Case Study: NTSB Reports

This notebook provides an example of MIKA capabilties via a case study on NTSB reports. The capabilities shown in this example include: - Information Retrieval - Topic Modeling - FMEA extraction through custom NER - Trend Analysis

Case Study set up:

• Package imports

• Data import

import sys, os
#sys.path.append(os.path.join(os.path.dirname(os.path.realpath(__file__)),"..","..")) #not working in notebook
sys.path.append(os.path.join("..",".."))
import numpy as np
import pandas as pd
from mika.utils import Data
from mika.ir import search
from datetime import datetime as dt
from mika.kd.topic_model_plus import Topic_Model_plus
from mika.kd.trend_analysis import plot_frequency_time_series, plot_metric_time_series, plot_metric_averages, make_pie_chart, chi_squared_tests, plot_risk_matrix, get_likelihood_FAA, identify_docs_per_fmea_row, calc_severity_per_hazard, add_hazards_to_docs, chi_squared_tests
from mika.kd import FMEA
from sklearn.feature_extraction.text import CountVectorizer
from sentence_transformers import SentenceTransformer
from torch import cuda
import matplotlib as mpl
import matplotlib.pyplot as plt

os.chdir('../')
os.chdir('../')

ntsb_filepath = os.path.join("data/NTSB/ntsb_full.csv")
ntsb_text_columns = ['narr_cause', 'narr_accf'] # narrative accident cause and narrative accident final
ntsb_document_id_col = 'ev_id'
ntsb_database_name = 'NTSB'
ntsb_data = Data()
ntsb_data.load(ntsb_filepath, preprocessed=False, id_col=ntsb_document_id_col, text_columns=ntsb_text_columns.copy(), name=ntsb_database_name, load_kwargs={'dtype':str})
ntsb_data.prepare_data(create_ids=False, combine_columns=ntsb_text_columns.copy(), remove_incomplete_rows=False)

Combining Columns…: 100%|██████████| 196535/196535 [00:04<00:00, 41292.74it/s]

data preparation:  0.08 minutes

years_of_interest = ['2011', '2012', '2013', '2014', '2015', '2016', '2017', '2018', '2019', '2020', '2021']
ntsb_data.data_df = ntsb_data.data_df.loc[ntsb_data.data_df['ev_year'].isin(years_of_interest)].drop_duplicates(subset='ev_id', keep="last").reset_index(drop=True) # keep the last record, this one has the phase of flight and mishap right before the accident
ntsb_data._Data__update_ids()
ntsb_data.data_df

	ev_id	damage	ev_highest_injury	inj_tot_f	ev_date	ev_year	ev_state	wind_dir_ind	wind_vel_ind	light_cond	...	narr_accf	narr_cause	acft_make	acft_model	flt_plan_filed	flight_plan_activated	total_seats	Phase	Mishap Category	Combined Text
0	20110103X01024	SUBS	FATL	1.0	2011-01-01 00:00:00	2011	MA	U	F	NITE	...	The pilot and passenger were on a pleasure fli...	The pilot did not maintain separation from tre...	CESSNA	310F	NONE		4.0	Approach-VFR Pattern Final	Control flight into terr/obj	The pilot did not maintain separation from tre...
1	20110103X35259	SUBS	FATL	1.0	2011-01-04 00:00:00	2011	MO	U	F	NITE	...	The accident occurred during the fourth leg of...	The pilot's loss of control for undetermined r...	CESSNA	172H	NONE		4.0	Enroute-Cruise	Loss of control in flight	The pilot's loss of control for undetermined r...
2	20110103X42941	SUBS	SERS	0.0	2011-01-03 00:00:00	2011	PA	U	F	NITE	...	The instrument-rated pilot was on the return l...	The pilot's failure to maintain clearance from...	PIPER	PA-28-161	NONE	N	4.0	Enroute-Cruise	Control flight into terr/obj	The pilot's failure to maintain clearance from...
3	20110103X63632	SUBS	NONE	0.0	2011-01-02 00:00:00	2011	NM	U	F	DAYL	...	The pilot stated that during landing he lost d...	The pilot's failure to maintain directional co...	BELLANCA	1419	NONE	N	4.0	Landing-Landing Roll	Landing gear collapse	The pilot's failure to maintain directional co...
4	20110104X52154	SUBS	NONE	0.0	2011-01-04 00:00:00	2011	AZ	U	F	DAYL	...	While parking the airplane, the student pilot ...	The student pilot's failure to maintain cleara...	PIPER	PA-28-181	NONE		4.0	Taxi-from Runway	Collision with terr/obj (non-CFIT)	The student pilot's failure to maintain cleara...
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
16909	20200908X33742	SUBS	FATL	3.0	2020-09-08 00:00:00	2020	TN	U	F	DAYL	...			Piper	PA28	NONE	N	4.0	Uncontrolled Descent	Collision with terr/obj (non-CFIT)
16910	20210929103995	SUBS	MINR	0.0	2021-09-28 00:00:00	2021	FL	U	F	DAYL	...			ROBINSON HELICOPTER COMPANY	R44 II			4.0	Standing-Engine(s) Operating	Loss of control on ground
16911	20190826X12752	SUBS	NONE	0.0	2019-08-26 00:00:00	2019	CA	U	F	NDRK	...			Lockheed	C130	VFIF	Y	7.0	Initial Climb	Part(s) separation from AC
16912	20200823X00819	SUBS	NONE	0.0	2020-08-22 00:00:00	2020	NC	U	F	DAYL	...			Aeronca	11AC	NONE		2.0	Landing-Landing Roll	Collision with terr/obj (non-CFIT)
16913	20200921X53937	DEST	FATL	1.0	2020-09-21 00:00:00	2020	FL	U	F	DAYL	...			Vans	RV 8	NONE		2.0	Enroute-Cruise	Fire/smoke (non-impact)

16914 rows × 22 columns

Information Retrieval

Two model options are available for IR: 1. fine-tuned model 2. pre-trained distilroberta model

# fine tuned model
model = SentenceTransformer("NASA-AIML/MIKA_Custom_IR")
#model = SentenceTransformer('all-distilroberta-v1') #uncomment to use pretrained model
ir_ntsb = search('narr_cause', ntsb_data, model)
embeddings_path = os.path.join('data', 'NTSB', 'ntsb_sentence_embeddings_finetune.npy')
ir_ntsb.get_sentence_embeddings(embeddings_path) # uncomment this if the embeddings do not yet exist
#ir_ntsb.load_sentence_embeddings(embeddings_path) # uncomment this if you wish to load sentence embeddings that already exist
queries = ['what components are vulnerable to fatigue crack', 'what are the consequences of a fuel leak', 'what are the risks of low visibility']
for query in queries:
    print(query)
    print(ir_ntsb.run_search(query, return_k=10, rank_k=10))

what components are vulnerable to fatigue crack
   top_hit_idx     top_hit_doc  top_hit_scores  \
0        37185  20121204X63622        0.746134
1        23081  20141027X62323        0.728395
2        39995  20141027X62323        0.728395
3        41744  20160114X73526        0.715234
4        24830  20160114X73526        0.715234
5        17989  20110809X03303        0.702911
6        34903  20110809X03303        0.702911
7        20253  20121130X01711        0.699882
8        37167  20121130X01711        0.699882
9        37185  20121204X63622        0.699882

                                        top_hit_text
0  The total loss of engine power as a result of ...
1  The private pilot and a sport pilot-rated pass...
2  The loss of engine power during cruise flight ...
3  Failure of the left wing in flight due to comp...
4  The sport pilot was conducting a personal cros...
5  The pilot had just leveled off to cruise fligh...
6  A sudden loss of engine thrust due to the sepa...
7  The airplane was operating as a night, schedul...
8  The total loss of engine power as a result of ...
9  The total loss of engine power as a result of ...
what are the consequences of a fuel leak
   top_hit_idx     top_hit_doc  top_hit_scores  \
0        18698  20120129X84717        0.756848
1        35612  20120129X84717        0.756848
2        22747  20140812X10218        0.723396
3        39661  20140812X10218        0.723396
4        33896  20110128X23759        0.705061
5        16982  20110128X23759        0.705061
6        27222  20170710X71845        0.704668
7        44136  20170710X71845        0.704668
8        47247  20190716X10219        0.679851
9        30333  20190716X10219        0.679851

                                        top_hit_text
0  The pilot stated that, during the preflight in...
1  The total loss of engine power due to fuel sta...
2  The pilot reported that the airplane's engine ...
3  The pilot’s failure to properly manage the air...
4  The pilot’s inadequate preflight inspection to...
5  The pilot requested that the airplane be “topp...
6  The pilot reported that, shortly after takeoff...
7  A total loss of engine power due to fuel starv...
8  The pilot's improper fuel planning, which resu...
9  The pilot reported that, after takeoff and whi...
what are the risks of low visibility
   top_hit_idx     top_hit_doc  top_hit_scores  \
0        16921  20110105X11652        0.562436
1        33835  20110105X11652        0.562436
2        16989  20110131X11636        0.526502
3        33903  20110131X11636        0.526502
4        42919  20160921X20513        0.518302
5        26005  20160921X20513        0.518302
6        22413  20140613X91656        0.513717
7        39327  20140613X91656        0.513717
8        22413  20140613X91656        0.484448
9        39327  20140613X91656        0.484448

                                        top_hit_text
0  During the approximately 5 hour and 25 minute ...
1  The pilot's failure to maintain control of the...
2  The pilot reported that he was practicing nigh...
3  The pilot's failure to maintain control of the...
4  The pilot's decision to land in an area of low...
5  While maneuvering at low altitude for a water ...
6  The pilot arrived at the fixed-base operator o...
7  The pilot's failure to maintain a positive cli...
8  The pilot arrived at the fixed-base operator o...
9  The pilot's failure to maintain a positive cli...

Topic Modeling

Here we implement BERtopic via topic model plus to create a taxonomy of failure information.

tm = Topic_Model_plus(text_columns=ntsb_text_columns, data=ntsb_data, results_path=os.path.join(os.getcwd(),"examples/Case_Study_NTSB"))
vectorizer_model = CountVectorizer(ngram_range=(1, 3), stop_words="english") #removes stopwords
BERTkwargs={"top_n_words": 10, 'min_topic_size':25}
tm.bert_topic(count_vectorizor=vectorizer_model, BERTkwargs=BERTkwargs, from_probs=False)
tm.save_bert_model()
tm.save_bert_results(from_probs=False)
tm.save_bert_taxonomy() #saves taxonomy #takes 15 min to run

taxonomy = pd.read_csv(os.path.join(tm.folder_path,'BERT_taxonomy.csv'), index_col=0) #print taxonomy
taxonomy = taxonomy.dropna(how='any').reset_index(drop=True)
taxonomy

	narr_cause	narr_accf	document IDs for row	number of documents for row
0	abort, abort takeoff, decision abort, decision...	airplane, pilot reported, pilot, reported, run...	['20120515X10453', '20120531X13740', '20120907...	10
1	abort, abort takeoff, decision abort, decision...	airplane, pilot, runway, landing, engine, left...	['20110609X25931', '20110706X70339', '20110805...	41
2	abort, abort takeoff, decision abort, decision...	carburetor, power, engine, carburetor heat, he...	['20120430X00440', '20120514X11605']	2
3	abort, abort takeoff, decision abort, decision...	fuel, tank, engine, fuel tank, power, tanks, p...	['20111221X54903', '20200920X32151']	2
4	abort, abort takeoff, decision abort, decision...	snow, airplane, snowcovered, pilot, reported, ...	['20120316X94235']	1
...	...	...	...	...
1149	wing, left wing, right wing, spar, right, fail...	airplane, pilot reported, pilot, reported, run...	['20120831X90624', '20130829X54643']	2
1150	wing, left wing, right wing, spar, right, fail...	airplane, pilot, runway, landing, engine, left...	['20110228X83526', '20110919X61206', '20120320...	19
1151	wing, left wing, right wing, spar, right, fail...	airplane, tailwheelequipped, reported, right, ...	['20200519X04334']	1
1152	wing, left wing, right wing, spar, right, fail...	flight, pilot, conditions, weather, accident, ...	['20150505X85410', '20180404X13226']	2
1153	wing, left wing, right wing, spar, right, fail...	taxiway, taxi, airplane, taxiing, wing, pilot,...	['20210727103561']	1

1154 rows × 4 columns

FMEA using Named-Entity Recognition

#definted according to FAA order 8040.4B: https://www.faa.gov/documentLibrary/media/Order/FAA_Order_8040.4B.pdf
def NTSB_severity(damage, inj_level, inj_tot_f, persons_onboard): #damage, ev_highest_injury, inj_tot_f
    if float(persons_onboard) == 0:
        persons_onboard = inj_tot_f
    if inj_tot_f != 0 :
        pct_fatal = inj_tot_f/persons_onboard
    else:
        pct_fatal = 0
    #minimal: no injuries, no damage.
    if inj_level == 'NONE' and damage == 'UKN':
        severity = 'Minimal'
    #minor: slight (MINR) damage, physical discomfort
    elif inj_level == 'MINR' or inj_level == 'NONE':
        #major: substaintail (SUBS) damage, injuries
        if damage == 'SUBS':
            severity = 'Major'
        elif damage == 'DEST':
            severity = 'Hazardous'
        else:
            severity = 'Minor'
    #hazardous: multiple serious injuries, fatalities<2, hull loss (DEST)
    elif inj_level == 'SERS' or (inj_level == 'FATL' and (inj_tot_f <= 2 or pct_fatal < 0.75)) or damage == 'DEST':
        severity = 'Hazardous'
    #catatrophic: fatalities > 2, or num person on board= num fatalities,  hull loss (DEST)
    elif inj_level == 'FATL' and (inj_tot_f > 2 or pct_fatal > 0.75):
        severity = 'Catastrophic'
    else:
        severity = 'Minimal' #case with no reported fatalities, injury level, or damage level
    return severity

def severity_func(df, numeric=True):
    severity_dict = {'Catastrophic':5, 'Hazardous': 4, 'Major':3, 'Minor':2, 'Minimal':1}
    severities = []
    for i in range(len(df)):
        severities.append(NTSB_severity(df.at[i, 'damage'], df.at[i, 'ev_highest_injury'], float(df.at[i, 'inj_tot_f'].replace('','0')), float(df.at[i, 'total_seats'].replace('','0'))))
    if numeric == True:
        df['severity'] = [severity_dict[severity] for severity in severities]
    else:
        df['severity'] = severities
    return df

#prepare the df for FMEA - drop repeat rows
fmea_input_df = ntsb_data.data_df.copy()
fmea_input_df = fmea_input_df.loc[~(fmea_input_df['Combined Text']=='')].reset_index(drop=True) # remove docs with no text

model_checkpoint = "NASA-AIML/MIKA_BERT_FMEA_NER"
print(model_checkpoint)

device = 'cuda' if cuda.is_available() else 'cpu'
cuda.empty_cache()
print(device)

fmea = FMEA()
fmea.load_model(model_checkpoint)
print("loaded model")
input_data = fmea.load_data('Combined Text','ev_id', df=fmea_input_df, formatted=False)
print("loaded data")
preds = fmea.predict()
df = fmea.get_entities_per_doc()
fmea.group_docs_with_meta(grouping_col='Mishap Category', additional_cols=['Phase'])
fmea.grouped_df.to_csv(os.path.join(os.getcwd(),"examples/Case_Study_NTSB/ntsb_fmea_raw.csv"))

models\FMEA-ner-model\checkpoint-1424
cuda
loaded model

Token indices sequence length is longer than the specified maximum sequence length for this model (3132 > 512). Running this sequence through the model will result in indexing errors

loaded data

fmea.calc_severity(severity_func, from_file=False)
fmea.calc_frequency(year_col="ev_year") #add year column
fmea.calc_risk()
fmea.post_process_fmea(phase_name='Phase', id_name='NTSB', max_words=10)

fmea.fmea_df.astype(str).to_csv(os.path.join(os.getcwd(),"examples/Case_Study_NTSB/NTSB_FMEA.csv"))

mishaps_of_interest = ['Birdstrike','Midair collision', 'Loss of control in flight','Loss of control on ground','Turbulence encounter', 'Ground collision']

fmea.fmea_df.loc[fmea.fmea_df.index.isin(mishaps_of_interest)].astype(str).to_csv(os.path.join(os.getcwd(),"examples/Case_Study_NTSB/NTSB_FMEA_truncated.csv"))
fmea.fmea_df.loc[fmea.fmea_df.index.isin(mishaps_of_interest)]

	Phase	Cause	Failure Mode	Effect	Control Process	Recommendations	Frequency	Severity	Risk	NTSB
cluster
Birdstrike	Approach-VFR Pattern Downwind; Enroute; Enrout...	at low, bird, surface, a, red - tailed, hawk, ...	in - flight, collision, with a, bird, large, p...	bird, substantial, damage, large, broke the fr...	was, towed to the gate, a, bird ingestion and ...	see the public, , enter, keep an, eye, on, land,	4	3.0114942528735638	12.045977011494251	20170626X02552
Ground collision	Approach-VFR Pattern Downwind; Standing-Engine...	', inadequate visual, lookout, failure, zodiac...	to see and avoid the, zodiac was, from the, pr...	hit, rear, vertical stabilize, were, destroyed...	radio, calls, position, reports, checked the t...	inform, , use caution, hold, pilot, clearance,...	4	2.878504672897196	11.514018691588785	20140603X83103
Loss of control in flight	Approach-VFR Pattern Downwind; Approach-IFR Fi...	pilot's, fatigue, pilot, departed, night, test...	pilot's loss of, entered a, descending left, f...	und, airplane, spiraled, down, impacting an op...	intermediate, stops, radar track, toxicology, ...	, conform to its type, certificate, documentat...	5	3.659551760939168	18.29775880469584	20190713X34059
Loss of control on ground	Approach-VFR Pattern Downwind; Approach-IFR Fi...	pre - existing crack in the weld, joint, const...	failure of the left main landing gear, st, lef...	the, structural, damage, to the, fuselage, rig...	right ailer, point, applied right rudder to, c...	, remain, reduce, land to the, north, take off...	5	3.0433925049309667	15.216962524654834	20111104X64432
Midair collision	Enroute; Enroute-Descent; Landing; Maneuvering...	failure of both pilots to see and avoid the ot...	midair, collision, airplanes, collided, collid...	impacted the, terrain, a utility, pole, to, re...	wingtip -, - mounted strobe anticollision, lig...	alter, course, pass well, not have passed over...	3	3.3968253968253967	10.19047619047619	20191205X95005
Turbulence encounter	Approach-VFR Pattern Downwind; Enroute; Enrout...	with, of, cumulonimbus, clouds, slowly, activi...	and, turbulence, tailwind, knots, tailwind sud...	indicated speed of the airplane quickly, incre...	captain activated the speed, brakes, disengage...	, expect light - to - moderate, before -, cabin	4	3.792307692307692	15.169230769230769	20181001X33722

Trend Analysis

Now that we have rows of mishaps and failure information, we can look at trends in the mishap. In this case, we look at trends in: 1. mishap frequency over time 2. mishap severity over time 3. average mishap severity 3. distribution of mishaps over activated flight plans 4. distribution of mishaps over visibility conditions

frequency, docs_per_row = identify_docs_per_fmea_row(ntsb_data.data_df, 'Mishap Category', 'ev_year', 'ev_id')

mishaps_of_interest = ['Birdstrike','Midair collision', 'Loss of control in flight','Loss of control on ground','Turbulence encounter', 'Ground collision',]
years_of_interest = ['2011', '2012', '2013', '2014', '2015', '2016', '2017', '2018', '2019', '2020', '2021']
frequency_set = {mishap:{year: frequency[mishap][year] for year in years_of_interest} for mishap in mishaps_of_interest}
doc_set = {mishap:{year: docs_per_row[mishap][year] for year in years_of_interest} for mishap in mishaps_of_interest}

plot_frequency_time_series(frequency_set, metric_name='Frequency', line_styles=[],
                               markers=[], title="Frequency from 2011-2021", time_name="Year", xtick_freq=2,
                               scale=False, save=False, yscale='log', legend=True,
                               figsize=(6,4), fontsize=24)

df_with_severities = severity_func(ntsb_data.data_df, numeric=True)

severities, total_severities_hazard = calc_severity_per_hazard(doc_set, df_with_severities, 'ev_id', metric='max')

plot_metric_time_series(metric_data=severities, metric_name="Severity", title="Average Severity from 2011-2021", time_name='Year', xtick_freq=2, show_std=False, save=False, figsize=(6,4), fontsize=24)

plot_metric_averages(metric_data=severities, metric_name="Severity", show_std=True, title="Average Severity", save=False, legend=False, figsize=(8,4),fontsize=24)

df_with_severities['sky_cond_nonceil'].unique()
sky_conditions_dict = {'CLER': 'clear',
'':'unknown',
'SCAT': 'scattered',
'FEW': 'few',
'UNK': 'unknown',
'OVCT': 'thin overcast',
'OVC': 'overcast',
'OBSC': 'obscured',
'BKNT': 'thin broken',
'BKN': 'broken',
'POBS': 'partially obscured',
'VV': 'indefinite',
'NONE': 'none'}
df_with_severities['sky_cond_nonceil_cleaned'] = [sky_conditions_dict[cond] for cond in df_with_severities['sky_cond_nonceil'].tolist()]

df_with_severities['flight_plan_activated_cleaned'] = [val if val!='' else 'U' for val in df_with_severities['flight_plan_activated'].tolist()]

make_pie_chart(doc_set, df_with_severities, 'flight_plan_activated_cleaned', mishaps_of_interest, 'ev_id', 'Activated Flight Plan', save=False, fontsize=12, pie_kwargs={'pctdistance':1.27}, figsize=(6,4), padding=10)

make_pie_chart(doc_set, df_with_severities, 'sky_cond_nonceil_cleaned', mishaps_of_interest, 'ev_id', 'Sky Condition', save=False, fontsize=12, pie_kwargs={'pctdistance':1.27}, figsize=(6,4), padding=10)

df_with_hazards = add_hazards_to_docs(df_with_severities, id_field='ev_id', docs=doc_set)
stats_df, counts_dfs = chi_squared_tests(df_with_hazards, mishaps_of_interest, predictors=['flight_plan_activated_cleaned','sky_cond_nonceil_cleaned'], pred_dict={'flight_plan_activated_cleaned':'flight plan','sky_cond_nonceil_cleaned': 'sky condition'})

stats_df

Predictor	flight plan		sky condition
Measure	p-val	chi-squared	p-val	chi-squared
Birdstrike	0.000	44.813	0.027	10.929
Midair collision	0.007	10.024	0.789	1.710
Loss of control in flight	0.000	30.626	0.000	34.186
Loss of control on ground	0.000	74.891	0.000	65.104
Turbulence encounter	0.000	319.912	0.000	98.286
Ground collision	0.005	10.670	0.040	10.004

for df in counts_dfs:
    display(counts_dfs[df])

		N	U	Y
Hazard	Present
Birdstrike	0	18.343739	4.985338	-23.329077
	1	-18.343739	-4.985338	23.329077
Midair collision	0	14.496985	-14.321509	-0.175476
	1	-14.496985	14.321509	0.175476
Loss of control in flight	0	42.169032	-86.260908	44.091877
	1	-42.169032	86.260908	-44.091877
Loss of control on ground	0	-118.701135	43.465236	75.235899
	1	118.701135	-43.465236	-75.235899
Turbulence encounter	0	71.030330	8.283020	-79.313350
	1	-71.030330	-8.283020	79.313350
Ground collision	0	2.819085	14.042805	-16.861890
	1	-2.819085	-14.042805	16.861890

		clear	unknown	few	scattered	thin overcast
Hazard	Present
Birdstrike	0	12.706515	-3.719641	-7.401206	-0.237436	-1.348232
	1	-12.706515	3.719641	7.401206	0.237436	1.348232
Midair collision	0	-3.161168	-1.408892	2.871940	1.083954	0.614166
	1	3.161168	1.408892	-2.871940	-1.083954	-0.614166
Loss of control in flight	0	19.721178	-80.587797	36.090635	20.597552	4.178432
	1	-19.721178	80.587797	-36.090635	-20.597552	-4.178432
Loss of control on ground	0	-83.986165	111.842143	-24.983505	-4.546825	1.674353
	1	83.986165	-111.842143	24.983505	4.546825	-1.674353
Turbulence encounter	0	54.640771	-54.730164	0.199894	0.792775	-0.903275
	1	-54.640771	54.730164	-0.199894	-0.792775	0.903275
Ground collision	0	7.663238	2.133144	-14.683576	3.370581	1.516613
	1	-7.663238	-2.133144	14.683576	-3.370581	-1.516613

severity_dict = {5:'Catastrophic Impact', 4:'Hazardous Impact', 3:'Major Impact', 2:'Minor Impact', 1:'Minimal Impact'}
rm_severities = {hazard: severity_dict[round(total_severities_hazard[hazard])] for hazard in total_severities_hazard}
rates = {hazard: sum([frequency_set[hazard][year] for year in frequency_set[hazard]])/len(years_of_interest) for hazard in frequency_set}
rm_likelihoods = get_likelihood_FAA(rates)

mpl.rcParams.update(mpl.rcParamsDefault)
plt.rcParams["font.family"] = "Times New Roman"

plot_risk_matrix(rm_likelihoods, rm_severities, figsize=(8,4), fontsize=12, max_chars=20, annot_font=10)