陳如清，李嘉春，尚 濤，張 俊

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改進(jìn)煙花算法和概率神經(jīng)網(wǎng)絡(luò)智能診斷齒輪箱故障

陳如清1，李嘉春2，尚 濤1，張 俊3

（1. 嘉興學(xué)院機(jī)電工程學(xué)院，嘉興 314001；2. 嘉興學(xué)院數(shù)理與信息工程學(xué)院，嘉興 314001；3. 浙江大學(xué)生物系統(tǒng)工程與食品科學(xué)學(xué)院，杭州 310058）

針對(duì)復(fù)雜環(huán)境下農(nóng)機(jī)設(shè)備的齒輪箱系統(tǒng)在故障診斷時(shí)存在易受現(xiàn)場(chǎng)噪聲干擾和故障識(shí)別率低等問(wèn)題，提出了一種基于改進(jìn)的煙花算法和概率神經(jīng)網(wǎng)絡(luò)的齒輪箱智能故障診斷方法。為提高現(xiàn)有概率神經(jīng)網(wǎng)絡(luò)模式分類方法的性能，定義了一項(xiàng)樣本相似度衡量指標(biāo)以提高建模過(guò)程中訓(xùn)練樣本的質(zhì)量。將煙花算法與概率神經(jīng)網(wǎng)絡(luò)技術(shù)有機(jī)融合提出了一種改進(jìn)的煙花算法-概率神經(jīng)網(wǎng)絡(luò)模式分類方法，利用煙花算法優(yōu)化概率神經(jīng)網(wǎng)絡(luò)的平滑參數(shù)以確定網(wǎng)絡(luò)參數(shù)的最優(yōu)值，提高模式分類與識(shí)別精度。將改進(jìn)的煙花算法-概率神經(jīng)網(wǎng)絡(luò)模式分類方法用于噪聲環(huán)境下齒輪箱的故障診斷建模，構(gòu)建故障特征參量與齒輪箱工作狀況間的復(fù)雜非線性映射關(guān)系。應(yīng)用結(jié)果表明，與基于BP神經(jīng)網(wǎng)絡(luò)、GABP（genetic algorithm back propagation）神經(jīng)網(wǎng)絡(luò)和概率神經(jīng)網(wǎng)絡(luò)的故障診斷模型相比，在不同程度噪聲影響下煙花算法-概率神經(jīng)網(wǎng)絡(luò)模型均具有最高故障識(shí)別率。當(dāng)噪聲控制系數(shù)為0.01、0.02、0.04和0.06時(shí)，模型的故障識(shí)別率分別為100%、95.83%、93.33%和88.33%。該研究可為非線性復(fù)雜系統(tǒng)的故障診斷提供了一種可行的解決方案。

齒輪；算法；噪聲；概率神經(jīng)網(wǎng)絡(luò)；故障診斷建模

0 引 言

農(nóng)業(yè)機(jī)械裝備是提高農(nóng)業(yè)生產(chǎn)效率及推動(dòng)農(nóng)業(yè)可持續(xù)發(fā)展不可或缺的工具。齒輪箱既是用于轉(zhuǎn)速調(diào)節(jié)和動(dòng)力傳遞的常用傳動(dòng)部件，也是農(nóng)機(jī)設(shè)備的重要機(jī)械部件。工作過(guò)程中其故障發(fā)生率較高，是引發(fā)機(jī)械設(shè)備故障的重要原因[1]。為確保其安全可靠運(yùn)行，對(duì)齒輪與軸承等關(guān)鍵部件進(jìn)行故障檢測(cè)與分類定位具有重要意義[2-3]。大型農(nóng)機(jī)設(shè)備通常具有系統(tǒng)結(jié)構(gòu)復(fù)雜、工作條件多樣且工作環(huán)境惡劣等特征，故障特征參量和設(shè)備工作狀況間形成了較為復(fù)雜的非線性映射關(guān)系[4-5]。機(jī)械設(shè)備故障機(jī)理分析和故障診斷方法研究一直受到廣泛關(guān)注，現(xiàn)有方法主要有模式識(shí)別方法、神經(jīng)網(wǎng)絡(luò)方法和專家系統(tǒng)方法等。隨著人工智能技術(shù)的發(fā)展，基于人工智能融合技術(shù)的故障診斷方法也成為一大研究熱點(diǎn)[6-7]。各種智能診斷理論和方法的集成和融合，如小波分析與神經(jīng)網(wǎng)絡(luò)集成、模糊系統(tǒng)與神經(jīng)網(wǎng)絡(luò)集成和進(jìn)化計(jì)算與神經(jīng)網(wǎng)絡(luò)融合等，較好構(gòu)建了故障征兆與故障類別之間的映射關(guān)系，有效實(shí)現(xiàn)了機(jī)械設(shè)備的故障診斷[8-10]。但對(duì)于齒輪箱等復(fù)雜非線性動(dòng)態(tài)系統(tǒng)，現(xiàn)有故障診斷方法存在故障建模復(fù)雜、易受噪聲干擾和診斷精度不高等缺陷[11-12]。

從機(jī)器學(xué)習(xí)角度看，機(jī)械設(shè)備的故障診斷本質(zhì)上是一個(gè)模式分類問(wèn)題。概率神經(jīng)網(wǎng)絡(luò)（probabilistic neural networks, PNN）是由Specht提出，其主要思想是將貝葉斯決策理論引入傳統(tǒng)神經(jīng)網(wǎng)絡(luò)，網(wǎng)絡(luò)結(jié)構(gòu)按照貝葉斯判別函數(shù)來(lái)設(shè)置，以實(shí)現(xiàn)錯(cuò)誤分類的期望風(fēng)險(xiǎn)最小[13]。PNN吸收了徑向基神經(jīng)網(wǎng)絡(luò)與經(jīng)典的概率密度估計(jì)原理的優(yōu)點(diǎn)，在模式分類與識(shí)別領(lǐng)域獲得廣泛應(yīng)用[14-15]。與傳統(tǒng)BP、RBF神經(jīng)網(wǎng)絡(luò)比較，PNN具有以下優(yōu)勢(shì)：網(wǎng)絡(luò)學(xué)習(xí)過(guò)程簡(jiǎn)單，學(xué)習(xí)速度快；分類更準(zhǔn)確，對(duì)錯(cuò)誤噪聲容忍性高；容錯(cuò)性好，分類能力強(qiáng)[16]。PNN的不足之處主要體現(xiàn)在以下2個(gè)方面：1）對(duì)訓(xùn)練樣本的代表性要求高，需要的存儲(chǔ)空間更大；2）網(wǎng)絡(luò)參數(shù)（如平滑參數(shù)）的選取直接影響PNN識(shí)別性能。此外，基本PNN通常對(duì)于每個(gè)模式類別平滑參數(shù)的取值均相同（即假設(shè)1=2=…=），不能將概率特性完整地表示出來(lái)，從而降低了PNN的識(shí)別精度。因此，如何提煉更具代表性的建模訓(xùn)練樣本和選定合適的參數(shù)是PNN研究的關(guān)鍵問(wèn)題。

為解決復(fù)雜環(huán)境下齒輪箱故障診斷系統(tǒng)易受噪聲干擾且故障識(shí)別率低等問(wèn)題，本文設(shè)計(jì)了一種代表性訓(xùn)練樣本提取方法，通過(guò)將PNN網(wǎng)絡(luò)與煙花算法（fireworks algorithm, FWA）有機(jī)結(jié)合提出了一種改進(jìn)的FWA-PNN方法，利用FWA算法優(yōu)化PNN的平滑參數(shù)，對(duì)于每個(gè)模式類別都不同（即→σ）。最后將本文所提出的方法用于農(nóng)業(yè)機(jī)械裝備領(lǐng)域齒輪箱系統(tǒng)的故障診斷與分類定位，應(yīng)用結(jié)果表明，基于改進(jìn)的FWA-PNN智能診斷方法可有效提高齒輪箱故障診斷的性能。

1 PNN模式分類模型

PNN模型包括輸入層、模式層、求和層和輸出層。假設(shè)特征向量維數(shù)為3，為方便闡述，以3類模式分類器為例（即=3），PNN模型可用圖1進(jìn)行描述[13,15]。圖1中，為輸入向量，11～33為訓(xùn)練樣本，11～33為模式層各節(jié)點(diǎn)的輸出，1()～3()為求和層各節(jié)點(diǎn)的輸出，Output為PNN的最終輸出，表示屬于哪一類。

Note: ，，, (i=1,2,3; n1=2, n2=2, n3=3; σ is the smoothing parameter of PNN).

輸入層神經(jīng)元個(gè)數(shù)為特征向量的維數(shù)。在輸入層中，網(wǎng)絡(luò)計(jì)算輸入向量與所有訓(xùn)練樣本向量之間的距離。樣本層神經(jīng)元個(gè)數(shù)為訓(xùn)練樣本的個(gè)數(shù)，通常其激活函數(shù)為高斯函數(shù)。求和層神經(jīng)元個(gè)數(shù)為類別個(gè)數(shù)，主要功能是將樣本層的輸出按類相加，相當(dāng)于個(gè)加法器。競(jìng)爭(zhēng)層的神經(jīng)元個(gè)數(shù)為1。整個(gè)網(wǎng)絡(luò)判決的結(jié)果通過(guò)競(jìng)爭(zhēng)層輸出，輸出結(jié)果中只有一個(gè)1，其余為0，概率值最大的那一類輸出結(jié)果為1。根據(jù)Speeht博士提出的PNN基本模型并參照現(xiàn)有研究文獻(xiàn)，基本PNN學(xué)習(xí)算法的總結(jié)如下[13-15]。

1）歸一化處理

式中為訓(xùn)練樣本矩陣，樣本個(gè)數(shù)為，樣本維數(shù)為，1k～x為矩陣中的一個(gè)元素。計(jì)算下面矩陣以求解歸一化因子。

2）將歸一化好的樣本送入網(wǎng)絡(luò)輸入層。歸一化處理后的學(xué)習(xí)樣本用表示，即

3）模式距離計(jì)算。計(jì)算待識(shí)別樣本矩陣與學(xué)習(xí)矩陣相對(duì)應(yīng)元素之間的距離（歐氏距離）。

4）激活模式層高斯函數(shù)的神經(jīng)元。學(xué)習(xí)樣本與待識(shí)別樣本歸一化處理后，通常取標(biāo)準(zhǔn)差=0.1的高斯型函數(shù)。激活后得到初始概率矩陣。

5）求和層求解各樣本屬于各類的初始概率和。

設(shè)樣本數(shù)為，可分為類，且各類樣本的數(shù)量相同。則樣本屬于各類的初始概率和為

6）計(jì)算概率，即第個(gè)待識(shí)別樣本屬于第類的概率，其中S為的第行第列元素，S為的第行第列元素。

2 模式分類代表樣本的獲取

為提高PNN模式分類方法的性能，建模過(guò)程對(duì)樣本的質(zhì)量要求較高。采用樣本間的相似度度量方法從原始樣本數(shù)據(jù)中篩選更具代表性的建模樣本。相似度分析時(shí)，常以樣本間的距離（如歐氏距離、馬氏距離和余弦距離等）作為度量方式。

由歐氏距離和余弦距離的定義可知，歐氏距離和余弦距離分別從不同的角度描述數(shù)據(jù)間的相似度。兩者區(qū)別主要體現(xiàn)在：余弦距離在描述數(shù)據(jù)間的相似度時(shí)強(qiáng)調(diào)兩組數(shù)據(jù)方向上的差異；歐氏距離則注重兩組數(shù)據(jù)的空間距離或位置上的差異。為更好度量數(shù)據(jù)間的相似度，發(fā)揮歐氏距離和余弦距離各自在描述數(shù)據(jù)間相似性的優(yōu)勢(shì)，將余弦距離和歐式距離2種度量方法有機(jī)融合，形成一種新的樣本相似度衡量指標(biāo)，即

式中dist和cos分別表示樣本間的歐氏距離和余弦距離，Abs為絕對(duì)值函數(shù)。相似度衡量指標(biāo)數(shù)值越大則表示2組數(shù)據(jù)間的差異性越大，反之亦然。采用新的相似度衡量方法對(duì)PNN模式分類原始建模數(shù)據(jù)進(jìn)行分析，提取更具代表性的建模樣本。獲取過(guò)程為：通過(guò)計(jì)算原始數(shù)據(jù)集中樣本兩兩之間的相似度值并設(shè)置相應(yīng)的閾值，當(dāng)相似度值小于設(shè)定閾值，則去除其中一個(gè)樣本。重復(fù)以上篩選過(guò)程，直至剩余樣本的數(shù)量滿足建模要求為止。提取后的樣本數(shù)據(jù)具有良好的代表性，即數(shù)據(jù)間的差異性最大或相似性最小，作為PNN的建模數(shù)據(jù)。

3 改進(jìn)的FWA-PNN模式分類算法

將PNN用于解決模式分類問(wèn)題時(shí)，平滑參數(shù)的選取直接影響PNN識(shí)別性能。通常平滑參數(shù)的選取并無(wú)統(tǒng)一規(guī)則，如何確定合適的參數(shù)是PNN建模的關(guān)鍵問(wèn)題。譚營(yíng)等[17-18]根據(jù)煙花爆炸產(chǎn)生火花這一現(xiàn)象提出煙花算法，其基本實(shí)現(xiàn)思路是將煙花視為最優(yōu)化問(wèn)題解空間中的一個(gè)可行解，通過(guò)煙花爆炸產(chǎn)生一定規(guī)模的火花，實(shí)現(xiàn)鄰域搜索最優(yōu)解。FWA屬于有導(dǎo)向的隨機(jī)性啟發(fā)式算法，作為一種新型群體智能優(yōu)化算法，相比傳統(tǒng)優(yōu)化方法，其具有魯棒性較強(qiáng)、全局優(yōu)化性能較好，局部和全局搜索能力自調(diào)節(jié)機(jī)制靈活等優(yōu)勢(shì)，受到不同領(lǐng)域?qū)W者的廣泛關(guān)注。目前已成功用于解決神經(jīng)網(wǎng)絡(luò)權(quán)值的訓(xùn)練、連續(xù)和離散系統(tǒng)的參數(shù)優(yōu)化及組合優(yōu)化問(wèn)題的求解等方面問(wèn)題，取得良好的應(yīng)用成效[19-21]。

針對(duì)現(xiàn)有PNN模式分類方法存在的分類識(shí)別精度不高和平滑參數(shù)難以確定等問(wèn)題，本文將FWA優(yōu)化算法與PNN神經(jīng)網(wǎng)絡(luò)技術(shù)有機(jī)融合提出了一種改進(jìn)的FWA-PNN模式分類方法。將FWA用于求解PNN平滑因子σ的優(yōu)化問(wèn)題，以提高PNN的模式分類與識(shí)別精度。

用于故障分類識(shí)別的改進(jìn)FWA-PNN算法，運(yùn)行過(guò)程具體包括以下6個(gè)步驟：

1）初始化設(shè)置。設(shè)定平滑因子σ的取值范圍，隨機(jī)產(chǎn)生規(guī)模為的維初始煙花種群1, …σ, …,σ∈R,1，表征平滑因子σ優(yōu)化問(wèn)題的個(gè)初始解，為待分類樣本模式的種類數(shù)；根據(jù)FWA算法的搜索機(jī)理初始化FWA的爆炸半徑及爆炸火花數(shù)調(diào)節(jié)常數(shù)、最大搜索次數(shù)和尋優(yōu)精度等相關(guān)參數(shù)；并設(shè)當(dāng)前代數(shù)=1；

3）產(chǎn)生爆炸火花和高斯變異火花，從煙花、爆炸火花和高斯變異火花種群中選擇個(gè)體作為下一次迭代計(jì)算的煙花種群；

4）更新迭代次數(shù)（即增加1）；

5）檢查并根據(jù)群體最優(yōu)適應(yīng)度值計(jì)算誤差，判斷是否滿足終止條件。若滿足則停止搜索，否則返回步驟2）；

6）利用FWA優(yōu)化算法得到的最優(yōu)平滑因子σ確定PNN的網(wǎng)絡(luò)模型，輸入測(cè)試樣本數(shù)據(jù)，完成故障分類識(shí)別。

4 故障診斷建模與驗(yàn)證

4.1 故障數(shù)據(jù)采集

齒輪箱是農(nóng)機(jī)設(shè)備傳動(dòng)系統(tǒng)中的重要部分，經(jīng)常工作在強(qiáng)噪聲干擾、重載和特殊介質(zhì)等惡劣條件下，齒輪和軸承的故障時(shí)有發(fā)生[22]?，F(xiàn)場(chǎng)運(yùn)行表明，較為常見的故障類型主要有齒輪崩齒、中間軸竄動(dòng)、輸入軸彎曲、軸承外圈有剝落坑和軸承內(nèi)圈劃傷等5類。

為獲取齒輪箱的故障建模數(shù)據(jù)，以JZQ250型齒輪箱（型號(hào)：ZQ-250；品牌：江蘇國(guó)茂；總中心距：250 mm；傳動(dòng)比：40.17）為對(duì)象在實(shí)驗(yàn)室模擬了6種工作狀態(tài)（含1種正常狀態(tài)和5種典型故障狀態(tài)）。利用信號(hào)采集系統(tǒng)的加速度傳感器獲取齒輪箱多處測(cè)試點(diǎn)的振動(dòng)信號(hào)（采樣點(diǎn)數(shù)設(shè)置為2 048，采樣頻率分別設(shè)置為800、1 000和1 250 Hz，對(duì)應(yīng)齒輪箱額定轉(zhuǎn)速分別為1 000、1 200和1 500 r/min。此外，為使所采集的振動(dòng)信號(hào)能更加全面和真實(shí)地反映齒輪箱的工作狀態(tài)，將測(cè)試點(diǎn)布置在齒輪箱箱體的平面和軸承座的受力方向上[23]。

齒輪箱故障診斷系統(tǒng)結(jié)構(gòu)如圖2所示。試驗(yàn)過(guò)程中，首先利用傳感器采集正常工況下齒輪箱的振動(dòng)信號(hào)。受客觀條件限制，短期內(nèi)難以收集大量故障狀態(tài)下的振動(dòng)信號(hào)用于故障診斷研究。通過(guò)在試驗(yàn)對(duì)象中間軸的相關(guān)部位人為設(shè)置齒輪箱的上述幾種典型故障狀態(tài)（包括齒輪崩齒、中間軸竄動(dòng)、輸入軸彎曲、軸承外圈有剝落坑、軸承內(nèi)圈劃傷等故障情況），模擬故障工況。試驗(yàn)過(guò)程中保持負(fù)載恒定，待齒輪箱轉(zhuǎn)速平穩(wěn)后再次利用壓電加速度傳感器（型號(hào)：YD-81D；品牌：秦皇島協(xié)力科技）分別測(cè)試故障工況下齒輪箱的振動(dòng)信號(hào)。

圖2 齒輪箱故障診斷系統(tǒng)結(jié)構(gòu)

4.2 故障特征描述與代表樣本獲取

對(duì)不同工況下從現(xiàn)場(chǎng)采集的齒輪箱振動(dòng)信號(hào)進(jìn)行預(yù)處理，并對(duì)其振動(dòng)特征進(jìn)行時(shí)域和頻域分析，得到反應(yīng)齒輪箱工況的21項(xiàng)時(shí)域特征參數(shù)（即最大值、最小值、均值、均方值、有效值、方差、方根幅值、絕對(duì)平均幅值、偏度、峭度、峰值、波形指標(biāo)、峰值指標(biāo)、脈沖指標(biāo)、裕度指標(biāo)、峭度指標(biāo)、偏態(tài)指標(biāo)、偏度系數(shù)、8階矩系數(shù)、16階矩系數(shù)和6階矩）和6項(xiàng)頻域特征參數(shù)（相關(guān)因子、諧波因子、譜原點(diǎn)矩、頻譜重心、均方譜和頻域方差）[24-25]。

為簡(jiǎn)化故障診斷模型，根據(jù)齒輪箱體的實(shí)際工作情況，進(jìn)行故障特征參數(shù)分析和故障敏感參數(shù)選取。采用KPCA方法對(duì)高維原始數(shù)據(jù)進(jìn)行特征提取，分析表明前7個(gè)特征值的累積貢獻(xiàn)率（即攜帶的變異信息）大于85%，可以用于進(jìn)行齒輪箱工作狀況識(shí)別。從特征參數(shù)集中提取對(duì)齒輪箱故障較為敏感的7個(gè)特征值，即波形指標(biāo)、峭度指標(biāo)、裕度指標(biāo)、偏態(tài)指標(biāo)、頻譜重心、頻域方差和相關(guān)因子，作為齒輪箱故障特征向量?；赑NN的故障診斷系統(tǒng)就是用PNN建立故障特征與故障類型間的映射關(guān)系。

通過(guò)對(duì)振動(dòng)信號(hào)的時(shí)域和頻域分析，得到波形指標(biāo)等7維故障特征向量。典型故障樣本如表1所示。診斷模型輸入為7維故障特征量，輸出為6維故障編碼。

表1 齒輪箱典型故障樣本

注：1～6分別代表齒輪箱正常工況、齒輪崩齒、中間軸竄動(dòng)、輸入軸彎曲、軸承外圈有剝落坑和軸承內(nèi)圈劃傷等6種工作狀態(tài)。故障編碼中“1”表示故障發(fā)生，“0”表示不發(fā)生。

Note: C1～C6 represent 6 working conditions of the gearbox, there are normal operating condition, fault of gear breaking, fault of intermediate shaft playing, fault of input shaft bending, fault of spalling pits on the bearing outer ring and fault of scratching on the bearing inner race. In the fault code, the number 1 indicates fault occurring and 0 indicates normal condition.

式中為人為添加的均值為0，方差為1的隨機(jī)噪聲；為噪聲控制系數(shù)，本文分別取=0.01, 0.02, 0.04, 0.06。利用式（13）在每類工作狀態(tài)下分別產(chǎn)生100組帶噪聲的樣本，歸一化處理后共600組樣本。針對(duì)不同程度噪聲下的故障樣本，采用前文所述“模式分類代表樣本的獲取”方法分別對(duì)6類工作狀態(tài)下的600組故障樣本進(jìn)行相似度分析并剔除其中的冗余樣本。

以=0.01情況下產(chǎn)生的故障樣本為例，代表樣本獲取過(guò)程為：計(jì)算預(yù)處理后故障樣本集中兩樣本間的歐氏距離、余弦距離和相似度值，得到矩陣D=(δ)×l(600，1)，≥時(shí)δ取值為0。根據(jù)預(yù)處理后故障樣本的實(shí)際情況設(shè)置閾值，即當(dāng)|δ|<0.18時(shí)去除當(dāng)中的一個(gè)樣本。處理后故障建模樣本規(guī)模由600組精簡(jiǎn)至339組。隨機(jī)選取其中的219組故障樣本（每類故障類別的樣本數(shù)量約36組）作為神經(jīng)網(wǎng)絡(luò)故障診斷建模的訓(xùn)練數(shù)據(jù)，其余120組作為測(cè)試數(shù)據(jù)。

4.3 基于改進(jìn)FWA-PNN的故障診斷建模與驗(yàn)證

將改進(jìn)的FWA-PNN模式分類方法用于齒輪箱故障診斷建模，根據(jù)齒輪箱的實(shí)際運(yùn)行工況，本文在進(jìn)行故障診斷建模時(shí)選取的PNN拓?fù)浣Y(jié)構(gòu)為7-219-6-6，即輸入層神經(jīng)元個(gè)數(shù)為7，對(duì)應(yīng)7維故障特征量；樣本層神經(jīng)元個(gè)數(shù)為219，對(duì)應(yīng)219組訓(xùn)練樣本的個(gè)數(shù)；求和層神經(jīng)元個(gè)數(shù)為6，對(duì)應(yīng)齒輪箱的6類工作狀態(tài)；競(jìng)爭(zhēng)層神經(jīng)元個(gè)數(shù)為6，與求和層相同，輸出故障診斷結(jié)果（即將求和層求解的具有最大后驗(yàn)概率密度的神經(jīng)元輸出為1，其余為0）。

為與FWA-PNN神經(jīng)網(wǎng)絡(luò)故障診斷建模方法形成對(duì)比，本文還引入了BP神經(jīng)網(wǎng)絡(luò)、GABP神經(jīng)網(wǎng)絡(luò)（遺傳算法優(yōu)化的BP神經(jīng)網(wǎng)絡(luò)）和PNN神經(jīng)網(wǎng)絡(luò)，分別建立不同類型的齒輪箱故障診斷模型。主要參數(shù)設(shè)置情況描述如下：

BP神經(jīng)網(wǎng)絡(luò)：結(jié)構(gòu)為7-13-6，學(xué)習(xí)算法為梯度下降法，學(xué)習(xí)率為0.01，最大迭代次數(shù)為5 000，網(wǎng)絡(luò)訓(xùn)練目標(biāo)為0.01；GABP神經(jīng)網(wǎng)絡(luò)：初始種群規(guī)模和維數(shù)分別為20和6，交叉概率p為0.65，變異概率p為0.01，網(wǎng)絡(luò)結(jié)構(gòu)及其他參數(shù)設(shè)置與BP神經(jīng)網(wǎng)絡(luò)相同；PNN神經(jīng)網(wǎng)絡(luò)：結(jié)構(gòu)為7-219-6-6，平滑參數(shù)=0.1；FWA-PNN神經(jīng)網(wǎng)絡(luò)：結(jié)構(gòu)為7-219-6-6，平滑參數(shù)σ(16)通過(guò)FWA優(yōu)化獲取。FWA優(yōu)化算法的煙花成員規(guī)模和維數(shù)分別為20和6、爆炸半徑及爆炸火花數(shù)調(diào)節(jié)常數(shù)分別為100和80、爆炸火花數(shù)上限和下限分別為20和1、高斯變異火花數(shù)=50，參數(shù)優(yōu)化過(guò)程最大迭代次數(shù)為3 000，優(yōu)化精度（求和層實(shí)際輸出與理想輸出之間的偏差）為0.01。

圖3為噪聲控制系數(shù)=0.01時(shí)，基于常規(guī)BP神經(jīng)網(wǎng)絡(luò)、GABP神經(jīng)網(wǎng)絡(luò)和FWA-PNN神經(jīng)網(wǎng)絡(luò)的訓(xùn)練樣本誤差變化曲線。由圖3可知：基于改進(jìn)的FWA-PNN故障診斷模型經(jīng)過(guò)3 000次迭代后訓(xùn)練精度達(dá)到0.101 6，誤差收斂速度和精度明顯優(yōu)于GABP神經(jīng)網(wǎng)絡(luò)和常規(guī)BP神經(jīng)網(wǎng)絡(luò)。展現(xiàn)出良好的容錯(cuò)性和較強(qiáng)的故障分類能力；相同條件下GABP神經(jīng)網(wǎng)絡(luò)經(jīng)3 000次迭代訓(xùn)練精度為0.471 2；而常規(guī)BP神經(jīng)網(wǎng)絡(luò)表現(xiàn)最差，經(jīng)3 000次迭代訓(xùn)練精度僅為0.865 7，經(jīng)過(guò)1 200迭代后收斂速度明顯減慢，訓(xùn)練精度無(wú)明顯變化，網(wǎng)絡(luò)陷入局部極值。

圖3 3種神經(jīng)網(wǎng)絡(luò)訓(xùn)練誤差曲線(噪聲控制系數(shù)a=0.01)

采用4種神經(jīng)網(wǎng)絡(luò)故障診斷模型，分別對(duì)不同噪聲控制系數(shù)下的測(cè)試樣本進(jìn)行故障診斷與分類定位試驗(yàn)，故障識(shí)別結(jié)果對(duì)比如表2所示。故障識(shí)別率為累計(jì)正確識(shí)別個(gè)數(shù)與測(cè)試驗(yàn)本總數(shù)之比值。

表2 3種故障診斷模型故障識(shí)別結(jié)果對(duì)比

由表2可知，故障樣本在噪聲控制系數(shù)取值較?。ㄈ?.01）的情況下，4種故障診斷模型的故障識(shí)別率均大于85%，故障識(shí)別性能較好，其中FWA-PNN模型性能最優(yōu)，故障識(shí)別率達(dá)到100%；隨著噪聲程度的遞增，由于常規(guī)BP神經(jīng)網(wǎng)絡(luò)噪聲適應(yīng)能力及容錯(cuò)能力較弱，模型的故障診斷精度有較大程度下降，在=0.06時(shí)，故障識(shí)別率僅為65%；GABP神經(jīng)網(wǎng)絡(luò)模型，將全局優(yōu)化性能較強(qiáng)的GA算法和BP神經(jīng)網(wǎng)絡(luò)有機(jī)融合，利用GA算法對(duì)神經(jīng)網(wǎng)絡(luò)的權(quán)閾值進(jìn)行優(yōu)化，有效提高了常規(guī)BP神經(jīng)網(wǎng)絡(luò)的非線性映射能力。故障識(shí)別率有一定程度提高，但噪聲抗干擾能力不夠強(qiáng)；PNN神經(jīng)網(wǎng)絡(luò)由于吸收了徑向基神經(jīng)網(wǎng)絡(luò)與經(jīng)典的概率密度估計(jì)原理的優(yōu)點(diǎn)，具有較強(qiáng)的噪聲抗干擾能力，在模式分類方面較BP網(wǎng)絡(luò)更有優(yōu)勢(shì)，整體故障識(shí)別性能優(yōu)于BP網(wǎng)絡(luò)；FWA-PNN神經(jīng)網(wǎng)絡(luò)由于采用FWA算法對(duì)每個(gè)模式類別的平滑參數(shù)σ進(jìn)行優(yōu)化，有效提高了PNN的識(shí)別精度，在不同程度的噪聲影響下FWA-PNN神經(jīng)網(wǎng)絡(luò)模型均具有最高的故障識(shí)別率。

5 結(jié) 論

復(fù)雜噪聲環(huán)境下齒輪箱的狀態(tài)監(jiān)測(cè)與故障診斷對(duì)于保障設(shè)備安全可靠運(yùn)行具有重要理論意義和實(shí)用價(jià)值。為更好地實(shí)現(xiàn)齒輪箱的智能故障診斷，本文融合煙花算法和概率神經(jīng)網(wǎng)絡(luò)，提出一種改進(jìn)的模式分類方法并成功用于噪聲環(huán)境下齒輪箱的故障診斷建模。主要結(jié)論為：

1）為解決現(xiàn)有PNN模式分類方法在實(shí)際應(yīng)用過(guò)程中存在對(duì)訓(xùn)練樣本的代表性要求高及平滑參數(shù)難以確定等問(wèn)題，一方面定義了一種樣本相似度衡量指標(biāo)并設(shè)計(jì)了一種代表性訓(xùn)練樣本提取方法，可有效提高PNN建模過(guò)程中訓(xùn)練樣本的質(zhì)量；另一方面引入一種全局優(yōu)化性能較強(qiáng)的FWA算法用于優(yōu)化PNN每個(gè)模式類別的平滑參數(shù)，以提高噪聲環(huán)境下PNN模式分類與識(shí)別的精度。

2）通過(guò)對(duì)6類典型故障情況下齒輪箱的振動(dòng)信號(hào)進(jìn)行分析和處理，得到相應(yīng)的故障特征向量。為模擬齒輪箱的實(shí)際工況，在典型故障樣本中人為添加不同程度的噪聲并產(chǎn)生相應(yīng)的故障診斷建模樣本。將提出的改進(jìn)FWA-PNN模式分類方法用于齒輪箱故障診斷建模，建立了故障特征參量與齒輪箱工作狀況間的非線性映射關(guān)系。試驗(yàn)結(jié)果表明在噪聲控制系數(shù)為0.01、0.02、0.04和0.06的情況下，該故障診斷模型的故障識(shí)別率分別為100%、95.83%、93.33%和88.33%，優(yōu)于BP-NN、GABP-NN和PNN 3種故障診斷模型。本文所構(gòu)建的模型能較為準(zhǔn)確地檢測(cè)齒輪箱的各種典型故障，有效地提高了現(xiàn)有方法的故障診斷性能，為復(fù)雜噪聲環(huán)境下齒輪箱等非線性復(fù)雜系統(tǒng)的故障診斷提供一種通用可行的解決方案。

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Intelligent fault diagnosis of gearbox based on improved fireworks algorithm and probabilistic neural network

Chen Ruqing1, Li Jiachun2, Shang Tao1, Zhang Jun3

(1.,,314001,; 2.,,314001,; 3.,,310058,)

In the field of agricultural machine and equipment, gearbox was a key mechanical part that was widely applied in speed regulation and power transmission. The gearbox had a high fault rate in actual operating process due to the severe working condition and its complex configuration. State monitoring and fault diagnosing were of great significance to guarantee the safety and stability of gearbox. A fault diagnosis method based on the improved fireworks algorithm (FWA) and probabilistic neural network (PNN) was proposed to overcome the shortcomings, such as the sensitivity to environmental noise and low fault recognition rate, when conducting the fault diagnosis system of gearbox under complex operating conditions. To enhance the pattern classifying performance of traditional methods based on PNN, a new similarity measure for samples was defined, which made the quality of PNN training data increase in modeling process. An improved FWA-PNN classification method was proposed by combining FWA optimization algorithm with PNN technology. The FWA was applied to optimize the smoothing parameters of PNN to determine the optimal values of network parameters, and thus in some way the pattern classification and identification accuracy of PNN could be improved. The proposed FWA-PNN classification method was applied in fault diagnosis modeling for gearbox under noisy environment, and the complex non-linear mapping relationship between fault characteristic parameters and equipment working conditions was constructed. Experiments were carried out on JZQ250 gearbox in laboratory and the process of the fault diagnosis modeling was summarized as follows: At first, 6 working states of the gearbox that included normal state and 5 typical fault states were simulated during the experiments. And then the vibration signals of the gearbox were gained by using the accelerometers of signal acquisition system under different working conditions. After the pretreatment, time and frequency domain analysis of vibration signals were carried out and 27 time and frequency parameters reflecting the working status of the gearbox were obtained. Kernel principal component analysis (KPCA) method was applied to extract the features of the original high-dimensional data, and 7 characteristic parameters were selected as the fault feature vectors of gearbox at last. As a result, the original fault samples were generated according to the fault feature vectors. Given that the fault vibration signals of gearbox were easy to be interfered by different noises in practice, the fault modeling sample sets were regenerated by adding random noises of different levels in the original fault samples. Two thirds of the samples were randomly selected as the training data and the remaining samples were as the test data to establish fault diagnosis model for gearbox based on FWA-PNN. Next, in order to validate the effectiveness and robustness of this new model, BP (back propagation) neural network (BP-NN), genetic algorithm based BP-NN (GABP-NN) and normal PNN methods were introduced to compare with the improved pattern classification method, and 4 different fault diagnosis models were built. The training results of different neural network models indicated that FWA-PNN had better performance in error convergence speed and precision than GABP-NN and BP-NN, which had an excellent fault tolerance and fault classification capability. Finally, 4 different models were applied in fault diagnosis and classification by using the noise samples as the test data. Comparison results indicated that FWA-PNN model could effectively improve the precision of fault detection due to the smooth parameters of all pattern categories optimized by FWA. Application results showed that by compared with the fault diagnosis models based on BPNN, GABPNN and traditional PNN, the FWA-PNN model had the highest fault recognition rate under different noise levels. In conclusion, a novel fault diagnosis program for nonlinear and complex mechanical systems is provided in this paper. It has good application prospects and popularized value in fault diagnosing for agricultural machinery and equipment.

gears; algorithms; noises; probabilistic neural network; fault diagnosis modeling

2018-01-29

2018-06-30

浙江省基礎(chǔ)公益研究計(jì)劃項(xiàng)目（LGG18F030011）；國(guó)家自然科學(xué)基金資助項(xiàng)目（61603154）

陳如清，副教授，博士，主要從事復(fù)雜工業(yè)過(guò)程建模、機(jī)械系統(tǒng)狀態(tài)監(jiān)測(cè)與故障診斷的有關(guān)研究。Email：10555322@qq.com

10.11975/j.issn.1002-6819.2018.17.025

TH165+.3; TH132.46

A

1002-6819(2018)-17-0192-07

陳如清，李嘉春，尚 濤，張 俊. 改進(jìn)煙花算法和概率神經(jīng)網(wǎng)絡(luò)智能診斷齒輪箱故障[J]. 農(nóng)業(yè)工程學(xué)報(bào)，2018，34(17)：192－198. doi：10.11975/j.issn.1002-6819.2018.17.025 http://www.tcsae.org

Chen Ruqing, Li Jiachun, Shang Tao, Zhang Jun. Intelligent fault diagnosis of gearbox based on improved fireworks algorithm and probabilistic neural network[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2018, 34(17): 192－198. (in Chinese with English abstract) doi：10.11975/j.issn.1002-6819.2018.17.025 http://www.tcsae.org