In ComtekAdvancedStructures/cmstatr: Statistical Methods for Composite Material Data
knitr::opts_chunk$set(echo = TRUE)
Summary
Strength data for composite materials used in aerospace applications,
such as carbon fiber and fiberglass reinforced composites, are normally analyzed
using statistical methods because of the
inherent variability in the constituent materials and in the processing.
The design standards for civil aviation requires that the probability
of structural failure due to this variability must be minimized, and to do
so, the designer must use what are called "Design Values" for each material
in stress analyses and ensure they
exceed the actual stresses experienced by those materials in service.
Design Values are set based on the one-sided lower confidence bound of the
material strength. For some types of structure, the content of this
lower confidence bound is $99\%$ with a confidence level of $95\%$;
in this case, the confidence bound is referred to as A-Basis.
For some other types of structure, the content of the lower
confidence bound is instead $90\%$ with a confidence level of $95\%$;
in this case, the confidence bound is referred to as B-Basis.
The statistical
methods for calculating these
basis values are outlined in Composite Materials Handbook, Volume 1,
Revision G, or CMH-17-1G in short [@CMH171G].
The use of these methods is widely accepted by industry and civil
aviation regulators.
Design Values are often adjusted to account for anticipated in-service
damage and other factors, however those adjustments are outside the scope
of the present software package.
For a detailed discussion of the theory and applications of tolerance bounds,
the reader is referred to @Meeker_Hahn_Escobar_2017 or
@Krishnamoorthy_Mathew_2008.
Currently, many users use MS Excel spreadsheets to perform these
analyses. The MS Excel spreadsheets typically used, such as
STAT-17 [@STAT-17],
ASAP [@Raju_Tomblin_2008] and CMH17-STATS [@CMH17-STATS], use
password-protected VBA macros to
perform the computations. As such, the code cannot be audited by
the user.
cmstatr is an R package that addresses this issue by implementing
the same statistical analysis techniques
found in CMH-17-1G in an open-source environment.
Statement of Need
The purpose of cmstatr is to:
- Provide a consistent user interface for computing A- and B-Basis
values and performing the related diagnostic tests in the
R
programming environment
- Allow auditing of the code used to compute A- and B-Basis values,
and performing the related diagnostic tests
- Enable users to automate computation workflows or to perform
simulation studies
Implementation Goals
cmstatr aims give a consistent interface for the user. Most functions
are written to work with the tidyverse [@tidyverse] and most functions
have similar argument lists. The intent is to make the package easy to
learn and use.
The implementation of cmstatr also aims to avoid the use of lookup
tables
that are prevalent in calculation spreadsheets and minimize the use of
approximations.
While this decision leads to increased computation time, the typically small
data sets (tens to hundreds
of observations) associated with composite material test data and the
speed of modern computers make this practical for interactive programming.
Example Usage
Normally, to use cmstatr the user will load cmstatr itself as well as
the tidyverse package.
library(cmstatr)
library(tidyverse)
cmstatr contains some example data sets, which can be used to demonstrate
the features of the package. One of those data sets --- carbon.fabric.2 ---
will be used in the following example. This data set contains results from
several mechanical tests of a typical composite material, and contains the
typical measurements obtained from a test lab. In the following
examples, results from tension testing in the warp fiber direction (WT)
will be used.
Part of this data set is shown below.
carbon.fabric.2 %>%
filter(test == "WT") %>%
head(10)
One common task is to calculate B-Basis values. There are several
statistical methods for doing so, depending on the distribution of
the data.
The single-point basis functions automatically perform the following
diagnostic tests:
- the maximum normed residual test for outliers within a batch [@CMH171G],
- the Anderson--Darling k-Sample test to check if batches are drawn from
the same (unspecified) distribution [@Scholz_Stephens_1987],
- the maximum normed residual test for outliers within the data, and
- the Anderson--Darling test for a particular probability
distribution [@Lawless_1982].
Assuming that the data from the warp tension (WT) tested at
elevated-temperature/wet condition (ETW) follows
a normal distribution, then this can be done using the function.
Note that all of the functions in cmstatr that compute
basis values default to computing tolerance bounds with a
content of $p=0.9$ and a confidence of $conf=0.95$, or
B-Basis.
carbon.fabric.2 %>%
filter(test == "WT") %>%
filter(condition == "ETW") %>%
basis_normal(strength, batch)
All of the various basis functions perform diagnostic tests for each of the
statistical tests mentioned above. If any
of the diagnostic tests failed, a warning is shown and the test failure
is also recorded in the returned object (and shown in that object's
print method). In the example above, the output shows that the
Anderson--Darling test for normality [@Lawless_1982] rejects the hypothesis
that the data is drawn from a normal distribution.
Two non-parametric basis calculations, based on @Guenther_1970 and
@Vangel_1994 are also implemented in cmstatr. These functions
perform the same
diagnostic tests, but omit the Anderson--Darling test for a particular
distribution.
The diagnostic test can be run directly using cmstatr as well.
For example, the failed diagnostic test above can be run as follows:
carbon.fabric.2 %>%
filter(test == "WT") %>%
filter(condition == "ETW") %>%
anderson_darling_normal(strength)
If the failure of a diagnostic test is decided to be acceptable,
the test result can be overridden to hide the warning in the basis function
output:
carbon.fabric.2 %>%
filter(test == "WT") %>%
filter(condition == "ETW") %>%
basis_normal(strength, batch, override = c("anderson_darling_normal"))
cmstatr also provides functions for calculating basis values from
data pooled across multiple testing environments, as recommended by [@CMH171G].
There are two methods of pooling: both calculate a measure of global variation
from the data in all tested environmental conditions,
then they calculate a basis value for each condition using the measure of
the global variation and the individual mean values of each
condition. The two methods of pooling have different underlying assumptions
and hence the data must pass a different set diagnostic tests for each of
the two functions.
Validation and Comparison With Existing Tools
Where possible, cmstatr has been verified against the examples given
in the articles in which the statistical methods were published. Unit
tests have been written so that this verification is re-checked routinely
to prevent unintended regressions. Agreement between cmstatr and the
examples in the original articles is within the expected numeric accuracy.
cmstatr has also been verified against existing software, such as
STAT-17 [@STAT-17], ASAP [@Raju_Tomblin_2008] and
CMH17-STATS [@CMH17-STATS] using several example data sets.
Agreement between cmstatr and the other software is generally good,
but some results differ slightly, likely due to various approximations used
in the software.
Comparison between cmstatr and the other software is performed
within various unit tests to guard against future regressions.
The tests are automatically run each time a change is made to the code
of cmstatr using a continuous integration service.
Reproducibility
It is envisioned that many users of cmstatr will use it within an
R Notebook or a Jupyter Notebook. It is further envisioned that this notebook
will be directly converted into the statistical analysis report. If this is
done, the reader of the statistical report will be able to verify all of the
detailed steps used in the statistical analysis.
Acknowledgement
The author would like to thank Mr. Billy Cheng for his contributions to
cmstatr and this paper. The author would also like to thank Comtek
Advanced Structures Ltd. for its support in developing and releasing
the cmstatr package.
References
ComtekAdvancedStructures/cmstatr documentation built on Nov. 20, 2024, 6:39 p.m.
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Summary
Strength data for composite materials used in aerospace applications, such as carbon fiber and fiberglass reinforced composites, are normally analyzed using statistical methods because of the inherent variability in the constituent materials and in the processing. The design standards for civil aviation requires that the probability of structural failure due to this variability must be minimized, and to do so, the designer must use what are called "Design Values" for each material in stress analyses and ensure they exceed the actual stresses experienced by those materials in service. Design Values are set based on the one-sided lower confidence bound of the material strength. For some types of structure, the content of this lower confidence bound is $99\%$ with a confidence level of $95\%$; in this case, the confidence bound is referred to as A-Basis. For some other types of structure, the content of the lower confidence bound is instead $90\%$ with a confidence level of $95\%$; in this case, the confidence bound is referred to as B-Basis. The statistical methods for calculating these basis values are outlined in Composite Materials Handbook, Volume 1, Revision G, or CMH-17-1G in short [@CMH171G]. The use of these methods is widely accepted by industry and civil aviation regulators.
Design Values are often adjusted to account for anticipated in-service damage and other factors, however those adjustments are outside the scope of the present software package.
For a detailed discussion of the theory and applications of tolerance bounds, the reader is referred to @Meeker_Hahn_Escobar_2017 or @Krishnamoorthy_Mathew_2008.
Currently, many users use MS Excel spreadsheets to perform these
analyses. The MS Excel spreadsheets typically used, such as
STAT-17 [@STAT-17],
ASAP [@Raju_Tomblin_2008] and CMH17-STATS [@CMH17-STATS], use
password-protected VBA macros to
perform the computations. As such, the code cannot be audited by
the user.
cmstatr is an R package that addresses this issue by implementing
the same statistical analysis techniques
found in CMH-17-1G in an open-source environment.
Statement of Need
The purpose of cmstatr is to:
- Provide a consistent user interface for computing A- and B-Basis
values and performing the related diagnostic tests in the
Rprogramming environment - Allow auditing of the code used to compute A- and B-Basis values, and performing the related diagnostic tests
- Enable users to automate computation workflows or to perform simulation studies
Implementation Goals
cmstatr aims give a consistent interface for the user. Most functions
are written to work with the tidyverse [@tidyverse] and most functions
have similar argument lists. The intent is to make the package easy to
learn and use.
The implementation of cmstatr also aims to avoid the use of lookup
tables
that are prevalent in calculation spreadsheets and minimize the use of
approximations.
While this decision leads to increased computation time, the typically small
data sets (tens to hundreds
of observations) associated with composite material test data and the
speed of modern computers make this practical for interactive programming.
Example Usage
Normally, to use cmstatr the user will load cmstatr itself as well as
the tidyverse package.
library(cmstatr) library(tidyverse)
cmstatr contains some example data sets, which can be used to demonstrate
the features of the package. One of those data sets --- carbon.fabric.2 ---
will be used in the following example. This data set contains results from
several mechanical tests of a typical composite material, and contains the
typical measurements obtained from a test lab. In the following
examples, results from tension testing in the warp fiber direction (WT)
will be used.
Part of this data set is shown below.
carbon.fabric.2 %>% filter(test == "WT") %>% head(10)
One common task is to calculate B-Basis values. There are several statistical methods for doing so, depending on the distribution of the data. The single-point basis functions automatically perform the following diagnostic tests:
- the maximum normed residual test for outliers within a batch [@CMH171G],
- the Anderson--Darling k-Sample test to check if batches are drawn from the same (unspecified) distribution [@Scholz_Stephens_1987],
- the maximum normed residual test for outliers within the data, and
- the Anderson--Darling test for a particular probability distribution [@Lawless_1982].
Assuming that the data from the warp tension (WT) tested at
elevated-temperature/wet condition (ETW) follows
a normal distribution, then this can be done using the function.
Note that all of the functions in cmstatr that compute
basis values default to computing tolerance bounds with a
content of $p=0.9$ and a confidence of $conf=0.95$, or
B-Basis.
carbon.fabric.2 %>% filter(test == "WT") %>% filter(condition == "ETW") %>% basis_normal(strength, batch)
All of the various basis functions perform diagnostic tests for each of the
statistical tests mentioned above. If any
of the diagnostic tests failed, a warning is shown and the test failure
is also recorded in the returned object (and shown in that object's
print method). In the example above, the output shows that the
Anderson--Darling test for normality [@Lawless_1982] rejects the hypothesis
that the data is drawn from a normal distribution.
Two non-parametric basis calculations, based on @Guenther_1970 and
@Vangel_1994 are also implemented in cmstatr. These functions
perform the same
diagnostic tests, but omit the Anderson--Darling test for a particular
distribution.
The diagnostic test can be run directly using cmstatr as well.
For example, the failed diagnostic test above can be run as follows:
carbon.fabric.2 %>% filter(test == "WT") %>% filter(condition == "ETW") %>% anderson_darling_normal(strength)
If the failure of a diagnostic test is decided to be acceptable, the test result can be overridden to hide the warning in the basis function output:
carbon.fabric.2 %>% filter(test == "WT") %>% filter(condition == "ETW") %>% basis_normal(strength, batch, override = c("anderson_darling_normal"))
cmstatr also provides functions for calculating basis values from
data pooled across multiple testing environments, as recommended by [@CMH171G].
There are two methods of pooling: both calculate a measure of global variation
from the data in all tested environmental conditions,
then they calculate a basis value for each condition using the measure of
the global variation and the individual mean values of each
condition. The two methods of pooling have different underlying assumptions
and hence the data must pass a different set diagnostic tests for each of
the two functions.
Validation and Comparison With Existing Tools
Where possible, cmstatr has been verified against the examples given
in the articles in which the statistical methods were published. Unit
tests have been written so that this verification is re-checked routinely
to prevent unintended regressions. Agreement between cmstatr and the
examples in the original articles is within the expected numeric accuracy.
cmstatr has also been verified against existing software, such as
STAT-17 [@STAT-17], ASAP [@Raju_Tomblin_2008] and
CMH17-STATS [@CMH17-STATS] using several example data sets.
Agreement between cmstatr and the other software is generally good,
but some results differ slightly, likely due to various approximations used
in the software.
Comparison between cmstatr and the other software is performed
within various unit tests to guard against future regressions.
The tests are automatically run each time a change is made to the code
of cmstatr using a continuous integration service.
Reproducibility
It is envisioned that many users of cmstatr will use it within an
R Notebook or a Jupyter Notebook. It is further envisioned that this notebook
will be directly converted into the statistical analysis report. If this is
done, the reader of the statistical report will be able to verify all of the
detailed steps used in the statistical analysis.
Acknowledgement
The author would like to thank Mr. Billy Cheng for his contributions to
cmstatr and this paper. The author would also like to thank Comtek
Advanced Structures Ltd. for its support in developing and releasing
the cmstatr package.
References
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