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畬族傳統(tǒng)服裝設(shè)色關(guān)聯(lián)規(guī)則分析

2023-07-04 13:46曹竟文賈靜徐平華林瑞冰孫曉婉
絲綢 2023年4期
關(guān)鍵詞:關(guān)聯(lián)規(guī)則可視化

曹竟文 賈靜 徐平華 林瑞冰 孫曉婉

摘要: 為清晰闡釋畬族傳統(tǒng)服裝設(shè)色分布及其關(guān)聯(lián)規(guī)則,文章利用圖像分析技術(shù)解析意象色彩配色關(guān)系。以散居于浙、贛、閩三地畬族為例,對(duì)田野調(diào)查采集的150幅典型傳統(tǒng)服裝圖像進(jìn)行色彩解析。通過利用自適應(yīng)聚類機(jī)制提取意象色彩,分別構(gòu)建三地服裝色彩譜系;設(shè)計(jì)基于向量集的Apriori算法,解析畬族服裝意象色之間的多元配色關(guān)系。實(shí)驗(yàn)結(jié)果表明,浙、贛、閩三地畬族服裝用色集中于黑、紅、藍(lán)等八色,主色較為接近;最小支持度優(yōu)選0.2時(shí),能夠有效區(qū)分三地服裝多元配色差異。其中浙江地區(qū)二元配對(duì)色組、江西地區(qū)三元配對(duì)色組表色相對(duì)豐富。改進(jìn)后的算法配色規(guī)則輸出平均耗時(shí)0.032 s,能夠快速解析畬族服裝設(shè)色關(guān)聯(lián)規(guī)則,為類似傳統(tǒng)服裝色彩分析和再生設(shè)計(jì)提供方法參考。

關(guān)鍵詞: 設(shè)色關(guān)系;關(guān)聯(lián)規(guī)則;自適應(yīng)聚類;色彩解析;色彩譜系;可視化

中圖分類號(hào): TS941.2;TP391.7

文獻(xiàn)標(biāo)志碼: A

文章編號(hào): 1001-7003(2023)04-0100-07

引用頁碼:

041201

DOI: 10.3969/j.issn.1001-7003.2023.04.013(篇序)

紡織品服裝同質(zhì)化、供需錯(cuò)配、設(shè)計(jì)決策遲緩等問題的長期顯現(xiàn),成為產(chǎn)業(yè)高質(zhì)量發(fā)展的瓶頸制約之一。隨著“東方美學(xué)”“新時(shí)尚”等消費(fèi)勢(shì)態(tài)的激活,再生傳統(tǒng)、民族、本土化的服飾精神和文化內(nèi)涵,為消費(fèi)增長開辟了新思路和新途徑。

畬族是分布在中國東南地區(qū)的散雜居少數(shù)民族,其服飾色彩獨(dú)具特色。相關(guān)學(xué)者從審美特征[1-3]、文化變遷[4],宗教信仰[5]及染色工藝發(fā)展[6]等方面對(duì)畬族傳統(tǒng)服飾進(jìn)行評(píng)述。夏帆等[2]以畬族相關(guān)史料典藏為線索,提出畬族服裝典型樣式中青、藍(lán)、黑為主要色系;陳敬玉[4]認(rèn)為畬族在歷史遷徙過程中與周邊民族的融合,使其在各地形成特有的服飾風(fēng)貌外觀;吳微微等[5]認(rèn)為畬族盛裝中所呈現(xiàn)的對(duì)紅色與黑色的尊崇,反映出畬族先民對(duì)太陽、火與黑暗的自然崇拜;段婷[6]則從面料印染角度出發(fā),認(rèn)為清代及后期畬族服飾色彩受到藍(lán)染工藝的影響,逐漸形成“衣尚青藍(lán)色”的服飾特色。當(dāng)前對(duì)畬族服裝設(shè)色多側(cè)重于感性認(rèn)知,缺乏系統(tǒng)性量化分析和地域性比對(duì)。近年來,圖像分析技術(shù)逐步應(yīng)用至色彩解析領(lǐng)域。徐平華等[7]、Hagtvedt等[8]量化分析各民族服飾所提取出的主色;劉肖健等[9-10]依托改進(jìn)的色彩網(wǎng)絡(luò)模型簡潔表達(dá)色彩量化元素;徐明慧等[11]針對(duì)品牌服裝構(gòu)建二元配色關(guān)系模型,但在意象色多元組合方面未作深入探討。

為此,本文重點(diǎn)以畬族傳統(tǒng)服裝為例,利用圖像分析技術(shù),構(gòu)建浙、贛、閩三地畬族服裝色彩譜系;使用改進(jìn)的Apriori算法,挖掘意象色多元配色關(guān)聯(lián)關(guān)系,為傳統(tǒng)服裝色彩再生設(shè)計(jì)提供配色基準(zhǔn)。

1 設(shè)色關(guān)聯(lián)規(guī)則挖掘

關(guān)聯(lián)分析又稱關(guān)聯(lián)挖掘,是對(duì)信息載體內(nèi)對(duì)象集合間頻繁模式的解析。對(duì)于服裝設(shè)色而言,針對(duì)批量服裝圖像色彩間配色關(guān)聯(lián)性,利用關(guān)聯(lián)規(guī)則算法挖掘其內(nèi)在賦色機(jī)制。

1.1 服裝用色數(shù)據(jù)集

為構(gòu)建系列服裝圖像用色數(shù)據(jù)集,對(duì)田野考察[12]獲得的畬族服裝圖像,按照浙、贛、閩三地進(jìn)行歸類。每個(gè)地區(qū)篩選了50幅代表性服裝樣本,三地共計(jì)150幅,所涉上裝為右衽大襟衣、下裝為筒裙或長褲等款式。對(duì)于含背景、噪聲的圖像,首先采用GrabCut[13]、高斯濾波[14]、伽馬光照自適應(yīng)校正[15]等算法對(duì)其進(jìn)行預(yù)處理,僅保留服裝主體內(nèi)容,背景則采用純白色標(biāo)記。

服裝用色基礎(chǔ)數(shù)據(jù)取自序列服裝圖像,在批量處理服裝樣本圖像時(shí),各樣本設(shè)色存在差異。在基礎(chǔ)數(shù)據(jù)集構(gòu)建階段,若采用常規(guī)K-means聚類,強(qiáng)制統(tǒng)一各樣本色彩聚類簇?cái)?shù),容易導(dǎo)致提色偏差。因此,本文采用二分K-均值自適應(yīng)聚類[16],自適應(yīng)提取每幅服裝色彩。在HSV色彩空間下,對(duì)序列樣本主色進(jìn)行提取;在此基礎(chǔ)上,橫向比對(duì)地域差異時(shí),采用K-means算法進(jìn)行二次聚類,獲得各地區(qū)服裝意象色。以浙江地區(qū)畬族服裝樣本為例,最終獲得如圖1所示的首次聚類提取色和二次聚類意象色。

1.2 關(guān)聯(lián)規(guī)則構(gòu)造

設(shè)色規(guī)則挖掘,是對(duì)色彩融合圖中超過一定閾值的配對(duì)色組,如二元、三元、四元等共現(xiàn)色組,進(jìn)行關(guān)聯(lián)度解析。當(dāng)前關(guān)聯(lián)規(guī)則挖掘算法中,Apriori算法[17]常用于挖掘數(shù)據(jù)關(guān)聯(lián)規(guī)則,以找出數(shù)據(jù)值頻繁出現(xiàn)的組合及其關(guān)聯(lián)關(guān)系。針對(duì)該算法中的連接和修剪耗時(shí)長等缺陷,相關(guān)學(xué)者提出如FP-Growth[18]、DHP[19]和頻繁閉項(xiàng)集法[20]等改進(jìn)算法,但當(dāng)數(shù)據(jù)維數(shù)較大時(shí),運(yùn)行效率較低。為快速挖掘頻繁項(xiàng)集,本文提出了一種基于布爾矩陣運(yùn)算的Apriori改進(jìn)算法。

算法主要包括兩個(gè)模塊,一是尋找頻繁項(xiàng)集的函數(shù)模塊,評(píng)價(jià)指標(biāo)為支持度,計(jì)算如下式所示:

Support(A,B)=P(A∪B)=NA,BN(1)

式中:P(A∪B)表示A、B項(xiàng)同時(shí)出現(xiàn)的比率,NA,B為A、B項(xiàng)同時(shí)出現(xiàn)的次數(shù),N為樣本數(shù)。

置信度反映了當(dāng)A出現(xiàn)時(shí),B出現(xiàn)的概率大小,如果置信度為100%,則表明A出現(xiàn)時(shí)必然伴隨著B出現(xiàn)的情況。

另一模塊是探索關(guān)聯(lián)規(guī)則的函數(shù)模塊,指標(biāo)為置信度,計(jì)算如下式所示:

Confidence(AB)=P(A|B)=NA,BNA(2)

式中:P(A|B)為條件概率,表示當(dāng)A出現(xiàn)時(shí),B出現(xiàn)的概率;NA為A出現(xiàn)的次數(shù)。

由于置信度A→B與B→A在色彩關(guān)聯(lián)規(guī)則挖掘中意義相同,為有效減少程序計(jì)算量,算法僅考慮支持度的影響。

1.3 關(guān)聯(lián)規(guī)則挖掘

將上述提取色聚類所對(duì)應(yīng)的意象色標(biāo)記結(jié)果構(gòu)建為布爾型矩陣Dn×k,下標(biāo)n為圖像樣本數(shù);k為二次聚類K-means設(shè)定的聚類中心數(shù),即指定的意象色彩數(shù)。矩陣元素Dij表達(dá)如下式所示:

Dij=1I→i=Cj0I→i≠Cj(3)

式中:1≤i≤n,1≤j≤k;Cj為第j個(gè)聚類中心。

當(dāng)?shù)趇幅圖像中存在提取色二次聚類歸為第j意象色時(shí),Dij為1;否則,置為0。如圖2所示,當(dāng)k取值為8時(shí),第1幅樣本圖像存在與意象色色號(hào)1、4、5、7、8相似的顏色,則對(duì)應(yīng)至矩陣首行相應(yīng)元素值為1,其余為0。類似地,計(jì)算矩陣Dn×k中其他元素值。

頻繁項(xiàng)集采用與操作運(yùn)算,如下式所示:

Fjt=Dj∧Dt=d1j∧d1td2j∧d2tdnj∧dnt, j,t∈(1,k)(4)

式中:Dj、Dt分別為矩陣任意兩列數(shù)據(jù)項(xiàng),由此計(jì)算j、t二元配對(duì)色的支持度Fjt。

計(jì)算如下式所示:

Support(Fjt)=1n∑ni=1(dij∧dit)(5)

類似地,增加公式與操作項(xiàng),完成多元色組支持度的計(jì)算。

具體步驟為:通過式(3)構(gòu)建色彩聚類結(jié)果對(duì)應(yīng)的布爾矩陣Dn×k,根據(jù)式(5)相應(yīng)地生成二元配對(duì)色組頻繁項(xiàng)集、三元配對(duì)色組頻繁項(xiàng)集,至多元配對(duì)色組頻繁項(xiàng)集。當(dāng)不再產(chǎn)生滿足最小支持度的頻繁項(xiàng)集,終止計(jì)算。

2 畬族服裝設(shè)色實(shí)證分析

2.1 畬族傳統(tǒng)服裝色彩構(gòu)成分析

文獻(xiàn)[2,21-22]對(duì)畬族服裝用色進(jìn)行解讀,指出常見色主要為黑、藍(lán)、青、紅、黃、赭、綠、灰8色。為具象化表述浙、贛、閩三地畬族服裝色彩構(gòu)成情況,本文采用圖形化方式展示意象色分布、占比及其十六進(jìn)制色值。實(shí)驗(yàn)中二次聚類數(shù)k同樣設(shè)為8,結(jié)果如圖3所示。

由H-S色環(huán)中顏色落點(diǎn)可以看出,三地意象色主要表現(xiàn)為黑、紅、藍(lán)等色,與文獻(xiàn)[2,21-22]基本一致,但分布存在著一定的差異。浙江、江西地區(qū)畬族服裝意象色多數(shù)落點(diǎn)在紅、

紫、藍(lán)象限,福建地區(qū)則主要落點(diǎn)在紅、黃、青象限。此外,意象色占比排序同樣存在一定的差異,若以占比50%內(nèi)意象色為主色,浙江地區(qū)主色為黑、藍(lán)和黃;江西為黑、灰和紅;福建則為黑、青和黃色。

該方法直觀地展示了不同地區(qū)畬族服裝色彩分布及其差異。進(jìn)一步地論證了畬族雖經(jīng)遷徙,但用色仍保持了相對(duì)穩(wěn)定,并隨著與本土民俗的融合,設(shè)色形態(tài)上適度演化,形成當(dāng)前的地域特征。

2.2 關(guān)聯(lián)規(guī)則支持度閾值選擇

關(guān)聯(lián)規(guī)則中支持度閾值的設(shè)定,直接影響到配對(duì)色組解析數(shù)量。支持度閾值范圍在0~1,閾值越大,解析的種類越少;反之,輸出的解析種類增多。為了橫向比較不同地區(qū)畬族服裝設(shè)色規(guī)則,選擇有效的支持度閾值,本文對(duì)不同閾值下關(guān)聯(lián)規(guī)則數(shù)進(jìn)行比較分析。實(shí)驗(yàn)中,以0.1為間隔,解析了0.1~1.0不同閾值下配對(duì)色組關(guān)系,結(jié)果如圖4所示。

總體來看,當(dāng)閾值由0.1逐步增大至1.0時(shí),二元、三元、四元、五元配對(duì)數(shù)逐漸遞減。當(dāng)閾值增大至0.5時(shí),浙江地區(qū)配對(duì)數(shù)均為0,江西和福建地區(qū)僅存二元配對(duì)色組;類似地,閾值為0.3、0.4時(shí),配對(duì)類較少,不利于區(qū)分三地配色關(guān)系。而當(dāng)閾值為0.1時(shí),配對(duì)關(guān)系數(shù)過多,不利于設(shè)計(jì)人員觀測(cè)內(nèi)在核心關(guān)系。當(dāng)閾值設(shè)置為0.2時(shí),二元、三元規(guī)則數(shù)量適中,能夠有效區(qū)分不同地區(qū)的畬族服裝設(shè)色關(guān)系。因此,實(shí)驗(yàn)中支持度閾值設(shè)置為0.2,用以進(jìn)一步地分析不同地區(qū)畬族服裝設(shè)色關(guān)系。

2.3 不同地區(qū)畬族服裝設(shè)色關(guān)系解析

為厘清畬族服裝色彩搭配關(guān)系和運(yùn)用機(jī)制,區(qū)分不同地區(qū)設(shè)色關(guān)系差異,本文對(duì)其關(guān)聯(lián)關(guān)系作進(jìn)一步探析。

表1顯示了三地畬族服裝二元配色關(guān)系及其支持度。其中,浙江地區(qū)雙色規(guī)則有18組、江西地區(qū)16組、福建地區(qū)14組,各配對(duì)色組支持度數(shù)值按序排列。

為可視化呈現(xiàn)三地畬族服裝二元配色規(guī)則,輸出形式設(shè)置為:線段兩端連接配色對(duì),線段粗細(xì)表示支持度大小,連線越粗即支持度越高,即二色共現(xiàn)頻次越高,結(jié)果如圖5所示。

由表1及圖5可知,三地畬族服裝色彩配對(duì)關(guān)系中,浙江地區(qū)居多,用色靈活多樣,配色形式豐富。福建地區(qū)較為簡潔,且其F8號(hào)色未出現(xiàn)于配色關(guān)系中,說明其與常用色搭配使用概率低于20%。

若以支持度不低于0.4配對(duì)色組為高頻配對(duì),則浙江地區(qū)畬族服裝用色Z1-Z2、Z1-Z3、Z1-Z5和Z1-Z6為高頻配對(duì),高占比Z1色號(hào)多與藍(lán)、黃和紅色相搭配呈現(xiàn);江西地區(qū)高頻配對(duì)色組僅為J1-J2,支持度為0.52,即江西地區(qū)畬族服裝常以黑、灰兩色高占比搭配出現(xiàn)頻次高于50%,用色深沉質(zhì)樸;福建地區(qū)高頻配對(duì)色為F1-F3、F1-F5與F1-F4三組。

此外,浙江地區(qū)畬族服裝還存在Z4、Z5、Z6與Z8四種色號(hào)交織低頻配對(duì),玫紅、土紅、深紅等深淺不一的搭配,服裝圖案中以紅色、水紅色為主、粉色為輔的色彩搭配,黑色則協(xié)調(diào)統(tǒng)一所有色彩;通過色彩搭配形成區(qū)域性的視覺中心點(diǎn),蘊(yùn)含著一定的服裝美學(xué)原則。福建地區(qū)中F3-F6、F4-F5與F4-F7配對(duì)色組支持度均為0.2,即福建地區(qū)畬族服裝存在少量紅、黃等點(diǎn)綴色作亮麗裝飾配色。

表2為三地畬族服裝三元配色關(guān)系及其支持度,其中浙江地區(qū)三色規(guī)則有3組、江西地區(qū)7組、福建地區(qū)5組。圖6為三地畬族服裝三元配色關(guān)系,三角形三條邊連接三種配對(duì)色,灰色越深表示支持度越高,即畬族服裝搭配中三色共現(xiàn)頻次越高。

由表2及圖6可知,江西地區(qū)畬族服裝三元色配對(duì)關(guān)系較為豐富,福建次之,浙江最少。其中,浙江地區(qū)中Z1-Z2-Z3配對(duì)色搭配頻次較高,為高占比黑—藍(lán)—黃對(duì)比色搭配。江西地區(qū)存在J1、J2號(hào)色與中低占比色搭配情況,即江西地區(qū)畬族服裝三元配色多存在黑、灰作主色,其余常用色點(diǎn)綴情況。福建地區(qū)中F1-F3-F5配對(duì)色為三地中三元配對(duì)頻次最高,支持度高達(dá)0.35,其畬族服裝整體呈現(xiàn)黑、青、不同深淺黃色三色相互配對(duì)的對(duì)比色搭配。

實(shí)驗(yàn)中,算法測(cè)試用計(jì)算機(jī)配置為:處理器AMD 3.59 GHz,機(jī)帶RAM為8.0 GB,利用Python編寫的關(guān)聯(lián)規(guī)則挖掘算法,配色規(guī)則平均耗時(shí)0.032 s。

3 結(jié) 論

本文利用圖像分析技術(shù),對(duì)田野調(diào)查采集的畬族服裝圖像進(jìn)行色彩解析。采用二分自適應(yīng)聚類提取圖像色彩數(shù)據(jù),再通過兩次聚類構(gòu)建浙、贛、閩三地畬族服裝意象色。利用改進(jìn)的Apriori算法解析服裝設(shè)色規(guī)則,以可視化方式闡釋不同地區(qū)設(shè)色形態(tài)和關(guān)聯(lián)關(guān)系。

實(shí)驗(yàn)結(jié)果表明,三地畬族服裝量化色與當(dāng)前文獻(xiàn)記載的畬族服裝用色基本吻合,色相整體呈現(xiàn)為黑、紅、藍(lán)等色。二元配色關(guān)系中,各地區(qū)畬族服裝色彩配對(duì)色組存在一定差異。浙江地區(qū)畬族服裝存在深淺不一的同類色交織搭配情形,呈現(xiàn)出豐富層次感;江西地區(qū)用色深沉樸素,其中黑灰搭配頻率大于50%;福建地區(qū)則存在少量紅、黃等點(diǎn)綴色搭配情況。三元配色關(guān)系中,江西地區(qū)畬族服裝配對(duì)較為豐富,浙江地區(qū)較為簡潔,福建地區(qū)整體呈現(xiàn)黑、青、深黃與淺黃相互配對(duì)關(guān)系。上述解析的三個(gè)地區(qū)畬族服裝設(shè)色關(guān)系,具象化表現(xiàn)出服裝用色規(guī)律和配色邏輯,有助于實(shí)現(xiàn)對(duì)畬族服裝色彩的數(shù)字化保護(hù)。此外,該方法客觀、可視化的方式表征服裝用色機(jī)制,為今后畬族服裝色彩活化設(shè)計(jì)應(yīng)用提供了賦色依據(jù),也進(jìn)一步為系統(tǒng)研究同類傳統(tǒng)服裝色彩提供方法參考。

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Coloration association rules parsing of She nationality costumes

CAO Jingwena, JIA Jinga, XU Pinghuaa,b,c, LIN Ruibinga, SUN Xiaowana

(a.School of Fashion Design & Engineering; b.Zhejiang Provincial Research Center of Fashion Engineering Technology; c.MOC Key Laboratoryof Silk Culture Heritage and Product Design Digital Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China)

Abstract:

Homogenization of textiles and garments, the mismatch between supply and demand, and slow design decisions have long been a bottleneck in the development of a high-quality industry. With the activation of consumer trends such as “oriental aesthetics” and “new fashion”, the regeneration of traditional, national and localized clothing spirit and cultural connotation has opened up new ideas and new ways for consumption growth. Color research based on image analysis technology is helpful to accurately, conveniently, and objectively characterize garment composition forms and color usage patterns and build a bridge between subjective perception and quantitative analysis, thus helping the development and application of intelligent color design for fashion products.

In order to clearly explain the color distribution and association rules of She traditional costumes, image analysis techniques were utilized to parse the imagery coloration relationship. Taking the She diaspora in Zhejiang, Jiangxi and Fujian provinces as an example, the coloration of 150 representative costumes images obtained from the field survey were analyzed. Firstly, the selected samples were subjected to image pre-processing operations. Secondly, in the construction stage of the base dataset, if conventional K-means clustering was used, the number of color clusters of each sample was forced to be uniform, which would easily lead to color lifting bias. Therefore, an improved dichotomy K-means adaptive clustering algorithm was used here to adaptively extract the color of each garment. Under HSV color space, the main colors of the sequence samples were extracted. On this basis, the K-means algorithm was used for secondary clustering when regional differences were compared horizontally, and the number of common color categories of She was determined according to relevant literature studies to unify the number of cluster centers and obtain the clothing imagery colors of each region. The improved vector set-based Apriori algorithm was used to resolve the multivariate color matching relationships among the imagery colors of She clothing, and to visually characterize the color patterns and correlations of different regional settings at the same time. Experimental results show that the quantified colors of She clothing in the three regions match the colors used in She clothing recorded in current literature, and the color palette as a whole presents black, red and blue. In the binary color matching relationship, there are some differences in the color matching color groups of She clothing in each region. In Zhejiang province, there are different shades of similar colors interwoven with each other, showing a rich sense of hierarchy; in Jiangxi province, the colors are deep and simple, with matching frequency of black and gray being greater than 50%, while in Fujian province, there are a small amount of red, yellow and other colors embellishing with each other. In the ternary color scheme relationship, the She clothing pairing is richer in Jiangxi province, simpler in Zhejiang province, and as a whole shows black, green, dark yellow and light yellow pairing relationships with each other in Fujian province. The average time cost of color matching rules parsing with the improved algorithm is 0.032 seconds, which can quickly parse the color correlation rules of She costumes coloration, and provides a referenced method of color analysis and regeneration design for other similar traditional costumes.

This study analyzes the color relationships of She clothing in Zhejiang, Jiangxi, and Fujian, and concretely represents the color usage patterns and color matching logic of clothing, which helps to realize the digital conservation of She clothing coloration. In addition, the objective and visualized way of characterizing the color mechanism of clothing provides a basis for color assignment for the future application of color activation and regeneration design of She clothing and further provides a methodological reference for the systematic study of similar traditional clothing colors.

Key words:

coloration relationship; association rules; adaptive clustering; color parsing; color spectrum; visualization

收稿日期:

2022-07-04;

修回日期:

2023-02-26

基金項(xiàng)目:

國家自然科學(xué)基金青年基金項(xiàng)目(61702460);國家社會(huì)科學(xué)基金重點(diǎn)項(xiàng)目(19AMZ009);浙江省高校重大人文社會(huì)科學(xué)攻關(guān)計(jì)劃項(xiàng)目(2023QN092);浙江理工大學(xué)科研業(yè)務(wù)費(fèi)專項(xiàng)資金資助項(xiàng)目(22076215-Y,2021Q057);服裝設(shè)計(jì)國家級(jí)虛擬仿真實(shí)驗(yàn)教學(xué)中心項(xiàng)目(zx20212004);浙江省服裝工程技術(shù)研究中心開放基金項(xiàng)目(2021FZKF05);浙江省教育廳科研基金項(xiàng)目(Y202250618);浙江理工大學(xué)教育教學(xué)改革研究重點(diǎn)項(xiàng)目(jgzd202202);浙江理工大學(xué)優(yōu)秀研究生學(xué)位論文培育基金項(xiàng)目(LW-YP2021053)

作者簡介:

曹竟文(1998),女,碩士研究生,研究方向?yàn)榉椛手腔墼O(shè)計(jì)。通信作者:徐平華,副教授,shutexph@163.com。

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