{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Building Blocks of a Timbre Simulation\n", "\n", "The example below represents a situation where one has a 21500 second hot dwell at 90.2 degrees pitch that they want to\n", "include in a schedule near January 1st, 2021. They want to know how much time at 148.95 degrees pitch that should be\n", "included in the schedule to balance this hot dwell from an ACA perspective.\n", "\n", "\n", "## Package Imports" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from cxotime import CxoTime\n", "from timbre import get_local_model, find_second_dwell" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Define Model Information\n", "\n", "This information defines the model being used, as well as initial starting conditions. These starting conditions do not significantly impact the results, however it is good practice to set them to be close to realistic values." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "msid = \"aacccdpt\"\n", "limit = -6.5\n", "date = \"2021:001:00:00:00\"\n", "aca_model_spec, aca_md5 = get_local_model(\"../timbre/tests/data/aca_spec.json\")\n", "model_init = {\"aacccdpt\": -6.5, \"aca0\": -6.5, \"eclipse\": False}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Define Dwell #1 Information\n", "\n", "Define the state information for the observation that one wants to balance, such as a known hot dwell to be\n", "included in a schedule. For the ACA model, we only need to define dwell time and pitch. Other models may need to have\n", "more information defined. For example, the DPA model would need FEP count, CCD count, SIM position, clocking state, and\n", "vid board state defined. Any information that the Xija model needs to run, that isn't defined in `model_init` needs to\n", "be defined in each of the dwell state definitions, `dwell1_state` and `dwell2_state`." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "t_dwell1 = 21500.0 # Seconds\n", "dwell1_state = {\"pitch\": 90.2}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Define Dwell #2 Information\n", "\n", "This state can be considered a candidate balancing dwell, such as a cooling attitude one wants to use to balance a hot\n", "attitude. In this case we want to calculate the cold time necessary to balance the hot dwell 1 state, so we do not\n", "define time as in input parameter. As with `dwell1_state`, `dwell2_state` still needs all information, not already in\n", "the initialization object `model_init`, necessary to run the Xija model." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "dwell2_state = {\"pitch\": 148.95}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculate Dwell #2 Time" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "results = find_second_dwell(\n", " date,\n", " dwell1_state,\n", " dwell2_state,\n", " t_dwell1,\n", " msid,\n", " limit,\n", " aca_model_spec,\n", " model_init,\n", " limit_type=\"max\",\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Explanation of Results\n", "\n", "The following information is returned by `find_second_dwell`:\n", "\n", " - `converged`: This is a boolean value that indicates whether or not a solution was possible. Solutions will not be\n", " possible in a number of situations:\n", "\n", " + Both dwells heat the location being modeled.\n", " + Both dwells cool the location being modeled.\n", " + One of the states neither sufficiently heats or cools the location being modeled (this will sometimes converge but\n", " not always reliably).\n", " + The `dwell1_state` is hot and the initial dwell time is long enough to heat this location from a steady state cold\n", " temperature to the specified hot limit, assuming the location is associated with a maximum temperature limit. In\n", " the case where a location is associated with a minimum temperature limit (e.g. PLINE03T), the opposite would apply,\n", " the `dwell1_state` is cold and is long enough to cool this location from a steady state hot temperature to the\n", " specified cold limit.\n", "\n", " - `unconverged_hot`: If the solution didn't converge, this will be `True` if the input values resulted in temperatures\n", " outside (e.g. above) the specified limit.\n", " - `unconverged_cold`: If the solution didn't converge, this will be `True` if the input values resulted in all\n", " temperatures within (e.g. below) the specified limit.\n", " - `min_temp`: This is the minimum temperature observed during the simulation (latter 2/3 actually to allow the model to\n", " reach a repeatable pattern - more on this later). This will be the limit for a converged solution in the case where\n", " the location is associated with a minimum temperature limit (e.g. PLINE03T).\n", " - `mean_temp`: This is the mean temperature observed during the simulation (latter 2/3)\n", " - `max_temp`: This is the maximum temperature observed during the simulation (latter 2/3). This will be the limit for a\n", " converged solution with a maximum temperature limit (e.g. AACCCDPT).\n", " - `temperature_limit`: This is the limit being used.\n", " - **`dwell2_time`: The dwell #2 time is what you are looking to calculate, and represents the dwell #2 state duration\n", " that balances the dwell #1 state at the specified duration, `t_dwell1`.**\n", " - `min_pseudo`: This is the min pseudo node temperature observed during the evaluated portion of the simulation. This\n", " is not implemented yet but is intended to eventually yield additional insight into the results.\n", " - `mean_pseudo`: This is the mean pseudo node temperature observed during the evaluated portion of the simulation. This\n", " is not implemented yet.\n", " - `max_pseudo`: This is the max pseudo node temperature observed during the evaluated portion of the simulation. This\n", " is not implemented yet.\n", " - `hotter_state`: This is an integer indicating which state is hotter, 1 or 2.\n", " - `colder_state`: This is an integer indicating which state is colder, 1 or 2, and is actually redundant with\n", " `hotter_state`.\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'converged': True,\n", " 'unconverged_hot': False,\n", " 'unconverged_cold': False,\n", " 'min_temp': -7.156585351574264,\n", " 'mean_temp': -6.791883371289597,\n", " 'max_temp': -6.5,\n", " 'temperature_limit': -6.5,\n", " 'dwell_2_time': 47284.94444514031,\n", " 'min_pseudo': nan,\n", " 'mean_pseudo': nan,\n", " 'max_pseudo': nan,\n", " 'hotter_state': 1,\n", " 'colder_state': 2}" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Batch Processing\n", "\n", "Multiple sets of cases can be run using a single function call, simplifying the generation of larger datasets." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Package Imports\n", "\n", "The only difference from above is the import of `run_state_pairs` and `numpy`." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from cxotime import CxoTime\n", "from timbre import get_local_model, run_state_pairs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Define Model Information\n", "\n", "This is the same setup as used above." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "msid = \"aacccdpt\"\n", "limit = -6.5\n", "date = \"2021:001:00:00:00\"\n", "aca_model_spec, aca_md5 = get_local_model(\"../timbre/tests/data/aca_spec.json\")\n", "model_init = {\"aacccdpt\": -6.5, \"aca0\": -6.5, \"eclipse\": False}\n", "t_dwell1 = 21500.0 # Seconds" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Define Dwell Cases\n", "\n", "This is the most significant departure from above, instead of defining separate `dwell1_state` and `dwell2_state` dictionary objects for a single case, pairs of `dwell1_state` and `dwell2_state` dictionary objects are combined into a larger data structure. The `run_state_pairs` function will run through this data structure one pair at a time.\n", "\n", "It should be noted that this set of cases will all use the same initial dwell time `t_dwell1` listed above.\n", "\n", "If one wishes the the return datatype for pitch to be a float, floats should be passed as inputs for all parameters of a given parameter (e.g. pitch)." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "state_pairs = (\n", " ({\"pitch\": 144.2}, {\"pitch\": 154.95}),\n", " ({\"pitch\": 90.2}, {\"pitch\": 148.95}),\n", " ({\"pitch\": 50.0}, {\"pitch\": 140.0}),\n", " ({\"pitch\": 90.0}, {\"pitch\": 100.0}),\n", " ({\"pitch\": 75.0}, {\"pitch\": 130.0}),\n", " ({\"pitch\": 170.0}, {\"pitch\": 90.0}),\n", " ({\"pitch\": 90.0}, {\"pitch\": 170.0}),\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculate Results" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Running simulations for state pair #: 1 out of 7.0\n" ] } ], "source": [ "results = run_state_pairs(\n", " msid,\n", " aca_model_spec,\n", " model_init,\n", " limit,\n", " date,\n", " t_dwell1,\n", " state_pairs,\n", " limit_type=\"max\",\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Explanation of Results Format\n", "\n", "The description of the results shown above is still valid for the similarly named items, however that information is\n", "still included here for completeness, along with descriptions of the additional included information.\n", "\n", " - `msid`: This is the MSID that represents the location of interest, and is the primary output of a given model.\n", " - `date`: This is the date for which the simulation is applicable.\n", " - `datesecs`: This is the same date described by `date` only in seconds using the standard Ska Chandra epoch\n", " - `limit`: This is the temperature limit being used.\n", " - `tdwell_1`: This is the initial, \"known\", time that corresponds to the dwell #1 state. This is fixed for a batch of\n", " `state_pairs`.\n", " - **`tdwell_2`: The dwell #2 time is what you are looking to calculate, and represents the dwell #2 state duration that\n", " balances the dwell #1 state at the specified duration, `t_dwell1`.**\n", " - `min_temp`: This is the minimum temperature observed during the simulation (latter 2/3 actually to allow the model to\n", " reach a repeatable pattern - more on this later). This will be the limit for a converged solution in the case where\n", " the location is associated with a minimum temperature limit (e.g. PLINE03T).\n", " - `mean_temp`: This is the mean temperature observed during the simulation (latter 2/3)\n", " - `max_temp`: This is the maximum temperature observed during the simulation (latter 2/3). This will be the limit for a\n", " converged solution with a maximum temperature limit (e.g. AACCCDPT).\n", " - `min_pseudo`: This is the min pseudo node temperature observed during the evaluated portion of the simulation. This\n", " is not implemented yet but is intended to eventually yield additional insight into the results.\n", " - `mean_pseudo`: This is the mean pseudo node temperature observed during the evaluated portion of the simulation. This\n", " is not implemented yet.\n", " - `max_pseudo`: This is the max pseudo node temperature observed during the evaluated portion of the simulation. This\n", " is not implemented yet.\n", " - `converged`: This is a boolean value that indicates whether or not a solution was possible. Solutions will not be\n", " possible in a number of situations:\n", "\n", " - Both dwells heat the location being modeled.\n", " - Both dwells cool the location being modeled.\n", " - One of the states neither sufficiently heats or cools the location being modeled (this will sometimes converge but\n", " not always reliably).\n", " - The `dwell1_state` is hot and the initial dwell time is long enough to heat this location from a steady state cold\n", " temperature to the specified hot limit, assuming the location is associated with a maximum temperature limit. In\n", " the case where a location is associated with a minimum temperature limit (e.g. PLINE03T), the opposite would apply,\n", " the `dwell1_state` is cold and is long enough to cool this location from a steady state hot temperature to the\n", " specified cold limit.\n", "\n", " - `unconverged_hot`: If the solution didn't converge, this will be `True` if the input values resulted in temperatures\n", " outside (e.g. above) the specified limit.\n", " - `unconverged_cold`: If the solution didn't converge, this will be `True` if the input values resulted in all\n", " temperatures within (e.g. below) the specified limit.\n", " - `hotter_state`: This is an integer indicating which state is hotter, 1 or 2.\n", " - `colder_state`: This is an integer indicating which state is colder, 1 or 2, and is actually redundant with\n", " `hotter_state`.\n", " - `pitch1`: This is the pitch used as an input to a given simulation corresponding to the dwell #1 state.\n", " - `eclipse1`: This is the eclipse state used as an input to a given simulation corresponding to the dwell #1 state.\n", " - `pitch2`: This is the pitch used as an input to a given simulation corresponding to the dwell #2 state.\n", " - `eclipse2`: This is the eclipse state used as an input to a given simulation corresponding to the dwell #2 state." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/html": [ "Table length=7\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
msiddatedatesecslimitt_dwell1t_dwell2min_tempmean_tempmax_tempmin_pseudomean_pseudomax_pseudoconvergedunconverged_hotunconverged_coldhotter_statecolder_statepitch1eclipse1pitch2eclipse2
str20str8float64float64float64float64float64float64float64float64float64float64boolboolboolint8int8float64boolfloat64bool
aacccdpt2021:001725846469.184-6.521500.0nan-8.393848298088113-8.342559970287693-8.30616855357068nannannanFalseFalseTrue12144.2False154.95False
aacccdpt2021:001725846469.184-6.521500.047250.373802043854-7.154068151351936-6.790040553689484-6.5nannannanTrueFalseFalse1290.2False148.95False
aacccdpt2021:001725846469.184-6.521500.0nan-7.411729330402032-6.956815970804288-6.785451637474314nannannanFalseFalseTrue2150.0False140.0False
aacccdpt2021:001725846469.184-6.521500.0nan-0.0129291278336146720.038144413339266010.10389656662600388nannannanFalseTrueFalse1290.0False100.0False
aacccdpt2021:001725846469.184-6.521500.0nan-3.2286628278301754-3.155946443627189-3.0047592290912712nannannanFalseTrueFalse1275.0False130.0False
aacccdpt2021:001725846469.184-6.521500.041364.30588583145-7.6912126491687705-7.1312558604180865-6.5nannannanTrueFalseFalse21170.0False90.0False
aacccdpt2021:001725846469.184-6.521500.010243.34267539528-6.897765606842965-6.7052851256062445-6.5nannannanTrueFalseFalse1290.0False170.0False
" ], "text/plain": [ "\n", " msid date datesecs limit ... pitch1 eclipse1 pitch2 eclipse2\n", " str20 str8 float64 float64 ... float64 bool float64 bool \n", "-------- -------- ------------- ------- ... ------- -------- ------- --------\n", "aacccdpt 2021:001 725846469.184 -6.5 ... 144.2 False 154.95 False\n", "aacccdpt 2021:001 725846469.184 -6.5 ... 90.2 False 148.95 False\n", "aacccdpt 2021:001 725846469.184 -6.5 ... 50.0 False 140.0 False\n", "aacccdpt 2021:001 725846469.184 -6.5 ... 90.0 False 100.0 False\n", "aacccdpt 2021:001 725846469.184 -6.5 ... 75.0 False 130.0 False\n", "aacccdpt 2021:001 725846469.184 -6.5 ... 170.0 False 90.0 False\n", "aacccdpt 2021:001 725846469.184 -6.5 ... 90.0 False 170.0 False" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import astropy\n", "\n", "astropy.table.Table(results)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "table = astropy.table.Table(results)\n", "table.write(\n", " \"run_state_pairs_example_output_table.rst\", format=\"ascii.rst\", overwrite=True\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Discussion of Results\n", "\n", "Each number corresponds to a row in the above results:\n", "\n", "1. This simulation included a dwell #1 pitch of 144.2 degrees, and a dwell #2 pitch of 154.95 degrees. Although the\n", " first dwell state is warmer, this state does not sufficiently heat this model at the given date to reach the\n", " specified limit, so these two states together result in an unconverged cold simulation.\n", "2. This simulation included a dwell #1 pitch of 90.2 degrees, and a dwell #2 pitch of 148.95 degrees. This solution\n", " converged with a dwell #2 duration of approximately 47250 seconds at 148.95 degrees pitch calculated to sufficiently\n", " balance 21500 seconds at 90.2 degrees pitch on 2021:001.\n", "3. This simulation included a dwell #1 pitch of 50.0 degrees, and a dwell #2 pitch of 140.0 degrees. This solution did \n", " not converge as both pitch values did not sufficiently heat this model at the given date to reach the specified limit.\n", "4. This simulation included a dwell #1 pitch of 90.0 degrees, and a dwell #2 pitch of 100.0 degrees. As both of these\n", " states heat this modeled location, no solution is possible.\n", "5. This simulation included a dwell #1 pitch of 75.0 degrees, and a dwell #2 pitch of 130.0 degrees. As both of these\n", " states heat this modeled location, no solution is possible.\n", "6. This simulation included a dwell #1 pitch of 170.0 degrees, and a dwell #2 pitch of 90.0 degrees. This solution\n", " converged with a dwell #2 duration of approximately 41364 seconds at 90.0 degrees pitch calculated to sufficiently\n", " balance 21500 seconds at 170.0 degrees pitch on 2021:001.\n", "7. This simulation included a dwell #1 pitch of 90.0 degrees, and a dwell #2 pitch of 170.0 degrees. This solution\n", " converged with a dwell #2 duration of approximately 10243 seconds at 170.0 degrees pitch calculated to sufficiently\n", " balance 21500 seconds at 90.0 degrees pitch on 2021:001.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Background: How Timbre Works\n", "\n", "The timbre package enables one to calculate the required contiguous cold time to balance a specified hot observation, or\n", "alternatively the maximum contiguous hot time yielded by a given cold observation, for a given Xija thermal model.\n", "\n", "Timbre accomplishes this by generating fictitious 30 day schedules that alternate between each of the two observations\n", "(and only those two observations), with the duration of the dwell time of interest (`t_dwell2`) being the only changing\n", "variable, for a single Xija thermal model. If a reasonable \"dwell time of interest\" (`t_dwell2`) can be found that\n", "results in the schedule reaching but not exceeding the specified limit for the thermal model being characterized, then\n", "this simulation has converged.\n", "\n", "### Detailed View of Converged Solution\n", "\n", "Below we take a look at such a schedule for the first converged solution from the table above.\n", "\n", " - The top plot primarily shows AACCCDPT temperature resulting from this Timbre simulation.\n", " - The bottom plot shows which dwell state is active.\n", " - The thin vertical shaded regions also highlight which dwell state is active.\n", "\n", " - The thin vertical lightly shaded regions are each 21500 seconds, corresponding to the length of `t_dwell1`.\n", " - The thin unshaded (white) regions in between the shaded regions are each approximately 53870 seconds,\n", " corresponding to the length of `t_dwell2`, which is the output of a Timbre calculation.\n", "\n", " - The dark shaded region on the left highlights the duration used to allow the schedule to reach a \"steady state\"\n", " oscillation, and is not used to evaluate convergence.\n", " - The simulation date is in the center of the evaluation period (2021:001).\n", " - Some small amount of instability in a Xija temperature prediction is not unusual.\n", " - Maximum temperatures in the evaluation region do not need to consistently reach the limit, they only need to be close\n", " for the ratio of `tdwell_1` to `t_dwell2` to be sufficiently accurate for the conditions being used.\n", " - Note that the dwell state transitions do not line up with the peaks and valleys. This is due to the \"momentum\" built\n", " into the model and accurately represents the thermal behavior of location being modeled." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from cxotime import CxoTime\n", "from timbre import get_local_model, run_state_pairs, create_opt_fun\n", "from timbre import calc_binary_schedule\n", "import plotly.io as pio\n", "\n", "from plot_code import *" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "line": { "color": "#666666", "shape": "hv", "width": 2 }, "mode": "lines", "name": "State Keys", "showlegend": false, "type": "scattergl", "x": [ "2020-12-12T00:50:00", "2020-12-12T06:48:19", "2020-12-12T06:48:20", "2020-12-12T19:55:49.374000", 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"%Y:%j" }, { "dtickrange": [ "M6", null ], "value": "%Y" } ], "ticks": "", "zeroline": false }, "yaxis": { "anchor": "x", "domain": [ 0, 0.19 ], "linecolor": "#666666", "linewidth": 1, "mirror": true, "range": [ 0.5, 2.5 ], "tickfont": { "color": "#666666", "family": "Arial", "size": 14 }, "ticktext": [ "State 1", "State 2" ], "tickvals": [ 1, 2 ], "zeroline": false }, "yaxis2": { "anchor": "x2", "domain": [ 0.2, 1 ], "linecolor": "#666666", "linewidth": 1, "mirror": true, "tickfont": { "color": "#666666", "family": "Arial", "size": 14 }, "title": { "font": { "color": "#666666", "family": "Arial", "size": 14 }, "text": "Simulation Temperature
(Celsius)" }, "zeroline": false } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "date = \"2021:001:00:00:00\"\n", "dwell1_state = {\"pitch\": 90.2}\n", "dwell2_state = {\"pitch\": 148.95}\n", "t_dwell1 = 21500.0\n", "msid = \"aacccdpt\"\n", "limit = -6.5\n", "model_spec, aca_md5 = get_local_model(\"../timbre/tests/data/aca_spec.json\")\n", "init = {\"aacccdpt\": -6.5, \"aca0\": -6.5, \"eclipse\": False}\n", "limit_type = \"max\"\n", "duration = 2592000\n", "t_backoff = 1725000\n", "n_dwells = 10\n", "\n", "datesecs = CxoTime(date).secs\n", "\n", "# This ensures three \"cycles\" of the two dwell states, within the portion of the\n", "# schedule used for evaluation. Subtract 1000 sec for extra padding.\n", "max_dwell = (t_backoff - t_dwell1) / 3 - 1000\n", "\n", "t_dwell2 = 47250.37380112706\n", "\n", "model_results, state_times, state_keys = calc_binary_schedule(\n", " datesecs,\n", " dwell1_state,\n", " dwell2_state,\n", " t_dwell1,\n", " t_dwell2,\n", " msid,\n", " model_spec,\n", " init,\n", " duration=duration,\n", " t_backoff=t_backoff,\n", ")\n", "\n", "\n", "tstart = model_results[\"aacccdpt\"].times[0]\n", "tstop = model_results[\"aacccdpt\"].times[-1]\n", "state_data = {\"state_times\": state_times, \"state_keys\": state_keys}\n", "plot_data = format_plot_data(\n", " model_results[\"aacccdpt\"], -6.5, state_data, dwell1_state, dwell2_state\n", ")\n", "shapes = format_shapes(state_data)\n", "shapes.extend(gen_unused_range(tstart, tstop))\n", "annotations = gen_range_annotations(tstart, tstop, -6.3, -6.3 + 0.01)\n", "annotations.extend(gen_limit_annotation(\"2021:001\", -6.51, -6.5, \"Celsius\"))\n", "annotations.extend(\n", " gen_shading_annotation(\n", " \"2021:010:12:00:00\",\n", " -5.7,\n", " f\"Pitch: {dwell1_state['pitch']}\",\n", " f\"Pitch: {dwell2_state['pitch']}\",\n", " )\n", ")\n", "plot_dict = generate_converged_solution_plot_dict(\n", " plot_data, shapes, annotations, tstart, tstop\n", ")\n", "pio.show(plot_dict)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plot above is intended to provide insight into what a balanced solution looks like, by demonstrating how alternating\n", "between two \"balanced\" dwells results in a relatively steady temperature profile, with the peak temperature reaching but\n", "not exceeding the limit. In the interest of minimizing unnecessary data generation this entire profile is not returned\n", "by Timbre, instead Timbre returns the duration of the second state, some descriptive information about the solution, and\n", "any inputs necessary for characterizing the each state (e.g. pitch, ccd_count, etc.) as described in the Basic and\n", "Batch Processing sections.\n", "\n", "The plot below demonstrates the conceptual output of Timbre:\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "marker": { "color": [ "#D62728", "#1F77B4" ] }, "text": [ "Dwell #1 State
Pitch: 90.2

Dwell Time: 21500s
(Input)", "Dwell #2 State
Pitch: 148.95

Dwell Time: 47250s
(Calculated)" ], "textfont": { "color": "white", "family": "Arial", "size": 16 }, "textposition": "inside", "type": "bar", "x": [ "Hot Dwell", "Cold Dwell" ], "y": [ 21500, 47250.37380112706, 1 ] } ], "layout": { "autosize": false, "height": 400, "hovermode": "closest", "margin": { "b": 70, "l": 50, "r": 50, "t": 50 }, "showlegend": false, "template": { "data": { "bar": [ { "error_x": { "color": "rgb(36,36,36)" }, "error_y": { "color": "rgb(36,36,36)" }, "marker": { "line": { "color": "white", "width": 0.5 } }, "type": "bar" } ], "barpolar": [ { "marker": { "line": { "color": "white", "width": 0.5 } }, "type": "barpolar" } ], "carpet": [ { "aaxis": { "endlinecolor": "rgb(36,36,36)", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "rgb(36,36,36)" }, "baxis": { "endlinecolor": "rgb(36,36,36)", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "rgb(36,36,36)" }, "type": "carpet" } ], "choropleth": [ { 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true, "ticks": "outside" }, "baxis": { "gridcolor": "rgb(232,232,232)", "linecolor": "rgb(36,36,36)", "showgrid": false, "showline": true, "ticks": "outside" }, "bgcolor": "white", "caxis": { "gridcolor": "rgb(232,232,232)", "linecolor": "rgb(36,36,36)", "showgrid": false, "showline": true, "ticks": "outside" } }, "title": { "x": 0.05 }, "xaxis": { "automargin": true, "gridcolor": "rgb(232,232,232)", "linecolor": "rgb(36,36,36)", "showgrid": false, "showline": true, "ticks": "outside", "title": { "standoff": 15 }, "zeroline": false, "zerolinecolor": "rgb(36,36,36)" }, "yaxis": { "automargin": true, "gridcolor": "rgb(232,232,232)", "linecolor": "rgb(36,36,36)", "showgrid": false, "showline": true, "ticks": "outside", "title": { "standoff": 15 }, "zeroline": false, "zerolinecolor": "rgb(36,36,36)" } } }, "title": { "font": { "color": "#666666", "family": "Arial", "size": 20 }, "text": "Timbre Produced Dwell Balance", "x": 0.5, "xanchor": "center", "y": 0.95, "yanchor": "top" }, "width": 600, "xaxis": { "anchor": "y", "domain": [ 0, 1 ], "linecolor": "#666666", "linewidth": 1, "mirror": true, "showticklabels": true, "tickfont": { "color": "#666666", "family": "Arial", "size": 14 } }, "yaxis": { "anchor": "x", "linecolor": "#666666", "linewidth": 1, "mirror": true, "tickfont": { "color": "#666666", "family": "Arial", "size": 14 }, "title": { "font": { "color": "#666666", "family": "Arial", "size": 14 }, "text": "Dwell Time (Kiloseconds)" } } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_dict = generate_example_balance_plot_dict(\n", " t_dwell1, t_dwell2, dwell1_state, dwell2_state\n", ")\n", "pio.show(plot_dict)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Dwell #2 Calculation Algorithm\n", "\n", "Now that a more detailed view of a converged solution has been presented, next we dive into how Timbre arrives at this solution. As stated earlier, the only dependant variable is the duration of the second dwell state, referred to as `t_dwell2` in the data returned by Timbre. There are a number of potential approaches to determining this parameter, from brute force to widely used optimization techniques, however the most robust and fastest technique for this particular application has been found to be a three pass brute force + interpolation method:\n", " 1. The first pass calculates the values for 1.e-6 and a pre-defined maximum dwell (approximately 500Ks). This serves to eliminate unncessary model runs when no viable solution exists. \n", " 2. The second pass calculates the results from N logarithmically (base 10) spaced guesses for `t_dwell2`, between 1.e-6 and the pre-defined maximum dwell. N is a keyword option, with a default value of 10. A logarithmically spaced set of guesses are used to yield more resolution at the smaller time durations, where the more useful (and likely more accurate) prediction data exists.\n", " 3. The third pass calculates the results from N linearly spaced guesses for `t_dwell2` between the two closest values calculated from the second pass.\n", " 4. The results of the third pass are used to interpolate the value of `t_dwell2`, using the values for the `t_dwell2` guesses and the resulting maximum temperatures observed (in the range of data used for evaluation) to determine the optimum value of `t_dwell2` at the limit.\n", " \n", "To provide a visual of what the second and third passes look like, please see the following plots:\n" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "line": { "color": "rgb(214.0, 39.0, 40.0)", "shape": "hv", "width": 2 }, "mode": "lines", "name": "t_dwell2 = 0.0", "showlegend": true, "type": "scattergl", "x": [ "2020-12-12T00:50:30.816000", "2020-12-12T00:55:58.816000", "2020-12-12T01:01:26.816000", "2020-12-12T01:06:54.816000", "2020-12-12T01:12:22.816000", "2020-12-12T01:17:50.816000", "2020-12-12T01:23:18.816000", "2020-12-12T01:28:46.816000", 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"rgb(36,36,36)" } } }, "title": { "font": { "color": "#666666", "family": "Arial", "size": 20 }, "text": "Timbre Second Pass Results", "x": 0.5, "xanchor": "center", "y": 0.95, "yanchor": "top" }, "width": 600, "xaxis": { "anchor": "y", "domain": [ 0, 1 ], "linecolor": "#666666", "linewidth": 1, "mirror": true, "range": [ "2020-12-12T00:50:30.816000", "2021-01-10T21:20:22.816000" ], "showticklabels": true, "tickangle": 30, "tickfont": { "color": "#666666", "family": "Arial", "size": 14 }, "tickformatstops": [ { "dtickrange": [ null, 60000000 ], "value": "%H:%M:%S\n%Y:%j" }, { "dtickrange": [ 60000000, 315360000 ], "value": "%Y:%j" }, { "dtickrange": [ 315360000, "M1" ], "value": "%e %b\n%Y:%j" }, { "dtickrange": [ "M1", "M6" ], "value": "%Y:%j" }, { "dtickrange": [ "M6", null ], "value": "%Y" } ], "zeroline": false }, "yaxis": { "anchor": "x", "linecolor": "#666666", "linewidth": 1, "mirror": true, "tickfont": { "color": "#666666", "family": "Arial", "size": 14 }, "title": { "font": { "color": "#666666", "family": "Arial", "size": 14 }, "text": "Resulting Temperatures for
Dwell #2 Guesses (Celsius)" }, "zeroline": false } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dwell2_range = np.logspace(1.0e-6, 1, n_dwells, endpoint=True) / n_dwells\n", "dwell2_range = (\n", " max_dwell * \\\n", " (dwell2_range - dwell2_range[0]) / (dwell2_range[-1] - dwell2_range[0])\n", ")\n", "\n", "# t_dwell2 = 47250.37380112706\n", "model_data = {}\n", "for t_guess in dwell2_range:\n", " model_results, state_times, state_keys = calc_binary_schedule(\n", " datesecs,\n", " dwell1_state,\n", " dwell2_state,\n", " t_dwell1,\n", " t_guess,\n", " msid,\n", " model_spec,\n", " init,\n", " duration=duration,\n", " t_backoff=t_backoff,\n", " )\n", " model_data[t_guess] = dict(\n", " zip(\n", " (\"model_results\", \"state_times\", \"state_keys\"),\n", " (model_results, state_times, state_keys),\n", " )\n", " )\n", "\n", "tstart = model_data[dwell2_range[0]][\"model_results\"][\"aacccdpt\"].times[0]\n", "tstop = model_data[dwell2_range[0]][\"model_results\"][\"aacccdpt\"].times[-1]\n", "\n", "plot_data = format_step_2_plot_data(model_data, limit, tstart, tstop)\n", "plot_dict = generate_step_2_plot_dict(\n", " plot_data, tstart, tstop, title=\"Timbre Second Pass Results\", units=\"Celsius\"\n", ")\n", "pio.show(plot_dict)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "line": { "color": "rgb(214.0, 39.0, 40.0)", "shape": "hv", "width": 2 }, "mode": "lines", "name": "t_dwell2 = 42078.0", "showlegend": true, "type": "scattergl", "x": [ "2020-12-12T00:50:30.816000", "2020-12-12T00:55:58.816000", "2020-12-12T01:01:26.816000", "2020-12-12T01:06:54.816000", "2020-12-12T01:12:22.816000", "2020-12-12T01:17:50.816000", "2020-12-12T01:23:18.816000", "2020-12-12T01:28:46.816000", "2020-12-12T01:34:14.816000", "2020-12-12T01:39:42.816000", "2020-12-12T01:45:10.816000", "2020-12-12T01:50:38.816000", "2020-12-12T01:56:06.816000", 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"ticks": "outside", "title": { "standoff": 15 }, "zeroline": false, "zerolinecolor": "rgb(36,36,36)" }, "yaxis": { "automargin": true, "gridcolor": "rgb(232,232,232)", "linecolor": "rgb(36,36,36)", "showgrid": false, "showline": true, "ticks": "outside", "title": { "standoff": 15 }, "zeroline": false, "zerolinecolor": "rgb(36,36,36)" } } }, "title": { "font": { "color": "#666666", "family": "Arial", "size": 20 }, "text": "Timbre Third Pass Results", "x": 0.5, "xanchor": "center", "y": 0.95, "yanchor": "top" }, "width": 600, "xaxis": { "anchor": "y", "domain": [ 0, 1 ], "linecolor": "#666666", "linewidth": 1, "mirror": true, "range": [ "2020-12-12T00:50:30.816000", "2021-01-10T11:08:06.816000" ], "showticklabels": true, "tickangle": 30, "tickfont": { "color": "#666666", "family": "Arial", "size": 14 }, "tickformatstops": [ { "dtickrange": [ null, 60000000 ], "value": "%H:%M:%S\n%Y:%j" }, { "dtickrange": [ 60000000, 315360000 ], "value": "%Y:%j" }, { "dtickrange": [ 315360000, "M1" ], "value": "%e %b\n%Y:%j" }, { "dtickrange": [ "M1", "M6" ], "value": "%Y:%j" }, { "dtickrange": [ "M6", null ], "value": "%Y" } ], "zeroline": false }, "yaxis": { "anchor": "x", "linecolor": "#666666", "linewidth": 1, "mirror": true, "tickfont": { "color": "#666666", "family": "Arial", "size": 14 }, "title": { "font": { "color": "#666666", "family": "Arial", "size": 14 }, "text": "Resulting Temperatures for
Dwell #2 Guesses (Celsius)" }, "zeroline": false } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dwell2_range = np.logspace(1.0e-6, 1, n_dwells, endpoint=True) / n_dwells\n", "dwell2_range = (\n", " max_dwell * \\\n", " (dwell2_range - dwell2_range[0]) / (dwell2_range[-1] - dwell2_range[0])\n", ")\n", "opt_fun = create_opt_fun(\n", " datesecs,\n", " dwell1_state,\n", " dwell2_state,\n", " t_dwell1,\n", " msid,\n", " model_spec,\n", " init,\n", " t_backoff,\n", " duration,\n", ")\n", "output_pass_2 = np.array(\n", " [opt_fun(t) for t in dwell2_range],\n", " dtype=[\n", " (\"duration2\", np.float64),\n", " (\"max\", np.float64),\n", " (\"mean\", np.float64),\n", " (\"min\", np.float64),\n", " ],\n", ")\n", "output_sorted = np.sort(output_pass_2, order=\"max\")\n", "ind = np.searchsorted(output_sorted[\"max\"], limit)\n", "\n", "# Generate a linearly spaced set of t_dwell2 guesses from the two closest guesses\n", "# from the second pass\n", "t_bound = (output_sorted[\"duration2\"][ind - 1], output_sorted[\"duration2\"][ind])\n", "dwell2_range = np.linspace(np.min(t_bound), np.max(t_bound), n_dwells, \n", " endpoint=True)\n", "\n", "model_data = {}\n", "for t_guess in dwell2_range:\n", " model_results, state_times, state_keys = calc_binary_schedule(\n", " datesecs,\n", " dwell1_state,\n", " dwell2_state,\n", " t_dwell1,\n", " t_guess,\n", " msid,\n", " model_spec,\n", " init,\n", " duration=duration,\n", " t_backoff=t_backoff,\n", " )\n", " model_data[t_guess] = dict(\n", " zip(\n", " (\"model_results\", \"state_times\", \"state_keys\", \"output\"),\n", " (model_results, state_times, state_keys),\n", " )\n", " )\n", "\n", "tstart = model_data[dwell2_range[0]][\"model_results\"][\"aacccdpt\"].times[0]\n", "tstop = model_data[dwell2_range[0]][\"model_results\"][\"aacccdpt\"].times[-1]\n", "\n", "plot_data = format_step_2_plot_data(model_data, limit, tstart, tstop)\n", "plot_dict = generate_step_2_plot_dict(\n", " plot_data, tstart, tstop, title=\"Timbre Third Pass Results\", units=\"Celsius\"\n", ")\n", "pio.show(plot_dict)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This plot is rather busy, making it difficult to estimate the likely optimum second dwell duration by eye. Instead lets look at a plot of just the maximum temperature for each run in the duration used for evaluation (see \"Converged Timbre Dwell Simulation\" plot above)." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "line": { "color": "black", "shape": "hv", "width": 2 }, "marker": { "cmax": 72708.08892451938, "cmin": 42078.01550748954, "color": [ 42078.01550748954, 45481.35699827063, 48884.69848905173, 52288.039979832814, 55691.38147061391, 59094.722961395004, 62498.0644521761, 65901.4059429572, 69304.74743373829, 72708.08892451938 ], "colorscale": [ [ 0, "rgb(214.0, 39.0, 40.0)" ], [ 0.1111111111111111, "rgb(193.66666666666666, 47.888888888888886, 55.55555555555556)" ], [ 0.2222222222222222, "rgb(173.33333333333334, 56.77777777777778, 71.11111111111111)" ], [ 0.3333333333333333, "rgb(153.0, 65.66666666666667, 86.66666666666666)" ], [ 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"xaxis": { "automargin": true, "gridcolor": "rgb(232,232,232)", "linecolor": "rgb(36,36,36)", "showgrid": false, "showline": true, "ticks": "outside", "title": { "standoff": 15 }, "zeroline": false, "zerolinecolor": "rgb(36,36,36)" }, "yaxis": { "automargin": true, "gridcolor": "rgb(232,232,232)", "linecolor": "rgb(36,36,36)", "showgrid": false, "showline": true, "ticks": "outside", "title": { "standoff": 15 }, "zeroline": false, "zerolinecolor": "rgb(36,36,36)" } } }, "title": { "font": { "color": "#666666", "family": "Arial", "size": 20 }, "text": "Maximum Temperature for Dwell #2 Guesses (Third Pass)", "x": 0.5, "xanchor": "center", "y": 0.95, "yanchor": "top" }, "width": 600, "xaxis": { "anchor": "y", "domain": [ 0, 1 ], "linecolor": "#666666", "linewidth": 1, "mirror": true, "showticklabels": true, "tickfont": { "color": "#666666", "family": "Arial", "size": 14 }, "zeroline": false }, "yaxis": { "anchor": "x", "linecolor": "#666666", "linewidth": 1, "mirror": true, "tickfont": { "color": "#666666", "family": "Arial", "size": 14 }, "title": { "font": { "color": "#666666", "family": "Arial", "size": 14 }, "text": "Temperature (Celsius)" }, "zeroline": false } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "output_pass_3 = np.array(\n", " [opt_fun(t) for t in dwell2_range],\n", " dtype=[\n", " (\"duration2\", np.float64),\n", " (\"max\", np.float64),\n", " (\"mean\", np.float64),\n", " (\"min\", np.float64),\n", " ],\n", ")\n", "\n", "plot_dict = generate_step_3_max_temp_plot_dict(\n", " output_pass_3,\n", " \"Maximum Temperature for Dwell #2 Guesses (Third Pass)\",\n", " t_dwell2,\n", " units=\"Celsius\",\n", ")\n", "pio.show(plot_dict)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This plot shows that when starting with a fixed initial dwell of 21500 seconds, at a pitch of 90.2 degrees, the ACA model needs 47250 seconds at 148.95 degrees pitch to maintain a balanced profile. See the plot \"Converged Timbre Dwell Simulation\" plot above for a more detailed view of the schedule that uses this interpolated dwell #2 time." ] } ], "metadata": { "kernelspec": { "display_name": "Python [conda env:ska3] *", "language": "python", "name": "conda-env-ska3-py" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.3" } }, "nbformat": 4, "nbformat_minor": 4 }