{
"cells": [
{
"cell_type": "markdown",
"id": "fc3195f0",
"metadata": {},
"source": [
"# Grama: Design Under Uncertainty\n",
"\n",
"*Purpose*: We don't model uncertainty just for fun: Once we have a model for uncertainty we can use it to do useful work, such as informing design decisions. In this exercise you will model a particular kind of uncertainty in built systems (variability in part geometry) and use your models to make design decisions that are resilient against the effects of uncertainty.\n"
]
},
{
"cell_type": "markdown",
"id": "53a8da54",
"metadata": {},
"source": [
"## Setup\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "fe025178",
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import grama as gr\n",
"import pandas as pd\n",
"DF = gr.Intention()\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"id": "9b9f9ff1",
"metadata": {},
"source": [
"# Uncertainty in Engineering Systems\n",
"\n",
"The previous exercises `e-grama06-fit-univar` and `e-grama07-fit-multivar` covered the \"how\" and \"why\" of modeling uncertainties with distributions. In this exercise we'll study how uncertainty in the *inputs* of a model *propagates* to uncertainty in its outputs.\n"
]
},
{
"cell_type": "markdown",
"id": "2c61332e",
"metadata": {},
"source": [
"## Perturbed Design Variables\n",
"\n",
"The realities of engineering manufacturing necessitate that built parts will be different from designed parts. In the previous exercise `e-grama07-fit-multivar` we saw a model for a circuit's performance. That system exhibited variability in its *realized component values*; we could pick the nominal (designed) component values `R, L, C`, but manufacturing variability would give rise to different as-made component values `Rr, Lr, Cr`.\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "6f53e520",
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from grama.models import make_prlc_rand\n",
"md_circuit = make_prlc_rand()\n"
]
},
{
"cell_type": "markdown",
"id": "e7870d7d",
"metadata": {},
"source": [
"As a reminder, let's take a look at designed `C` and realized `Cr` values of the circuit capacitance."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "41f2b867",
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"eval_sample() is rounding n...\n"
]
},
{
"data": {
"text/html": [
"
\n",
"\n",
"
\n",
" \n",
"
\n",
"
\n",
"
C
\n",
"
Cr_lo
\n",
"
Cr_mu
\n",
"
Cr_up
\n",
"
\n",
" \n",
" \n",
"
\n",
"
0
\n",
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50.0005
\n",
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42.887234
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64.404955
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87.447509
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\n",
" \n",
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\n",
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"
],
"text/plain": [
" C Cr_lo Cr_mu Cr_up\n",
"0 50.0005 42.887234 64.404955 87.447509"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# NOTE: No need to edit; run and inspect\n",
"(\n",
" md_circuit\n",
" >> gr.ev_sample(n=1e3, df_det=\"nom\")\n",
" \n",
" >> gr.tf_summarize(\n",
" C=gr.mean(DF.C),\n",
" Cr_lo=gr.quant(DF.Cr, p=0.05),\n",
" Cr_mu=gr.mean(DF.Cr),\n",
" Cr_up=gr.quant(DF.Cr, p=0.95),\n",
" )\n",
")"
]
},
{
"cell_type": "markdown",
"id": "6a2ab229",
"metadata": {},
"source": [
"The results above indicate that the designed capicitance was around `50`, but values as low as `42.2` and as high as `87.8` occur too.\n"
]
},
{
"cell_type": "markdown",
"id": "1e0e76ee",
"metadata": {},
"source": [
"### __q1__ Interpret the following density plot\n",
"\n",
"The nominal value for `Design 1` is `x = 0.5`, while the nominal value for `Design 2` is `x = 1.5`. However, parts manufactured according to both designs are subject to manufacturing variability, as depicted by the following densities. Answer the questions under *observations* below.\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "c02bd48c",
"metadata": {
"collapsed": false,
"jupyter": {
"source_hidden": true
},
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mg_1 = gr.marg_mom(\"norm\", mean=+0.5, sd=0.1)\n",
"mg_2 = gr.marg_mom(\"norm\", mean=+1.5, sd=0.1)\n",
"\n",
"(\n",
" gr.df_make(x=gr.linspace(0, +2, 100))\n",
" >> gr.tf_mutate(\n",
" y_1=mg_1.d(DF.x),\n",
" y_2=mg_2.d(DF.x),\n",
" )\n",
" \n",
" >> gr.ggplot(gr.aes(\"x\"))\n",
" + gr.annotate(\"segment\", x=+0.5, xend=+0.5, y=0, yend=4.25, linetype=\"dashed\")\n",
" + gr.annotate(\n",
" \"text\",\n",
" x=+0.5, y=4.5,\n",
" label=\"Design 1\",\n",
" )\n",
" + gr.annotate(\"segment\", x=+1.5, xend=+1.5, y=0, yend=4.25, linetype=\"dashed\")\n",
" + gr.annotate(\n",
" \"text\",\n",
" x=+1.5, y=4.5,\n",
" label=\"Design 2\",\n",
" )\n",
" + gr.geom_line(gr.aes(y=\"y_1\"), color=\"salmon\")\n",
" + gr.geom_line(gr.aes(y=\"y_2\"), color=\"cyan\")\n",
" \n",
" + gr.theme_minimal()\n",
" + gr.labs(\n",
" x=\"Realized Design Variable\",\n",
" y=\"Density\"\n",
" )\n",
")"
]
},
{
"cell_type": "markdown",
"id": "66e48de8",
"metadata": {},
"source": [
"*Observations*\n",
"\n",
"For the following questions, assume that you can measure the Realized Design Variable `x` with *perfect* accuracy.\n",
"\n",
"- Suppose you have a part with `x == 0.61`. Which design specification was this most likely manufactured according to?\n",
" - `Design 1`\n",
"- Suppose you selected a random part of `Design 2` off the manufacturing line and found that `x == 1.40`. Would you be surprised by this?\n",
" - Unsurprising; we can see that `x == 1.40` is well-within the distribution around the nominal `Design 2` value.\n",
""
]
},
{
"cell_type": "markdown",
"id": "0df97445",
"metadata": {},
"source": [
"### __q2__ Set up a perturbation model\n",
"\n",
"Implement a model for a perturbed design variable $x_r$ following\n",
"\n",
"$$x_r = x + \\Delta x$$\n",
"\n",
"where $\\Delta x$ is normally distributed with mean $\\mu = 0$ and standard deviation $\\sigma = 0.1$.\n",
"\n",
"*Hint 1*: To do this, you'll need to add a function to the model that computes $x_r$, and a random variable for $\\Delta x$.\n",
"\n",
"*Hint 2*: The previous exercises `e-grama06-fit-univar` and `e-grama07-fit-multivar` cover how to model an uncertain quantity.\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "4809095a",
"metadata": {
"collapsed": false,
"tags": []
},
"outputs": [],
"source": [
"## TASK: Implement the model for x_r stated above\n",
"\n",
"md_dx = (\n",
" gr.Model(\"Perturbation\")\n",
" >> gr.cp_vec_function(\n",
"\n",
" fun=lambda df: gr.df_make(\n",
" x_r=df.x + df.dx,\n",
" ),\n",
" var=[\"x\", \"dx\"],\n",
" out=[\"x_r\"],\n",
" )\n",
" >> gr.cp_bounds(x=(-1, +1))\n",
"\n",
" >> gr.cp_marginals(\n",
" dx=gr.marg_mom(\"norm\", mean=0, sd=0.1),\n",
" )\n",
" >> gr.cp_copula_independence()\n",
")\n",
"\n",
"## NOTE: Use this to check your work\n",
"gr.eval_sample(md_dx, n=1, df_det=\"nom\")\n",
" \n",
"assert \\\n",
" 'dx' in md_dx.density.marginals.keys(), \\\n",
" 'No density for dx'\n",
"assert \\\n",
" md_dx.density.marginals['dx'].d_param['loc'] == 0., \\\n",
" \"Density for dx has wrong mean\"\n",
"assert \\\n",
" md_dx.density.marginals['dx'].d_param['scale'] == 0.1, \\\n",
" \"Density for dx has wrong standard deviation\"\n",
" "
]
},
{
"cell_type": "markdown",
"id": "f596f8ac",
"metadata": {},
"source": [
"## Uncertainty Propagation\n",
"\n",
"Often, we model engineering outcomes *deterministically*; assuming certain inputs $x$ are known exactly, we produce a predictable output value $y$ based on a mathematical model $y = f(x)$.\n",
"\n",
"For example, we've previously looked at a model for the buckling strength of a rectangular plate\n",
"\n",
"$$\\sigma_{cr} = k_{cr} \\frac{\\pi^2 E}{12 (1 - \\mu^2)} \\left(\\frac{t}{b}\\right)^2.$$\n",
"\n",
"This is a *deterministic* model for the buckling strength $\\sigma_{cr}$ that depends on the plate geometry, such as the plate thickness $t$.\n"
]
},
{
"cell_type": "markdown",
"id": "9afaa1cd",
"metadata": {},
"source": [
"However, if the input values cannot be controlled exactly, it may be more appropriate to think of the model as having *perturbed* inputs $x_r = x + \\Delta x$. With perturbed inputs, the output is no longer precisely known, but is now subject to *uncertainty propagation*. We can think of this mathematically as \n",
"\n",
"$$y(x) = f(x_r) = f(x + \\Delta x).$$\n",
"\n",
"Where the input that the function \"sees\" is the perturbed input, rather than the deterministic input. This leads to uncertainty in the output $y$---the uncertainty *propagates* from the input to the output.\n",
"\n",
"Returning to the buckling strength example, if there were manufacturing variability in the plate thickness $t_r = t + \\Delta t$, then there would be uncertainty in the buckling strength\n",
"\n",
"$$\\sigma_{cr} = k_{cr} \\frac{\\pi^2 E}{12 (1 - \\mu^2)} \\left(\\frac{t + \\Delta t}{b}\\right)^2.$$\n"
]
},
{
"cell_type": "markdown",
"id": "b61a3d5d",
"metadata": {},
"source": [
"The following images depict uncertainty propagation schematically. First, let's look at a linear function $f(x)$."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "ced9a0cd",
"metadata": {
"collapsed": false,
"jupyter": {
"source_hidden": true
},
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# NOTE: No need to edit; this illustrates uncertainty propagation\n",
"md_line = (\n",
" md_dx\n",
" >> gr.cp_vec_function(\n",
" fun=lambda df: gr.df_make(y=0.5*df.x_r + 1),\n",
" var=[\"x_r\"],\n",
" out=[\"y\"],\n",
" )\n",
")\n",
"\n",
"y_baseboard = 0.5\n",
"\n",
"(\n",
" md_line\n",
" >> gr.ev_sample(\n",
" n=5,\n",
" df_det=gr.df_make(x=(0.5, 1.5)),\n",
" seed=101,\n",
" )\n",
" \n",
" >> gr.ggplot(gr.aes(\"x_r\", \"y\"))\n",
" + gr.geom_hline(yintercept=y_baseboard, color=\"grey\", size=1)\n",
" + gr.geom_abline(intercept=1, slope=0.5, color=\"salmon\")\n",
" \n",
" + gr.geom_segment(gr.aes(xend=\"x_r\", yend=y_baseboard), linetype=\"dotted\")\n",
" + gr.geom_segment(gr.aes(xend=\"x\", y=y_baseboard, yend=y_baseboard), linetype=\"dotted\")\n",
" + gr.geom_segment(gr.aes(x=\"x\", xend=\"x\", y=0, yend=y_baseboard))\n",
" + gr.geom_point(size=1)\n",
" + gr.geom_point(gr.aes(y=y_baseboard), size=1)\n",
" + gr.geom_point(gr.aes(x=\"x\", y=0), size=1)\n",
" + gr.annotate(\n",
" \"text\",\n",
" x=0.9,\n",
" y=y_baseboard-0.1,\n",
" label=\"Realized x\",\n",
" )\n",
" \n",
" + gr.scale_x_continuous(limits=(0, 2))\n",
" + gr.theme_minimal()\n",
" + gr.labs(\n",
" x=\"Designed x\",\n",
" y=\"Resulting output y\",\n",
" )\n",
")"
]
},
{
"cell_type": "markdown",
"id": "f92cebfd",
"metadata": {},
"source": [
"Here we have designed values of $x$ at $x = 0.5$ and $x = 1.5$. However, perturbations lead to variability in the realized values $x_r$, which in turn lead to variability in the output $y$.\n",
"\n",
"The variability in $y$ is roughly the same at both designed values $x$. However, a different function can lead to quite different results.\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "b5314a93",
"metadata": {
"collapsed": false,
"jupyter": {
"source_hidden": true
},
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# NOTE: No need to edit; this illustrates uncertainty propagation\n",
"md_exp = (\n",
" md_dx\n",
" >> gr.cp_vec_function(\n",
" fun=lambda df: gr.df_make(y=gr.exp(df.x_r)),\n",
" var=[\"x_r\"],\n",
" out=[\"y\"],\n",
" )\n",
")\n",
"\n",
"y_baseboard = 0.5\n",
"\n",
"(\n",
" md_exp\n",
" >> gr.ev_sample(\n",
" n=5,\n",
" df_det=gr.df_make(x=(0.5, 1.5)),\n",
" seed=101,\n",
" )\n",
" \n",
" >> gr.ggplot(gr.aes(\"x_r\", \"y\"))\n",
" + gr.geom_hline(yintercept=y_baseboard, color=\"grey\", size=1)\n",
" + gr.geom_line(\n",
" data=md_exp\n",
" >> gr.ev_nominal(df_det=gr.df_make(x=gr.linspace(0.2, 1.8, 100))),\n",
" mapping=gr.aes(\"x\"),\n",
" color=\"salmon\",\n",
" )\n",
" \n",
" + gr.geom_segment(gr.aes(xend=\"x_r\", yend=y_baseboard), linetype=\"dotted\")\n",
" + gr.geom_segment(gr.aes(xend=\"x\", y=y_baseboard, yend=y_baseboard), linetype=\"dotted\")\n",
" + gr.geom_segment(gr.aes(x=\"x\", xend=\"x\", y=0, yend=y_baseboard))\n",
" + gr.geom_point(size=1)\n",
" + gr.geom_point(gr.aes(y=y_baseboard), size=1)\n",
" + gr.geom_point(gr.aes(x=\"x\", y=0), size=1)\n",
" + gr.annotate(\n",
" \"text\",\n",
" x=0.96,\n",
" y=y_baseboard-0.2,\n",
" label=\"Realized x\",\n",
" )\n",
" \n",
" + gr.theme_minimal()\n",
" + gr.labs(\n",
" x=\"Designed x\",\n",
" y=\"Resulting output y\",\n",
" )\n",
")"
]
},
{
"cell_type": "markdown",
"id": "a4bdbfb4",
"metadata": {},
"source": [
"Once again we see variability in the realized values. However, note that the variability in the realized output `y` \n"
]
},
{
"cell_type": "markdown",
"id": "71d8219c",
"metadata": {},
"source": [
"### __q3__ Do a sweep with propagated uncertainty\n",
"\n",
"Use your perturbation model `md_dx` to study how variability propagates through the function\n",
"\n",
"$$y(x) = f(x_r) = x_r^4.$$\n",
"\n",
"Sweep the design variable $x$ from at least $0.1$ to $1.0$, and make sure to use a sufficient number of observations in your random sample. Answer the questions under *observations* below.\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "e9fc1a38",
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"## TASK: Evaluate a sweep with with propagated uncertainty\n",
"df_dx = (\n",
" md_dx\n",
" # NOTE: No need to edit; this composes the output function\n",
" # with the perturbation model you implemented above\n",
" >> gr.cp_vec_function(\n",
" fun=lambda df: gr.df_make(y=df.x_r**4),\n",
" var=[\"x_r\"],\n",
" out=[\"y\"],\n",
" )\n",
" \n",
"\n",
" >> gr.ev_sample(\n",
" n=100,\n",
" df_det=gr.df_make(x=gr.linspace(0.1, 1.0, 20)),\n",
" )\n",
")\n",
"\n",
"## NOTE: Use this to check your work\n",
"assert \\\n",
" isinstance(df_dx, pd.DataFrame), \\\n",
" \"df_dx is not a DataFrame; make sure to evaluate md_dx\"\n",
"assert \\\n",
" df_dx.x.min() <= 0.1, \\\n",
" \"Make sure to sweep to a value as low as x == 0.1\"\n",
"assert \\\n",
" df_dx.x.max() >= 1.0, \\\n",
" \"Make sure to sweep to a value as high as x == 1.0\"\n",
"assert \\\n",
" len(set(df_dx.x)) >= 10, \\\n",
" \"Make sure to use a sufficient number of points in your sweep\"\n",
"assert \\\n",
" len(set(df_dx.dx)) >= 100, \\\n",
" \"Make sure to use a sufficient number of points in your sample\"\n",
"\n",
"# Visualize\n",
"(\n",
" df_dx\n",
" >> gr.ggplot(gr.aes(\"x\", \"y\"))\n",
" + gr.geom_point()\n",
")"
]
},
{
"cell_type": "markdown",
"id": "18f7f007",
"metadata": {},
"source": [
"*Observations*\n",
"\n",
"- What does the horizontal axis in the plot above represent: The designed value of `x` or the realized value of `x`?\n",
" - The horizontal axis in the plot above represents the designed value of `x`.\n",
"- Why is there variability in `y`?\n",
" - There is variability in `y` because we are visualizing the designed value of `x`, while the realized value `x_r` varies randomly.\n",
"- Where (along the horizontal axis) is the variability in `y` large? Where is it small?\n",
" - The variability is smallest at small values of $x$, and largest at large values of $x$.\n",
"- What about the underlying function `y = f(x)` explains the trends in variability you noted above?\n",
" - Since the function is $y = x_r^4$, variability in $x_r$ is amplified by the function. A highly quantitative way to think of this is in terms of the derivative $\\frac{dy}{dx_r} = 4 x_r^3 = 4 (x + \\Delta x)^3$; note that larger values of the designed value lead to a larger slope in $y$. (I don't necessarily expect you to come up with that argument on your own!)\n",
""
]
},
{
"cell_type": "markdown",
"id": "d47e6432",
"metadata": {},
"source": [
"## Summarizing variability\n",
"\n",
"Visualizing variability with a scatterplot is a good first-step, but there are more effective ways to *summarize* variability.\n"
]
},
{
"cell_type": "markdown",
"id": "98f623a3",
"metadata": {},
"source": [
"### __q4__ Summarize variability across a sweep\n",
"\n",
"Summarize the variability in $y$ at each value of $x$ by computing the mean `y_mu`, the 5% quantile `y_lo`, and the 95% quantile `y_up`. Answer the questions under *observations* below.\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "df936163",
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df_dx_summary = (\n",
" df_dx\n",
"\n",
" >> gr.tf_group_by(DF.x)\n",
" >> gr.tf_summarize(\n",
" y_lo=gr.quant(DF.y, p=0.05),\n",
" y_mu=gr.mean(DF.y),\n",
" y_up=gr.quant(DF.y, p=0.95),\n",
" )\n",
" ## NOTE: Clean up the grouping\n",
" >> gr.tf_ungroup()\n",
")\n",
"\n",
"## NOTE: No need to edit; use this to check your work\n",
"assert \\\n",
" set(df_dx.x) == set(df_dx_summary.x), \\\n",
" \"Incorrect grouping for df_dx_summary\"\n",
"assert \\\n",
" \"y_lo\" in df_dx_summary.columns, \\\n",
" \"Make sure to compute a lower quantile y_lo\"\n",
"assert \\\n",
" \"y_up\" in df_dx_summary.columns, \\\n",
" \"Make sure to compute an upper quantile y_up\"\n",
"# Check the quantiles\n",
"df_dx_check = (\n",
" df_dx\n",
" >> gr.tf_left_join(df_dx_summary, by=\"x\")\n",
" >> gr.tf_filter(DF.x == gr.min(DF.x))\n",
" >> gr.tf_summarize(\n",
" p_lo=gr.pr(DF.y <= DF.y_lo),\n",
" p_up=gr.pr(DF.y <= DF.y_up),\n",
" )\n",
")\n",
"assert \\\n",
" abs(df_dx_check.p_lo[0] - 0.05) < 1e-3, \\\n",
" \"Lower quantile value is incorrect\"\n",
"assert \\\n",
" abs(df_dx_check.p_up[0] - 0.95) < 1e-3, \\\n",
" \"Upper quantile value is incorrect\"\n",
"\n",
"(\n",
" df_dx_summary\n",
" >> gr.ggplot(gr.aes(\"x\"))\n",
" + gr.geom_ribbon(\n",
" mapping=gr.aes(ymin=\"y_lo\", ymax=\"y_up\"),\n",
" alpha=1/3,\n",
" )\n",
" + gr.geom_line(gr.aes(y=\"y_mu\"))\n",
")"
]
},
{
"cell_type": "markdown",
"id": "641a5cb7",
"metadata": {},
"source": [
"*Observations*\n",
"\n",
"*Note*: This plot uses `geom_ribbon()`, which takes the aesthetics `ymin` and `ymax`. A ribbon is a useful way to visualize a region bounded by lower and upper values, such as quantiles!\n",
"\n",
"- Contrast this plot with the scatterplot from q3: What can you see in this ribbon plot that is harder to see in the scatterplot?\n",
" - Some examples: We can see the mean trend quite clearly, while the mean trend is harder to judge by eye in the scatterplot. We can also see particular quantiles; if we wanted to make decisions based on the middle 90% of the data, these would be ideal bounds to use. If we wanted to use a different fraction of the data (say, 99%) we could adjust the quantiles (say, `0.005` and `0.995`).\n"
]
},
{
"cell_type": "markdown",
"id": "250d2893",
"metadata": {},
"source": [
"# Designing for uncertainty\n",
"\n",
"We've seen that uncertainty can propagate through systems---what can we do about that? There are various ways we can design systems to mitigate the effects of uncertainty: We can seek *robust* designs, we can explicitly design for *reliability*, and we can *set tolerances* to achieve design targets.\n"
]
},
{
"cell_type": "markdown",
"id": "c83fab65",
"metadata": {},
"source": [
"## Robustness\n",
"\n",
"Sometimes, the best nominal performance does not result in the overall \"best\" design. Since uncertainty can propagate, a design that is highly sensitive to input variability can fail to live up to the promise of its best nominal performance. The following example will guide you through thinking about designs that are *robust*, in the sense that they are resistant to uncertainty.\n"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "9fc36af9",
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"## NOTE: No need to edit; this sets up a model with\n",
"## a perturbed input and a complex output function\n",
"md_poly = (\n",
" gr.Model(\"Polynomial\")\n",
" >> gr.cp_vec_function(\n",
" fun=lambda df: gr.df_make(\n",
" x_r=df.x + df.dx\n",
" ),\n",
" var=[\"x\", \"dx\"],\n",
" out=[\"x_r\"],\n",
" name=\"Realized design\"\n",
" )\n",
" >> gr.cp_vec_function(\n",
" fun=lambda df: gr.df_make(\n",
" y=(df.x_r + 0.6) \n",
" *(df.x_r + 0.4) \n",
" *(df.x_r - 0.65)\n",
" *(df.x_r - 0.55)\n",
" *13.5 * (1 + gr.exp(8.0 * df.x_r))\n",
" ),\n",
" var=[\"x_r\"],\n",
" out=[\"y\"],\n",
" name=\"Realized output\"\n",
" )\n",
" >> gr.cp_bounds(x=(-1, +1))\n",
" >> gr.cp_marginals(dx=gr.marg_mom(\"norm\", mean=0, sd=0.03))\n",
" >> gr.cp_copula_independence()\n",
")"
]
},
{
"cell_type": "markdown",
"id": "728d557d",
"metadata": {},
"source": [
"### __q5__ Interpret this plot\n",
"\n",
"Run the following code and inspect the plot. Answer the questions under *observations* below.\n"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "22e76f68",
"metadata": {
"collapsed": false,
"jupyter": {
"source_hidden": true
},
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"## NOTE: No need to edit; run and inspect\n",
"# Evaluate model without uncertainty\n",
"df_poly_nom = (\n",
" md_poly\n",
" >> gr.ev_nominal(\n",
" df_det=gr.df_make(x=gr.linspace(-1, +1, 100)),\n",
" )\n",
")\n",
"\n",
"# Evaluate with uncertainty, take quantiles\n",
"df_poly_mc = (\n",
" md_poly\n",
" >> gr.ev_sample(\n",
" df_det=gr.df_make(x=gr.linspace(-1, +1, 100)),\n",
" n=40,\n",
" seed=101,\n",
" )\n",
" >> gr.tf_group_by(\"x\")\n",
" >> gr.tf_summarize(\n",
" y_lo=gr.quant(DF.y, p=0.05),\n",
" y_mu=gr.median(DF.y),\n",
" y_up=gr.quant(DF.y, p=0.95),\n",
" )\n",
" >> gr.tf_ungroup()\n",
")\n",
"\n",
"# Visualize\n",
"(\n",
" df_poly_mc\n",
" >> gr.tf_mutate(source=\"Quantiles\")\n",
" >> gr.ggplot(gr.aes(\"x\"))\n",
" + gr.geom_line(\n",
" data=df_poly_nom\n",
" >> gr.tf_mutate(source=\"Nominal\"),\n",
" mapping=gr.aes(y=\"y\"),\n",
" )\n",
" + gr.geom_ribbon(\n",
" mapping=gr.aes(ymin=\"y_lo\", ymax=\"y_up\"),\n",
" alpha=1/3,\n",
" )\n",
" \n",
" + gr.scale_y_continuous(breaks=(-10, -5, 0, +5, +10, +15, +20))\n",
" + gr.coord_cartesian(ylim=(-10, 20))\n",
" + gr.theme_minimal()\n",
" + gr.guides(color=None)\n",
" + gr.labs(\n",
" x=\"Designed input value x\",\n",
" y=\"Realized output value y\",\n",
" )\n",
")"
]
},
{
"cell_type": "markdown",
"id": "0145ca5f",
"metadata": {},
"source": [
"*Observations*\n",
"\n",
"For this example, *lower* values of `y` are better. The solid curve depicts the `Nominal` output value, while the shaded region visualizes the 5% to 95% quantiles.\n",
"\n",
"- *Approximately*, what is the lowest value `y` value the `Nominal` curve (solid curve) achieves across the values of `x` depicted above?\n",
" - $y_{\\min} \\approx -5$\n",
"- *Approimately*, what is the value of `y` for the `Nominal` curve at `x = -0.5`?\n",
" - $y(x = -0.5) \\approx 0$\n",
"- Note the spread between the `Quantiles` at $x \\approx 0.6$. *Approximately* what range of `y` values would you expect to result from releated manufacturing at $x \\approx 0.6$?\n",
" - $y \\in [-5, 1]$\n",
"- Note the spread between the `Quantiles` at $x \\approx -0.5$. *Approximately* what range of `y` values would you expect to result from releated manufacturing at $x \\approx -0.5$?\n",
" - $y \\in [0, 0]$\n",
"- Suppose you plan to manufacture many parts according to this process, test all specimens, and choose the best 5%. Which design (value of `x`) would you pick, and why?\n",
" - I would choose $x = 0.6$ for the design, as we would likely see a large number of highly negative (desirable) values. Post-manufacturing selection would allow us to collect a subset of highly-performing specimens.\n",
"- Suppose you plan to manufacture many parts according to this process, all of which must work at an acceptable level. Which design (value of `x`) would you pick, and why?\n",
" - I would choose $x = -0.5$ for the design, as we need the performance of the parts to be consistent.\n",
""
]
},
{
"cell_type": "markdown",
"id": "c732bf63",
"metadata": {},
"source": [
"## Reliability\n",
"\n",
"While *robustness* is about reducing variability, *reliability* is about avoiding unwanted failures. A *reliable* design is a design that has a low probability of failure. With a model for a system and its uncertainties, we can use uncertainty propagation to quantify the probability of failure, and use the model to test the reliability of different designs.\n",
"\n",
"For the remainder of this exercise, let's use the cantilever beam model as an example.\n"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "4cfae052",
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"model: Cantilever Beam\n",
"\n",
" inputs:\n",
" var_det:\n",
" w: [2, 4]\n",
" t: [2, 4]\n",
"\n",
" var_rand:\n",
" H: (+1) norm, {'mean': '5.000e+02', 's.d.': '1.000e+02', 'COV': 0.2, 'skew.': 0.0, 'kurt.': 3.0}\n",
" V: (+1) norm, {'mean': '1.000e+03', 's.d.': '1.000e+02', 'COV': 0.1, 'skew.': 0.0, 'kurt.': 3.0}\n",
" E: (+0) norm, {'mean': '2.900e+07', 's.d.': '1.450e+06', 'COV': 0.05, 'skew.': 0.0, 'kurt.': 3.0}\n",
" Y: (-1) norm, {'mean': '4.000e+04', 's.d.': '2.000e+03', 'COV': 0.05, 'skew.': 0.0, 'kurt.': 3.0}\n",
"\n",
" copula:\n",
" Independence copula\n",
"\n",
" functions:\n",
" cross-sectional area: ['w', 't'] -> ['c_area']\n",
" limit state: stress: ['w', 't', 'H', 'V', 'E', 'Y'] -> ['g_stress']\n",
" limit state: displacement: ['w', 't', 'H', 'V', 'E', 'Y'] -> ['g_disp']"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from grama.models import make_cantilever_beam\n",
"md_beam = make_cantilever_beam()\n",
"md_beam\n"
]
},
{
"cell_type": "markdown",
"id": "0b59adee",
"metadata": {},
"source": [
"### __q6__ Compare the reliability of designs\n",
"\n",
"Estimate the probability of failure due to `stress` for the following cantilever beam designs. Make sure to compute lower and upper confidence interval bounds for your estimate, and choose a large enough sample size so that the CI for the designs do not overlap. Answer the questions under *observations* below.\n",
"\n",
"*Hint*: Remember that we learned about estimating probabilities of failure (and related confidence intervals) in `e-stat05-CI`.\n"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "3d6250c9",
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"eval_sample() is rounding n...\n",
" design pof_lo pof_mu pof_up\n",
"0 Square 0.473439 0.4863 0.499179\n",
"1 Tall 0.282503 0.2941 0.305970\n",
"2 Wide 0.928253 0.9349 0.940971\n"
]
}
],
"source": [
"## TASK: Estimate the reliability for the following beam designs\n",
"\n",
"# NOTE: No need to edit; evaluate these designs\n",
"df_beam_designs = gr.df_make(\n",
" design=[\"Wide\", \"Tall\", \"Square\"],\n",
" w=[4, 2, gr.sqrt(8)],\n",
" t=[2, 4, gr.sqrt(8)],\n",
")\n",
"\n",
"## TASK: Complete the following code\n",
"df_beam_results = (\n",
" md_beam\n",
"\n",
" >> gr.ev_sample(\n",
" n=1e4, \n",
" df_det=df_beam_designs, \n",
" seed=101,\n",
" )\n",
" >> gr.tf_group_by(DF.design)\n",
" >> gr.tf_summarize(\n",
" pof_lo=gr.pr_lo(DF.g_stress <= 0),\n",
" pof_mu=gr.pr(DF.g_stress <= 0),\n",
" pof_up=gr.pr_up(DF.g_stress <= 0),\n",
" )\n",
" >> gr.tf_ungroup()\n",
")\n",
"\n",
"print(df_beam_results)\n",
"\n",
"## NOTE: No need to edit below; use this to check your work\n",
"assert \\\n",
" isinstance(df_beam_results, pd.DataFrame), \\\n",
" \"df_beam_results is not a DataFrame; make sure to evaluate and summarize\"\n",
"assert \\\n",
" {\"Square\", \"Tall\", \"Wide\"} == set(df_beam_results.design), \\\n",
" \"df_beam_results does not contain rows for each design; make sure to group appropriately\"\n",
"assert \\\n",
" \"pof_lo\" in df_beam_results.columns, \\\n",
" \"CI lower bound pof_lo not found in df_beam_results; make sure to compute a lower CI bound\"\n",
"assert \\\n",
" \"pof_up\" in df_beam_results.columns, \\\n",
" \"CI upper bound pof_up not found in df_beam_results; make sure to compute an upper CI bound\"\n",
"assert \\\n",
" df_beam_results[df_beam_results.design==\"Tall\"].pof_up.values[0] < \\\n",
" df_beam_results[df_beam_results.design==\"Square\"].pof_lo.values[0], \\\n",
" \"CI overlap; make sure to use a sufficiently large sample size\"\n",
"assert \\\n",
" df_beam_results[df_beam_results.design==\"Square\"].pof_up.values[0] < \\\n",
" df_beam_results[df_beam_results.design==\"Wide\"].pof_lo.values[0], \\\n",
" \"CI overlap; make sure to use a sufficiently large sample size\"\n"
]
},
{
"cell_type": "markdown",
"id": "1ebe913f",
"metadata": {},
"source": [
"*Observations*\n",
"\n",
"- Which design has the lowest probability of failure?\n",
" - The `Tall` design has the lowest probability of failure.\n",
"- All of these designs have the same cross-sectional area; they vary from wide to square to tall in their rectangular cross-section shape. Based on the result above, does the *nominal* width or tallness of the cross-section seem to be more important for safe operation?\n",
" - Tallness seems to be most important, based on these results.\n",
""
]
},
{
"cell_type": "markdown",
"id": "569ea611",
"metadata": {},
"source": [
"## Setting Tolerances\n",
"\n",
"Once we represent uncertainty in a model, we can make modifications to that model to make quantitative statements about system performance. For instance, modeling the tolerances for a manufactured component will allow us to test different tolerance scenarios. This can help us decide whether to ask manufacturing to tighten specific tolerances.\n",
"\n",
"The following code adds a perturbation model for tolerances on the width and tallness of the cantilever beam. You'll use this model below to test different tolerance scenarios.\n"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "cff6fcbb",
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/zach/Git/py_grama/grama/marginals.py:336: RuntimeWarning: divide by zero encountered in double_scalars\n"
]
},
{
"data": {
"text/plain": [
"model: None\n",
"\n",
" inputs:\n",
" var_det:\n",
" t0: [2, 4]\n",
" w0: [2, 4]\n",
"\n",
" var_rand:\n",
" H: (+0) norm, {'mean': '5.000e+02', 's.d.': '1.000e+02', 'COV': 0.2, 'skew.': 0.0, 'kurt.': 3.0}\n",
" V: (+0) norm, {'mean': '1.000e+03', 's.d.': '1.000e+02', 'COV': 0.1, 'skew.': 0.0, 'kurt.': 3.0}\n",
" E: (+0) norm, {'mean': '2.900e+07', 's.d.': '1.450e+06', 'COV': 0.05, 'skew.': 0.0, 'kurt.': 3.0}\n",
" Y: (+0) norm, {'mean': '4.000e+04', 's.d.': '2.000e+03', 'COV': 0.05, 'skew.': 0.0, 'kurt.': 3.0}\n",
" dw: (+0) uniform, {'mean': '0.000e+00', 's.d.': '1.000e-01', 'COV': inf, 'skew.': 0.0, 'kurt.': 1.8}\n",
" dt: (+0) uniform, {'mean': '0.000e+00', 's.d.': '1.000e-01', 'COV': inf, 'skew.': 0.0, 'kurt.': 1.8}\n",
"\n",
" copula:\n",
" Independence copula\n",
"\n",
" functions:\n",
" Design perturbations: ['w0', 't0', 'dw', 'dt'] -> ['w', 't']\n",
" Cantilever Beam: ['w', 'Y', 't', 'V', 'E', 'H'] -> ['c_area', 'g_stress', 'g_disp']"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"## NOTE: NO need to edit; this adds tolerances to the cantilever beam model\n",
"md_beam_tolerances = (\n",
" gr.Model()\n",
" >> gr.cp_vec_function(\n",
" fun=lambda df: gr.df_make(\n",
" w=df.w0 + df.dw,\n",
" t=df.t0 + df.dt,\n",
" ),\n",
" var=[\"w0\", \"t0\", \"dw\", \"dt\"],\n",
" out=[\"w\", \"t\"],\n",
" name=\"Design perturbations\",\n",
" )\n",
" ## NOTE: gr.cp_md_det() is an advanced tool I'm using to\n",
" ## avoid re-defining the entire beam model. You could\n",
" ## accomplish the same thing with gr.cp_vec_function()\n",
" ## and the beam equations\n",
" >> gr.cp_md_det(md_beam)\n",
" ## Define the input space\n",
" >> gr.cp_bounds(\n",
" w0=(2, 4),\n",
" t0=(2, 4),\n",
" )\n",
" >> gr.cp_marginals(\n",
" # Uncertainties from the original model\n",
" H=gr.marg_mom(\"norm\", mean=500, sd=100),\n",
" V=gr.marg_mom(\"norm\", mean=1000, sd=100),\n",
" E=gr.marg_mom(\"norm\", mean=2.9e7, sd=1.45e6),\n",
" Y=gr.marg_mom(\"norm\", mean=40000, sd=2000),\n",
" # Variability in width and tallness\n",
" dw=gr.marg_mom(\"uniform\", mean=0, sd=1e-1),\n",
" dt=gr.marg_mom(\"uniform\", mean=0, sd=1e-1),\n",
" )\n",
" >> gr.cp_copula_independence()\n",
")\n",
"md_beam_tolerances \n"
]
},
{
"cell_type": "markdown",
"id": "29252113",
"metadata": {},
"source": [
"First, let's evaluate the baseline tolerance model to assess the probability of failure for a few designs.\n"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "5f1648fe",
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"eval_sample() is rounding n...\n"
]
},
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