JP3877838B2 - Tire pitch arrangement determination method - Google Patents

Description

【００３４】
但し、上記の表中の記号は次を表すものである。

【００３５】
なお、上記音響心理パラメータについては、E.Zwicker 著、山田由紀子訳「心理音響学」にも記載がある。以下の説明では、表１に示した数式を（１）式と総称して用いる。
【００３６】
本発明者は、音響心理パラメータと従来の音圧レベル評価とを実車計器音質評価法により比較実験し、次の結果を得た。
【００３７】
図２に示すように、実車計器音質評価法による測定は、タイヤ３０を備えた車両２０の後部に、車両２０の走行速度を検出するための速度計２８を取り付けて行った。車両２０内には乗員２２が着座するが、その着座した乗員２２の頭部で左右の各耳の近傍位置にマイクロフォン２４、２６が取り付けられている。これらのマイクロフォン２４、２６の各々によって、乗員２２が左右の耳から聴取すべき音を取得することができる。なお、上記測定では、乗員２２に模擬したダミー人形の左右の耳にマイクロフォンを埋め込んだダミーヘッド（マイク付ヘッド）を用いて測定を行った。
【００３８】
ここでは、新特殊路Ｐ／Ｎ路の路面において、所定速度範囲（３８〜６０ｋｍ／ｈ）で惰行（Ｄレンジ）走行した場合を測定した。
【００３９】
図３は、タイヤＴ１，Ｔ２の各々を車両に装着して走行させたときにマイクロフォン２４、２６から得られた音の音圧レベルに対する周波数特性を示したものであり、図３（１）は左耳の近傍位置のマイクロフォンによる検出結果を示し、図３（２）は右耳の近傍位置のマイクロフォンによる検出結果を示したものである。この図３から理解されるように、音圧レベルからではタイヤＴ１，Ｔ２の各々に対して差異はみられない。
【００４０】
次に、上記車両２０に複数の異なるタイヤ３０を装着し、各々のタイヤについてオペレ−タがフィ−リング評価を行うと共に、マイクロフォン２４、２６から得られる音を用いて音響心理パラメータと従来の音圧レベルとを求めた。
【００４１】
図４には、フィ−リング評点の値を縦軸にすると共に、音圧レベル及び音響心理パラメータの値を横軸にした各座標系に、複数の異なるタイヤの結果をプロットしたものである。図中、ｒの値は相関係数を示している。この図４から理解されるように、音質的にみれば、ラウドネス、シャープネス、ラフネスは、各値とフィ−リング評点との間には、相関関係がみられず、分散したプロットになった。一方、トナリティＫ、及びフラクチュエーション・ストレングスＦの各々には音響心理パラメータの値とフィ−リング評点との間に相関関係があることが理解される。
【００４２】
以上の結果から、本発明者は、音の目立ち易さやうなり感に関係する音質によるものが走行時の騒音を少なくする、すなわち静寂性を向上させることに大きく起因するという観点から、音響心理パラメータのうちトナリティＫ、及びフラクチュエーション・ストレングスＦを注目し、これら２つの音響心理パラメータを目的関数として設定し、タイヤのピッチ配列を最適化することを勘案した。
【００４３】
図８は、第１実施の形態のプログラムの処理ルーチンを示すものある。ステップ１００〜１０４では、タイヤのトレッドに形成されるピッチ配列を数値的・解析的に求めるためのピッチ配列基本モデルを求める。ここで、モデル化とは、ピッチ配列を、疑似乱数に基づいて作成しコンピュータプログラムへのインプットデータ形式に数値化することをいう。
【００４４】
詳細には、ステップ１００では、静寂なピッチ配列を決定する際に、必要とするまたは経験的に求められる以下の各値が設定値として入力される。
【００４５】
〔設定値〕

【００４６】
なお、上記設定値として、静寂性を評価するときのタイヤの回転速度（例えば車速から求めた回転速度）、およびピッチ配列を音化するための矩形波のパルス幅（詳細は後述する）を設定することができる。
【００４７】
ステップ１０２では、ピッチ比の数Ｍ（Ｍは自然数、本実施の形態では２〜９のいずれか１つ）を決定し、ステップ１０４においてピッチ配列に含まれるピッチ比の種類の数がＭ個でありピッチの総数がＮ個であるピッチ配列Ｖを擬似乱数アルゴリズムによって複数生成し、この複数ピッチ配列Ｖのうち、隣合うピッチの比に関する制約条件を満足する１つのピッチ配列を初期値として選択する。
【００４８】
すなわち、Ｍ個のピッチ比を１〜９までの自然数に対応させ、擬似乱数アルゴリズムによってＮ桁の配列を生成することによって、ピッチ比が配列値である自然数の各桁に対応して表現されるピッチ配列Ｖを生成する。次に、隣合うピッチの比に関する制約条件を満足する１つのピッチ配列を初期値として選択する。なお、本実施の形態では、このピッチ比の数Ｍとして、Ｍ＝２、３、・・９の場合を順にして処理を行うものとする。
【００４９】
ここで、上記目的関数の詳細を説明する。本実施の形態では、計算を単純化するため、目的関数として用いる音響心理パラメータであるトナリティＫ、及びフラクチュエーション・ストレングスＦを以下のようにして近似している。
【００５０】
まず、タイヤに形成されたピッチ配列により発生される音を得るため、すなわちピッチ配列を音化するため、上記ピッチ配列Ｖを配列デ−タとして、その配列デ−タを時間軸上のパルス列に置き換えて、時間周波数分析等で解析可能としている。すなわち、ピッチ配列を音について解析可能な形式に変換している。このように、本実施の形態では、ピッチ配列を音化するためにピッチ配列である配列デ−タを時間軸上のパルス列に置き換えている。一例として、３個または５個のピッチ比を１〜９までのいずれかの自然数に対応させ、ピッチ配列を得るタイヤＡ〜Ｃを表２に示した。
【００５１】
【表２】

【００５２】
上記のようにしてピッチ比が配列値である自然数の各桁に対応して表現されるピッチ配列Ｖを生成したのち、そのピッチ配列について矩形波の連続からなるパルス列に変換する。図５に一例を示すように、パルス列は、パルス幅が予め定めた一定幅の矩形波の周期をピッチ比に応じて伸長させたものである。図５の例は、ピッチ配列の一部として「２、１、３」の部分のパルス列を示すものであり、ピッチ比の配列値「２」に対応してパルス幅Ｐｗでかつ時間（周期）ｔａ、ピッチ比の配列値「１」に対応してパルス幅Ｐｗでかつ時間（周期）ｔｂ、ピッチ比の配列値「３」に対応してパルス幅Ｐｗでかつ時間（周期）ｔｃからなるパルス列の一部を示している。なお、時間（周期）ｔａ、ｔｂ、ｔｃは、ピッチ比に対応し長短の時間になるものであり、図５の例では、ｔｂ＞ｔａ＞ｔｃとなる。なお、パルス幅Ｐｗは、予め実験によって定めたものであり、本実施の形態では、５００μｓに設定している。このようにして設定したパルス列は、時間周波数分析等によって音化することができる。
【００５３】
次に、トナリティＫ及びフラクチュエーション・ストレングスＦの計算を単純化するため、区分スペクトルという概念を導入した。この区分スペクトルは、図７に示すように、タイヤ１回転のピッチ配列による長さを基本幅すると共に該基本幅を所定数で分割（本実施の形態では、３分割）した長さを区分幅として、基本幅内を区分幅を一部を所定ずらし量だけ重複させて所定回抽出したものを定義したものである。
【００５４】
トナリティＫは、主に音の目立ち易さを表すものであるから、この区分スペクトルを用いて、個々の区分スペクトル内の偏差に対応させる。本実施の形態では、基本幅の１／３を区分幅と設定すると共に、ずらし量を７５％に設定している。これによって、１２個の区分スペクトルを得ることができる。なお、このときの窓関数はハニングを設定している。
【００５５】
また、フラクチュエーション・ストレングスＦは、うなり感を表すものであり、区分スペクトルを用いて、個々の区分スペクトルの間のエネルギー差に対応させている。本実施の形態では、トナリティＫの場合と同様に、基本幅の１／３を区分幅と設定する。これと共に、ずらし量は９６％に設定して、７２個の区分スペクトルを得ている。
【００５６】
従って、目的関数による最適化は、次の（２）式に示すように、トナリティＫについては区分スペクトル内の偏差、すなわち区分スペクトル毎に音化したその各区分スペクトル内における音圧レベルに関する最大値と最小値とのレベル差（振幅）のばらつきを最小化することに相当する（図６参照）。
【００５７】
Ｍｉｎ｛Ｄｍｉｎ｝ ・・・（２）
但し、Ｍｉｎ：｛｝内の最小値を求める関数
Ｄｍｉｎ：区分スペクトル内の最大音圧レベルと最小音圧レベルのレベル差
【００５８】
また、フラクチュエーション・ストレングスＦについては、次の（３）式に示すように、区分スペクトル間のエネルギー差、すなわち区分スペクトル毎に音化したその音圧レベルのレベル差を最小化することに相当する。
【００５９】
Ｍｉｎ｛Ｅｍａｘ−Ｅｍｉｎ｝ ・・・（３）
但し、Ｅｍａｘ：区分スペクトル内のエネルギー（音圧レベル）の最大値
Ｅｍｉｎ：区分スペクトル内のエネルギー（音圧レベル）の最小値
【００６０】
次のステップ１０６では、図９に示した最適化ルーチンによって初期値として選択されたピッチ配列Ｖを最適化する。次に、ステップ１３２において、設計変数Ｐ_i の初期値Ｐｏにおける目的関数ＯＢＪの初期値ＯＢＪｏ及び制約条件Ｇの初期値Ｇｏを演算する。この目的関数ＯＢＪの初期値ＯＢＪｏについて、トナリティＫは区分スペクトル内の偏差を求めるもので、フラクチュエーション・ストレングスＦは区分スペクトル間のエネルギー差を求めるものである。これらの区分スペクトル内の偏差や区分スペクトル間のエネルギー差は、音化装置からのデ−タを用いても良いし、コンピュ−タ本体において求めてもよい。
【００６１】
次のステップ１３４では、基本モデルを変化させるために設計変数Ｐ_i を各々ΔＰ_i ずつ変化させる。ステップ１３６では、設計変数をΔＰ_i 変化させた後のピッチ配列を決定する。
【００６２】
ステップ１３８では、ステップ１３６で求めたピッチ配列について設計変数をΔＰ_i 変化させた後の目的関数の値ＯＢＪ（Ｐ_i ＋ΔＰ_i ）、制約条件の値Ｇ（Ｐ_i ＋ΔＰ_i ）を演算し、ステップ１４０で以下の式（４）に従って、設計変数の単位変化量に対する目的関数の変化量の割合である目的関数の感度ΔＯＢＪ／ΔＰ_i 及び設計変数の単位変化量に対する制約条件の変化量の割合である制約条件の感度ΔＧ_i ／ΔＰ_i を各設計変数毎に演算する。この目的関数の値である、トナリティＫ及びフラクチュエーション・ストレングスＦは、上記ステップ１３２の演算と同様にして求める。
【００６３】
【数１】

【００６４】
この感度によって、設計変数をΔＰ_i 変化させたときに目的関数の値及び制約条件の値がどの程度変化するか予測することができる。なお、この感度は、タイヤ騒音のモデル化に用いた手法や設計変数の性質によっては、解析的に求められる場合があるので、その際にはステップ１３８の演算は不要になる。
【００６５】
次のステップ１４２では、目的関数の初期値ＯＢＪｏ、制約条件の初期値Ｇｏ、設計変数の初期値Ｐｏ及び感度を用いて、数理計画法により制約条件を満たしながら目的関数の値を最小にする、すなわちトナリティＫ及びフラクチュエーション・ストレングスＦの値を最小にする設計変数の変化量を予測する。この設計変数の予測値を用いて、ステップ１４４でステップ１３６と同様の方法によりピッチ配列を決定すると共に、目的関数値を演算する。ステップ１４６において、ステップ１４４で演算した目的関数値ＯＢＪとステップ１３２で演算した目的関数の初期値ＯＢＪｏとの差と、予めインプットされたしきい値とを比較することで目的関数の値が収束したか否かを判断し、目的関数の値が収束していない場合にはステップ１４２で求められた設計変数の値を初期値として、ステップ１３２からステップ１４６を繰り返し実行する。目的関数の値が収束したと判断されたときには、このときの設計変数の値をもって制約条件を満たしながら目的関数を最小にする設計変数の値とし、ステップ１４８においてこの設計変数の値を用いてタイヤの最適化されたピッチ配列を決定する。
【００６６】
次のステップ１０８では、上記のようにして最適化されたピッチ配列のピッチ比を正規化する。すなわち、ピッチ比の数Ｍに基づいて、以下の式（５）に従って正規化された初期ピッチ比ｒｉを求める。
【００６７】
【数２】

【００６８】
ここで、ｒ_max は最大ピッチ長の比、ｒ_min は最小ピッチ長の比である。
次に、以下の式（６）に従って、最適化されたピッチ長Ｐｉをピッチ長の平均値で除算する。
【００６９】
【数３】

【００７０】
上記最適化されかつ平均値で除算された値ＡＰｉを、最も近い正規化されたピッチ比で置換した後、ピッチ比の数Ｍでピッチ配列を再表現する。
【００７１】
次のステップ１１０では、ピッチ比の数Ｍで表現されたピッチ配列の各ピッチ比を図１０に示したピッチ比の最適化ルーチンにより最適化する。図１０の最適化ルーチンは、最初と最後のピッチ比ｒ₁ 、ｒ_M の値を保持したまま、目的関数が最小になるように、その間のピッチ比ｒ₂ 〜ｒ_M-1 の値を最適化する。この最適化ルーチンのステップ１６０では、ピッチ比ｒ₂ 〜ｒ_M-1 の値を各々増減するための増減値Δｒを演算する。本実施の形態では、（ｒ_M −ｒ₁ ）／１０の値を増減値Δｒとして演算する。次のステップ１６２では、初期目的関数の値ＯＢＪｏを演算する。次のステップ１６４では、ピッチ比ｒ₂ 〜ｒ_M-1 の何れか１つを選択し、ステップ１６６で選択したピッチ比ｒｉを増加または減少させてステップ１６８において新たに目的関数の値ＯＢＪを演算する。次のステップ１７０でピッチ比ｒ₂ 〜ｒ_M-1 に関する増減を全て（２（Ｍ−２）回）演算したか否かを判断し、全て演算した場合には、ステップ１７２において、ステップ１６８で演算した２（Ｍ−２）個の目的関数の内、最低になる目的関数値を演算する。次のステップ１７４では、初期目的関数値とステップ１７２で演算した最低目的関数値とを比較し、最低目的関数値が初期目的関数値より大きい場合には、これ以上改良されないことを示しているので、ステップ１７８において最適なピッチ比ｒ₁ 〜ｒ_M を出力する。一方、ステップ１７４において初期目的関数値より最低目的関数値が小さいと判断された場合には、ステップ１７６において隣り合うピッチ比ｒｉ，ｒｉ₊₁（ｉ＝１〜Ｍ−１）の差が或る値（予め定めた所定値）より小さいか否かを次の式（７）を用いて判断し、小さくなっていないときには、ステップ１６２へ進み小さい場合にはステップ１７８へ進み、最適なピッチ比ｒ₁ 〜ｒ_M を出力する。
【００７２】
【数４】

【００７３】
次のステップ１１２では、ピッチ配列Ｖを１００個生成したか否かを判断し、１００個生成するまで、ステップ１０４〜ステップ１１０を繰り返す。ピッチ配列Ｖを１００個生成すると、ステップ１１４において目的関数が最低であるピッチ配列及びピッチ比を選択する。
【００７４】
次のステップ１１６では、全ピッチ比の数Ｍについて上記処理が終了したか否かを判断し、否定判断の場合には、ステップ１０２からステップ１１４までを実行する。一方、全ピッチ比の数Ｍについてピッチ比及びピッチ配列の最適化が終了したときは、ステップ１１８へ進み、ピッチ比の数毎に最適化されたピッチ比及びピッチ配列から目的関数が最低である、すなわちトナリティＫ及びフラクチュエション・ストレングスＦの値が最小となるピッチ比及びピッチ配列を選択し、本ルーチンを終了する。
【００７５】
このようにして、ピッチ比及びピッチ配列を決定することにより、予め定めた初期配列に対応した複数（１００個）の最適なピッチ配列から音質を考慮した、すなわち発生ノイズの音色の目立ちやすさ及びうなり感が抑制された最適なピッチ配列を選択でき、少ない演算で確度よく、静寂なタイヤを設計することができる。
【００７６】
本実施の形態では、音響心理パラメータのうちトナリティＫ、及びフラクチュエーション・ストレングスＦの各々を最適化する場合について説明したが、トナリティＫ、及びフラクチュエーション・ストレングスＦのいずれか一方のパラメータを最適化してもよい。また、トナリティＫ、及びフラクチュエーション・ストレングスＦの少なくとも一方と、音圧レベルのピークの最小化、すなわち発生ノイズの音圧レベルの最大値の最小化を行ってもよい。このようにすれば、音質を考慮し、発生ノイズの音色の目立ちやすさ及びうなり感が抑制されると共に、発生ノイズの振幅値のばらつきが最小となるホワイトノイズ化された最適なピッチ配列を選択でき、少ない演算で確度よく、静寂なタイヤを設計することができる。
【００７７】
ここで、本発明者は、音響心理パラメータを目的関数に用いてピッチ配列を最適化したタイヤを含む種々のタイヤについて、フィ−リングテストを行い、次の結果を得た。
【００７８】
このフィ−リングテストでは、１０個のタイヤについて、フィ−リング評点の基準を５（良好）、３（普通）、１（悪い）と対応させて、８人の熟練者にヒヤリング実験を行ったものである。次の表３にその結果を示した。なお、基準タイヤは８人の熟練者全てが平均的と思われたタイヤを１０個のうちから１つを選択設定したものである。
【００７９】
【表３】

【００８０】
図１１（２）には、上記１０個のタイヤのフィ−リング評点の平均値と、トナリティＫとの対応を示した。なお、トナリティＫは、上記で説明したようにピッチ配列を、パルス列に変換して区分スペクトルから求めたものである。また、図１１（３）には、上記１０個のタイヤのフィ−リング評点の平均値と、フラクチュエ−ション・ストレングスＦとの対応を示した。なお、フラクチュエ−ション・ストレングスＦも上記と同様に区分スペクトルを用いて求めたものである。
【００８１】
これらの図から理解されるように、フィ−リング評点の平均値と、トナリティＫ及びフラクチュエ−ション・ストレングスＦと、は相関関係を有している。そこで、各々について重回帰分析を行い、次式に示すように、トナリティＫ及びフラクチュエ−ション・ストレングスＦから推定評点Ｙを得るための推定式を求めた。
【００８２】
Ｙ＝４．７５−（２．８・Ｋ＋０．９３・Ｆ）
但し、Ｙ：推定評点
Ｋ：トナリティの値
Ｆ：フラクチュエ−ション・ストレングスの値
【００８３】
図１１（１）には、上記１０個のタイヤのフィ−リング評点の平均値と、推定評点Ｙとの対応を示した。これらの対応は相関が高く（相関係数ｒ＝０．９１６）フィ−リング評点と、音質を考慮した、すなわちトナリティＫ及びフラクチュエ−ション・ストレングスＦによる推定評点とが確度よく対応された。
【００８４】
図１２には、本発明者が行った、従来の音圧レベルで最適化したピッチ配列で規定されるタイヤ、及び上記実施の形態による最適化により定まるピッチ配列で規定されるタイヤについて、トナリティＫを求めた実験結果（図１２（１）参照）、及びフラクチュエ−ション・ストレングスＦを求めた実験結果（図１２（２）参照）を示した。図１２（１）から理解されるように、トナリティＫの値は抑制され、図１２（２）から理解されるように、フラクチュエ−ション・ストレングスＦの値も抑制されている。これにより、音質が良好に改善されたピッチ配列を決定できることになる。
【００８５】
次に、タイヤのピッチ配列を山型とする山型配列を基本として最適なピッチ配列及びピッチ比を決定する第２実施の形態を説明する。なお、本実施の形態は、図１３を参照して説明するが、図８と対応する部分には同一符号を付して詳細な説明を省略する。
【００８６】
このピッチ配列を山型とするピッチ配列（以下、山型ピッチ配列という）は、図１５に示したように、ピッチ比の数がＭ個のとき、小ピッチから大ピッチへ、大ピッチから小ピッチへ順に変化するピッチ配列をいう。また、山型ピッチ配列中にある大ピッチが連続する１つの群を１つの山として、図１５の場合は山の数が２つになる。また、この山型ピッチ配列におけるピッチの大きさが変化するときの階段数Ｈは、以下の式（８）で表せる。
【００８７】
Ｈ ＝ ２Ｃ＋２Ｃ・（Ｍ−２） ＝ ２Ｃ・（Ｍ−１） −−（８）
但し、Ｃ：山の数（図１５の場合、２）
Ｍ：ピッチ比の数
ステップ２００では、上記と同様に、静寂なタイヤを決定する際に必要とするまたは経験的に求められる設定値が入力され、次のステップ１０２においてピッチ比の数Ｍを設定する。本実施の形態では、山型ピッチ配列であるため、上記実施の形態のランダムピッチ配列のときに設定した、隣合うピッチ比に関する制約は省略される。
【００８８】
ここで、目的関数ＯＢＪ、制約条件Ｊ、設計変数は、次の通りである。

【００８９】
次のステップ２０２では、タイヤの周に含まれる山の数Ｃを設定する。本実施の形態では、この山の数Ｃとして、１〜９までの値を順に設定して以下を処理する。次のステップ２０４では、上記式（８）に基づいてピッチ比の数Ｍ及び山の数Ｃから演算される階段数Ｈがピッチの総数Ｎより小さいか否かを判断し、肯定判断のとき、ステップ２０６へ進む。
【００９０】
ステップ２０６では、擬似乱数アルゴリズムによって、２・Ｃ・（Ｍ−１）個の階段の各々に含まれるピッチの数Ｕ_j （ｊ：１〜２・Ｃ・（Ｍ−１））を決定する。すなわち、２・Ｃ・（Ｍ−１）個の階段を１〜９までの自然数に対応させ、擬似乱数アルゴリズムによって配列を生成し、配列値である自然数の各桁に対応して階段の各々に含まれるピッチの数Ｕ_j が表現されるピッチ配列Ｖを１つ生成して、初期値とする。図１５には、山の数Ｃが２つのときを例に、上記のようにして決定された山型ピッチ配列におけるピッチの大きさと階段に含まれるピッチの数との関係を示した。図中、階段部分に下線を付した数字は、階段部分に含まれるピッチの数Ｕ_j を示している。
【００９１】
次のステップ２０８では、図１４に示した最適化ルーチンによって初期値として選択された山型ピッチ配列を最適化する。図１４の最適化ルーチンのステップ２３２では、初期値として選択された山型ピッチ配列について決定された目的関数ＯＢＪの初期値ＯＢＪｏを演算する。次のステップ２３４では、山型ピッチ配列の何れか２つの階段部分についてピッチの数を増減する。例えば、山の数Ｃが２つでかつ、小ピッチの階段部分２２のピッチの数Ｕが３、中ピッチの階段部分２４のピッチの数Ｕが２、大ピッチの階段部分２６のピッチの数Ｕが３の山型ピッチ配列が初期値として選択された場合に（図１５参照）、図１６に２重下線で示したように、小ピッチの階段部分２２のピッチの数を１減少して中ピッチの階段部分２４のピッチの数を１増加させる。また、中ピッチの階段部分２４のピッチの数を１減少して大ピッチの階段部分２６のピッチの数を１する例は、図１７に２重下線で示した。
【００９２】
このようにピッチの数を増減した山型ピッチ配列における目的関数の値をステップ２３６において演算する。この階段部分間のピッチ数の交換が全ての階段部分について終了するまで上記処理を繰り返し（ステップ２３８）、目的関数ＯＢＪの初期値ＯＢＪｏと対比して求められた複数の目的関数の値の最小の値である山型ピッチ配列をステップ２４０において選択する。ステップ２４２では、目的関数ＯＢＪの初期値ＯＢＪｏと対比することによって目的関数の値が収束したか否かを判断し、収束していない場合にはステップ２４６においてステップ２４０で選択されたピッチ配列を初期のピッチ配列に置換してステップ２３２へ戻り、目的関数の値が収束するまで、上記処理を実行する。目的関数の値が収束すると、ステップ２４４において、目的関数の値が収束した時点での山型ピッチ配列を最適なピッチ配列として決定する。
【００９３】
次に、上記実施の形態と同様に、最初と最後のピッチ比ｒ₁ 、ｒ_M の値を保持したまま、目的関数が最小になるように、その間のピッチ比ｒ₂ 〜ｒ_M-1 の値を最適化し（ステップ１１０、図１０）、ピッチ配列Ｖを１００個生成したか否かを判断し、１００個生成されたピッチ配列Ｖから目的関数が最低であるピッチ配列及びピッチ比を選択する（ステップ１１２、１１４）。
【００９４】
次のステップ２１０では、山の数Ｃの各々について、最適化されたピッチ比及びピッチ配列が演算されたか否かを判断し、否定判断の場合には、ステップ２０２へ戻り、全ての山の数Ｃについて最適化されたピッチ比及びピッチ配列の演算が終了するまで上記処理を繰り返す。
【００９５】
次のステップ１１６では、全ピッチ比の数Ｍについて上記処理が終了したか否かを判断し、否定判断の場合には、ステップ１０２へ戻り、全ピッチ比の数Ｍについてピッチ比及びピッチ配列の最適化が終了するまで上記処理を繰り返す。次のステップ２１２では、山の数Ｃを含めてピッチ比の数毎に最適化されたピッチ比及びピッチ配列から目的関数が最低であるピッチ比及びピッチ配列を選択し、本ルーチンを終了する。
【００９６】
このように、本実施の形態では、予め定められた山型ピッチ配列について各々に対応した複数の最適なピッチ配列を求め、この複数のピッチ配列から音質を考慮し、発生ノイズの音色の目立ちやすさ及びうなり感が抑制される最適なピッチ配列を選択している。このため、外観的な美観を保持しつつ静寂なタイヤを提供するためのピッチ比及びピッチ配列を、少ない演算で確度よく、求めることができ、静寂かつ見栄えのよいタイヤを設計することができる。
【００９７】
次に、第３実施の形態について説明する。本実施の形態は、ピッチ配列を遺伝的にアルゴリズムによって設計するものである。図１８は、第３実施の形態のプログラムの処理ルーチンを示すものである。ステップ３００では、Ｎ個のピッチ配列を疑似乱数に基づいて求める。なお、Ｎは予め使用者がインプットする。本実施の形態で用いる基本モデルは、第１実施の形態と同一である。
【００９８】
次のステップ３０２では、タイヤ性能評価用物理量を表す目的関数、隣り合うピッチ長の比、最大ピッチ長と最小ピッチ長の比、各ピッチ長に属するピッチの数の連続する同一ピッチ長の数、及び性能評価物理量の少なくとも１つを制約する制約条件及びＮ個のピッチ配列を決定する設計変数を決定する。本実施の形態では、騒音性能、すなわち音質性能が良好なピッチ配列を設計するため、目的関数ＯＢＪ及び制約条件Ｇを次のように定めている。
【００９９】

【０１００】
これをＮ回繰り返すことにより、目的関数ＯＢＪ、制約条件Ｇ及びＮ個のタイヤモデルの各々の設計変数ｒ_iJ（Ｊ＝１，２，・・・，Ｎ）を決定した後、図１８のステップ３０４において、Ｎ個のタイヤモデルの各々の設計変数ｒ_iJの各々の目的関数ＯＢＪ_J 及び制約条件Ｇ_J を演算する。
【０１０１】
次のステップ３０６では、ステップ３０４で求めたＮ個のピッチ配列の各々の目的関数ＯＢＪ_J 及び制約条件Ｇ_J を用いて、Ｎ個のピッチ配列の各々の適応関数Ｆ_J を以下の式（９）に従って演算する。本実施の形態では、例えば区分スペクトル偏差を最小にするため、適応関数による値（適応度）は、区分スペクトル偏差が小さくなると大きくなる。
【０１０２】
【数５】

【０１０３】
ｃ：定数
γ：ペナルティ係数
Φ_min ＝ｍｉｎ（Φ₁ 、Φ₂ 、・・・Φ_N ）
Φ_J ：Ｎ個のピッチ配列のＪ番目のピッチ配列のペナルティ関数
（Ｊ＝１、２、３、・・・Ｎ）
なお、ｃ及びγは使用者が予め入力する。
【０１０４】
次のステップ３０８では、Ｎ個のピッチ配列の中から交叉させるピッチ配列を２個選択する。選択方法としては、一般に知られている適応度比例戦略を用い、Ｎ個のピッチ配列のある個体ｅが各々選択で選ばれる確率Ｐ_e は以下の式で表わされる。
【０１０５】
【数６】

【０１０６】
但し、 Ｆ_e ：Ｎ個のピッチ配列の中のある個体ｅの適応関数
Ｆ_J ：Ｎ個のピッチ配列のＪ番目の適応関数
Ｊ＝１、２、３、・・・Ｎ
上記実施の形態では、選択方法として適応度比例戦略を用いたが、この他、遺伝的アルゴリズム（北野宏明 編）に示されている様な、期待値戦略、ランク戦略、エリート保存戦略、トーナメント選択戦略、あるいはＧＥＮＩＴＯＲアルゴリズム等を用いてもよい。
【０１０７】
次のステップ３１０では、選択された２個のピッチ配列を、使用者が予め入力した確率Ｔによって交叉させるか否かを決定する。ここでいう、交叉とは、後述するように、２個のピッチ配列の要素の一部を交換することをいう。否定判定で交叉させない場合は、ステップ３１２において現在の２個のピッチ配列をそのままの状態でステップ３１６へ進む。一方、肯定判定で交叉させる場合には、ステップ３１４において後述するように２個のピッチ配列を交叉させる。
【０１０８】
２個のピッチ配列の交叉は、図１９に示す交叉ルーチンによって行われる。先ず、上記のステップ３０８において選択された２個のピッチ配列をピッチ配列ａ及びピッチ配列ｂとすると共に、各々のピッチ配列ａ，ｂの設計変数について並びを含む設計変数ベクトルＶｒで表し、
ピッチ配列ａの設計変数ベクトルを
Ｖｒ^a ＝（ｒ₁ ^a 、ｒ₂ ^a 、・・・、ｒ_i ^a 、・・・、ｒ_n-1 ^a ）、
ピッチ配列ｂの設計変数ベクトルを
Ｖｒ^b ＝（ｒ₁ ^b ，ｒ₂ ^b 、・・・ｒ_i ^b 、・・・ｒ_n-1 ^b ）
とする。先ず、図１９のステップ３５０では、予め定めた規則に従い乱数を生成し、この乱数に応じてピッチ配列ａ，ｂの設計変数ベクトルに関する交叉場所ｉを決定する。次のステップ３５２では、決定された交叉場所ｉに基づいて、新しい設計変数ｒ_i ^'a，ｒ_i ^'bを求める。この新しい設計変数ｒ_i ^'a，ｒ_i ^'bの決定を図２０及び図２１を用いて詳細に説明する。
【０１０９】
図２０の例のピッチ配列は山型ピッチ配列であり、ピッチ比の大きさが大中小の３種類からなり、ピッチの数が２２個でかつ、小ピッチ比から大ピッチ比へ、大ピッチ比から小ピッチ比へ順に変化している。また、山型ピッチ配列中にある大ピッチ比のピッチが連続する１つの群を１つの山とし、山の数が２つである。図中、階段部分に下線を付した数字は、階段部分に含まれるピッチの数を示している。ピッチの大きさについて、大ピッチ比を３、中ピッチ比を２、小ピッチ比を１とすると、図２０のピッチ配列ａ，ｂ（以下、親▲１▼、親▲２▼という。）は、以下に示す［親ピッチ配列］のように表せる。
【０１１０】
［親ピッチ配列］
親▲１▼ ：１１１２２３３３２２２１１２２２３３２２２２
親▲２▼ ：１１２２２３３３３２１１１１２２３３３２２２
【０１１１】
次に、例えば、乱数により、７番目の位置で交叉させると決定されたときには、親のピッチ配列から、次に示す［ピッチ配列の交叉過程］のように子孫配列が生成される。
【０１１２】
［ピッチ配列の交叉過程］
親▲１▼ ：１１１２２３３／３２２２１１２２２３３２２２２
親▲２▼ ：１１２２２３３／３３２１１１１２２３３３２２２
子孫▲１▼：１１１２２３３／３３２１１１１２２３３３２２２
子孫▲２▼：１１２２２３３／３２２２１１２２２３３２２２２
【０１１３】
すなわち、親▲１▼の交叉点前半の配列部分と、親▲２▼の交差点後半の配列部分とを繋げて、親▲１▼を基準として交叉させた後のピッチ配列（以下、子孫▲１▼という）を生成する。同様に、親▲２▼の交差点前半の配列部分と、親▲１▼の後半の配列部分を繋げて、親▲２▼を基準として交叉させた後のピッチ配列（以下、子孫▲２▼という。）を生成する。この場合、図から理解されるように子孫▲１▼、子孫▲２▼のピッチ配列について共に山型ピッチ配列の性質を有している。
【０１１４】
しかしながら、図２１に示すように、交叉させる位置が中ピッチ比または小ピッチ比である場合には、子孫▲２▼は山型配列の性質を有するが、子孫▲１▼では山型ピッチ配列の性質を有しないことになる。従って、常時、山型ピッチ配列を得るようにするためには、制約条件Ｇが山型ピッチ配列でない場合に、正の値を有するように予め設定すれば、山型ピッチ配列以外のピッチ配列が支配的になることを防ぐことができる。
【０１１５】
このようにして、ｒ_i ^'a，ｒ_i ^'bを求めた後、ステップ３５４で新しい設計変数の並びである設計変数ベクトルＶｒ^'a，ｒ_i ^'bは以下のように求められる。
Ｖｒ’^a ＝（ｒ₁ ^a 、ｒ₂ ^a 、・・・ｒ_i ^'a、ｒ_i+1 ^b 、・・・、ｒ_n-1 ^b ）
Ｖｒ’^b ＝（ｒ₁ ^b 、ｒ₂ ^b 、・・・ｒ_i ^'b、ｒ_i+1 ^a 、・・・、ｒ_n-1 ^a ）
【０１１６】
なお、上記例では交叉場所ｉは１ヶ所であるが、この他に遺伝的アルゴリズム（北野 宏明 編）に示されているような、複数点交叉または一様交叉等を用いてもよい。
【０１１７】
このような交叉によって新規な２個のピッチ配列を生成した後、図１８のステップ３１６では、使用者が予め入力した確率Ｓで、突然変異させるか否かを決定する。この突然変異は、後述するように、設計変数の一部を微小に変更することをいい、最適な設計変数となりうる母集団に当該ピッチ配列を含む確度を高くするためである。ステップ３１６で、否定判定で突然変異させない場合には、ステップ３１８では現在の２個のピッチ配列のまま、次のステップ３２２へ進む。肯定判定で突然変異させる場合には、次のステップ３２０で以下のように突然変異処理を行う。
【０１１８】
この突然変異は、図２２に示す突然変異ルーチンによって行われる。先ず、ステップ３５６では乱数を生成し、乱数によって突然変異の場所ｉを決定する。次に、ステップ３５８において、新しい設計変数ｒ_i ’を乱数を用いて与えられたピッチ比の中の整数に変更する。このようにして、設計変数ｒ_i ’を求めた後、ステップ３６０で求められる、新しい設計変数の並びである設計変数ベクトルＶｒ’は以下のようになる。
【０１１９】
Ｖｒ’＝（ｒ₁ 、ｒ₂ 、・・・ｒ_i ’、ｒ_i+1 、・・・、ｒ_n-1 ）
このようにして、新たに生成された２個のピッチ配列について、目的関数の値と制約条件の値を図１８のステップ３２２で演算する。次のステップ３２４では、得られた目的関数の値と制約条件の値から前記と同様に式（９）を用いて適応関数を演算する。
【０１２０】
次のステップ３２６では、上記２個のピッチ配列を保存する。次のステップ３２８では、ステップ３２６で保存したピッチ配列の数が、Ｎ個に達したか否かを判断し、Ｎ個に達していない場合は、Ｎ個になるまでステップ３０８からステップ３２８を繰り返し実行する。一方、ピッチ配列の数がＮ個に達した場合には、ステップ３３０で収束判定をし、収束していない場合には、Ｎ個のピッチ配列をステップ３２６で保存されたピッチ配列に更新し、ステップ３０８からステップ３３０を繰り返し実行する。一方、ステップ３３０で収束したと判断された場合には、Ｎ個のピッチ配列の中で制約条件を略満たしながら目的関数の値が最小となるピッチ配列の設計変数の値をもって制約条件を略満たしながら目的関数を最大にする設計変数の値とし、ステップ３３２においてこの設計変数の値を用いてピッチ配列を決定する。
【０１２１】
なお、ステップ３３０の収束判定は以下の条件のいずれかを満足したら収束とみなす。
【０１２２】
１）世代数がＭ個に達した
２）一番目的関数の値が大きい線列の数が全体のｑ％以上になった
３）最大の目的関数の値が、続くｐ回の世代で更新されない。
【０１２３】
但し、Ｍ、ｑ、ｐは使用者が予め入力しておく。
【０１２４】
以上、本発明の実施例について説明したが、本発明の実施例には特許請求の範囲に記載した要件以外に、次のような各種の技術事項の実施態様を有するものである。
【０１２５】
前記請求項１のタイヤのピッチ配列決定方法において、前記ステップ（ａ）では、複数個のピッチ配列基本モデルからなる選択対象集団を定め、該選択対象集団の各ピッチ配列基本モデルについて、前記目的関数、前記設計変数、及び前記制約条件を定めると共に、前記目的関数及び前記制約条件から評価できる適応関数を定め、前記ステップ（ｂ）では、適応関数に基づいて前記選択対象集団から２つのピッチ配列基本モデルを選択し、所定の確率で各ピッチ配列基本モデルの設計変数を交叉させて新規のピッチ配列モデルを生成すること及び少なくとも一方のピッチ配列基本モデルの設計変数の一部を変更させて新規のピッチ配列モデルを生成することの少なくとも一方を行い、設計変数を変化させたピッチ配列モデルの目的関数、制約条件及び適応関数を求めて該ピッチ配列モデル及び設計変数を変化させなかったピッチ配列モデルを保存しかつ保存したピッチ配列モデルが所定数になるまで繰り返し、保存した所定数のピッチ配列モデルからなる新規集団が所定の収束条件を満たすか否かを判断し、収束条件を満たさないときには該新規集団を前記選択対象集団として該選択対象集団が所定の収束条件を満たすまで繰り返すと共に、該所定の収束条件を満たしたときに保存した所定数のピッチ配列モデルのなかで制約条件を考慮しながら目的関数の最適値を与える設計変数の値を求める。
【０１２６】
なお、前記初期配列は、ピッチの大きさが段階状に変化するように順にピッチが並べられると共に各階位に含まれるピッチの数が予め定められ、前記ステップ（ｂ）では異なる階位間で該階位に含まれるピッチの数を変化させ、前記ステップ（ｃ）では目的関数の最適値を与える各階位が含むピッチの数に基づいてタイヤのピッチ配列を求めることができる。
【０１２７】
上記の実施態様によれば、具体的に、前記ステップ（ａ）では、複数個のピッチ配列からなる選択対象集団を定め、該選択対象集団の各ピッチ配列について、タイヤ性能評価用物理量を表す目的関数、ピッチ配列を決定する設計変数、隣り合うピッチ長さの比、最大ピッチ長と最小ピッチ長の比、各ピッチ長に属するピッチの数、連続する同一ピッチ長の数及び性能評価用物理量の少なくとも１つを制約する制約条件、及び目的関数及び制約条件から評価できる適応関数を定め、前記ステップ（ｂ）では、適応関数に基づいて前記選択対象集団から２つのピッチ配列を選択し、所定の確率で各ピッチ配列の設計変数を交叉させて新規のピッチ配列を生成すること及び少なくとも一方のピッチ配列の設計変数の一部を変更（突然変異）させて新規のピッチ配列を生成することの少なくとも一方を行い、設計変数を変化させたピッチ配列の目的関数、制約条件及び適応関数を求めて該ピッチ配列及び設計変数を変化させなかったピッチ配列を保存しかつ保存したピッチ配列が所定数になるまで繰り返し、保存した所定数のピッチ配列からなる新規集団が所定の収束条件を満たすか否かを判断し、収束条件を満たさないときには該新規集団を前記選択対象集団として該選択対象集団が所定の収束条件を満たすまで繰り返すと共に、該所定の収束条件を満たしたときに保存した所定数のピッチ配列のなかで制約条件を考慮しながら目的関数の最適値を与える設計変数の値を求める。
【０１２８】
このステップ（ｂ）では、設計変数を変化させたピッチ配列について、設計変数の単位変化量に対する目的関数の変化量の割合である目的関数の感度及び設計変数の単位変化量に対する制約条件の変化量の割合である制約条件の感度に基づいて制約条件を考慮しながら目的関数の最適値を与える設計変数の変化量を予測すると共に、設計変数を予測量に相当する量変化させたときの目的関数の値及び設計変数を予測量に相当する量変化させたときの制約条件の値を演算し、目的関数の値及び制約条件の値から適応関数を求めて該ピッチ配列及び設計変数を変化させなかったピッチ配列を保存しかつ保存したピッチ配列が所定数になるまで繰り返すことができる。
【０１２９】
上記のステップ（ｂ）では、設計変数の単位変化量に対する目的関数の変化量の割合である目的関数の感度及び設計変数の単位変化量に対する制約条件の変化量の割合である制約条件の感度に基づいて制約条件を考慮しながら目的関数の最適値を与える設計変数の変化量を予測すると共に、設計変数を予測量に相当する量変化させたときの目的関数の値及び設計変数を予測量に相当する量変化させたときの制約条件の値を演算し、予測値と演算値とに基づいて、制約条件を考慮しながら目的関数の最適値を与える設計変数の値を求めることができる。
【０１３０】
また、設計変数は、ピッチ配列を表す関数とすることができる。
設計変数としてピッチ配列を表す関数を定めたときには、ステップ（ｂ）で設計変数を変化させたときにピッチ長が所定範囲になるように制約条件を定めてステップ（ｂ）を実行することにより、制約条件を考慮しながら目的関数の最適値を与える設計変数の値を求めればよい。
【０１３１】
また、ピッチの大きさが段階状に変化するように順にピッチが並べられると共に各階位に含まれるピッチの数が予め定められた初期配列毎に、ステップ（ａ）ではタイヤの各ピッチから発生する騒音パルスのモデル、タイヤ騒音性能評価用物理量を表す目的関数を定め、ステップ（ｂ）では異なる階位間で該階位に含まれるピッチの数を変化させ、ステップ（ｃ）では目的関数の最適値を与える各階位が含むピッチの数に基づいてタイヤのピッチ配列を求める、各ステップを繰り返して、複数の初期配列に対応した複数のピッチ配列を求め、求められた複数のピッチ配列から目的関数の最適値が最適となるピッチ配列を選択することもできる。
【０１３２】
また、トレッドに形成されるピッチは、規則性を有する方が外観的に見栄えが良い。そこで、前記ステップ（ａ）では、タイヤの各ピッチから発生する騒音パルスのモデル、及びタイヤ騒音評価用物理量を表す目的関数を定める。このタイヤの騒音パルスのモデルには、路面とタイヤのピッチから発生する音のレベルとピッチ長等を対応させたモデルを適用できる。
【０１３３】
次のステップ（ｂ）では、異なる階位間で該階位に含まれるピッチの数を変化させる。例えば、隣接する階位間で一方のピッチの数を増加させると共に他方のピッチの数を減少させることによってピッチの数を変更する。この場合、ピッチ配列中に含まれるピッチの総数は変化しない。
【０１３４】
そして、ステップ（ｃ）では、目的関数の最適値を与える各階位が含むピッチの数に基づいてタイヤの騒音パルスのモデル等を変更することによりピッチ配列を求める。
【０１３５】
この各ステップを、ピッチの大きさが段階状に変化するように順にピッチが並べられると共に各階位に含まれるピッチの数が予め定められた初期配列毎に、例えば各々の階位に含まれるピッチの数が設定されかつ小ピッチから大ピッチまたは大ピッチから小ピッチに大きさが段階状に変化するように順にピッチを並べたタイヤのピッチ配列の初期配列毎に繰り返す。これによって、複数の初期配列に対応した複数のピッチ配列が求められる。この求められた複数のピッチ配列から目的関数の最適値が最適となるピッチ配列を選択することによって複数ある最適なピッチ配列から更に最適なタイヤのピッチ配列を決定できる。この決定されたピッチ配列に基づいてタイヤを設計することにより、外観的な美観を保持しつつ静寂なタイヤを提供することができる。
【０１３６】
【発明の効果】
以上説明したように本発明によれば、制約条件を考慮し音質に対応する目的関数の最適値を与える設計変数を求め、この設計変数からピッチ配列等を決定してタイヤを設計しているので、ベストモードのタイヤ設計を行うことができる、という効果が得られる。
【０１３７】
本発明の決定方法に基づいて決定されたピッチ配列及びピッチ比からタイヤを設計・開発した場合、従来の思考錯誤を基本とした設計・開発とことなり、コンピュータ演算を主体にしてベストモードの設計から設計されたタイヤの騒音性能評価までが、ある程度可能となり、著しい効率化を達成でき、開発にかかるコストが削減可能となる。
【図面の簡単な説明】
【図１】本発明の実施の形態に使用されるパーソナルコンピュータの概略図である。
【図２】実車計器音質評価法の概略構成を示すブロック図である。
【図３】タイヤを車両に装着し走行させたときの音の周波数特性を示し、（１）は左耳の近傍位置、（２）は右耳の近傍位置の結果を示したものである。
【図４】フィ−リング評点と、音圧レベル及び音響心理パラメータとの対応関係を示す線図である。
【図５】タイヤのピッチ配列を音化するためのパルス列を説明するための説明図である。
【図６】トナリティを目的関数としたときの最適化を説明するための線図である。
【図７】タイヤ１回転のピッチ配列に対応された区分スペクトルを説明するための線図である。
【図８】本発明の第１実施の形態の処理ルーチンを示す流れ図である。
【図９】図８のステップ１０６のピッチ配列の最適化ルーチンを示す流れ図である。
【図１０】図８のステップ１１０のピッチ比の最適化ルーチンを示す流れ図である。
【図１１】フィ−リング評点と演算値との対応関係を示す線図であり、（１）は演算による推定評点、（２）はトナリティ、（３）はフラクチュエ−ション・ストレングスの対応関係を示している。
【図１２】音圧レベルで最適化したピッチ配列及び第１実施の形態の最適化で定まるピッチ配列の、音響心理学的な感覚尺度の関係を示す線図であり、（１）はトナリティ、（２）はフラクチュエ−ション・ストレングスの関係を示している。
【図１３】本発明の第２実施の形態の処理ルーチンを示す流れ図である。
【図１４】図１３のステップ２０８のピッチ配列の最適化ルーチンを示す流れ図である。
【図１５】山型ピッチ配列を示すイメージ図である。
【図１６】山型ピッチ配列を最適化する過程を説明するためのイメージ図である。
【図１７】山型ピッチ配列を最適化する過程を説明するための他の例を示すイメージ図である。
【図１８】本発明の第３実施の形態の処理ルーチンを示す流れ図である。
【図１９】交叉処理ルーチンを示す流れ図である。
【図２０】交叉処理される過程の山型ピッチ配列を示すイメージ図であり、（ａ）はピッチ配列ａを示し、（ｂ）はピッチ配列ａ，ｂを親とし交叉後のピッチ配列を示し、（ｃ）はピッチ配列ｂを示し、（ｄ）はピッチ配列ａ，ｂを親とし交叉後のピッチ配列を示す。
【図２１】図２０と異なる山型ピッチ配列について、交叉処理される過程の山型ピッチ配列を示すイメージ図である。
【図２２】突然変異処理ルーチンを示す流れ図である。
【符号の説明】
１０ キーボード
１２ コンピュータ本体
１４ ＣＲＴ[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a tire pitch arrangement determining method, and more particularly to a tire pitch arrangement determining method for determining a tire pitch arrangement that improves tire noise performance.
[0002]
[Prior art]
In recent years, there has been a steady increase in the recognition of safe and relatively quiet automotive tires while driving on dry, wet and icy road conditions, and recently there is a theoretical approach to designing quiet tires. It ’s becoming a reality. The grooves and the like formed in the tire tread are designed by a plurality of variable pitch iterative design cycles in accordance with mathematically calculated standards.
[0003]
The tire is divided into a lateral groove and a circumferential groove that define the pitch and pitch arrangement on the tire circumference by manually carving into the tread based on the above design values or forming with a tire mold. A tread having a formed land portion (hereinafter referred to as a design element) is formed. Here, the pitch refers to the relative length of the design elements, and the pitch arrangement refers to the order of pitches used on the tire circumference.
[0004]
In JP-A-4-232105, each pitch can have various different lengths. However, for practical purposes, the pitch is limited to about nine types or less, and the specific length of a specific pitch in a certain pitch arrangement is the tire length. It is stated that it depends on the circumference. As a result, when the second tire travels at a lower speed than the first tire, the specific pitch arrangement of the designated relative length pitches on the first tire having a diameter larger than the diameter of the second tire is the same pitch. The same acoustic fingerprint as that of the second tire with the ratio of length and pitch (simulated with a characteristic string plot. The string plot is the number of times the tire makes one revolution when it makes sound. The amplitude, that is, the sound pressure <ordinate> is plotted against the harmonic number <abscissa> indicating whether it vibrates.
[0005]
Although the gist is also introduced in the above prior art, the design method of a specific tread was disclosed by Landers (US Pat. Nos. 4,327,792 and 4,474,223), and in addition to this, an approach for optimizing the tread design was proposed by Frechner. (U.S. Pat. No. 4,598,747). The Frickner approach cuts each protrusion and reduces the wavelength and amplitude of the cut relative to the dimensions of the protrusion to meet other criteria. In addition to these, a mathematical design method has been disclosed by Campo et al. (US Pat. No. 4,598,748).
[0006]
Validation of the approach is determined by physically forming a tire that is sized for the tread design to be tested and testing the tire. The tire test for “noise level and quality” is based on the experience of skilled trainees who have sensitive and trained ears when four (or less) test tires are mounted on an automobile wheel rim and exercised or run. It is common to specify by feeling.
[0007]
Also, as a convenient and reliable method for testing the noise generation characteristics of the tread design, there is a technique disclosed by Parker et al. That simulates actual tire tread noise when traveling on a road surface by a computer. (US Pat. No. 4,727,501).
[0008]
[Problems to be solved by the invention]
However, in order to obtain a quiet tire, it is not sufficient to specify tire noise based only on the value of the sound pressure, and a test of “noise level and quality” is necessary. However, because the “noise level and quality” test depends on the senses of experts, the evaluation varies, and it is not possible to feed back to the tread shape caused by the “noise level and quality”. Tire could not be obtained.
[0009]
An object of the present invention is to obtain a tire pitch arrangement determining method that efficiently and easily determines a tire pitch arrangement that improves tire noise performance in consideration of the above facts.
[0010]
[Means for Solving the Problems]
  In order to achieve the above-mentioned object, the present inventors have made various studies. As a result, when considering tire noise, it is considered that it is not sufficient to capture only the sound pressure, and the knowledge that sound quality should be taken into account. All the studies have been made and the present invention has been achieved. Specifically, the tire pitch arrangement determination method according to the first aspect of the present invention includes: (a) a pitch arrangement basic model representing a tire pitch arrangement;At least one of a predetermined sound component physical quantity in a predetermined band that represents the psychoacoustic conspicuousness and a predetermined low frequency fluctuation amount that represents the psychoacoustic feeling of acoustic psychologyAn objective function representing a physical quantity for evaluating tire noise performance corresponding to sound quality, a design variable for determining pitch arrangement, and a constraint condition for restricting the pitch arrangement; and (b) determining an optimum value of the objective function while considering the constraint condition. Each step includes a step of obtaining a value of a design variable to be given, and a step of obtaining a pitch array based on (c) a design variable that gives an optimum value of the objective function.
[0011]
  In step (a) of the invention of claim 1, a pitch arrangement basic model representing the pitch arrangement of tires,At least one of a predetermined sound component physical quantity in a predetermined band that represents the psychoacoustic conspicuousness and a predetermined low frequency fluctuation amount that represents the psychoacoustic feeling of acoustic psychologyAn objective function representing a physical quantity for tire noise evaluation corresponding to sound quality, a design variable for determining a pitch arrangement, and a constraint condition for restricting the pitch arrangement are defined. As the tire pitch arrangement basic model, an arrangement model in which a predetermined number of tire pitches, that is, pitch length and pitch ratio, can be applied. In addition, as a pitch arrangement basic model, a pulse signal in which a predetermined rectangular waveform signal is associated with each pitch in order to obtain sound from a tire in which a predetermined number of pitches are arranged (that is, the pitch arrangement is sounded). A sound pulse model can be applied. The tire sound pulse model can be determined by setting the pulse width in advance and changing the time between pulses according to the size of each pitch, that is, by changing the period. Since the sound generated from the tire may vary depending on the rotation speed of the tire, the rotation speed of the tire may be given as attribute information. The objective function for optimizing the arrangement model may not be consistent with the listener's sense only by a physical quantity such as the sound pressure level, that is, the sound component that the listener feels troublesome may remain. The listener feels the sound from the sound quality that is directly independent of the sound pressure level and the sound pressure level. Therefore, an objective function representing a physical quantity for tire noise evaluation corresponding to at least sound quality is used. Note that the sound pressure level may be further added to the objective function. As a design variable for determining the pitch arrangement, a pitch length, a function representing the pitch arrangement, or the like can be used. Constraint conditions that restrict the pitch arrangement include the pitch ratio of adjacent pitches, the maximum and minimum values of the pitch ratio, and the like. Note that the objective function, the design variable, and the constraint condition are not limited to the above example, and various ones can be determined according to the tire design purpose.
[0012]
In the next step (b), the value of the design variable that gives the optimum value of the objective function is obtained in consideration of the constraint conditions. As a result, the value of the design variable when the value of the objective function is optimal is obtained in consideration of the constraint conditions. In step (c), the pitch arrangement is obtained by changing the pitch arrangement basic model representing the tire pitch arrangement based on the design variable that gives the optimum value of the objective function.
[0013]
In the pitch arrangement thus obtained, the sound quality in accordance with the listener's sense is optimally determined, and a quiet tire can be designed based on this pitch arrangement.
[0014]
According to a second aspect of the present invention, there is provided the tire pitch arrangement determining method according to the first aspect, wherein each of a plurality of predetermined initial arrangements is determined by the tire pitch arrangement determining method according to the first aspect. The pitch arrangement corresponding to the initial arrangement is obtained, and the pitch arrangement that optimizes the optimum value of the objective function is selected from the obtained pitch arrangements corresponding to the plurality of initial arrangements.
[0015]
According to the invention of claim 2, by repeating the above steps for each predetermined initial arrangement, a plurality of pitch arrangements corresponding to the plurality of initial arrangements are obtained, and the objective function is determined from the obtained plurality of pitch arrangements. The optimum tire pitch arrangement is selected from a plurality of optimum pitch arrangements by selecting the pitch arrangement that optimizes the optimum value, for example, the psychological psychological conspicuousness and the groaning feeling that are objective functions are minimized. Can be determined. Based on this determined pitch arrangement, a quiet tire can be designed.
[0016]
A third aspect of the present invention is the tire pitch arrangement determining method according to the first or second aspect, wherein in the step (b), the ratio of the change amount of the objective function to the unit change amount of the design variable. Based on the sensitivity of the objective function and the sensitivity of the constraint condition, which is the ratio of the change amount of the constraint condition to the unit change amount of the design variable, while predicting the change amount of the design variable that gives the optimum value of the objective function while considering the constraint condition The value of the objective function when the design variable is changed by an amount corresponding to the predicted amount and the value of the constraint condition when the design variable is changed by the amount corresponding to the predicted amount are calculated. Based on the predicted value and the calculated value Thus, the value of the design variable that gives the optimum value of the objective function is obtained while considering the constraint conditions.
[0017]
According to the invention of claim 3, in the step (b), the value of the design variable that gives the optimum value of the objective function while satisfying the constraint condition is obtained. In this case, the constraint is based on the sensitivity of the objective function, which is the ratio of the change amount of the objective function to the unit change amount of the design variable, and the sensitivity of the constraint condition, which is the ratio of the change amount of the constraint condition to the unit change amount of the design variable. The amount of change in the design variable that gives the optimum value of the objective function while satisfying the conditions is predicted, and the value of the objective function and the amount of change in the design variable that correspond to the prediction amount when the design variable is changed by the amount equivalent to the prediction amount It is effective to calculate the value of the constraint condition when it is set, and to obtain the value of the design variable that gives the optimum value of the objective function while satisfying the constraint condition based on the predicted value and the calculated value. As a result, the value of the design variable when the constraint condition is satisfied and the value of the objective function is optimal is obtained.
[0018]
When a function representing a pitch arrangement is defined as a design variable, the constraint condition is determined so that the pitch length is within a predetermined range when the design variable is changed, and step (b) is executed, thereby satisfying the constraint condition. If the value of the design variable that gives the optimum value of the objective function is obtained, the pitch length included in the pitch array is within a predetermined range, and there is no extremely large pitch or extremely small pitch.
[0019]
  In the tire pitch arrangement determining method of the present invention,Step (a)InIn addition, as a physical quantity for tire noise performance evaluation corresponding to the sound quality, a sound component physical quantity in a predetermined band representing the psychoacoustic conspicuousness, and a predetermined low frequency representing a psychoacoustic beat feeling It is characterized in that at least one of the fluctuation amounts is determined as an objective function.
[0020]
As a result of various investigations, the present inventors have focused on applying a sensory scale used in psychoacoustics to a special field called tires, and tried various investigations to determine the tire pitch arrangement method. Established as.
[0021]
  That is, a psychoacoustic parameter can be used as the objective function representing the physical quantity for tire noise evaluation corresponding to the sound quality, and the psychoacoustic parameter includes a sensory scale representing the loudness, Sensory scale that expresses sharpness, sensory scale that expresses roughness of sound,EyeThere is a sensory scale that represents ease of standing and a sensory scale that represents a feeling of beating. The sensory scale representing the loudness corresponds to the sound pressure level, and the sensory scale representing the sharpness of the sound is obtained from the magnitude of the ratio including the loudness component (the sensory scale representing the loudness) on the high frequency side. be able to. The sensory scale representing the roughness of the sound can be obtained from a value obtained by weighting and adding the modulation degree in the critical band with a predetermined band as a critical band among a plurality of predetermined bands. A sensory scale representing conspicuousness can be obtained from the ratio of pure tone components and narrowband noise components contained in the sound. In addition, pure sounds and narrow-band noise may be canceled depending on the volume of the sound. Therefore, when seeking for conspicuousness, the cancellation of pure tones and narrow-band noise (masking effect) should be considered according to the volume of the sound. Is preferred. A sensation scale that expresses a feeling of roaring can be obtained from the amount of fluctuation in which the vibration amplitude of a predetermined frequency that is determined in advance fluctuates. This feeling of beating appears more prominently as the fluctuation amplitude of the loudness is larger.
[0022]
The pitch arrangement obtained in this way is optimally determined for the sound quality in line with the listener's senses, that is, psychoacoustic conspicuousness and beating, etc. Based on this pitch arrangement, a quiet tire is designed. can do.
[0023]
  The invention according to claim 4 is any one of claims 1 to 3.The tire pitch arrangement determining method according to claim 1, wherein a physical quantity representing a sound pressure level is further determined as the objective function.
[0024]
In the above, the tire noise evaluation physical quantity corresponding to the sound quality, that is, the psychoacoustic parameter, is used as the objective function, but in order to obtain a quiet tire, the tire noise is specified by the magnitude of the sound pressure. Considering evaluation by value, it is more effective. For example, as a physical quantity for tire noise performance evaluation corresponding to sound quality, a predetermined low-frequency sound component physical quantity representing easiness of psychoacoustics, and a predetermined low frequency representing psychoacoustic beating At least one of the fluctuation amount and the peak of the sound pressure level are minimized, that is, the maximum value of the sound pressure level of the generated noise is minimized. This makes it possible to determine the optimal pitch arrangement with white noise that minimizes the variation in the amplitude value of the generated noise, while suppressing the conspicuousness of the timbre of the generated noise and the feeling of humming in consideration of the sound quality. Tires can be designed.
[0025]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. FIG. 1 shows an outline of a personal computer for carrying out the tire pitch arrangement determining method of the present invention. The personal computer includes a keyboard 10 for inputting data and the like, a computer main body 12 that calculates design variables that satisfy constraints and optimize, for example, maximize or minimize an objective function according to a program stored in advance. It is composed of a CRT 14 that displays the calculation results of the main body 12. The computer main body 12 is composed of a microcomputer composed of a CPU, ROM, and RAM (not shown).
[0026]
A sound generator 16 is connected to the computer main body 12, and speakers 18 </ b> A and 18 </ b> B are connected to the sound generator 16. The sound generator 16 converts the pitch array into sound information, for example, sound pressure level / frequency characteristics, in accordance with a pulse train composed of a series of rectangular waves corresponding to the pitch array output from the computer main body 12, and the sound information. Is output to the speakers 18A and 18B. Between the computer main body 12 and the sound generator 16, exchange of a pulse train generated by the computer main body 12 and information on the sound of the pulse train, for example, sound information such as sound pressure level / frequency characteristics, etc., are exchanged. . As an example of the sound generator 16, BAS II. Manufactured by HEAD acoustics Co., Ltd. is used. 3E (No. 42516103).
[0027]
In the first embodiment, in order to reduce noise during traveling, that is, to improve quietness, an optimum pitch arrangement and pitch length ratio (hereinafter referred to as pitch ratio) is determined in consideration of sound quality. Is. This embodiment will be described based on a random pitch arrangement having no regularity in the pitch arrangement.
[0028]
As a result of various studies on the pitch arrangement of the tire, the inventor has found that the badness of pattern noise generated from a tire having a predetermined pitch arrangement is due to the sound quality, for example, the sound noise rather than the sound pressure level. We obtained knowledge that things related to conspicuousness and groaning are largely attributed, and tried all kinds of studies, leading to the introduction of sensory scales used in psychoacoustics.
[0029]
Further, the present inventor has found that the sound quality of the sound generated from the tire is related to the arrangement of the primary region (number of pitches × frequency) of the pattern pitch, and optimization of the objective function based on the spectrum of all the arrangement numbers ( For example, in the flattening of the spectrum and minimization of the sound pressure level, it has been found that it is difficult to reduce the poor sound quality associated with the arrangement on the time axis.
[0030]
Next, a psychoacoustic sensory scale for obtaining a tire with improved quietness in consideration of sound quality, that is, a psychoacoustic parameter will be described. The psychoacoustic parameters include a sensation scale (loudness) that represents the loudness of the sound, a sensation scale (sharpness) that represents the sharpness of the sound, a sensation scale (roughness) that represents the roughness of the sound, and a sensation scale that represents conspicuousness (tonality) ), And a sensory scale (fractation strength) that expresses a sense of roar. Although the loudness corresponds to the sound pressure level, it is closer to the actual sense than the sound pressure level dB (A), and is obtained in consideration of the sound masking effect, and is standardized by ISO532B. The sharpness can be obtained from the size of the ratio including the loudness component on the high frequency side. Further, the roughness can be obtained from a value obtained by weighting and adding the modulation degree in the critical band with a predetermined band among a plurality of predetermined bands as a critical band. Tonality can be obtained from the ratio of pure tone components and narrowband noise components contained in the sound. In addition, pure sounds and narrow-band noise may be canceled depending on the volume of the sound. Therefore, when seeking for conspicuousness, the cancellation of pure tones and narrow-band noise (masking effect) should be considered according to the volume of the sound. Is preferred. The fracture strength can be obtained from the amount of fluctuation in which the vibration amplitude of a predetermined frequency is changed. This feeling of beating appears more prominently as the fluctuation amplitude of the loudness is larger.
[0031]
Each of these psychoacoustic parameters can be obtained from the following Table 1.
As described above, the tonality K can be obtained from the ratio of pure tone components and narrowband noise components contained in the sound. If the obtained ratio is calculated in consideration of the masking effect of loudness, the tonality K is displayed on the spectrum. -There are moss. Therefore, in the equation shown in Table 1 below, for the peaks existing on the spectrum, the tonality K is set such that the smaller the peak (bandwidth) width (weight w1) and the closer the frequency to 700 Hz (weight w2). ), The larger the peak level (weight w1), the larger factor, and the product of the S / N ratio factor for these noises as seen in loudness. Note that the conspicuousness of the pitch primary corresponds to signal extraction by adding a bandpass filter of 400 to 500 Hz.
[0032]
In addition, the fractionation strength can be obtained from the amount of fluctuation in which the vibration amplitude of a predetermined frequency varies in advance, but in the expression shown in Table 1 below, the fluctuation frequency increases as the loudness fluctuation amplitude increases. It becomes larger as it gets closer to 4 Hz.
[0033]
[Table 1]

[0034]
However, the symbols in the above table represent the following.

[0035]
The psychoacoustic parameters are also described in E.Zwicker's translation by Yukiko Yamada “Psychoacoustics”. In the following description, the mathematical formulas shown in Table 1 are generically used as the formula (1).
[0036]
The inventor conducted a comparative experiment between the psychoacoustic parameters and the conventional sound pressure level evaluation by the actual vehicle instrument sound quality evaluation method, and obtained the following results.
[0037]
As shown in FIG. 2, the measurement by the actual vehicle instrument sound quality evaluation method was performed by attaching a speedometer 28 for detecting the traveling speed of the vehicle 20 to the rear portion of the vehicle 20 including the tire 30. An occupant 22 is seated in the vehicle 20, and microphones 24 and 26 are attached to positions near the left and right ears on the head of the seated occupant 22. Each of these microphones 24 and 26 can acquire sound that the occupant 22 should listen to from the left and right ears. In the above measurement, the measurement was performed using a dummy head (a head with a microphone) in which a microphone was embedded in the left and right ears of a dummy doll simulated by the occupant 22.
[0038]
Here, the case of coasting (D range) in a predetermined speed range (38 to 60 km / h) on the road surface of the new special road P / N was measured.
[0039]
FIG. 3 shows the frequency characteristics with respect to the sound pressure level of the sound obtained from the microphones 24 and 26 when the tires T1 and T2 are mounted on the vehicle and run, and FIG. FIG. 3 (2) shows the detection result by the microphone in the vicinity of the right ear. FIG. 3 (2) shows the detection result by the microphone in the vicinity of the left ear. As can be understood from FIG. 3, there is no difference from the sound pressure level for each of the tires T1 and T2.
[0040]
Next, a plurality of different tires 30 are mounted on the vehicle 20, and the operator performs a filling evaluation on each tire, and the psychoacoustic parameters and conventional sounds are obtained using sounds obtained from the microphones 24 and 26. The pressure level was determined.
[0041]
FIG. 4 plots the results of a plurality of different tires in each coordinate system with the feeling score value on the vertical axis and the sound pressure level and psychoacoustic parameter values on the horizontal axis. In the figure, the value of r indicates the correlation coefficient. As can be understood from FIG. 4, in terms of sound quality, no correlation was observed between each value and the feeling score of the loudness, sharpness, and roughness, and the plots were dispersed. On the other hand, it is understood that each of the tonality K and the fractionation strength F has a correlation between the value of the psychoacoustic parameter and the filling score.
[0042]
From the above results, the present inventor has found that the psychoacoustic parameter is based on the fact that the sound quality related to the ease of sound conspicuousness and the feeling of beating is largely attributable to reducing noise during driving, that is, improving quietness. Of these, attention was paid to tonality K and fractionation strength F, and these two psychoacoustic parameters were set as objective functions, and the pitch arrangement of tires was optimized.
[0043]
FIG. 8 shows a processing routine of the program according to the first embodiment. In steps 100 to 104, a pitch arrangement basic model for obtaining the pitch arrangement formed on the tire tread numerically and analytically is obtained. Here, modeling refers to creating a pitch array based on pseudo-random numbers and digitizing it into an input data format for a computer program.
[0044]
Specifically, in step 100, the following values that are necessary or empirically obtained when determining a quiet pitch arrangement are input as set values.
[0045]
[Setting value]

[0046]
In addition, the rotation speed of the tire (e.g., the rotation speed obtained from the vehicle speed) when evaluating the quietness, and the pulse width (details will be described later) of the rectangular wave for sounding the pitch arrangement are set as the set values. can do.
[0047]
In step 102, the number M of pitch ratios (M is a natural number, in this embodiment, any one of 2 to 9) is determined. In step 104, the number of types of pitch ratios included in the pitch array is M. A plurality of pitch arrays V in which the total number of pitches is N is generated by a pseudo-random algorithm, and one pitch array satisfying the constraint condition regarding the ratio of adjacent pitches is selected as an initial value from the plurality of pitch arrays V. .
[0048]
That is, by making the M pitch ratios correspond to natural numbers from 1 to 9, and generating an N-digit array by a pseudo-random algorithm, the pitch ratio is expressed corresponding to each digit of the natural number that is the array value. A pitch array V is generated. Next, one pitch arrangement that satisfies the constraint on the ratio of adjacent pitches is selected as an initial value. In this embodiment, the number M of pitch ratios is assumed to be processed in the order of M = 2, 3,.
[0049]
Here, the details of the objective function will be described. In the present embodiment, in order to simplify the calculation, the tonality K, which is the psychoacoustic parameter used as the objective function, and the fractionation strength F are approximated as follows.
[0050]
First, in order to obtain sound generated by the pitch arrangement formed on the tire, that is, to synthesize the pitch arrangement, the pitch arrangement V is used as arrangement data, and the arrangement data is converted into a pulse train on the time axis. It can be replaced by time frequency analysis. That is, the pitch arrangement is converted into a format that can be analyzed for sound. As described above, in this embodiment, the array data which is the pitch array is replaced with the pulse train on the time axis in order to make the pitch array into a sound. As an example, Table 2 shows tires A to C in which a pitch ratio of 3 or 5 is made to correspond to any natural number from 1 to 9 to obtain a pitch arrangement.
[0051]
[Table 2]

[0052]
As described above, after generating the pitch array V expressed corresponding to each digit of the natural number whose pitch ratio is the array value, the pitch array is converted to a pulse train composed of continuous rectangular waves. As shown in FIG. 5, the pulse train is obtained by extending a period of a rectangular wave having a predetermined pulse width according to a pitch ratio. The example of FIG. 5 shows a pulse train of “2, 1, 3” as part of the pitch arrangement, and has a pulse width Pw and time (period) corresponding to the arrangement value “2” of the pitch ratio. Ta, a pulse train having a pulse width Pw corresponding to the pitch ratio array value “1” and time (period) tb and a pulse width Pw corresponding to the pitch ratio array value “3” and time (period) tc Some of them are shown. Note that the times (cycles) ta, tb, and tc correspond to the pitch ratio and are long and short times, and in the example of FIG. 5, tb> ta> tc. The pulse width Pw is determined in advance by experiment, and is set to 500 μs in this embodiment. The pulse train set in this way can be sounded by time frequency analysis or the like.
[0053]
Next, in order to simplify the calculation of tonality K and fractionation strength F, the concept of a piecewise spectrum was introduced. As shown in FIG. 7, this segmented spectrum is obtained by dividing the basic width by the pitch arrangement of one rotation of the tire and dividing the basic width into a predetermined number (in this embodiment, three divisions). Are defined by extracting a predetermined number of times by overlapping a part of the basic width within the basic width by a predetermined shift amount.
[0054]
Since the tonality K mainly represents the conspicuousness of the sound, this segmented spectrum is used to correspond to the deviation in each segmented spectrum. In the present embodiment, 1/3 of the basic width is set as the segment width, and the shift amount is set to 75%. As a result, 12 segmented spectra can be obtained. Note that Hanning is set for the window function at this time.
[0055]
Moreover, the fractionation strength F represents a feeling of beating, and uses the segmented spectrum to correspond to the energy difference between the individual segmented spectra. In the present embodiment, as in the case of tonality K, 1/3 of the basic width is set as the segment width. At the same time, the shift amount is set to 96%, and 72 segmented spectra are obtained.
[0056]
Therefore, as shown in the following equation (2), the optimization based on the objective function is performed with respect to the tonality K, the deviation in the segmented spectrum, that is, the maximum value regarding the sound pressure level in each segmented spectrum that is sounded for each segmented spectrum. This corresponds to minimizing the variation in level difference (amplitude) between the minimum value and the minimum value (see FIG. 6).
[0057]
Min {Dmin} (2)
However, Min: a function for obtaining the minimum value in {}
Dmin: Level difference between the maximum sound pressure level and the minimum sound pressure level in the segmented spectrum
[0058]
Further, as to the fractionation strength F, as shown in the following equation (3), it corresponds to minimizing the energy difference between the divided spectra, that is, the level difference of the sound pressure level generated for each divided spectrum. To do.
[0059]
Min {Emax-Emin} (3)
However, Emax: Maximum value of energy (sound pressure level) in the segmented spectrum
Emin: Minimum value of energy (sound pressure level) in the segmented spectrum
[0060]
In the next step 106, the pitch array V selected as the initial value by the optimization routine shown in FIG. 9 is optimized. Next, at step 132, the design variable P_iThe initial value OBJo of the objective function OBJ and the initial value Go of the constraint condition G are calculated. With respect to the initial value OBJo of the objective function OBJ, the tonality K is for obtaining a deviation in the segmented spectrum, and the fractionation strength F is for obtaining an energy difference between the segmented spectra. The deviation in the segmented spectrum and the energy difference between the segmented spectra may be obtained from data from the sounding device or may be obtained in the computer main body.
[0061]
In the next step 134, the design variable P is used to change the basic model._iEach with ΔP_iChange it step by step. In step 136, the design variable is ΔP._iThe pitch arrangement after the change is determined.
[0062]
In step 138, the design variable is set to ΔP for the pitch arrangement obtained in step 136._iThe value of the objective function OBJ (P_i+ ΔP_i), G (P_i+ ΔP_i), And in step 140, the sensitivity ΔOBJ / ΔP of the objective function, which is the ratio of the change amount of the objective function to the unit change amount of the design variable, according to the following equation (4)_iAnd the sensitivity ΔG of the constraint that is the ratio of the variation of the constraint to the unit variation of the design variable_i/ ΔP_iIs calculated for each design variable. The tonality K and the fractionation strength F, which are the values of the objective function, are obtained in the same manner as the calculation in step 132 above.
[0063]
[Expression 1]

[0064]
With this sensitivity, the design variable is ΔP_iIt is possible to predict how much the value of the objective function and the value of the constraint condition change when changed. Note that this sensitivity may be obtained analytically depending on the method used for tire noise modeling and the nature of the design variables, and in this case, the calculation in step 138 is not necessary.
[0065]
In the next step 142, using the initial value OBJo of the objective function, the initial value Go of the constraint condition, the initial value Po of the design variable, and the sensitivity, the value of the objective function is minimized while satisfying the constraint condition by mathematical programming. That is, the amount of change in the design variable that minimizes the values of the tonality K and the fractionation strength F is predicted. Using the predicted value of the design variable, in step 144, the pitch arrangement is determined by the same method as in step 136, and the objective function value is calculated. In step 146, the value of the objective function has converged by comparing the difference between the objective function value OBJ calculated in step 144 and the initial value OBJo of the objective function calculated in step 132 with a threshold value input in advance. If the value of the objective function has not converged, the value of the design variable obtained in step 142 is used as the initial value, and steps 132 to 146 are repeatedly executed. When it is determined that the value of the objective function has converged, the value of the design variable at this time is set as the value of the design variable that minimizes the objective function while satisfying the constraint condition. In step 148, the value of the design variable is used to Determine an optimized pitch array.
[0066]
In the next step 108, the pitch ratio of the pitch arrangement optimized as described above is normalized. That is, based on the number M of pitch ratios, an initial pitch ratio ri normalized according to the following formula (5) is obtained.
[0067]
[Expression 2]

[0068]
Where r_maxIs the ratio of the maximum pitch length, r_minIs the ratio of the minimum pitch length.
Next, according to the following formula (6), the optimized pitch length Pi is divided by the average value of the pitch lengths.
[0069]
[Equation 3]

[0070]
After replacing the optimized value APi divided by the average value with the nearest normalized pitch ratio, the pitch arrangement is re-expressed with the number M of pitch ratios.
[0071]
In the next step 110, each pitch ratio of the pitch arrangement represented by the number M of pitch ratios is optimized by the pitch ratio optimization routine shown in FIG. The optimization routine of FIG. 10 uses the first and last pitch ratio r₁, R_MThe pitch ratio r between the objective functions is minimized so that the value of₂~ R_M-1Optimize the value of. In step 160 of this optimization routine, the pitch ratio r₂~ R_M-1An increase / decrease value Δr for increasing / decreasing each of the values is calculated. In this embodiment, (r_M-R₁) / 10 is calculated as an increase / decrease value Δr. In the next step 162, the value OBJo of the initial objective function is calculated. In the next step 164, the pitch ratio r₂~ R_M-1Is selected, the pitch ratio ri selected in step 166 is increased or decreased, and a new objective function value OBJ is calculated in step 168. In step 170, the pitch ratio r₂~ R_M-1It is determined whether or not all the increases and decreases have been calculated (2 (M−2) times). If all have been calculated, in step 172, of the 2 (M−2) objective functions calculated in step 168. The objective function value that becomes the lowest is calculated. In the next step 174, the initial objective function value is compared with the lowest objective function value calculated in step 172. If the lowest objective function value is larger than the initial objective function value, it indicates that no further improvement is made. In step 178, the optimum pitch ratio r₁~ R_MIs output. On the other hand, if it is determined in step 174 that the minimum objective function value is smaller than the initial objective function value, the adjacent pitch ratios ri, ri are determined in step 176.₊₁It is determined whether or not the difference of (i = 1 to M−1) is smaller than a certain value (predetermined predetermined value) using the following equation (7). If it is smaller, the process proceeds to step 178 and the optimum pitch ratio r₁~ R_MIs output.
[0072]
[Expression 4]

[0073]
In the next step 112, it is determined whether or not 100 pitch arrays V have been generated, and steps 104 to 110 are repeated until 100 pitch arrays V are generated. When 100 pitch arrays V are generated, in step 114, the pitch array and the pitch ratio having the lowest objective function are selected.
[0074]
In the next step 116, it is determined whether or not the above processing has been completed for the number M of all pitch ratios. If the determination is negative, steps 102 to 114 are executed. On the other hand, when the optimization of the pitch ratio and pitch arrangement is completed for the number M of all pitch ratios, the process proceeds to step 118, and the objective function is the lowest from the pitch ratio and pitch arrangement optimized for each number of pitch ratios. That is, the pitch ratio and pitch arrangement that minimize the values of the tonality K and the fractional strength F are selected, and this routine is terminated.
[0075]
In this way, by determining the pitch ratio and pitch arrangement, the sound quality is considered from a plurality (100) of optimum pitch arrangements corresponding to the predetermined initial arrangement, that is, the timbre of generated noise is easily noticeable and An optimal pitch arrangement with suppressed feeling of beating can be selected, and a quiet tire can be designed accurately with few calculations.
[0076]
In this embodiment, the case of optimizing each of the tonality K and the fractionation strength F among the psychoacoustic parameters has been described. However, the parameter of either the tonality K or the fractionation strength F is optimized. May be. Further, at least one of the tonality K and the fractionation strength F and the peak of the sound pressure level may be minimized, that is, the maximum value of the sound pressure level of the generated noise may be minimized. In this way, considering the sound quality, the optimal pitch arrangement with white noise that minimizes the variation in the amplitude value of the generated noise is selected while suppressing the conspicuousness and humming of the generated noise timbre. It is possible to design a quiet tire with high accuracy and few calculations.
[0077]
Here, the inventor performed a filling test on various tires including tires in which the pitch arrangement was optimized using the psychoacoustic parameters as objective functions, and obtained the following results.
[0078]
In this filling test, hearing tests were conducted on 8 tires for 10 tires, with the criteria of the filling score corresponding to 5 (good), 3 (normal), and 1 (bad). Is. The results are shown in Table 3 below. The reference tire is a set of 10 tires that are considered average by all eight skilled workers.
[0079]
[Table 3]

[0080]
FIG. 11 (2) shows the correspondence between the average value of the filling scores of the ten tires and the tonality K. The tonality K is obtained from the segmented spectrum by converting the pitch arrangement into a pulse train as described above. FIG. 11 (3) shows the correspondence between the average value of the feeling scores of the ten tires and the fraction strength F. The fraction strength F is also obtained using the segmented spectrum in the same manner as described above.
[0081]
As understood from these figures, the average value of the filling score and the tonality K and the fraction strength F have a correlation. Therefore, multiple regression analysis was performed for each, and an estimation formula for obtaining the estimated score Y from the tonality K and the fraction strength F was obtained as shown in the following formula.
[0082]
Y = 4.75− (2.8 · K + 0.93 · F)
Y: Estimated score
K: Tonality value
F: Fracture strength value
[0083]
FIG. 11 (1) shows the correspondence between the average score of the 10 tires and the estimated score Y. These correspondences were highly correlated (correlation coefficient r = 0.916), and the rating score was accurately associated with the estimated score based on the tonality K and the fractional strength F considering the sound quality.
[0084]
FIG. 12 shows the tonality K for the tire defined by the pitch arrangement optimized by the conventional sound pressure level performed by the inventor and the tire defined by the pitch arrangement determined by the optimization according to the above embodiment. The experimental result (refer FIG. 12 (1)) which calculated | required and the experimental result (refer FIG. 12 (2)) which calculated | required the fraction strength F were shown. As understood from FIG. 12 (1), the value of tonality K is suppressed, and as understood from FIG. 12 (2), the value of fraction strength F is also suppressed. As a result, it is possible to determine a pitch arrangement with improved sound quality.
[0085]
Next, a description will be given of a second embodiment in which an optimum pitch arrangement and pitch ratio are determined based on a mountain arrangement in which the tire pitch arrangement is a mountain shape. Although the present embodiment will be described with reference to FIG. 13, the same reference numerals are given to portions corresponding to those in FIG. 8, and detailed description thereof will be omitted.
[0086]
As shown in FIG. 15, the pitch arrangement in which this pitch arrangement is a mountain shape (hereinafter referred to as a mountain shape pitch arrangement), when the number of pitch ratios is M, is changed from a small pitch to a large pitch and from a large pitch to a small pitch. A pitch arrangement that changes in order to the pitch. In addition, in the case of FIG. 15, the number of peaks is two in the case where one group of continuous large pitches in the peak-shaped pitch array is defined as one peak. In addition, the number of steps H when the pitch size in the mountain pitch arrangement changes can be expressed by the following formula (8).
[0087]
H = 2C + 2C. (M-2) = 2C. (M-1)-(8)
Where C is the number of peaks (2 in the case of FIG. 15)
M: Number of pitch ratios
In step 200, as described above, a setting value necessary or empirically obtained for determining a quiet tire is input, and in the next step 102, the number M of pitch ratios is set. In the present embodiment, since it is a mountain-shaped pitch arrangement, the restriction on the adjacent pitch ratio set in the case of the random pitch arrangement in the above embodiment is omitted.
[0088]
Here, the objective function OBJ, the constraint condition J, and the design variables are as follows.

[0089]
In the next step 202, the number C of peaks included in the tire circumference is set. In this embodiment, as the number C of peaks, values from 1 to 9 are set in order and the following is processed. In the next step 204, it is determined whether the number of steps H calculated from the number M of pitch ratios and the number C of peaks is smaller than the total number N of pitches based on the above equation (8). Proceed to step 206.
[0090]
In step 206, the number of pitches U included in each of 2 · C · (M−1) stairs is determined by a pseudorandom algorithm._j(J: 1 · 2 · C · (M−1)) is determined. That is, 2 · C · (M−1) stairs are made to correspond to natural numbers from 1 to 9, an array is generated by a pseudo-random algorithm, and each stairs is assigned to each digit of the natural number that is the array value. Number of pitches included U_jOne pitch array V in which is expressed is generated and set as an initial value. FIG. 15 shows the relationship between the pitch size and the number of pitches included in the stairs in the mountain pitch arrangement determined as described above, taking as an example the case where the number of peaks C is two. In the figure, the number with the underlined staircase is the number of pitches U included in the staircase_jIs shown.
[0091]
In the next step 208, the mountain-shaped pitch array selected as the initial value by the optimization routine shown in FIG. 14 is optimized. In step 232 of the optimization routine of FIG. 14, the initial value OBJo of the objective function OBJ determined for the mountain-shaped pitch array selected as the initial value is calculated. In the next step 234, the number of pitches is increased or decreased for any two step portions of the mountain-shaped pitch arrangement. For example, the number C of the peaks is 2, the number U of the pitches of the small pitch staircase portion 22 is 3, the number of pitches U of the medium pitch staircase portion 24 is 2, and the number of pitches of the large pitch staircase portion 26. When the U-shaped pitch arrangement with U = 3 is selected as the initial value (see FIG. 15), the number of pitches of the small-step staircase portion 22 is decreased by 1 as shown by the double underline in FIG. The number of pitches of the medium pitch step portion 24 is increased by one. In addition, an example in which the number of pitches of the staircase portion 24 having a large pitch is reduced by 1 and the number of pitches of the staircase portion 26 having a large pitch is reduced to 1 is indicated by a double underline in FIG.
[0092]
In step 236, the value of the objective function in the mountain pitch arrangement in which the number of pitches is increased or decreased is calculated. The above processing is repeated until the exchange of the pitch numbers between the staircase portions is completed for all the staircase portions (step 238), and the minimum of the values of the plurality of objective functions obtained in comparison with the initial value OBJo of the objective function OBJ is obtained. A chevron pitch array which is a value is selected in step 240. In step 242, it is determined whether or not the value of the objective function has converged by comparing with the initial value OBJo of the objective function OBJ. If not, the pitch array selected in step 240 in step 246 is initialized. And the above processing is executed until the value of the objective function converges. When the value of the objective function converges, in step 244, the mountain-shaped pitch arrangement at the time when the value of the objective function converges is determined as the optimum pitch arrangement.
[0093]
Next, as in the above embodiment, the first and last pitch ratio r₁, R_MThe pitch ratio r between the objective functions is minimized so that the value of₂~ R_M-1Is optimized (step 110, FIG. 10), whether or not 100 pitch arrays V have been generated is determined, and the pitch array and pitch ratio having the lowest objective function are selected from the 100 generated pitch arrays V (Steps 112 and 114).
[0094]
In the next step 210, it is determined whether or not the optimized pitch ratio and pitch arrangement have been calculated for each of the number of peaks C. If the determination is negative, the process returns to step 202, where the number of all peaks is determined. The above processing is repeated until the calculation of the pitch ratio and pitch arrangement optimized for C is completed.
[0095]
In the next step 116, it is determined whether or not the above processing has been completed for the number M of all pitch ratios. If the determination is negative, the process returns to step 102 and the pitch ratio and pitch arrangement of the number M of all pitch ratios are returned. The above process is repeated until the optimization is completed. In the next step 212, the pitch ratio and pitch arrangement having the lowest objective function are selected from the pitch ratio and pitch arrangement optimized for each number of pitch ratios including the number C of peaks, and this routine is terminated.
[0096]
As described above, in the present embodiment, a plurality of optimum pitch arrangements corresponding to each of the predetermined mountain-shaped pitch arrangements are obtained, and the tone quality of the generated noise is easily noticeable from the plurality of pitch arrangements. An optimal pitch arrangement is selected that suppresses the sense of beat and beat. For this reason, the pitch ratio and the pitch arrangement for providing a quiet tire while maintaining the appearance and appearance can be obtained accurately and with few operations, and a quiet and good-looking tire can be designed.
[0097]
Next, a third embodiment will be described. In this embodiment, the pitch arrangement is genetically designed by an algorithm. FIG. 18 shows a processing routine of the program according to the third embodiment. In step 300, N pitch arrays are obtained based on pseudo random numbers. Note that N is input in advance by the user. The basic model used in this embodiment is the same as that in the first embodiment.
[0098]
In the next step 302, the objective function representing the physical quantity for tire performance evaluation, the ratio of adjacent pitch lengths, the ratio of the maximum pitch length and the minimum pitch length, the number of consecutive identical pitch lengths of the number of pitches belonging to each pitch length, And a constraint that constrains at least one of the performance evaluation physical quantities and a design variable that determines N pitch arrays. In the present embodiment, the objective function OBJ and the constraint condition G are determined as follows in order to design a pitch arrangement with good noise performance, that is, sound quality performance.
[0099]

[0100]
By repeating this N times, the objective function OBJ, the constraint G, and the design variable r for each of the N tire models_iJAfter determining (J = 1, 2,..., N), in step 304 of FIG. 18, the design variable r for each of the N tire models is determined._iJEach objective function OBJ_JAnd constraint G_JIs calculated.
[0101]
In the next step 306, the objective function OBJ of each of the N pitch arrays obtained in step 304 is displayed._JAnd constraint G_J, The adaptive function F for each of the N pitch arrays_JIs calculated according to the following equation (9). In the present embodiment, for example, in order to minimize the segmented spectral deviation, the value (fitness) by the adaptive function increases as the segmented spectral deviation decreases.
[0102]
[Equation 5]

[0103]
c: Constant
γ: Penalty coefficient
Φ_min= Min (Φ₁, Φ₂・ ・ ・ ・ ・ ・ Φ_N)
Φ_J: Penalty function of Jth pitch array of N pitch arrays
(J = 1, 2, 3, ... N)
Note that c and γ are input in advance by the user.
[0104]
In the next step 308, two pitch arrays to be crossed are selected from the N pitch arrays. As a selection method, a generally known fitness proportional strategy is used, and a probability P that an individual e having N pitch arrangements is selected by selection is selected._eIs represented by the following equation.
[0105]
[Formula 6]

[0106]
However, F_e: Adaptive function of an individual e in N pitch arrays
F_J: Jth adaptive function of N pitch arrays
J = 1, 2, 3, ... N
In the above embodiment, the fitness proportional strategy was used as the selection method, but in addition to this, the expected value strategy, rank strategy, elite conservation strategy, tournament selection as shown in the genetic algorithm (Hiroaki Kitano) A strategy, a GENERTOR algorithm, or the like may be used.
[0107]
In the next step 310, it is determined whether or not the two selected pitch arrays are to be crossed according to the probability T input in advance by the user. Crossing here refers to exchanging a part of the elements of two pitch arrangements, as will be described later. If no crossover is made in the negative determination, the process proceeds to step 316 in step 312 with the current two pitch arrangements intact. On the other hand, when crossing is made with an affirmative determination, in step 314, two pitch arrays are crossed as will be described later.
[0108]
Crossing of the two pitch arrangements is performed by a crossover routine shown in FIG. First, the two pitch arrays selected in the above step 308 are set as a pitch array a and a pitch array b, and the design variables of each pitch array a and b are represented by a design variable vector Vr including a sequence,
Design variable vector of pitch array a
Vr^a= (R₁ ^a, R₂ ^a... r_i ^a... r_n-1 ^a),
Design variable vector of pitch array b
Vr^b= (R₁ ^b, R₂ ^b... r_i ^b... r_n-1 ^b)
And First, in step 350 of FIG. 19, a random number is generated according to a predetermined rule, and a crossing location i regarding the design variable vectors of the pitch arrays a and b is determined according to the random number. In the next step 352, based on the determined crossover location i, a new design variable r_i ^'a, R_i ^'bAsk for. This new design variable r_i ^'a, R_i ^'bThe determination will be described in detail with reference to FIGS.
[0109]
The pitch arrangement in the example of FIG. 20 is a mountain-shaped pitch arrangement, and there are three types of pitch ratios, large, medium and small. The number of pitches is 22, and the large pitch ratio is changed from small pitch ratio to large pitch ratio. It changes in order from small pitch ratio. Further, one group in which pitches having a large pitch ratio in the mountain pitch arrangement are continuous is defined as one mountain, and the number of mountains is two. In the figure, the number with the underline in the staircase portion indicates the number of pitches included in the staircase portion. With respect to the size of the pitch, if the large pitch ratio is 3, the medium pitch ratio is 2, and the small pitch ratio is 1, the pitch arrangements a and b (hereinafter referred to as parent (1) and parent (2)) in FIG. It can be expressed as [Parent pitch arrangement] shown below.
[0110]
[Parent pitch arrangement]
Parent (1): 1112233222112223322222
Parent (2): 112223333211112233222
[0111]
Next, for example, when it is determined by crossing at the seventh position by random numbers, a descendant array is generated from the parent pitch array as shown in [Pitch array crossover process] shown below.
[0112]
[Pitch array crossover process]
Parent (1): 11212233/322211222323222
Parent (2): 1122233/33211112233222
Descendants (1): 111233/33211112233222
Offspring (2): 1122233/322211222323222
[0113]
That is, the pitch array (hereinafter referred to as the descendant (1)) after connecting the array part of the first half of the intersection of the parent (1) and the array part of the second half of the intersection of the parent (2) and crossing with the parent (1) as a reference ▼). Similarly, the pitch arrangement (hereinafter referred to as a descendant (2)) after connecting the arrangement portion of the first half of the intersection of the parent (2) and the arrangement portion of the second half of the parent (1) and crossing with the parent (2) as a reference. .) Is generated. In this case, as understood from the figure, the pitch arrangement of the descendant (1) and the descendant (2) has the property of a mountain-shaped pitch arrangement.
[0114]
However, as shown in FIG. 21, when the crossing position is a medium pitch ratio or a small pitch ratio, the descendant (2) has a mountain-shaped arrangement property, but the descendant (1) has a mountain-shaped pitch arrangement characteristic. It will not have properties. Therefore, in order to always obtain a mountain-shaped pitch arrangement, if the constraint condition G is not a mountain-shaped pitch arrangement, and a preset value is set so as to have a positive value, a pitch arrangement other than the mountain-shaped pitch arrangement can be obtained. It can prevent becoming dominant.
[0115]
In this way, r_i ^'a, R_i ^'bIn step 354, the design variable vector Vr, which is a new design variable sequence, is obtained.^'a, R_i ^'bIs obtained as follows.
Vr ’^a= (R₁ ^a, R₂ ^a... r_i ^'a, R_{i + 1} ^b... r_n-1 ^b)
Vr ’^b= (R₁ ^b, R₂ ^b... r_i ^'b, R_{i + 1} ^a... r_n-1 ^a)
[0116]
In the above example, the number of crossover locations i is one, but a multipoint crossover or uniform crossover as shown in the genetic algorithm (edited by Hiroaki Kitano) may also be used.
[0117]
After two new pitch arrays are generated by such crossover, in step 316 in FIG. 18, it is determined whether or not to mutate with the probability S previously input by the user. As will be described later, this mutation means that a part of a design variable is slightly changed, and this is to increase the accuracy of including the pitch arrangement in a population that can be an optimum design variable. If it is determined in step 316 that the mutation is not to be made in the negative determination, the process proceeds to the next step 322 with the current two pitch arrangements maintained in step 318. If mutation is to be made in the affirmative determination, mutation processing is performed in the next step 320 as follows.
[0118]
This mutation is performed by the mutation routine shown in FIG. First, in step 356, a random number is generated, and a mutation location i is determined by the random number. Next, in step 358, a new design variable r_i'Is changed to an integer in a given pitch ratio using a random number. In this way, the design variable r_iAfter obtaining ', a design variable vector Vr', which is a new design variable sequence obtained in step 360, is as follows.
[0119]
Vr '= (r₁, R₂... r_i', R_{i + 1}... r_n-1)
In this way, the value of the objective function and the value of the constraint condition are calculated in step 322 in FIG. 18 for the two newly generated pitch arrays. In the next step 324, an adaptive function is calculated using the equation (9) in the same manner as described above from the obtained value of the objective function and the value of the constraint condition.
[0120]
In the next step 326, the two pitch arrangements are saved. In the next step 328, it is determined whether or not the number of pitch arrays stored in step 326 has reached N. If not, the steps 308 to 328 are repeated until N. Execute. On the other hand, when the number of pitch arrays reaches N, the convergence determination is made at step 330, and when not converged, the N pitch arrays are updated to the pitch array stored at step 326, and Steps 308 to 330 are repeatedly executed. On the other hand, if it is determined in step 330 that the convergence has occurred, the constraint condition is substantially satisfied by the value of the design variable of the pitch array that minimizes the value of the objective function while substantially satisfying the constraint condition among the N pitch arrays. However, the value of the design variable that maximizes the objective function is set, and in step 332, the pitch arrangement is determined using the value of the design variable.
[0121]
Note that the convergence determination at step 330 is regarded as convergence if any of the following conditions is satisfied.
[0122]
1) The number of generations reached M
2) The number of line trains with the largest objective function value is more than q% of the total.
3) The value of the maximum objective function is not updated in the subsequent p generations.
[0123]
However, the user inputs M, q, and p in advance.
[0124]
As mentioned above, although the Example of this invention was described, the Example of this invention has the aspect of the following various technical matters besides the requirements described in the claim.
[0125]
In the tire pitch arrangement determination method according to claim 1, in the step (a), a selection target group including a plurality of pitch arrangement basic models is defined, and the objective function is determined for each pitch arrangement basic model of the selection target group. The design variable and the constraint condition are determined, and an adaptive function that can be evaluated from the objective function and the constraint condition is determined. In the step (b), two pitch arrangement basics are selected from the selection target group based on the adaptive function. A model is selected, a design variable of each pitch array basic model is crossed with a predetermined probability to generate a new pitch array model, and a part of the design variable of at least one pitch array basic model is changed to create a new pitch array model. The objective function and constraints of the pitch array model with at least one of generating the pitch array model and changing the design variables The pitch arrangement model in which the pitch arrangement model and the design variable are not changed by obtaining the condition and the adaptive function are stored, and the stored pitch arrangement model is repeated until the predetermined number is reached, and a new number of the saved pitch arrangement models is formed. It is determined whether the group satisfies a predetermined convergence condition. When the convergence condition is not satisfied, the new group is used as the selection target group and the selection target group is repeated until the predetermined convergence condition is satisfied. The value of the design variable that gives the optimum value of the objective function is obtained among the predetermined number of pitch arrangement models stored when the condition is satisfied while considering the constraint conditions.
[0126]
In the initial arrangement, the pitches are arranged in order so that the pitch changes stepwise, and the number of pitches included in each rank is determined in advance. By changing the number of pitches included in the rank, in step (c), the pitch arrangement of the tires can be obtained based on the number of pitches included in each rank that gives the optimum value of the objective function.
[0127]
According to the above embodiment, specifically, in the step (a), a selection target group consisting of a plurality of pitch arrangements is defined, and the tire performance evaluation physical quantity is expressed for each pitch arrangement of the selection target group. Function, design variable that determines pitch arrangement, ratio of adjacent pitch lengths, ratio of maximum pitch length to minimum pitch length, number of pitches belonging to each pitch length, number of consecutive identical pitch lengths, and physical quantity for performance evaluation A constraint condition that constrains at least one and an adaptive function that can be evaluated from the objective function and the constraint condition are determined. In the step (b), two pitch arrays are selected from the selection target group based on the adaptive function, Create a new pitch array by crossing design variables of each pitch array with probability, and change (mutate) a part of the design variables of at least one pitch array to create a new one And generating the pitch array objective function, constraint condition and adaptive function by changing the design variable, storing the pitch array and the pitch array without changing the design variable, and Iterate until the number of stored pitch arrangements reaches a predetermined number, determine whether a new group consisting of the stored number of pitch arrangements satisfies a predetermined convergence condition, and if the convergence condition is not satisfied, select the new group as the selection target The selection target group is repeated as a group until the predetermined convergence condition is satisfied, and an optimum value of the objective function is given while considering the constraint condition in the predetermined number of pitch arrangements stored when the predetermined convergence condition is satisfied Find the value of a design variable.
[0128]
In this step (b), the sensitivity of the objective function, which is the ratio of the change amount of the objective function to the unit change amount of the design variable, and the change amount of the constraint condition relative to the unit change amount of the design variable for the pitch arrangement with the design variable changed Based on the sensitivity of the constraint condition, which is the ratio of the ratio, predict the change amount of the design variable that gives the optimal value of the objective function while considering the constraint condition, and at the same time change the objective variable when the design variable is changed by the amount corresponding to the prediction amount The constraint condition value when the value of the value and the design variable are changed by an amount corresponding to the predicted amount is calculated, the adaptive function is obtained from the value of the objective function and the constraint condition, and the pitch array and the design variable are not changed. The pitch arrangement can be stored and repeated until the stored pitch arrangement reaches a predetermined number.
[0129]
In the step (b), the sensitivity of the objective function, which is the ratio of the change amount of the objective function to the unit change amount of the design variable, and the sensitivity of the constraint condition, which is the ratio of the change amount of the constraint condition to the unit change amount of the design variable. Based on this, the change amount of the design variable that gives the optimum value of the objective function is predicted while considering the constraint conditions, and the value of the objective function and the design variable when the design variable is changed by an amount corresponding to the prediction amount are used as the prediction amount. The value of the constraint condition when the corresponding amount is changed can be calculated, and the value of the design variable that gives the optimum value of the objective function can be obtained based on the predicted value and the calculated value while considering the constraint condition.
[0130]
The design variable can be a function representing the pitch arrangement.
When a function representing a pitch arrangement is defined as a design variable, by defining a constraint condition so that the pitch length falls within a predetermined range when the design variable is changed in step (b), executing step (b) What is necessary is just to obtain | require the value of the design variable which gives the optimal value of an objective function, considering a constraint condition.
[0131]
Further, the pitches are arranged in order so that the size of the pitch changes stepwise, and the number of pitches included in each rank is generated from each pitch of the tire in step (a) for each predetermined initial arrangement. An objective function representing a noise pulse model and a physical quantity for evaluating tire noise performance is defined. In step (b), the number of pitches included in the rank is changed between different ranks, and in step (c), an optimal objective function is determined. Obtain tire pitch arrangement based on the number of pitches included in each rank giving value, repeat each step to obtain a plurality of pitch arrangements corresponding to a plurality of initial arrangements, and obtain objective function from the obtained plurality of pitch arrangements It is also possible to select a pitch arrangement that optimizes the optimum value.
[0132]
Further, the pitch formed on the tread is better in appearance when it has regularity. Therefore, in the step (a), a noise pulse model generated from each pitch of the tire and an objective function representing a tire noise evaluation physical quantity are determined. As the tire noise pulse model, a model in which the level of the sound generated from the road surface and the pitch of the tire, the pitch length, and the like are associated can be applied.
[0133]
In the next step (b), the number of pitches included in the rank is changed between different ranks. For example, the number of pitches is changed by increasing the number of one pitch between adjacent levels and decreasing the number of the other pitch. In this case, the total number of pitches included in the pitch array does not change.
[0134]
In step (c), the pitch arrangement is obtained by changing the tire noise pulse model or the like based on the number of pitches included in each rank that gives the optimum value of the objective function.
[0135]
For each step, the pitches are arranged in order so that the pitch changes stepwise, and the number of pitches included in each rank is predetermined for each initial arrangement, for example, the pitch included in each rank Is repeated for each initial arrangement of the pitch arrangement of tires in which pitches are arranged in order so that the size changes stepwise from small pitch to large pitch or from large pitch to small pitch. Thereby, a plurality of pitch arrangements corresponding to the plurality of initial arrangements are obtained. By selecting a pitch arrangement that optimizes the optimum value of the objective function from the obtained plurality of pitch arrangements, a further optimum tire pitch arrangement can be determined from the plurality of optimum pitch arrangements. By designing the tire based on the determined pitch arrangement, it is possible to provide a quiet tire while maintaining its external appearance.
[0136]
【The invention's effect】
As described above, according to the present invention, the design variable that gives the optimum value of the objective function corresponding to the sound quality in consideration of the constraint condition is obtained, and the tire is designed by determining the pitch arrangement and the like from this design variable. The best mode tire design can be achieved.
[0137]
When designing and developing tires based on the pitch arrangement and pitch ratio determined based on the determination method of the present invention, it is different from conventional design and development based on thought and error. It is possible to evaluate the noise performance of the designed tires to a certain extent, achieving significant efficiency and reducing development costs.
[Brief description of the drawings]
FIG. 1 is a schematic diagram of a personal computer used in an embodiment of the present invention.
FIG. 2 is a block diagram showing a schematic configuration of an actual vehicle instrument sound quality evaluation method.
FIGS. 3A and 3B show the frequency characteristics of sound when a tire is mounted on a vehicle, and FIG. 3A shows the result of the position near the left ear, and FIG. 3B shows the result of the position near the right ear.
FIG. 4 is a diagram showing a correspondence relationship between a feeling score, a sound pressure level, and a psychoacoustic parameter.
FIG. 5 is an explanatory diagram for explaining a pulse train for sounding a tire pitch arrangement.
FIG. 6 is a diagram for explaining optimization when tonality is an objective function.
FIG. 7 is a diagram for explaining a segmented spectrum corresponding to a pitch arrangement of one rotation of the tire.
FIG. 8 is a flowchart showing a processing routine of the first embodiment of the present invention.
FIG. 9 is a flowchart showing a pitch arrangement optimization routine in step 106 of FIG. 8;
FIG. 10 is a flowchart showing a pitch ratio optimization routine in step 110 of FIG. 8;
FIG. 11 is a diagram showing the correspondence between a filling score and a calculated value, where (1) is an estimated score by calculation, (2) is a tonality, and (3) is a correspondence of a fraction strength. Show.
FIG. 12 is a diagram showing the relationship between the psychoacoustic sensory scale of the pitch arrangement optimized by the sound pressure level and the pitch arrangement determined by the optimization of the first embodiment, (1) is the tonality; (2) shows the relationship of the fracture strength.
FIG. 13 is a flowchart showing a processing routine of the second embodiment of the present invention.
FIG. 14 is a flowchart showing a pitch arrangement optimization routine in step 208 of FIG. 13;
FIG. 15 is an image diagram showing a mountain-shaped pitch arrangement.
FIG. 16 is an image diagram for explaining a process of optimizing the mountain pitch arrangement.
FIG. 17 is an image diagram showing another example for explaining the process of optimizing the mountain-shaped pitch arrangement.
FIG. 18 is a flowchart showing a processing routine of a third embodiment of the present invention.
FIG. 19 is a flowchart showing a crossover processing routine.
FIG. 20 is an image diagram showing a mountain-shaped pitch arrangement in the process of crossover processing, where (a) shows pitch arrangement a, (b) shows pitch arrangement after crossover with pitch arrangements a and b as parents, (C) shows the pitch arrangement b, and (d) shows the pitch arrangement after crossing with the pitch arrangements a and b as parents.
FIG. 21 is an image diagram showing a mountain-shaped pitch arrangement in the process of crossover processing for a mountain-shaped pitch arrangement different from FIG. 20;
FIG. 22 is a flowchart showing a mutation processing routine.
[Explanation of symbols]
10 Keyboard
12 Computer body
14 CRT

Claims (4)

A tire pitch arrangement determination method including the following steps.
(A) Pitch arrangement basic model representing tire pitch arrangement , sound component physical quantity in a predetermined band representing acoustic psychological conspicuousness, and predetermined low frequency fluctuation representing psychoacoustic feeling A step of determining an objective function representing a physical quantity for evaluating tire noise performance corresponding to at least one of the sound qualities, a design variable for determining a pitch arrangement, and a constraint condition for restricting the pitch arrangement.
(B) A step of obtaining a value of a design variable that gives an optimum value of the objective function while considering the constraint condition.
(C) A step of obtaining a pitch arrangement based on a design variable that gives an optimum value of the objective function.   According to the tire pitch arrangement determining method according to claim 1, a pitch arrangement corresponding to the initial arrangement is obtained for each of the plurality of predetermined initial arrangements, and the pitch arrangement corresponding to the obtained plurality of initial arrangements is determined. The tire pitch arrangement determination method according to claim 1, wherein a pitch arrangement that optimizes the optimum value of the objective function is selected.   In the step (b), based on the sensitivity of the objective function that is the ratio of the change amount of the objective function to the unit change amount of the design variable and the sensitivity of the constraint condition that is the ratio of the change amount of the constraint condition to the unit change amount of the design variable. In addition to predicting the amount of change in the design variable that gives the optimal value of the objective function while considering the constraints, the value of the objective function and the design variable when the design variable is changed by the amount equivalent to the prediction amount are equivalent to the prediction amount The value of the constraint condition when the amount to be changed is calculated, and the value of the design variable that gives the optimum value of the objective function is obtained based on the predicted value and the calculated value while considering the constraint condition. The method for determining the pitch arrangement of the tire. The tire pitch arrangement determination method according to any one of claims 1 to 3, wherein a physical quantity representing a sound pressure level is further determined as the objective function .

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