5 with predicted and observed values on Probability of failure
The observation was based on rejection and replacement strategy following the bathtub curve where the failure rate remains constant, decreasing and increasing. The outcome in Table 7-4 illustrates that policymakers, manufacturers, designers and maintenance engineers can make better maintenance decision based on cost as a safety factor and the rate of failure of components. The practitioners can decide at what stage the entire components should be replaced with new components, that is, where the numbers of expected renewal are slightly above half of the total of 36 components.
The life of a population of NGVs can be described as early life, useful life and wear-out or ageing. The values of β in Table 7-4 signify an early wear-out when β value is > 1 and < 2. In the analysis, components in an assembly show a slight wear-out condition because the value of β parameter is greater than 1. The outcome leads to an optimal time of replacement analysis based on total cost of maintenance. Few early ageing failures are observed which increases over time in cycles. The β parameter for all methods gives a better predictability of the scenario with variance showing through-life performance of NGVs in an assembly.
The early wear-out with β is constant for the six overhaul states. In OS1, LSM predicted the rejection of the 3 while MLE estimated 4. For OS2, quantity of NGVs rejected are 9 for both LSM and MLE. This difference resulted from (a) failure modes, and (b) reuse of existing NGVs relative to time interval. In OS3, degraded
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NGVs are 5 – this outcome can be attributed to optimum renewal (replacement) of rejected NGVs in OS2. However, in OS4, 21 NGVs are projected to fail using LSM, while 19 NGVs are estimated to reject with the MLE method. This occurrence can be ascribed to minimal renewal in OS3 and the time interval. The reliability of a majority of the NGVs are based on the renewal principles, hence, the high number of rejections in OS4. The same can be said of OS5 and OS6. The WTPPM predicts the number of rejections and optimal renewal (replacement). LSM has a total number of NGVs renewals at 74 and MLE projected a through-life performance quantity of NGVs rejected as 70. These outcomes can be attributed to β parameters – high β leads to less number of rejections and low β produces a high number of rejections. The outcome can be seen in the first overhaul state, but the reverse is the case for the rejections at subsequent overhauls.
The replacement cost of individual NGV, maintenance, repair, overhaul and logistics can be high regarding the engine for each OS. At each OS, if the cost of replacing the NGVs in an assembly is 50% of the cost of replacing the entire NGVs in an assembly, the expert advice would be to scrap and replace. The LSM and MLE have been described as reliable methods for parameter estimation.
In calculating the minimised error values, η and β parameters are passed through the model. Equation 6-39 (MAE) is called to calculate the outcome from predicted rejection values and observed rejected values as shown in Figure 7-8. The outcome is a single error value based on the estimated Weibull parameters. The error values are presented in a 20 x 20 matrix for back-fitting as shown in Figure 7-9. The matrix representation is a generic enumeration approach, which is calibrated into different shades of green and red. While green colour indicates a region with the closest deviation, red colour specifies a region with the farthest deviation. The effect of the failure modes affects the characteristic life of the population of NGVs. While red region indicates that NGVs cannot be reused, green region illustrates the population of NGVs can be reused.
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Figure 7-9 Single system (a) LSM β = 1.6 and (b) MLE β = 1.5 with error values, η and β parameters
The representation shows robustness of the WTPPM for reliability purposes. Optimal η and β values based on the residuals can be used for decision making. The region with the closest residuals of observed data is highlighted around the green area. The region indicates optimised fit for predicting values of η and β of the Weibull distribution. The predicted η and β parameters are used to estimate number of future rejections, and when they will occur. The 3D surface map is a representation of maximum and minimum error values seen in the Wireframe contour map is numerically analysed and illustrated in appendix L.
Further analysis shows that the generated parameters from GOT as shown in Figure 7-10 are calculated as failure probability in the Weibull distribution. The failure data are solved to represent RUL of components. Table 7-5 shows the estimated and optimised η and β parameters.
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Figure 7-10 Single system (a) LSM β = 1.6 and (b) MLE β = 1.5 with error values and optimised η and β parameters
Table 7-5 Outcomes of the optimised values from LSM and MLE methods
Method Initial η
Initial β
Zoom-in (optimised)η β
LSM 4353.8 1.6 High η and Low β 8103.8 0.98
Low η and High β 3353.8 2.6
MLE 4523.5 1.5 High η and Low β 8273.5 1.0
Low η and High β 3523.5 2.5 The RUL results in Figure 7-11 are presented as “RUL with High η Low β” and “RUL with Low η High β” with values in Table 7-5. The distribution can be used to highlight the RUL of components from each data point in the trajectory. RUL distribution is reliable and appropriate because it depicts multiple renewals of multi-component in an assembly.
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Figure 7-11 RUL for single system (a) LSM β = 1.6 and (b) MLE β = 1.5 for optimised η and β parameters
The results of predicted rejected NGV in an assembly historical data are required for the remaining useful life prediction derived from probability of failure distribution illustrated in Figure 6-7. The data analysed for a single system with an outcome of underlying predicted rejection rate and observed rejection rate with time are based on the historical data.
A cost indicator discussed in chapter 6 creates a known threshold of when it is uneconomically viable to continue replacing components in the assembly. If cost at any overhaul state equals average total cost of an assembly replacement, the assembly should be replaced with new NGVs in the assembly as shown in Figure 7-12.
173 Multiple engines and overhauls analysis
The application of multiple engines and overhaul states present the following results. The GOT capability aims to get the most realistic η and β parameters relating to error values (see Figure 7-13). The GOT process is initiated until the function reaches ends of the matrix. The residuals of estimated η and β parameters are recalculated using GOT. The representation shows a variation of residuals /error values with respect to the η and β parameters. The variation of results comes from failure modes which affect NGVs in their environmental operating condition. A representation of the variation of error values is presented in a 3D surface map (see Figure 7-14), which represents a real-world entity behaviour of components in an assembly in service. The variation can be described as noise, which reflects failure modes and the characteristic life of NGVs. Most of the low error values of the estimated η and β parameters have various gradients or shades of green with same error values. Invariably, error values are similar, but appear the same due to approximation problem. The value with the lowest decimal has bright green colour; others have low and high decimal approximate values respectively with different shades of green.
The model evaluation is conducted with selected error values, η and β parameters in green region as outcome from GOT functionality, the Weibull function is then applied to the last selected optimised η and β values to generate a Weibull distribution for probability of failure and converted to remaining useful life. The graphed red distribution results from the minimum η value, while the blue distribution from the maximum η. The outcomes relate to the actual historical data as shown in Figure 7-15.
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Figure 7-14 3D surface map: β = 1.5 with errors values, realistic η and β
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