JP4159890B2 - Method for determining the presence or absence of tropical cyclone damage and method and apparatus for predicting tropical cyclone damage - Google Patents

Description

また、分散σ^２ _ｘｋ は次の(2)式のようになる。
【００２８】
【数２】

パターン空間のｋ次元（１≦ｋ≦ｎ）の正規化を示す。標本パターンのｋ次元の数値データｘ_ｉｊｋ を正規化したｙ_ｉｊｋ は、ｋ次元の平均￣ｘ_ｋ と標準偏差σ_ｘｋ により次の(3)式となる。
【００２９】
【数３】

これ以降は、(4)式の正規化された標本パターンｙ_ｉｊ を用いて、パターン認識理論を説明する。
【００３０】
ｙ_ｉｊ＝［ｙ_ｉｊ１，ｙ_ｉｊ２，・・・，ｙ_ｉｊｎ］^Ｔ ・・・(4)
(4)フィッシャーの評価関数
多変量解析における判別分析は、代表的な識別志向の線形特別抽出法である。判別分析の評価関数は、クラス間の差異を考慮に入れたフィッシャー(Fisher)の評価関数Ｊ(d)である。評価関数Ｊ(d)は、次の(5)式となる。
【００３１】
【数４】

ここに、ｄはパターンを射影するｎ次元列ベクトルである。Ｂはクラス間共分散行列の推定値、Ｗはクラス内共分散行列の推定値であり、それぞれ、次の(6)(7)式で定義される。
【００３２】
【数５】

また、ｐ_ｉ はクラスｉの事前確率の推定値、μ_ｙｉ は正規化されたクラスｉの標本パターン平均列ベクトルであり、次の(8)(9)式で示される。
【００３３】
【数６】

前記(5)式の分子のｄ^Ｔ Ｂｄは、パターン空間からの射影ベクトルｄで生成される一次元特徴空間（部分空間）上におけるクラス間分散の和であり、各クラスの平均値間の自乗距離の和を表している。また、分母のｄ^Ｔ Ｗｄは、ｄで生成される一次元特徴空間上におけるクラス内分散和である。したがって、(5)式のフィッシャーの評価関数を最大にすることは、各クラス間の分散を大きく、クラス内の分散を小さくすることである。つまり、クラス内の標本パターンはかたまるように、クラス間は離れるように射影することにより、判別が容易になる。
【００３４】
(5)特徴抽出
フィッシャーの評価関数を最大にするベクトルｄは、周知のように、行列Ｗ^−１Ｂの最大固有値に対する固有ベクトルｄ_１ である。行列Ｂのランクは(6)式より明らかにクラス数から１を減じたｍ−１である。したがって、行列Ｗ^−１Ｂの固有値は、λ１≧λ２≧・・・≧λm-1≧λm＝・・・＝λn＝０となる。したがって、０以外の固有値に対する固有ベクトルｄ１，ｄ２，・・・，ｄm-1を各一次元特徴空間への射影ベクトルとして、ｍ−１次元の特徴空間を構成する。特徴空間へのパターン空間からの射影行列Ｄは、固有ベクトルにより、次の(10)式と定義される。
【００３５】
Ｄ＝［ｄ１，ｄ２，・・・，ｄm-1］ ・・・(10)
(10)式を用いた、パターン空間上のクラスｉのｊ番目の標本パターン列ベクトルｙ_ｉｊ の特徴空間への射影値列ベクトルｚ_ｉｊ は次の(11)式のようになる。
【００３６】
ｚ_ｉｊ ＝Ｄ^Ｔｙ_ｉｊ ・・・(11)
つまり、ｍ−１次元特徴空間上におけるクラスｉのｊ番目の標本パターン列ベクトルｚ_ｉｊ は次の(12)式である。
【００３７】
ｚ_ｉｊ ＝［ｚ_ｉｊ１，ｚ_ｉｊ２，・・・，ｚ_{ｉｊ（ｍ−１）}］^Ｔ ・・・(12)
先に示した諸定義における特徴空間の次元数は、下記の(13)式のようになる。
【００３８】
ｌ＝（ｍ−１） ・・・(13)
(6)判別分析
フィッシャーの評価関数により、クラス間分散和を最大に、クラス内分散和を最小にする判別に有効な(10)式の射影行列が与えられ、ｌ次元特徴空間が構成された。事故判別は、この特徴空間での識別問題に帰着できる。
【００３９】
特徴空間における各クラスの分布を正規分布と仮定すれば、クラスｉの分布ｆ_ｉ(z)は、次の(14)式の確率密度関数で表現することができる。
【００４０】
【数７】

ここに、μ_ｚｉ，Σ_ｚｉ は、特徴空間へ射影されたクラスｉの標本パターンｚ_ｉｊ
（１≦ｊ≦Ｎ_ｉ）を用いて計算され、次の(15)(16)式のようになる。
【００４１】
【数８】

各クラスの分布が(14)式で特徴空間においてパラメトリックに与えられた場合、属するクラスが未知であるパターンが被害「あり」「なし」である各クラスのいずれから生起したかを識別するのが検討すべき課題である。
(7)未知パターンの被害ありなしの判別
属するクラスが未知のパターンは、事故情報項目を軸とするパターン空間上でｎ次元の列ベクトルｘ_ｕとして与えられる。未知パターンｘ_ｕ を、標本パターンと同様に正規化したｙ_ｕ１，ｙ_ｕ２，・・・，ｙ_ｕｎのｎ個の実数の組からなる未知パターンｙ_ｕのｋ次元のｙ_ｕｋは前記(1)(2)式により、次の(17)式となる。
【００４２】
【数９】

未知パターンｘ_ｕ は正規化されｙ_ｕとした後、（10）式のＤを用いて、特徴空間に射影された未知パターンｚ_ｕは、次の(18)式で与えられ、特徴空間での識別がなされる。
【００４３】
ｚ_ｕ ＝Ｄ^Ｔｙ_ｕ ・・・(18)
この識別において、未知パターンｚ_ｕは、(15)(16)式により、次の(19)式のマハラノビス（Maharanois）の汎距離ｒ_ｉ を最小にするクラスｉから生起したと考えるのが自然であり、かつ合理的である。
【００４４】
【数１０】

この識別は、確率論的には、尤度関数を最大にするクラスを求めることに相当する。識別方法を再度記すと、次の(20)式のようになり、該(20)式の規範により定まるクラスｉ^＊に未知パターンを対応させることになる。
【００４５】
【数１１】

(8)判別結果
日本に襲来した９９１８号（１９９９年の第１８番目に発生した台風番号）台風以外の１９個の熱帯性低気圧に関し、九州電力（株）の８５営業所のデータを用いて判別モデルを構築し、構築に使用していない９９１８号台風のやはり８５営業所のデータを用いて、本発明の統計的パターン認識手法の判別精度を確かめたところ、図４(a)のようになった。図から明らかなように、本発明の統計的パターン認識手法では、構築用データで全て８割以上の成功率を示すと共に、評価用（９９１８号熱帯性低気圧）データにおいても８割以上の成功率となった。一方、判別分析手法では、図４(b)に示すように、構築用データでほぼ全て８割以上の成功率を示すと共に、評価用データにおいて、７割、８割台の成功率であった。
【００４６】
このように、統計的パターン認識手法は、部分空間法に比べて、有効な判別結果となった。また、統計的パターン認識手法は演算面でも有利なため、被害ありなしの予測方法に統計的パターン認識手法を用いるのが好適であるしたがって、被害ありなしの判別には、統計的パターン認識手法を用いるのが良いことがわかった。
【００４７】
なお、風速の閾値で被害のありなしを判別する従来法と比べると、本発明方法の改善効果は著しく大きいことが分かる。
【００４８】
以上の本実施形態の処理を要約すると、図５のようになる。ステップＳ１１では、被害予測に使用する変数の組（標本パターン）ｘ_ｉｊ を次のように定義する。
ｘ_ｉｊ＝［ｘ_ｉｊ１，ｘ_ｉｊ２，・・・，ｘ_ｉｊｎ］^Ｔ
ステップＳ１２では、該標本パターンｘ_ｉｊ を正規化し、正規化された標本パターンｙ_ｉｊ を得る。
ｙ_ｉｊ＝［ｙ_ｉｊ１，ｙ_ｉｊ２，・・・，ｙ_ｉｊｎ］^Ｔ
ステップＳ１３では、フィッシャーの評価関数Ｊ(d)を用いて、Ｊ(d)を大きくするベクトルｄ、すなわち「被害あり」と「被害なし」のクラス間を離し、クラス内を纏めるベクトルｄを選定する。
【００４９】
ステップＳ１４では、特徴抽出を行う。パターン空間から特徴空間への射影行列ＤをＤ＝［ｄ_１，ｄ_２，・・・，ｄ_ｍ−１］と定義する。ここに、ｄ_kは行列Ｗ^−１Ｂの最大からｋ番目の固有値に対する固有ベクトルである。ｍはクラス数であり、本発明では「被害あり」と「被害なし」の２つであるため、ｍ＝２となる。
【００５０】
ステップＳ１５では、標本パターン列ベクトルｙ_ｉｊ の特徴空間への射影値列ベクトルｚ_ｉｊをｚ_ｉｊ＝Ｄ^Ｔ ｙ_ｉｊで求める。特徴空間の次元数ｌは、ｌ＝（ｍ−１）＝１となる。
【００５１】
ステップＳ１６では、特徴空間への射影値列ベクトルｚ_ｉｊを用いて、クラスの分布、すなわち「被害あり」「被害なし」の分布ｆ_ｉ(z)を求める。
【００５２】
以上の処理が、図３のステップＳ１に対応する。
【００５３】
次に、ステップＳ１７では、未知パターンが「被害あり」か「被害なし」かのいずれのクラスに属するかの判別を行う。まず、未知パターンを正規化し、射影行列Ｄ似て、特徴空間に射影する。射影された特徴空間において、未知パターンがどちらのクラス（「被害あり」と「被害なし」）に近いかを判別する。
【００５４】
この処理は、図３のステップＳ２に対応する。
【００５５】
次に、本発明の第２実施形態の原理を、図６のフローチャートを参照して説明する。
【００５６】
図のステップＳ２１では、既知の被害データと状況データから、重回帰モデルを構築する。ステップＳ２２では、該構築された重回帰モデルを用いて、熱帯性低気圧に対する未知の被害を予測する。
【００５７】
以下に、本実施形態を詳細に説明する。
【００５８】
熱帯性低気圧による被害予測には、重回帰分析法を使用する。被害（目的変数：Ｙ）は、それに影響を与える変数（Ｘ１，Ｘ２，・・・，Ｘｍ）と、その影響度合いを示す係数（ａ１，ａ２，・・・，ａｍ）にて説明できるため、予測式は次の(21)式で表せる。
【００５９】
Ｙ＝ａ１・Ｘ１＋ａ２・Ｘ２＋ａ３・Ｘ３＋・・・・＋ａｍ・Ｘｍ ・・・(21)
該(21)式の係数（ａ１，ａ２，・・・，ａｍ)は、過去に被害のあったｍ個の熱帯性低気圧の各々の被害数（目的変数Ｙ）と、各熱帯性低気圧における風速などの各既知の変数（Ｘ１，Ｘ２，・・・，Ｘｍ）を(21)式に代入して、係数（ａ１，ａ２，・・・，ａｍ)からなるｍ個以上の式を形成する。そして、これらの式を最小自乗法で解くことにより、前記係数（ａ１，ａ２，・・・，ａｍ)を求める。
【００６０】
運用時に熱帯性低気圧が襲来した時の被害の予測は、前記のようにして求めた係数（ａ１，ａ２，・・・，ａｍ)を前記(21)式に入れる。そして、予測する時刻の風速、強風継続時間、電力線支持物支線数、山間部比率、電線サイズ比率などの変数（Ｘ１，Ｘ２，・・・，Ｘｍ）の値を前記(21)式に代入することで、目的変数Ｙ、すなわち被害数を具体的に導出する。
【００６１】
以上のように、前記実施形態では、被害のありなしの判別、および被害数の予測をすることができるようになる。
また、同様に、被害データ（被害の種類）として、家屋の倒壊率や損害金額の少なくとも一つを用いて、ある地域の被害予測状況を示す変数（状況データ）を選定することで被害予測を実施できる。この場合の該変数は、風速、強風継続時間、熱帯性低気圧襲来回数、鉄筋施工比率、人口密度、雨量などを挙げることができる。種々の設備や構造物の被害率や損害金額を被害データ（被害の種類）とし、状況を示す変数（状況変数）を風速、強風継続時間、雨量などとすることで被害予測を実施できる。
また、同様に、被害データ（被害の種類）として、特定の農産物の損害率や損害金額の少なくとも一つを用いて、ある地域の被害予測状況を示す変数（状況データ）を選定することで被害予測を実施できる。この場合の該変数は、風速、強風継続時間、熱帯性低気圧襲来回数、雨量などを挙げることができる。種々の農産物の被害率や損害金額を被害データ（被害の種類）とし、状況を示す変数（状況変数）を風速、強風継続時間、雨量などとすることで被害予測を実施できる。
【００６２】
【発明の効果】
以上の説明から明らかなように、本発明によれば、複数の状況データを用い、かつパターン認識を用いるようにしたので、従来の風速の閾値で被害のありなしを判別する方法に比べて、被害のありなしの予測を精度よく行うことができるようになる。
【００６３】
また、本発明によれば、既知の被害データと状況データとから重回帰モデルを構築し、該モデルを用いて被害の予測を行うようにしたので、該被害の予測を従来より正確に行うことができるようになる。
【図面の簡単な説明】
【図１】 本発明が適用されるシステム例を示す図である。
【図２】 本発明の一実施形態の機能ブロック図である。
【図３】 本発明の第１実施形態の原理を説明するフローチャートである。
【図４】 第１実施形態の効果を説明する図である。
【図５】 第１実施形態の一具体例の概略を説明するフローチャートである。
【図６】 本発明の第２実施形態の原理を説明するフローチャートである。
【符号の説明】
２・・・気象表示装置、３・・・熱帯性低気圧風速・被害予測装置、３ａ・・・熱帯性低気圧処理装置、３ｂ・・・風速・被害予測装置、４・・・ＬＡＮ、１１・・・通信装置、１２・・・状況データ入力装置、１３・・・記憶部、１４・・・被害予測演算部、１５・・・表示部。[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a method for determining the presence or absence of tropical cyclone damage and a method and apparatus for predicting tropical cyclone damage, and in particular, facilities in various locations (power lines, supports, structures such as houses, etc.) associated with the passage of tropical cyclones. Or, damage such as crops can be automatically predicted regardless of human judgment from state data such as tropical cyclone wind speed, wind direction, strong wind duration, and rainfall after several hours in advance. The present invention relates to a method for determining the presence or absence of tropical cyclone damage and a method and apparatus for predicting tropical cyclone damage.
[0002]
[Prior art]
Tropical cyclones occur in the area centering on the equator of the earth, causing great damage to the surrounding area. Conventionally, the tropical nature of each region is estimated from the tropical cyclone center position, central atmospheric pressure, direction, strong winds and storms predicted several hours later by information providers such as TV and radio broadcasting weather information. The damage caused by the cyclone was predicted with reference to past experiences of tropical cyclones.
[0003]
[Problems to be solved by the invention]
However, it was difficult to predict damage from the characteristics of tropical cyclones experienced by humans in the past and the tropical cyclones that are currently approaching. Moreover, the prediction of the damage by the conventional tropical cyclone greatly depends on the experience of the predictor, and the prediction of the inexperienced person is extremely difficult. Another problem is that the prediction of damage caused by human experience is not always accurate.
[0004]
The present invention has been made in view of the above-described problems of the prior art, and its purpose is more accurately determining whether there is damage and predicting the magnitude of damage without relying on human experience or judgment. It is an object of the present invention to provide a method for determining the presence or absence of tropical cyclone damage and a method and apparatus for predicting tropical cyclone damage.
[0005]
[Means for Solving the Problems]
In order to achieve the above-described object, the present invention is a method for determining the presence or absence of damage in a certain region in a tropical cyclone, and extracts features of presence or absence of damage from known damage data and situation data. 1 and a second step of determining whether or not there is damage to an unknown tropical cyclone using the extracted features. The first and second steps are performed using pattern recognition. The first feature is that it is executed.
[0006]
According to this feature, it is possible to accurately determine whether or not the tropical cyclone is damaged.
[0007]
In addition, the present invention is a method for predicting the number or rate of damage of tropical cyclones, which is a multiple regression from known damage data and situation data including only damage that has occurred in the past or no damage. A second feature is that it includes a first step of constructing a model and a second step of predicting damage to an unknown tropical cyclone using the constructed multiple regression model.
[0008]
According to this feature, damage can be predicted more accurately than the conventional method. That is, a coefficient that is a feature indicating the presence / absence of damage from known data and a coefficient of a multiple regression model that predicts damage from known data having actual damage are calculated in advance. At the time of operation, the tropical cyclone that is attacking this time is set as an unknown tropical cyclone and the presence or absence of damage is determined using a coefficient that has been derived in advance, and the number or rate of damage is derived in advance for damage. This is a method of predicting from the coefficient.
[0009]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, the present invention will be described in detail with reference to the drawings. FIG. 1 is a schematic system diagram of a tropical cyclone wind speed / damage prediction system to which the tropical cyclone damage determination method and tropical cyclone damage prediction method of the present invention are applied. Here, power systems where damage prediction is important for recovery measures are targeted. The term “tropical cyclone” in the present invention includes typhoons, hurricanes, cyclones and the like.
[0010]
For example, a weather display device 2 that displays the location of a tropical cyclone by Weathernews, and a power company and an affiliated company that need wind speed prediction for power system damage prediction. For example, a tropical cyclone wind speed / damage prediction device 3 of Kyushu Electric Power Co., Inc. is connected by a communication line such as LAN 4. The tropical cyclone wind speed / damage prediction device 3 includes a tropical cyclone processing device 3a that mediates data and a wind speed / damage prediction device 3b that performs wind speed / damage prediction.
[0011]
When a tropical cyclone occurs, the weather display device 2 provides tropical cyclone characteristic prediction information. The tropical cyclone characteristic prediction information includes the tropical cyclone center position (latitude and longitude) and the central atmospheric pressure after 1, 6, 12, 24, 36, 48, and 72 hours from the time of issue (actual information). Is provided. The wind speed / damage prediction device 3b receives the tropical cyclone characteristic prediction information via the LAN 4 and predicts the wind speed from the received tropical cyclone central pressure and the central position, and then the tropical cyclone of the present invention. The tropical cyclone damage is predicted according to the damage determination method and the tropical cyclone damage prediction method.
[0012]
FIG. 2 is a block diagram showing functions related to the present invention of the wind speed / damage prediction device 3b.
[0013]
In the figure, a communication device 11 is connected to the LAN 4 and acquires current tropical cyclone information or various data. The situation data input unit 12 inputs situation data to be described later. The status data may be acquired from another device by the communication device 11. The storage unit 13 is used to predict the data acquired by the communication device 11, the data input from the situation data input unit 12, the coefficient used for determining the presence or absence of damage derived in advance, and the number or rate of damage derived in advance. Stores the coefficient used. Based on the data accumulated in the storage unit 13, the damage prediction calculation unit 14 predicts the magnitude of damage when there is no damage and when there is damage by a method described later. The display unit 15 displays the result obtained by the damage prediction calculation unit 14.
[0014]
FIG. 3 is a flowchart showing the principle of an embodiment of the method for determining whether or not there is damage due to tropical cyclones according to the present invention.
[0015]
As shown in the figure, in step S1, characteristics of presence / absence of damage are extracted from known damage data and situation data. Next, in step S2, the presence or absence of damage to an unknown tropical cyclone is determined using the extracted features. In the present embodiment, the processes of steps S1 and S2 are executed using pattern recognition. The feature extraction in step S1 is executed in advance, and only the determination of the presence or absence of damage in step S2 is performed during operation.
[0016]
Hereinafter, this embodiment will be described in detail.
[0017]
(1) As an example of damage data (damage type), use at least one of breakage, overturning, tilting, runoff, power line disconnection, structures and crops of power line supports.
[0018]
Also, select variables (situation data) used to predict damage in a certain area. The variables include wind speed, strong wind duration, wind direction, power pole column ratio, power consumer density, mountain area ratio, plain ratio, span length, number of tropical cyclones, soil quality, power pole safety factor , Electric wire size ratio, number of branch lines attached to power line support, rainfall, and the like.
[0019]
In addition, as the wind speed, the maximum value of the average wind speed accompanying the tropical cyclone that will be observed at one or several observation points, the average value of the maximum value of each point, or the tropical cyclone passing It is preferable to use an average of the maximum instantaneous wind speed at each point and at least one of the maximum instantaneous wind speeds. The strong wind duration may be at least one of a time equal to or higher than a certain wind speed associated with passing through a tropical cyclone, an integrated value of wind speed equal to or higher than a certain wind speed, and an integrated value of square of wind speed equal to or greater than a certain wind speed. Is preferred.
[0020]
(2) Explanation of terms and various definitions In the present invention, pattern recognition theory is used as a method for discriminating whether there is no damage (for example, whether there is damage such as breakage of the power line support or toppling). I do.
[0021]
Pattern space: Multi-dimensional space pattern that shows each information item (situation data) of the cause of damage as an axis. In the pattern space, a column vector feature space composed of a set of numerical data for each information item of the damage: a feature axis suitable for discrimination obtained by projection onto a subspace created by linear combination of each axis of the pattern space Number of spatial dimensions spanned: Number of axes spanning the space Feature extraction: Determining the axes that make up the feature space from the pattern space Class: “Damaged” and “Damaged” to be distinguished are called classes. The class contains damage data patterns for the same accident.
[0022]
Specimen pattern: Pattern of damage data that is known to have no damage Unknown pattern: Pattern base vector to be discriminated (identified) that is unknown to no damage: Vector norm of magnitude 1 orthogonal to each other spanning a certain space: Euclidean space Euclidean distance between the above two points Next, mathematical definitions are made as preparations for explaining the pattern recognition theory.
[0023]
n: number of dimensions in pattern space l: number of dimensions in feature space m: number of classes Ni: number of sample patterns of class i N = ΣNi: number of all sample patterns In the non-damaged discrimination method of the present invention, an n-dimensional Euclidean space Let R ⁿ be a pattern space, and consider each point as a pattern. Therefore, the pattern α is expressed as follows by a set of real values α1, α2,..., Αn which are numerical data of n damage information items.
[0024]
α = [α1, α2,..., αn] ^T
Where α ^T is the transpose of α.
[0025]
When it is known that there is no damage, that is, the class to which it belongs is known, the j (≦ Ni) -th sample pattern x _ij belonging to the class i is expressed as follows.
x _ij = [x _ij1 , x _ij2 ,..., x _ijn ] ^T
Representing a sample pattern y _ij of the sample pattern x _ij normalized as follows.
y _ij = [y _ij1 , y _ij2 ,..., y _ijn ] ^T
The expression of the sample pattern in the feature space is expressed as z _ij as follows.
z _ij = [z _ij1 , z _ij2 ,..., z _ijn ] ^T
(3) The determination of whether there is no damage by recognition of the normalized pattern of data is based on the distance defined in the Euclidean space set by the damage information item. Therefore, the size of the real value (average and variance of all the sample patterns) of each axis spanning the pattern space affects the pattern recognition result. Therefore, it is necessary to make the average and variance of all sample patterns equal on each axis. This is called normalization.
[0026]
Normalization is performed using all sample patterns in each axis spanning the pattern space, and the average and variance of each axis are made equal to one. The average ￣x _k of all sample patterns of k (1 ≦ k ≦ n) dimensions (axis) in the n-dimensional pattern space is expressed by the following equation (1).
[0027]
[Expression 1]

Further, the variance σ ² _xk is expressed by the following equation (2).
[0028]
[Expression 2]

The k-dimensional (1 ≦ k ≦ n) normalization of the pattern space is shown. _{Y ijk} a k-dimensional numerical data _{x ijk} sample pattern was normalized by the mean of the k-dimensional ¯x _k and the standard deviation sigma _xk by the following equation (3).
[0029]
[Equation 3]

In the following, the pattern recognition theory will be described using the normalized sample pattern y _ij in equation (4).
[0030]
y _ij = [y _ij1 , y _ij2 ,..., y _ijn ] ^T (4)
(4) Fisher's evaluation function Discriminant analysis in multivariate analysis is a typical identification-oriented linear special extraction method. The evaluation function of discriminant analysis is Fisher's evaluation function J (d) taking into account differences between classes. The evaluation function J (d) is expressed by the following equation (5).
[0031]
[Expression 4]

Here, d is an n-dimensional column vector for projecting the pattern. B is the estimated value of the interclass covariance matrix, and W is the estimated value of the intraclass covariance matrix, which are defined by the following equations (6) and (7), respectively.
[0032]
[Equation 5]

Further, p _i is an estimated value of the prior probability of class i, μ _yi is a normalized sample pattern average column vector of class i, and is expressed by the following equations (8) and (9).
[0033]
[Formula 6]

The d ^T Bd of the numerator in the equation (5) is the sum of the variances between classes on the one-dimensional feature space (subspace) generated by the projection vector d from the pattern space, and the square between the average values of the classes. It represents the sum of distances. The denominator d ^T Wd is the intra-class variance sum on the one-dimensional feature space generated by d. Therefore, maximizing the Fisher's evaluation function in equation (5) is to increase the variance between classes and to reduce the variance within the classes. That is, it is easy to discriminate by projecting the classes so that the sample patterns in the class are accumulated and separated from each other.
[0034]
(5) The vector d that maximizes the feature extraction Fisher's evaluation function is the eigenvector d ₁ for the maximum eigenvalue of the matrix W ⁻¹ B, as is well known. The rank of the matrix B is m−1 obtained by subtracting 1 from the number of classes clearly from the equation (6). Therefore, the eigenvalues of the matrix W ⁻¹ B are λ1 ≧ λ2 ≧... ≧ λm−1 ≧ λm =. Therefore, an m-1 dimensional feature space is constructed by using eigenvectors d1, d2,..., Dm-1 for eigenvalues other than 0 as projection vectors onto each one-dimensional feature space. The projection matrix D from the pattern space to the feature space is defined as the following equation (10) by the eigenvector.
[0035]
D = [d1, d2,..., Dm-1] (10)
The projection value sequence vector z _ij onto the feature space of the j-th sample pattern sequence vector y _ij of class i on the pattern space using the formula (10) is expressed by the following formula (11).
[0036]
z _ij = D ^T y _ij (11)
That is, the j-th sample pattern string vector z _ij of class i on the m−1-dimensional feature space is expressed by the following equation (12).
[0037]
z _ij = [z _ij1 , z _ij2 ,..., z _{ij (m−1)} ] ^T (12)
The number of dimensions of the feature space in the above definitions is as shown in the following equation (13).
[0038]
l = (m−1) (13)
(6) Discriminant analysis Fisher's evaluation function gives the projection matrix of equation (10), which is effective for discriminating to maximize the inter-class variance sum and minimize the intra-class variance sum, and the l-dimensional feature space is constructed. . Accident discrimination can result in an identification problem in this feature space.
[0039]
Assuming that the distribution of each class in the feature space is a normal distribution, the distribution f _i (z) of the class i can be expressed by the probability density function of the following equation (14).
[0040]
[Expression 7]

Here, μ _zi and Σ _zi are sample patterns z _{ij of} class i projected onto the feature space.
It is calculated using (1 ≦ j ≦ N _i ), and the following equations (15) and (16) are obtained.
[0041]
[Equation 8]

When the distribution of each class is given parametrically in the feature space in equation (14), it is possible to identify from which of the classes where the pattern to which the class belongs is unknown is `` Yes '' or `` No '' This is an issue to be considered.
(7) Discrimination without damage of unknown pattern A pattern whose class belongs is unknown is given as an n-dimensional column vector x _u on the pattern space with the accident information item as an axis. The unknown pattern _{x u, y} u1, _y u2 normalized similarly to the sample _pattern, ···, _{y uk} of k-dimensional unknown pattern _{y u} of n real numbers set of _{y un} are the (1) From the equation (2), the following equation (17) is obtained.
[0042]
[Equation 9]

After the unknown pattern x _u which was normalized y _u, (10) with a D of formula unknown pattern z _u is which is projected in the feature space, given by the following equation (18), in feature space Identification is made.
[0043]
z _u = D ^T y _u (18)
In this identification, it is natural to think that the unknown pattern z _u originated from the class i that minimizes the general distance r _i of the following equation (19) according to the equations (15) and (16). Yes and reasonable.
[0044]
[Expression 10]

This identification is stochastically equivalent to finding a class that maximizes the likelihood function. When the identification method is described again, the following equation (20) is obtained, and the unknown pattern is made to correspond to the class i ^* determined by the norm of the equation (20).
[0045]
[Expression 11]

(8) Discrimination result No. 9918 (the 18th typhoon number that occurred in 1999) that hit Japan. Regarding 19 tropical cyclones other than typhoons, we used data from 85 sales offices of Kyushu Electric Power Co., Inc. A discrimination model was constructed and the discrimination accuracy of the statistical pattern recognition method of the present invention was confirmed using data from the 85 office of the No. 9918 typhoon that was not used for construction, as shown in FIG. 4 (a). became. As is clear from the figure, the statistical pattern recognition method of the present invention shows a success rate of 80% or more in the construction data and 80% or more in the evaluation (9918 tropical cyclone) data. Became a rate. On the other hand, in the discriminant analysis method, as shown in FIG. 4 (b), almost all of the construction data showed a success rate of 80% or more, and the evaluation data showed a success rate of 70% or 80%. .
[0046]
As described above, the statistical pattern recognition method is more effective than the subspace method. In addition, since the statistical pattern recognition method is advantageous in terms of computation, it is preferable to use the statistical pattern recognition method for the prediction method without damage. It turned out to be good to use.
[0047]
In addition, it can be seen that the improvement effect of the method of the present invention is remarkably large as compared with the conventional method in which the presence or absence of damage is determined by the wind speed threshold.
[0048]
The above-described processing of the present embodiment is summarized as shown in FIG. In step S11, a set of variables (sample pattern) x _ij used for damage prediction is defined as follows.
x _ij = [x _ij1 , x _ij2 ,..., x _ijn ] ^T
In step S12, the sample pattern x _ij is normalized to obtain a normalized sample pattern y _ij .
y _ij = [y _ij1 , y _ij2 ,..., y _ijn ] ^T
In step S13, using Fisher's evaluation function J (d), a vector d that increases J (d), that is, a vector d that separates the “damaged” and “no damage” classes and summarizes the class is selected. To do.
[0049]
In step S14, feature extraction is performed. A projection matrix D from the pattern space to the feature space is defined as D = [d ₁ , d ₂ ,..., D _m−1 ]. Here, d _k is an eigenvector for the k-th eigenvalue from the maximum of the matrix W ⁻¹ B. m is the number of classes, and in the present invention, there are two, “damaged” and “no damage”, so m = 2.
[0050]
In step S15, a projection value sequence vector z _ij to the feature space of the sample pattern sequence vector y _ij is obtained by z _ij = D ^T y _ij . The dimension number l of the feature space is l = (m−1) = 1.
[0051]
In step S16, using the projection value sequence vector z _ij to the feature space, a class distribution, that is, a distribution f _i (z) of “damaged” and “no damage” is obtained.
[0052]
The above processing corresponds to step S1 in FIG.
[0053]
Next, in step S17, it is determined whether the unknown pattern belongs to the class “damaged” or “no damage”. First, the unknown pattern is normalized and projected onto the feature space in a manner similar to the projection matrix D. In the projected feature space, it is determined which class (“damaged” or “no damage”) the unknown pattern is close to.
[0054]
This process corresponds to step S2 in FIG.
[0055]
Next, the principle of 2nd Embodiment of this invention is demonstrated with reference to the flowchart of FIG.
[0056]
In step S21 in the figure, a multiple regression model is constructed from known damage data and situation data. In step S22, unknown damage to the tropical cyclone is predicted using the constructed multiple regression model.
[0057]
Hereinafter, this embodiment will be described in detail.
[0058]
Multiple regression analysis is used to predict damage caused by tropical cyclones. Damage (objective variable: Y) can be explained by variables (X1, X2,..., Xm) that affect the damage and coefficients (a1, a2,. The prediction formula can be expressed by the following formula (21).
[0059]
Y = a1, X1 + a2, X2 + a3, X3 +,... + Am, Xm (21)
The coefficients (a1, a2,..., Am) of the equation (21) are the number of damages (objective variable Y) of each of the m tropical cyclones that have been damaged in the past, and the tropical cyclones. Substituting each known variable (X1, X2,..., Xm) such as wind speed in Eq. (21) to form m or more formulas consisting of coefficients (a1, a2,..., Am) To do. Then, the coefficients (a1, a2,..., Am) are obtained by solving these equations by the method of least squares.
[0060]
For predicting damage when a tropical cyclone hits during operation, the coefficients (a1, a2,..., Am) obtained as described above are put into the equation (21). Then, the values of variables (X1, X2,..., Xm) such as the wind speed at the predicted time, the strong wind duration, the number of power line support branch lines, the mountain area ratio, and the wire size ratio are substituted into the equation (21). Thus, the objective variable Y, that is, the number of damages is specifically derived.
[0061]
As described above, in the embodiment, it is possible to determine whether there is damage or not and to predict the number of damages.
Similarly, the damage prediction (situation data) is selected by selecting a variable (situation data) that indicates the damage prediction status of a certain area, using at least one of the collapse rate of the house and the amount of damage as damage data (type of damage). Can be implemented. Examples of the variables in this case include wind speed, strong wind duration, number of times of tropical cyclone attack, rebar construction ratio, population density, and rainfall. Damage prediction can be carried out by using the damage rate (damage type) as the damage rate and damage amount of various facilities and structures, and the variables (situation variables) indicating the situation as wind speed, strong wind duration, and rainfall.
Similarly, the damage data (type of damage) can be determined by selecting a variable (situation data) that indicates the damage prediction status of a certain region using at least one of the damage rate and damage amount of a specific agricultural product. Can make predictions. Examples of the variables in this case include wind speed, strong wind duration, number of tropical cyclone intrusions, and rainfall. Damage can be predicted by using the damage rate and damage amount of various agricultural products as damage data (type of damage), and the variables indicating the situation (situation variables) as wind speed, strong wind duration, and rainfall.
[0062]
【The invention's effect】
As is clear from the above description, according to the present invention, since a plurality of situation data is used and pattern recognition is used, compared to the conventional method of determining whether there is damage by using a wind speed threshold value, It becomes possible to accurately predict whether there is damage.
[0063]
Further, according to the present invention, a multiple regression model is constructed from known damage data and situation data, and damage is predicted using the model, so that the damage can be predicted more accurately than before. Will be able to.
[Brief description of the drawings]
FIG. 1 is a diagram illustrating an example of a system to which the present invention is applied.
FIG. 2 is a functional block diagram of an embodiment of the present invention.
FIG. 3 is a flowchart illustrating the principle of the first embodiment of the present invention.
FIG. 4 is a diagram illustrating the effect of the first embodiment.
FIG. 5 is a flowchart for explaining an outline of a specific example of the first embodiment;
FIG. 6 is a flowchart illustrating the principle of the second embodiment of the present invention.
[Explanation of symbols]
2 ... Weather display device, 3 ... Tropical cyclone wind speed / damage prediction device, 3a ... Tropical cyclone processing device, 3b ... Wind velocity / damage prediction device, 4 ... LAN, 11 ... Communication device, 12 ... Status data input device, 13 ... Storage unit, 14 ... Damage prediction calculation unit, 15 ... Display unit.

Claims (13)

A method of determining the presence or absence of damage in a certain area in a tropical cyclone,
A first step of extracting features of presence or absence of damage from damage data and situation data at the time of a tropical cyclone attack in the past;
A second step of determining whether or not there is damage to an unknown tropical cyclone using the extracted features;
A method for determining the presence or absence of tropical cyclone damage, wherein the first and second steps are executed using pattern recognition. The method for determining the presence or absence of tropical cyclone damage according to claim 1,
As the damage data, at least one of structure collapse, breakage, fall, tilt, runoff, breakage of power line support, fall, tilt, runoff, power line disconnection, and crops is used as a target, and the damage A method for determining the presence or absence of tropical cyclone damage characterized by determining the presence or absence. The method for determining the presence or absence of tropical cyclone damage according to claim 1,
As the above situation data, wind speed, strong wind duration, wind direction, power pole column rate, power consumer density, mountain area ratio, plain ratio, span length of power line support, number of tropical cyclone intrusions, soil quality, utility pole And a method for determining the presence or absence of tropical cyclone damage, comprising at least one of a safety factor of the structure, a wire size ratio, the number or rate of branch lines attached to a power line support, and rainfall. In the method for determining the presence or absence of tropical cyclone damage according to claim 3,
The wind speed is the maximum average wind speed associated with passing tropical cyclones that would be observed at one or several observation points, the average of the maximum values of each point, and the maximum of each point associated with passing tropical cyclones. A method for determining the presence or absence of tropical cyclone damage, comprising using at least one of an average value of instantaneous wind speeds and a maximum instantaneous wind speed value. In the method for determining the presence or absence of tropical cyclone damage according to claim 3,
The strong wind duration is at least one of a time equal to or greater than a certain wind speed associated with passing through a tropical cyclone, an integrated value of wind speed equal to or greater than a certain wind speed, and an accumulated value of square of wind speed equal to or greater than a certain wind speed. How to determine whether or not tropical cyclone damage. The method for determining the presence or absence of tropical cyclone damage according to claim 1,
A method for discriminating the presence or absence of tropical cyclone damage, wherein a partial space classification method or a discriminant analysis method is used for the pattern recognition. A method for predicting damage from tropical cyclones,
A first step of constructing a multiple regression model from known damage data and situation data including only damage that has been past or not damaged; and
A tropical cyclone damage prediction method comprising the second step of predicting the number or rate of damage to an unknown tropical cyclone using the constructed multiple regression model. In the tropical cyclone damage prediction method according to claim 7,
Using the damage data as a target for at least one of structure collapse, breakage, fall, tilt, runoff, breakage of power line support, fall, tilt, runoff, power line disconnection, and crops, the number of damage Alternatively, a tropical cyclone damage prediction method characterized by predicting the damage rate. In the tropical cyclone damage prediction method according to claim 7,
As the above situation data, wind speed, strong wind duration, wind direction, power pole column rate, power consumer density, mountain area ratio, plain ratio, span length of power line support, number of tropical cyclone intrusions, soil quality, utility pole And a tropical cyclone damage prediction method comprising: at least one of a safety factor of a structure, a wire size ratio, the number or rate of branch lines attached to a power line support, and rainfall. In the tropical cyclone damage prediction method according to claim 9,
The wind speed is the maximum average wind speed associated with passing tropical cyclones that would be observed at one or several observation points, the average of the maximum values of each point, and the maximum of each point associated with passing tropical cyclones. A tropical cyclone damage prediction method using an average value of instantaneous wind speed and at least one of the maximum instantaneous wind speed. In the tropical cyclone damage prediction method according to claim 9,
The strong wind duration is at least one of a time equal to or greater than a certain wind speed associated with passing through a tropical cyclone, an integrated value of wind speed equal to or greater than a certain wind speed, and an accumulated value of square of wind speed equal to or greater than a certain wind speed. To predict tropical cyclone damage. The current tropical cyclone to be damaged is assumed to be an unknown tropical cyclone, and the presence or absence of damage is determined by the determination method according to claim 1, and if there is damage, the tropical cyclone damage prediction method according to claim 7 A tropical cyclone damage prediction method characterized by predicting the number of damages or damage rate at A means to input tropical cyclone current data, forecast data, and status data;
Means for storing the input data;
Means for obtaining in advance the coefficient used for the presence or absence of damage and prediction;
Means for storing the previously determined coefficient;
Means for determining the presence or absence of damage based on the stored data and coefficients;
If it is determined that there is no damage, the number or rate of damage is zero, and if there is damage, means for predicting the number or rate of damage based on the stored data and coefficient,
A damage prediction apparatus comprising: means for displaying the calculated damage prediction.

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