鐜嬫矙锛屾潹蹇楀畨锛屼换涓含

(娴庡崡澶у鐞嗗闄紝灞变笢娴庡崡250022)

鎽樿锛欬/span>浜掍俊鎭嚱鏁板弽鏄犵殑鏄郴缁熶腑鐨勯潪绾挎€у叧鑱旓紝鏄皢绾挎€х殑鍏宠仈鍑芥暟瀵归潪绾挎€х郴缁熺殑涓€绉嶆帹骞匡紝鍔ㄦ€佸厜鏁ｅ皠棰嗗煙鐩墠鏈鍒扮敤璁＄畻浜掍俊鎭嚱鏁拌繘琛屽垎鏋愮殑鎶ラ亾銆傛湰鏂囦腑閫氳繃璁＄畻浜掍俊鎭嚱鏁帮紝瀵瑰姩鎬佸厜鏁ｅ皠妫€娴嬬數鏈鸿浆閫熺殑鏃堕棿搴忓垪杩涜鍒嗘瀽锛岀爺绌惰〃鏄庯紝浜掍俊鎭嚱鏁版硶鑳藉噯纭湴娴嬪嚭鐢垫満杞€熴€傚悓鏃讹紝鐢变簬浜掍俊鎭嚱鏁拌嚜韬殑浼樼偣鈥斺€旇兘瀹為檯鍦板弽鏄犲嚭鏁版嵁涔嬮棿鐨勭浉浜掑叧鑱旓紝鍥犳锛屼笌鑷浉鍏冲嚱鏁版硶姣旇緝锛屼簰淇℃伅鍑芥暟娉曞弽鏄犲嚭浜嗘洿澶氱殑鍔ㄥ姏瀛︿俊鎭€傜洰鍓嶆鍦ㄦ妸浜掍俊鎭嚱鏁板垎鏋愭硶鐢ㄤ簬妫€娴嬮绮掔矑寰勭殑瀹為獙褰撲腑銆傚笇鏈涘埄鐢ㄤ簰淇℃伅鍑芥暟鍒嗘瀽鐨勬柟娉曪紝鍦ㄥ姩鎬佸厜鏁ｅ皠妫€娴婞/span>椤咟/span>绮掔矑寰勭殑瀹為獙褰撲腑寰楀埌鏇村鐨勫姩鍔涘淇℃伅銆傚苟杩涗竴姝ュ簲鐢ㄤ簬绾崇背椤咟/span>绮掔矑寰勭殑鍔ㄦ€佸厜鏁ｅ皠妫€娴嬩腑銆侟/span>

鍏抽敭璇嶏細浜掍俊鎭嚱鏁帮紱鍔ㄦ€佸厜鏁ｅ皠锛涜嚜鐩稿叧鍑芥暟銆侟/span>

鏈枃鍒╃敤浜掍俊鎭嚱鏁板鍔ㄦ€佸厜鏁ｅ皠娉曟祴鐢垫満杞€熺殑瀹為獙杩涜浜嗙爺绌讹紝鍑嗙‘娴嬪嚭浜嗙數鏈虹殑杞€熴€傛枃涓瘮杈冧簡浜掍俊鎭嚱鏁版硶涓庤嚜鐩稿叧鍑芥暟娉旤/span>^[2]涓ょ鏂规硶鐨勪紭鍔ｃ€侟/span>

1.鍘熺悊

鎸堻/span>Shannon鐨勪俊鎭悊璁猴紝璁近/span>S琛ㄧず涓€缁勮鍙蜂负s₁锛孅/span>s₂锛屸€︼紝s_n鐨勭郴缁燂紝鍑虹幇s₁鐨勬鐜嘃/span>P_s(s_褨)锛孅/span>i= 1锛孅/span>2锛屸€︼紝n銆傚鍙︿竴缁勮鍙蜂负q₁锛孅/span>q₂锛屸€︼紝q_n鐨勭郴缁烖/span>Q锛屽嚭鐜?/span>q_j鐨勬鐜囨槸P_q(q_j),j= 1锛孅/span>2锛屸€︼紝n銆侟/span>s_褨鍜孅/span>q_jq鍚屾椂鍑虹幇鐨勬鐜嘃/span>P_sq(s_褨,q_j)銆備簰淇℃伅鐨勫畾涔変负^[3]

I(S,Q)搴﹂噺鐨勬槸鍙橀噺S涓嶞/span>Q涔嬮棿鐨勪竴鑸€у叧鑱旂▼搴︼紝鎴栨瘮鍊稽/span>P_sq(s_褨,q_j)/P_s(s_褨j)P_q(q_j)鐨勬暣浣撲笉骞虫暣绋嬪害銆備簰淇℃伅瓒婂ぇ锛屽彉绔?/span>S涓嶞/span>Q涔嬮棿鐨勫叧鑱旂▼搴﹁秺寮猴紝绯荤粺鐨勪笉骞虫暣绋嬪害瓒婇珮锛岀郴缁熻秺涓嶅潎鍖€锛涗簰淇℃伅瓒婂皬锛孅/span>S涓嶞/span>Q涔嬮棿鐨勫叧鑱旂▼搴﹁秺寮憋紝绯荤粺鐨勪笉骞虫暣绋嬪害瓒婁綆锛岀郴缁熻秺鍧囧寑銆侟/span>

鍦ㄥ厜瀛愪簰淇℃伅娉曟娴嬬數鏈鸿浆閫熺殑瀹為獙鐮旂┒涓紝涓昏鍏冲績鐨勬槸娴嬮噺鏁版嵁闅忓欢杩熸椂闂滁/span>T鐨勫懆鏈熸€э紝浠庤€屽緱鍑虹數鏈虹殑杞€熴€傚湪璁＄畻涓紝瀵规煇缁欏畾鐨勫欢杩熸椂闂滁/span>T锛屼护[s,q]=[x(t),x(t+T)]锛岃繖鏃朵簰淇℃伅I鏄欢杩熸椂闂滁/span>T鐨勫嚱鏁?/span>I(T)銆侟/span>

鍥犱负鐢垫満杞姩鏄懆鏈熸€х殑鍔ㄥ姏绯荤粺锛屽叾鐘舵€侀殢鏃堕棿鐨勬紨鍖栧彲琛ㄧず鎴忺/span>s=x(T)= Sint锛屽垯寤惰繜鍧愭爣鍙〃绀烘垚q=x(t+T)= sin(t+T)锛屽叾涓?/span>T鏄欢杩熸椂闂淬€傚綋寤惰繜T₁=0鏃讹紝q=x(t+T)= sin(t+0)=sint锛岃繖鏃迭/span>s涓嶞/span>q鏄悓涓€鍙橀噺涓庯紝s涓嶞/span>q闂寸殑鍏宠仈鏈€寮猴紝杩欐椂I(T₁)鍙栨瀬澶у€笺€傝绯荤粺鍛ㄦ湡鏄?/span>蟿锛屽綋

T₂=蟿鏃讹紝q=x(t+蟿)= sin(t+蟿)=sint锛屼娇浜掍俊鎭?/span>I(T₂)鍙堝彇鏋佸ぇ鍊硷紝鍒欎袱涓瀬澶х偣涔嬪樊T₂-T₁= 蟿鍗充负绯荤粺鐨勫懆鏈熴€傛墍浠ュ彧瑕佹壘鍑轰簰淇℃伅I鐨勪袱涓浉閭绘瀬澶у€兼墍瀵瑰簲鐨勬瀬澶х偣T₁鍜孅/span>T₂锛屽叾宸€稽/span>蟿=T₂-T₁灏辨槸绯荤粺鐨勫懆鏈熴€傚綋鍛ㄦ湡蟿纭畾鍚庯紝灏卞彲姹傚嚭杞€熴€傚彟澶栧埄鐢ㄧ敱浜掍俊鎭?/span>I(T)鐨勬瀬澶у€兼潵纭畾鍛ㄦ湡锛屾槗浜庤鲸鍒拰璁＄畻銆侟/span>

鍦ㄦ祴鐢垫満杞€熺殑瀹為獙涓紝鐢变簬鐢垫満鎵€甯﹀姩鐨勮浆鍔ㄥ渾鐩樻槸涓嶅畬鍏ㄥ潎鍖€鐨勶紝鍦ㄨ浆鍔ㄧ殑杩囩▼涓紝浠庡叾涓婇潰鏁ｅ皠鐨勫厜灏变細鍛堢幇鍛ㄦ湡鎬с€傛垜浠鍏堢敤鎺㈡祴鍣ㄦ潵鎺ユ敹杩欎簺鏁ｅ皠鍏夛紝寰楀埌鏁ｅ皠鍏夌殑鏃堕棿搴忓垪锛涘叾娆＄紪鍒跺嚭璁＄畻浜掍俊鎭殑绋嬪簭锛岃绠楀嚭缁欏畾寤惰繜鏃堕棿T鍊间笅鐨勪簰淇℃伅鍊稽/span>I(T)锛屽緱鍑轰簰淇℃伅鍑芥暟鏇茬嚎锛涙渶鍚庡埄鐢ㄤ簰淇℃伅鍑芥暟鏇茬嚎锛屾眰鍑鸿浆鍔ㄧ殑鍛ㄦ湡鎬э紝浠庤€屾眰鍑鸿浆閫熴€侟/span>

2.瀹為獙瑁呯疆

瀹為獙绯荤粺濡傚浘1鎵€绀恒€侟/span>

1.姘哥鐩存祦鐢靛姩鏈猴紱2.鍦嗙洏锛汓/span>3.5.鍏夐槕鍥撅紱4.閫忛暅锛汓/span>6.璁℃暟鍣ㄥ浘

鍥近/span>1瀹為獙绯荤粺缁撴瀯绀烘剰鍥近/span>

鍥近/span>2鍙栨牱鐐瑰鍏夊瓙鏁伴殢鏃堕棿鐨勫彉鍖朁/span>

鐢ㄧ洿娴佺數鍔ㄦ満甯﹀姩鍦嗙洏杞姩锛岀數鏈鸿浆閫熷彲璋冦€傚湪涓€瀹氱殑娴嬮噺鏃堕棿鍐咃紝閲囬泦鐨勫厜瀛愭暟闅忔椂闂村彉鍖栫殑鏇茬嚎濡傚浘2鎵€绀恒€備粠鍥近/span>3鍙互鐪嬪嚭浜掍俊鎭鐞嗗懆鏈熷彉鍖栫殑淇″彿鏄剧幇鍑烘潵銆侟/span>

3锛庣敱瀹為獙鏁版嵁璁＄畻鐢垫満杞€烖/span>

瀵圭數鏈洪噰闆嗘煇涓€杞€熶笅闅忔椂闂村彉鍖栫殑鍏夊瓙鏁帮紝鐢ㄨ嚜缂栬蒋浠跺閲囬泦鍒扮殑鏁版嵁璁＄畻浜掍俊鎭嚱鏁帮紝鍙緱鍒颁簰淇℃伅鐨勫嚱鏁版洸绾军/span>I(T)銆傚垎鏋愪簰淇℃伅鍑芥暟鏇茬嚎鐨勫懆鏈熺壒鎬э紝鍙绠楀嚭鐩稿簲鐨勮浆閫熴€侟/span>

鍥近/span>3瀵瑰疄楠屾暟鎹殑浜掍俊鎭鐞咟/span>

鍥近/span>4鍚屼竴缁勫疄楠屾暟鎹殑鑷浉鍏冲嚱鏁板浘

瀵逛竴缁勬暟鎹殑浜掍俊鎭洸绾匡紙濡傚浘3锛夎繘琛岀浉搴旇浆閫熻绠楋細鐢变簰淇℃伅鏋佸ぇ鐐瑰彲鐭ュ渾鐩樿浆鍔ㄥ懆鏈熶负25 x 2 ms锛岃浆閫烖/span>n = 60/25脳2脳10^-3= 1200 r/min銆傛墍寰楃粨鏋滀笌鏂嘃/span>^[2]鎵€鐢ㄧ殑鑷浉鍏冲嚱鏁版硶锛堝浘4锛夋墍璁＄畻鍑虹殑鐢垫満杞€熺浉鍚屻€傝繖璇存槑鎶婁簰淇℃伅鍑芥暟娉曞簲鐢ㄤ簬鍔ㄦ€佸厜鏁ｅ皠娴嬬數鏈鸿浆閫熺殑瀹為獙涓槸鍙鐨勩€侟/span>

4锛庤璁裹/span>

鏈枃灏嗕簰淇℃伅鍑芥暟搴旂敤浜庡姩鎬佸厜鏁ｅ皠妫€娴嬬數鏈鸿浆閫熺殑鐮旂┒锛屽噯纭緱娴嬪嚭鐢垫満杞€燂紝杩欎竴缁撴灉涓庤嚜鐩稿叧鍑芥暟娉曠殑缁撴灉涓€鑷淬€傚苟涓斾簰淇℃伅鍑芥暟娉曟槸鐪熸鎰忎箟涓婄殑鐩镐簰鍏宠仈锛屽彲寰楀埌鏇村绯荤粺鐨勫姩鍔涘淇℃伅锛岃繖浜涗俊鎭父甯歌娣规病浜庡櫔澹颁腑銆侟/span>

鐩墠姝ｅ湪鎶婁簰淇℃伅鍑芥暟鍒嗘瀽娉曠敤浜庢娴嬮绮掔矑寰勭殑瀹為獙褰撲腑銆傚笇鏈涘埄鐢ㄤ簰淇℃伅鍑芥暟鍒嗘瀽鐨勬柟娉曪紝鍦ㄥ姩鎬佸厜鏁ｅ皠妫€娴嬮绮掔矑寰勭殑瀹為獙褰撲腑锛屽緱鍒版洿澶氱殑鍔ㄥ姏瀛︿俊鎭€傚苟杩涗竴姝ュ簲鐢ㄤ簬绾崇背棰楃矑绮掑緞鐨勫姩鎬佸厜鏁ｅ皠妫€娴嬩腑銆侟/span>

鍙傝€冩枃鐚細

[1]寰愮閾?/span>.淇″彿鍒嗘瀽涓庣浉鍏虫妧鏈?/span>[M].鍖椾含:绉戝鍑虹増绀近/span>, 1981.

[2]绐﹀溅鐜秉/span>,绛堻/span>.鍏夊瓙鐩稿叧娉曟娴嬬數鏈鸿浆閫熺殑瀹為獙鐮旂┒[J].娴庡崡澶у瀛︽姤, 2003, 17(11).

[3]姒傜巼璁裹/span>[M].鍖椾含:浜烘皯鏁欒偛鍑虹増绀近/span>, 1979.

[4]鏉ㄥ織瀹堻/span>,绛堻/span>.鐢ㄧ瓑闂磋窛鏍煎瓙娉曡绠椾簰淇℃伅鍑芥暟纭畾寤惰繜鏃堕棿[J].璁＄畻鐗╃悊, 1995, 12(4): 443.

Analysis On the Mutual Information Function

for Testing Dynamic Light Scattering Method

WANG Sha. YANG Zhi-an, REN Zhong-jing

(Science School, Jinan University, Jinan 250022, China )

Abstract:The mutual information function is adapted to develop the experiment of testing the rotational speed of the electrical machinery by the Photon Correlation Technique and picked up the rotational speed's information of the electrical machinery. It indicated that the mutual information function could be applicable to the experiment of testing the electrical machinery by the photon correlation technique as same as the autocorrelation function. At the same time, because of the advantage of the mutual information function, it could actually reflect the mutual correlation of the data and paid more attention to the details. So it could reflect a lot of dynamics鈥 subtle information.

Key words:mutual information function锛汓/span>dynamic light scattering锛汓/span>autocorrelation function