m*****n
发帖数: 1513 | 1 【 以下文字转载自 Military 讨论区 】
发信人: mitcoin (米特币), 信区: Military
标 题: BBC：Bayesian Stat.可找MH370，曾成功找到法航残骸
发信站: BBS 未名空间站 (Sat Mar 22 11:06:03 2014, 美东)
MH370 Malaysia plane: How maths helped find an earlier crash
Statisticians helped locate an Air France plane in 2011 which was missing
for two years. Could mathematical techniques inspired by an 18th Century
Presbyterian minister be used to locate the mysterious disappearance of
Malaysia Airlines Flight MH370?
In June 2009, Air France flight 447 went missing flying from Rio de Janeiro
in Brazil to Paris, France.
Debris from the Airbus A330 was found floating on the surface of the
Atlantic five days later, but the mystery of why the plane crashed could
only be answered by finding the black box and the cockpit voice recorder.
You may think that having found the debris it would be easy to find the rest
of the plane, but it's not that simple - after a number of days, the
material would have moved with the ocean current.
Software does exist that can simulate how the debris has travelled from the
initial impact. It is used regularly by the US coast guard.
But in this case, because this area near the equator is known for
unpredictable currents - particularly at that time of year - it was no help.
Debris from the Air France crash is laid out in a warehouse
Debris from the Air France crash is laid out for investigation in 2009
American, Brazilian and French ships, planes and submarines all searched for
the plane, but they couldn't find it.
At this point France's aviation accident investigation authority, BEA, made
a call to a group of statisticians in the US who had expertise in finding
objects lost at sea.
Senior analyst Colleen Keller flew to France to help.
Continue reading the main story
More or Less: Behind the stats
Listen to More or Less on BBC Radio 4 and the World Service, or download the
free podcast
Download the More or Less podcast
More stories from More or Less
"The French BEA had already done a wonderful job of coming up with different
theories for why the aircraft might have crashed," she says.
They also had lots of data about historical crashes and the results of the
searches that had already been carried out.
To turn all this information into numbers and probability, Keller and her
team from Metron Inc in Virginia, relied on Bayesian statistics named after
a British Presbyterian minister called Thomas Bayes.
This type of thinking allows you to assess various scenarios at once - even
contradictory ones. The probability of each being true is brought together
to give you the most likely solution. And if you find new information, you
can revise your model easily.
Keller and her colleagues went through all the available information and
assessed the uncertainties of each piece of data - applying Bayesian
principles of probability to work out the most likely location of the plane.
The team split up the search area into a grid, and applied to each cell a
figure representing the probability that the plane would be found there.
A small Brazilian Air Force radar plane prepares to leave an airport strip
in front of a green, rocky, hill
A Brazilian Air Force radar plane prepares to leave Fernando de Noronha
airport to search for Flight 447
To calculate these figures, they first looked at the theories about what
caused the plane to crash. For instance, they assessed the likeliness of
various mechanical failures, and came up with a probability for each
scenario.
They then assessed historical data from previous crashes, noting, for
example, that planes were usually found very close to where they were last
known to have been.
Finally, Keller and her team lowered the probability of the plane being
found in locations that had already been searched.
"There are two components to Bayesian maths which make it unique. It allows
you to consider all the data you have including the uncertainties which is
very important because nothing is certain," says Keller.
"And to combine it all - it even allows you to combine views that contradict
each other.
"For instance with the Malaysian search, you have that arc to the north and
the arc to the south. It's either one or the other but it can't have gone
both ways, but [Bayes] allows you to preserve all your theories and weight
them."
The second benefit is that the Bayesian approach is very flexible, Keller
says. It allows you to update your body of knowledge at any time. If
something new comes up, you factor it in and update the probability map.
A Meteosat-9 infrared satellite image shows weather conditions over
Atlantic
A 2009 infrared satellite image shows weather conditions off the Brazilian
coast and the plane search area
In the case of the Air France plane, they could be sure that the plane had
come down within a 40-mile radius of the last location pinged out by its on-
board computer system.
Continue reading the main story
Who was Thomas Bayes?
Reverend Thomas Bayes
Born in London, 1702, the eldest of seven children
Studied logic and theology at University of Edinburgh from 1719 until 1722
Became the The Reverend Thomas Bayes, serving as minister in a Presbyterian
chapel
But as a Nonconformist, he did not follow Church of England doctrines or
practices
Best known for his mathematical work on probability, giving rise to Bayes'
Theorem
Bayesian probability estimates are used all over the world, built into
software that forecasts events including financial markets and weather
Died in Royal Tunbridge Wells in 1761
Yet this area was so huge that the investigators were struggling to know
where to look.
The probability map Keller provided gave, by contrast, a much tighter area
to search.
A team went out there, hoping that finally the mystery would be solved. But
those hopes were dashed. There was no sign of the plane.
It seemed the statisticians could not help after all.
Some months later, though, Air France got back in touch and asked Keller to
make one last attempt to analyse the data.
This time, she and her colleagues decided they were not happy with one of
their initial assumptions.
The historical data showed that after a crash, the black box will be
emitting a signal in 90% of cases.
In the immediate aftermath of the crash, search teams had spent a lot of
time sweeping the areas close to the last known location, listening for the
ping of the black box or voice recorder.
They had heard nothing. So Keller and her team had decided there was a very
low probability the plane would be found there.
But what if neither the black box nor the voice recorder were sending a
signal?
Alain Bouillard, investigator-in-charge of flight Air France 447 safety
investigation from French agency Bureau of Enquiry and Analysis for Civil
Aviation Safety (BEA), speaks during a press conference focused on the AF447
Rio-Paris plane flight black boxes (screen), on May 12, 2011
Alain Bouillard of the BEA speaking about the Air France 447 black boxes,
found in 2011
The Metron statisticians now adapted their model to this possible scenario
and came up with a new area of highest probability.
A team returned to the scene to look - and this time they found the plane.
The mystery of the crash was solved. The black box and voice recorder data
appear to show that the pilots were given faulty speed readings, responded
inappropriately, and lost control of the plane.
Continue reading the main story
“
Start Quote
It's very likely if we don't get any breakthroughs, [Malaysia Airlines
flight MH370 is] at the bottom of the Indian Ocean and we will never find it
, sadly”
Colleen Keller
"It still was a minor miracle that we found it," says Keller.
"It was lucky that the wreckage was on the bottom of the ocean floor, on a
very sandy area. There were some areas down there that looked like the
Himalayas - in terms of mountains, crags, and valleys."
If the plane had been in one of those areas, she says, "it could have been
undetected forever".
Keller says she is not sure Malaysia Airlines Flight 370 will be found.
"It's a big world out there. And I know people are saying - how could you
possibly hide or not find a Boeing 777?
"[But] it's very likely if we don't get any breakthroughs, it's at the
bottom of the Indian Ocean and we will never find it, sadly."
Even finding debris might not mean finding the bulk of the plane.
"If we found wreckage at this point, it would tell us it was in one body of
water rather than the other," Keller says. "But it's so long since the plane
would have crashed that I don't think the wreckage is going to be very
helpful." |
|
