段垚奇， 劉克格， 趙麗娜， 閆楚良

(北京飛機(jī)強(qiáng)度研究所 北京，100083)

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飛機(jī)載荷標(biāo)定試驗(yàn)數(shù)據(jù)的多元回歸選元方法*

段垚奇， 劉克格， 趙麗娜， 閆楚良

(北京飛機(jī)強(qiáng)度研究所 北京，100083)

進(jìn)行飛機(jī)載荷標(biāo)定試驗(yàn)時(shí)，由于載荷與應(yīng)變參數(shù)之間存在耦合相關(guān)性，采用逐步回歸法判斷自變量是否顯著時(shí)具有一定的主觀性。針對(duì)飛機(jī)載荷標(biāo)定試驗(yàn)數(shù)據(jù)處理提出了一種多元回歸選元方法，將回歸項(xiàng)的變異系數(shù)作為誤差控制指標(biāo)和選元的判據(jù)，逐步剔除變異系數(shù)最大的自變量，直至選出最優(yōu)的自變量參數(shù)組合，以此得到較佳的回歸結(jié)果。此方法已成功應(yīng)用于多個(gè)型號(hào)飛機(jī)起落架航向、垂向、側(cè)向載荷的飛行實(shí)測(cè)。

飛行載荷實(shí)測(cè)； 載荷標(biāo)定試驗(yàn)； 多元回歸； 選元

引言

飛機(jī)在研制和使用過(guò)程中需要進(jìn)行載荷實(shí)測(cè)，以獲得在真實(shí)使用條件下的載荷時(shí)間歷程，這是進(jìn)行強(qiáng)度設(shè)計(jì)、可靠性分析和全尺寸疲勞試驗(yàn)的前提。在采用應(yīng)變計(jì)測(cè)量載荷時(shí)，需對(duì)結(jié)構(gòu)部件進(jìn)行載荷標(biāo)定試驗(yàn)，建立輸入載荷與應(yīng)變電橋輸出量值之間的定量關(guān)系。將這種確定的關(guān)系應(yīng)用在飛機(jī)使用過(guò)程中實(shí)測(cè)到的應(yīng)變量值上，可將應(yīng)變時(shí)間歷程轉(zhuǎn)換為載荷時(shí)間歷程[1]。

載荷標(biāo)定試驗(yàn)記錄的原始數(shù)據(jù)由兩部分組成：a.載荷向量y為一個(gè)n維的向量(n為標(biāo)定試驗(yàn)中記錄數(shù)據(jù)的次數(shù))；b. 應(yīng)變參數(shù)矩陣x為一個(gè)n×m的矩陣(m為應(yīng)變參數(shù)的個(gè)數(shù))。由于應(yīng)變參數(shù)始終處于線彈性范圍變化，因此多元線性回歸方法適用于載荷標(biāo)定數(shù)據(jù)的處理[2]。載荷標(biāo)定方程中并非包含越多的自變量越好，引入不恰當(dāng)?shù)膽?yīng)變參數(shù)會(huì)降低實(shí)測(cè)載荷的精度。如何對(duì)應(yīng)變參數(shù)進(jìn)行優(yōu)選，是載荷標(biāo)定數(shù)據(jù)處理的關(guān)鍵問(wèn)題。目前，常用的多元回歸選元方法是逐步回歸法[3]，逐步回歸法的方法步驟是按偏回歸平方的大小次序?qū)⒆宰兞恐饌€(gè)引入方程，對(duì)引入方程的每個(gè)自變量偏相關(guān)系數(shù)進(jìn)行檢驗(yàn)，效果顯著的自變量保留在回歸方程中，循環(huán)繼續(xù)遴選下一個(gè)自變量，如果效應(yīng)不顯著，則停止引入新自變量。由于新自變量的引入，原已引入方程中的自變量由于變量之間的相互作用，其效應(yīng)有可能變得不顯著，經(jīng)統(tǒng)計(jì)檢驗(yàn)確認(rèn)后要隨時(shí)從方程中剔除，只保留效應(yīng)顯著的自變量，直至不再引入和剔除自變量為止，從而得到最優(yōu)的回歸方程。

逐步回歸法在判斷自變量是否顯著時(shí)具有一定的主觀性，而且由于載荷與應(yīng)變參數(shù)之間有復(fù)雜的耦合相關(guān)性，往往會(huì)導(dǎo)致最終載荷標(biāo)定精度的不穩(wěn)定。以某型飛機(jī)起落架載荷實(shí)測(cè)試驗(yàn)采用逐步回歸法得到的實(shí)測(cè)載荷-時(shí)間歷程為例，在轉(zhuǎn)彎時(shí)，左主起落架航向載荷有明顯的變化趨勢(shì)，而在剎車時(shí)，航向載荷卻未表現(xiàn)出明顯的變化趨勢(shì)，這與理論分析及類似機(jī)型的測(cè)試結(jié)果相矛盾，因此認(rèn)為逐步回歸法不完全適用于載荷測(cè)量的所有情況。本研究建立了一種新的多元回歸選元方法，能夠有效控制實(shí)測(cè)載荷的誤差。

1 理論模型

實(shí)測(cè)載荷的標(biāo)定方程[1]可表示為

y=b1x1+b2x2+…+bmxm

(1)

其中：x1～xm為各實(shí)測(cè)應(yīng)變參數(shù)；b1～bm為對(duì)應(yīng)于各實(shí)測(cè)應(yīng)變參數(shù)的真實(shí)系數(shù)；y為實(shí)測(cè)載荷參數(shù)。

對(duì)載荷應(yīng)變參數(shù)進(jìn)行回歸選元的最終目的是控制實(shí)測(cè)載荷的誤差。實(shí)測(cè)載荷的誤差可用實(shí)測(cè)載荷變異系數(shù)的絕對(duì)值K來(lái)衡量，由于x1～xm為實(shí)測(cè)得到的應(yīng)變值，可忽略其誤差，K可表示為

(2)

其中：Sy為實(shí)測(cè)載荷的方差；Sb1～Sbm為各項(xiàng)系數(shù)b1～bm的方差。

因?yàn)镾b1～Sbm均為誤差來(lái)源，而x1～xm為實(shí)測(cè)應(yīng)變值，是尚未確定的變量，所以在標(biāo)定數(shù)據(jù)處理時(shí)，無(wú)法根據(jù)式(2)直接對(duì)實(shí)測(cè)載荷的誤差進(jìn)行控制。

設(shè)

(3)

因?yàn)?/p>

(4)

所以有如下關(guān)系

(5)

將式(5)整理得到

K≤ZP

(6)

由于b1～bm為對(duì)應(yīng)于各實(shí)測(cè)應(yīng)變參數(shù)的真實(shí)系數(shù)，x1～xm為實(shí)測(cè)應(yīng)變值，所以P中沒(méi)有誤差來(lái)源，因此可將Z作為實(shí)測(cè)載荷的誤差指標(biāo)來(lái)進(jìn)行控制。

2 回歸步驟

設(shè)有m個(gè)應(yīng)變參數(shù)x1～xm可能與載荷參數(shù)y存在相關(guān)關(guān)系，設(shè)標(biāo)定試驗(yàn)共進(jìn)行了n次數(shù)據(jù)采集。方法流程如圖1所示，步驟如下。

圖1 方法流程圖Fig.1 Flow chart

1) 計(jì)算式(7)～(9)

(7)

(8)

(9)

2) 計(jì)算各項(xiàng)系數(shù)及各項(xiàng)系數(shù)的標(biāo)準(zhǔn)差[4]

各項(xiàng)系數(shù)

b=Cl0

(10)

各項(xiàng)系數(shù)的標(biāo)準(zhǔn)差

(11)

3) 按照式(9)計(jì)算各項(xiàng)系數(shù)的Z值(記為Zi)，挑出Zi值最大的項(xiàng)，并記錄最大的Zi值為A

(12)

4) 從第2次循環(huán)開(kāi)始，如果第3步計(jì)算出的A大于上一次循環(huán)中計(jì)算出的A值，那么循環(huán)結(jié)束，上一步的回歸結(jié)果為最優(yōu)；否則，將Zi值最大的應(yīng)變參數(shù)項(xiàng)刪除，重新執(zhí)行下一循環(huán)的第1～3步。需要注意的是，下一循環(huán)中的m應(yīng)在當(dāng)前m的基礎(chǔ)上減1。

5) 將最終的回歸結(jié)果代入實(shí)測(cè)應(yīng)變曲線，得到實(shí)測(cè)載荷-時(shí)間歷程，具體方法參考文獻(xiàn)[5-8]。

3 實(shí)例驗(yàn)證

選取一段標(biāo)定試驗(yàn)的數(shù)據(jù)進(jìn)行測(cè)試，此數(shù)據(jù)來(lái)源于某型飛機(jī)水平尾翼載荷標(biāo)定試驗(yàn)的數(shù)據(jù)，如表1所示。其中，y為載荷參數(shù)，在回歸時(shí)y作為因變量。根據(jù)理論分析和對(duì)試驗(yàn)數(shù)據(jù)的觀察結(jié)果，從眾多應(yīng)變參數(shù)中選出與載荷參數(shù)線性相關(guān)性較好的x1～x5作為回歸自變量。

表1 測(cè)試數(shù)據(jù)

按照本研究方法進(jìn)行處理，得到的結(jié)果如表2所示。第3次回歸的結(jié)果為最終結(jié)果，最終結(jié)果的A值等于0.008 2。對(duì)x1～x5所有可能的組合情況分別進(jìn)行回歸處理，計(jì)算各種組合情況下的A值，如表3所示。

表2 基于本研究方法的處理結(jié)果

表3 所有組合情況分別回歸的結(jié)果

為了比較本研究方法與逐步回歸法的效果，用SPASS軟件對(duì)表1中的數(shù)據(jù)進(jìn)行逐步線性多元回歸處理，結(jié)果如式(13)所示，A值等于0.019 5，大于用本研究方法得到選元結(jié)果的A值。從表2，3以及與SPASS處理結(jié)果的比較可以看出，利用本研究方法處理載荷-應(yīng)變線性多元回歸問(wèn)題時(shí)，選出結(jié)果的A值小于用逐步回歸法得到的結(jié)果和其他所有可能的組合情況。

y=-0.009 75x2-0.011 59x3-0.008 75x5

(13)

4 工程應(yīng)用

某型飛機(jī)主起落架為四輪車架式，主起由四輪車架、主支柱、側(cè)撐桿、前撐桿、扭力臂及收放作動(dòng)筒等主要構(gòu)件組成。為了測(cè)量其在實(shí)際使用過(guò)程中的受載情況，在主起落架上進(jìn)行了應(yīng)變計(jì)粘貼，共有應(yīng)變參數(shù)39個(gè)。起落架倒裝在試驗(yàn)臺(tái)架上進(jìn)行標(biāo)定，其在試驗(yàn)臺(tái)上的連接方式與在飛機(jī)上相同，起落架機(jī)輪用假輪代替。通過(guò)在假輪上的加載點(diǎn)進(jìn)行航向、垂向、側(cè)向載荷的加載，且載荷按單向加載、雙向加載、三向加載多種工況分別進(jìn)行，具體的標(biāo)定技術(shù)可參考文獻(xiàn)[5-9]。通過(guò)地面標(biāo)定試驗(yàn)得到了載荷標(biāo)定試驗(yàn)的原始數(shù)據(jù)。

根據(jù)本研究方法對(duì)載荷標(biāo)定試驗(yàn)數(shù)據(jù)進(jìn)行回歸處理，得到了主起落架航向載荷、垂向載荷和側(cè)向載荷的標(biāo)定方程。為了驗(yàn)證標(biāo)定載荷的正確性，在標(biāo)定試驗(yàn)之后進(jìn)行了驗(yàn)證加載，驗(yàn)證加載的理論和方法可參考文獻(xiàn)[10-11]。表4為起落架驗(yàn)證加載時(shí)實(shí)際加載載荷與標(biāo)定方程計(jì)算載荷分析?？梢钥闯?，標(biāo)定方程計(jì)算載荷與實(shí)際加載載荷的誤差均不超過(guò)5%，這滿足顧客方提出的精度要求。

表4 起落架載荷標(biāo)定結(jié)果驗(yàn)證

Tab.4 Verification of the load calibration result of landing gears

載荷參數(shù)實(shí)際載荷/kN計(jì)算載荷/kN相對(duì)誤差/%航向載荷-62．859-61．0232．92垂向載荷148．111143．3613．21側(cè)向載荷-61．785-61．9910．33

圖2 利用本研究方法得到的某機(jī)型左主起落架實(shí)測(cè)載荷-時(shí)間歷程Fig.2 Load of landing gears with the method proposed in this paper

如圖2所示，將實(shí)測(cè)應(yīng)變-時(shí)間歷程代入標(biāo)定方程得到實(shí)測(cè)載荷-時(shí)間歷程。該機(jī)型主起落架為支柱式起落架，沒(méi)有安裝內(nèi)束角，圖2和圖3的第1個(gè)轉(zhuǎn)彎過(guò)程中沒(méi)有剎車，因此航向載荷不應(yīng)有明顯的變化趨勢(shì)(如圖2)，而圖3中的航向載荷表現(xiàn)出明顯的負(fù)向變化趨勢(shì)，這是不符合事實(shí)的。在剎車過(guò)程中主起應(yīng)受到逆航向的載荷，圖2中可以明顯看到這種趨勢(shì)，但圖3中的航向載荷在剎車時(shí)卻沒(méi)有明顯的變化趨勢(shì)，這也是不符合事實(shí)的。圖2與圖3相比，載荷變化規(guī)律能更好地符合理論分析結(jié)果及類似機(jī)型的經(jīng)驗(yàn)。

圖3 利用逐步回歸法得到的某機(jī)型左主起落架實(shí)測(cè)載荷-時(shí)間歷程Fig.3 Load of landing gears with the stepwise regression

5 結(jié)束語(yǔ)

提出了一種基于回歸項(xiàng)變異系數(shù)進(jìn)行誤差控制的多元回歸選元方法。利用實(shí)測(cè)數(shù)據(jù)對(duì)此方法進(jìn)行了驗(yàn)證。結(jié)果表明，該方法處理載荷-應(yīng)變線性多元回歸問(wèn)題時(shí)，可以得到較佳的結(jié)果且計(jì)算量小，便于實(shí)際應(yīng)用。此方法成功應(yīng)用于某型飛機(jī)起落架的載荷實(shí)測(cè)試驗(yàn)，得到了起落架的實(shí)測(cè)載荷-時(shí)間歷程。

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[10]Raymer D P. Aircraft design: a vonceptual approach-third edition[M]. Washington D C: AIAA，1999：7-10.

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Abstract When an airplane load is calibrated, there is some subjectivity in judging whether an independent variable is significant due to coupled correlation between load and strain. A selection method of multiple regression elements for processing calibration test data in airplane structural load measurements is given that uses the coefficient of variation as a standard for selecting multiple regression elements. The biggest coefficient of variation is selected and excluded until optimal results are obtained. This method has been successfully applied to the loads measurement of landing gears.

Keywords flight load measurement; load calibration test; multiple regression; selected element

The Research for the Degradation of the Spindle of Machine Tool Based on Lempel-Ziv Index

DongXinfeng1，ZhangWeimin1,2，DengSong1

(1.School of Mechanical Engineering ,Tongji University Shanghai, 201804, China)(2.Chinese-German School for Postgraduate Studies, Tongji University Shanghai, 201804, China)

In order to estimate the states of the machine tool spindle system during the course of its operation, this paper proposes a deterioration method based on the complexity of the nonlinear system by monitoring the relative index. The vibration signals generated by the workpiece spindle when the grinder machine tool operation is idling were used as the objects of analysis, and the complexity relevant index is used to judge the states of the workpiece spindle of the grinding machine during several months of operation. The analysis results showed that the complexity of the vibration signals generated by the workpiece spindle system increased as the time in use increased. In order to verify the validity of the deterioration analysis, the complexity index is used to analyze the dates of the deterioration bearing published by CWRU. The results showed that the complexity is an effective method for deterioration analysis.

complexity; degradation; machine tool spindle system; bearing; fault

Selection of Regularization Matrixes for Moving Force Identification Based on Truncated Generalized Singular Value Decomposition

ChenZhen1,2,YuLing2

(1.School of Civil Engineering and Communication, North China University of Water Resources and Electric Power Zhengzhou, 450045, China)(2.Key Laboratory of Disaster Forecast and Control in Engineering of Ministry of Education, Jinan University Guangzhou, 510632, China)

Abstract Based on the time domain method (TDM) theory, a truncated generalized singular value decomposition(TGSVD) method for moving force identification has been developed by introducing a regularization matrix. The influence of TGSVD identification can be identified by comparing it with different regularization matrixes. Then, when comparing the TGSVD method with the TDM method, the numerical simulation of two-axle moving force loads shows that regularization matrixes have great influence on such properties as identification accuracy, robustness, etc. With appropriate regularization matrixes, the proposed TGSVD method has many good properties compared with TDM, such as better identification accuracy and robust noise with bending moment responses or acceleration responses. TGSVD has prominent advantages with single responses type or less responses number, which is beneficial for the application of TGSVD in the field identification of dynamic axle loads on bridges.

Keywords bridge; moving force; identification; ill-posed problem; time domain method; truncated generalized singular value decomposition; regularization matrixes

Defect,Improvement and Verification of Seismic Multi-supported Response Spectrum Model

LiuGuohuan1, 2,LianJijian1, 2,GuoWei3,GengChen4,TianLi5

(1.State Key Laboratory Hydraulic Engineering Simulation and Safety, Tianjin University Tianjin, 300072, China) (2.School of Civil Engineering, Tianjin University Tianjin, 300072, China)(3.School of Civil Engineering, Central South University Changsha, 410075, China)(4.School of Civil Engineering, Tianjin Chengjian University Tianjin, 300384, China)(5.School of Civil and Hydraulic Engineering, Shandong University Jinan, 250100, China)

Abstract The multiple support response spectrum (MSRS) theory formula based on displacement and the displacement-velocity model are induced and given. Then, the irrationality and unconvergency of the responses, which are calculated from the displacement-multiple support response spectrum (D-MSRS) model and derived from the current displacement input model, are explained. This paper also addresses the accidence in deducing processing, and necessity in calculation results of MSRS deduced from the acceleration model. The deriving processing and numerical results show that the displacement velocity-multiple support response spectrum (DV-MSRS) is strict and logical. The D-MSRS can induce the unreasonable and unconvergent internal force of the bottom element. The reasonability of A-MSRS (acceleration-multiple support response spectrum) derived from the two negligible terms can be counteracted, but is suitable for a classic damping system.

Keywords seismic ground motion; multi-support response spectrum(MSRS); acceleration input model; displacement input model; displacement-velocity input model; classical damping

Dynamic Performance of a Solar Array Deployable Mechanism with Multiple Clearances

GuYongxia1,YangTianfu2,GuoFeng2

(1.School of Material and Mechanical Engineering, Beijing Technology and Business University Beijing, 100048, China)(2.State Key Laboratory of Tribology, Tsinghua University Beijing, 100084, China)

Abstract All large spacecrafts have deployable structures like solar arrays, which are folded during launch and deployed in orbit. The clearances between the deployable joints greatly impact the system′s dynamics. A multi-body model consisting of a satellite, solar panels, clearance revolute joints and flexible panels is established with ADAMS software. The deployment progress of multiple clearances is numerically simulated, and the comparison between models with different numbers of clearance joints is analyzed by calculating the impact force and relative trail of the shaft mass centroid in the joint. The results show that increasing the clearance number brings in more complexity, and that the joint near the spacecraft base has a stronger influence.

Keywords spacecraft; deployable mechanism; joint clearance; impact

Separation of Real-Time Dynamic Deflection Signals for Long-Span Bridges

YangHong1,LiuXiaping2,CuiHaixia3,PengJun1,SunZhuo2

(1.School of Physics & Electronic Engineering, Guangzhou University Guangzhou, 510006, China)(2.School of Civil Engineering, Guangzhou University Guangzhou, 510006, China)(3.School of Physics and Telecommunication Engineering, South China Normal University Guangzhou, 510006, China)

Abstract The real-time dynamic deflection signal separation of the long-span bridge is an effective new method for the long-span bridge fault diagnosis. Because empirical mode decomposition (EMD) can decompose nonlinear and non-stationary signals into a set of linear and stationary intrinsic mode functions, a blind source separation (BSS) method based on EMD is proposed that combines the respective advantages of BSS and EMD for single-channel long-span bridge deflection signal separation, while EMD can decompose the nonlinear and non-stationary signals into a set of linear and stationary intrinsic mode functions. The source number is estimated using singular value decomposition (SVD), and then to composes the multi-channel input signals with the single-channel deflection signal and its intrinsic mode functions according to the source number. Finally, the method separates the source signals using the fast independent component analysis (Fast ICA) algorithm and obtains the separation value of each component of the bridge deflection signal. Simulation research indicates that this is a good solution for estimating the quantity of source number estimation for the independent component analysis (ICA) model and single-channel deflection signal BSS problem.

Keywords filtering; empirical mode decomposition; independent component analysis; singular value decomposition; deflection signal separation

Prediction and Optimization Method for the Longitudinal Stiffness of V-type Thrust Rod

KeJun1,ShiWenku1,TengTeng2,ZhouYufei2,LiuTianyun3,WuZhiyong3

(1.State Key Laboratory of Automobile Simulation and Control, Jilin University Changchun, 130022, China)(2.China Faw Group Corporation R&D Center Changchun, 130011, China)(3.Changchun Cheng Yun Auto Parts Limited Company Changchun, 130114, China)

Abstract In order to forecast and optimize the longitudinal stiffness of the V-type thrust rod applied to heavy-duty commercial vehicles, the hyperelastic constitutive model of rubber material in the V-type thrust rod is built based on uniaxial tension and compression experiment for rubber specimens. Then the dynamic finite element simulation for the work process of the V-type thrust rods are carried out using Abaqus software. The longitudinal stiffness of the V-type thrust rods is predicted using the post processor module of Abaqus software. The relationship between the V-type thrust rod's longitudinal stiffness and the structure of the spherical hinge is studied according to the strain contours of the rubber layer. The simulation results demonstrates that increasing the width of the plastic layer in the spherical hinge can improve the V-type thrust rod's longitudinal stiffness, because this structure can change the volume and vulcanization area of the rubber layer and block rubber layer extend to end covers. Bench tests for the samples of the primary structure and optimized structure are carried out, and the results show that the prediction and optimization method is valid. This method can shorten the R&D period of the V-type thrust rod and dramatically improve its longitudinal stiffness.

Keywords thrust rod; constitutive model; finite element analysis; stiffness optimize; tandem suspension

Order Selection for Wavelet Series Decomposition in Dynamic Load Identification

YangFan,ZhangFang

(State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics Nanjing, 210016, China)

Abstract Based on orthogonal wavelet series decomposition, there is often inaccuracy or huge amounts of calculation when identifying the load due to improper choice of wavelet series order. The envelope line of the wavelet series coefficient amplitude is proposed, which tends to converge with the increasing order through the matrix spectral decomposition and Parseval theorem of which represents that the total energy in the time-domain and frequency-domain is equivalent. The non-analytical wavelet coefficient is analyzed, and the function between the wavelet series order and the relative error of the identified load is obtained. The wavelet series order is thus chosen according to the error level of the engineering requirements. The theoretical basis of the order selection when using the series decomposition in the dynamic load to be identified is proposed. Both the computer simulation in the form of the single-frequency and multi-frequency, real signal as well as the lab test in the form of the impact signal confirm that the proposed approach is feasible and effective. The results show that the proposed approach is applicable to all forms of the loads.

Keywords load identification; series order determination; wavelet series; orthogonal wavelet basis; structural dynamics

High-Rise Structure Damage Identification Based on Pseudo-Transfer Function

LiWanrun1,2,3,DuYongfeng1,2,NiYiqing3,LiHui1,2

(1.Key Laboratory of Disaster Prevention and Mitigation in Civil Engineering of Gansu Province, Lanzhou University of Technology Lanzhou, 730050, China)(2.Institute of Earthquake Protection and Disaster Mitigation, Lanzhou University of Technology Lanzhou, 730050, China)(3.Shenzhen Research Institute of Hong Kong Polytechnic University Shenzhen, 518057, China)

Abstract A novel damage location method, which is based on the pseudo-transfer function (PTF) established by the ARX model (autoregressive model with eXogenous input), is proposed based on the conception of the transform function reflected the relationship of the input-output (structural characteristics). According to the correlation with the degree of freedom (DOF), the DOF is grouped, the response of one DOF is chosen as a reference channel (which is the ARX model output), and the response of the other DOF correlating with the reference channel is taken as the input of the ARX model. The reference PTF is established using the responses of the health structure. After creating the reference PTF, these models are used to predict the data from the damaged structure. The difference between the fit ratios is used as the damage feature. The methodology is applied to the reduced finite element model of the Canton Tower, and the threshold of damage is established using the change of the fit ratios of the responses with Gaussian white noise of the health structure. The results show that this methodology is successful in damage identification and localization, and can also determine the severity of damage under noise effects.

Keywords pseudo-transform function; ARX model(autoregressive model with exogenous input); damage identification; fit ratio; high-rise structure

Dynamics Modeling Method and Test of Sliding Crawler Travel System

ZhangHong1,KangPeng2,SongYang2,ZhangXiaokun2

(1.School of Mechanical Engineering, Taiyuan University of Science and Technology Taiyuan, 030024，China)(2.Taiyuan Institute of China Coal Technology & Engineering Group Corp Taiyuan, 030006, China)

Abstract In this paper, the operational status of the sliding crawler is studied under special conditions in the underground mine. With the continuous miner as the research object, the interaction between the sliding crawler in a continuous miner coal cutter and the underground as well as the contact characteristics of the various components within the crawler system are analyzed. The contact characteristics of the various components within the crawler system are established. Then, the multi-body interaction mechanics model of the sliding crawler is established to simulate the coal-rock road and running state of the track sliding friction. The crawler system operating parameters of the tractive force and support force at different tensioning displacements, as well as the simulation feature data extraction and conversion are obtained. Then, the machine's total travel power is indirectly calculated by the characteristic data of the machine's total travel power. On this basis, the power-time history curve of the actual real time operating state of the continuous miner is drew according to the underground field test to obtain the power time history curve of actual operating state. The order of magnitude of the conversion power of the simulation results is shown to be within a permissible range of the measured power of the experimental results. The study provides a reliable basis and valid path for the structure optimization and power matching of the crawler system.

Keywords sliding crawler; internal and external friction resistance; physical simulation; underground test

Research on Parameters Identification Method for Local Boundary of Rotor-Bearing System

TanZhen1,2，LiChaofeng2，TaiXingyu2，WenBangchun2

(1.School of Technology, Shen Yang Radio & TV University Shenyang, 110003, China)(2.School of Mechanical Engineering and Automation, Northeastern University Shenyang, 110819, China)

Abstract A whole dynamical model is often built to analyze the dynamic characteristics of exactly one part, because the rotor system has a complex structure and a strong coupling effect between its parts. For example, in a plate or blade, the degrees of freedom of the complete machine finite element model are enormous, and the computational efficiency is low. A constrained parameters identification method for the local restriction is proposed to increase the computational efficiency and make it easier to analyze the part's vibration. A constrained parameters identification method for local restriction is present, considering the subsystem coupling effects in a complex system. The rotor system is resolved and decomposed into the axis and plate and the subsystem and main system are established. Considering the subsystem coupling effects in the complex system, the restrain stiffness and dampness of the boundary unit can be identified by deducing the dynamical equation. The nodes response of the finite element model can be computed and compared with the corresponding nodes of the whole model. The results show that the equations are correct. This method can be used in the vibration analysis modeling of the rotating structure to save computing resources.

Keywords rotor system; parameter identification; dynamical model; stiffness; damp

Method for On-Line Forecasting of Gyro's Drift Based on Wavelet-Strong Tracking Filter Algorithm

ZhangWei1，DuDangbo2，HuChanghua2，ZhouZhijie2，ZhangJianxun2

(1.Department of Information, Xi′an Institute of Hi-Tech Xi′an, 710025, China)(2.Department of Automation, Xi′an Institute of Hi-Tech Xi′an, 710025, China)

Abstract An on-line forecasting method based on the wavelet-suboptimal multiple fading kalman filtering algorithm is proposed in order to advance the forecasting precision of the gyro′s drift coefficients for its data mutation and strong trend according to the characteristics of the gyro′s drift coefficients non-stationary time series. The experimental results indicate that the gyro′s drift can be precisely forecasted, which can effectively improve the problem of inaccurate results brought by the data mutation and the strong trend.

Keywords wavelet analysis; strong tracking filter; gyro′s drift; suboptimal multiple fading factor

Numerical Characteristic and Theory Modeling for Parameter Uncertainty Propagation in Complex System

TangBingsong1,HanXiaolin2,YangHuifeng3

(1.The State Key Laboratory of Structure Analysis of Industrial Equipment, Dalian University of Technology Dalian, 116024, China)(2.Jiangsu Key Laboratory of Engineering Mechanics, Southeast University Nanjing, 210096, China)(3.The State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics Nanjing, 210016, China)

Abstract Parameter uncertainty of measurements is nominally an experimental value fluctuating around a true value in the condition of a definite confidence level. This is a very important tool for describing the accuracy of parameters besides error measures. The concept of uncertainty measurements is developed that multivariable parameters uncertainty is proposed. The basic property of generalized uncertainty is discussed later. Both the propagating characteristic of generalized uncertainty in the complex system and the classification of the propagating characteristic are investigated. The property and mode of parameter uncertainty propagation in one single subsystem are very important research contents. There is significant influence on the calculating result and the absolute value of the elements in the propagation matrix. The comparison between all the subsystems′ parameters uncertainty propagation is discussed, and the corresponding criterion is simultaneously achieved. The examples show the effectiveness and feasibility of this theory when it is applied in the parameter uncertainty propagation problem for a complex system.

Keywords complex system; uncertainty of measurement; propagation matrix; propagation mode

Aero-Engine Fault Diagnosis Based on Dynamic PCA and Improved SVM

CuiJianguo1,YanXue1,PuXueping2,QiYiwen1,JiangLiying1,ShiJianqiang2

(1.School of Automatization, Shenyang Aerospace University Shenyang, 110136, China)(2.China Gas Turbine Establishment Chengdu, 610500, China )

Abstract In order to effectively diagnose aero-engine faults and ensure safety in aircraft flights, a method based on dynamic principal component analysis (PCA) and the improved support vector machine is put forth. It combines the advantages of dynamic PCA in the feature extraction and improves the support vector machine (SVM) in the fault diagnosis. The dynamic PCA method can complete the pre-treatment through de-noising, dimension reduction, and eliminating correlation on the processing variables. The improved SVM method can diagnose faults with the eigenvector. The proposed method can solve such problems as the lubrication system like, low accuracy of the aero-engine model, and limited measurement parameters, all of which are problems that can lead to low efficiency, ease of misdiagnosis, and other issues. A certain type of lubrication system of the aero-engine is taken as an example to verify the effectiveness of the proposed method. The results show that using the dynamic PCA and improved SVM fault diagnosis method can effectively improve accuracy and realize the fault diagnosis performance of the lubrication system of the aero-engine. Furthermore, it has good prospects for future application.

Keywords aero-engine; lubrication system; dynamic principal component analysis; improved support vector machine; fault diagnosis

A Fault Diagnostic Rules Gaining Method for Aviation Electronic Equipment under Incomplete Information Condition

ZhaoLiangliang1，XiaoMingqing1，ShengSheng1，ZhiHuilai2，ZhangLei1

(1.College of Aeronautics and Astronautics Engineering, Air Force Engineering University Xi′an, 710038, China)(2.School of Computer Science and Technology, Henan Polytechnic University Jiaozuo, 454000, China)

Abstract Uncertainty caused by incomplete information brings great challenges to fault diagnostic rules gaining method for aviation electronic equipment. In order to solve the problem, by defining the incompleteness from the two angles of narrow sense and broad sense respectively, the consistency first completer algorithm is designed to solve the inconsistency problem caused by incomplete information based on maximal confidence and attribute value expectation, which exists in indirect completing algorithms. The symptom attributes concept lattice and diagnostic decision-making attributes concept lattice are constructed, and the equivalent relationship on the symptom attributes concept is introduced. Based on this, the disjunctive normal form discernibility function of the maximum inconsistent symptom attributes concept set is computed, then the optimal reduced attribute set is obtained based on which diagnostic rules are gained. Taking the weapon launching system as an example, the approach is validated with a precision of 83.3%. It can be concluded that the approach is better than the existing representative approach in dealing with incomplete information, accuracy and intuitionism of the diagnosis knowledge display.

Keywords incompleteness; discernibility matrix; concept lattice; reduction; diagnostic rules

A Mode-Control-Decoupling Linear Ultrasonic Motor with a Tower-Type Stator

ChenQianwei1,JuQuanyong1,HuangWeiqing2,ShiYunlai2

(1.School of Mechatronic Engineering, Jinling Institute of Technology Nanjing, 211169, China)(2.State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics Nanjing, 210016, China)

Abstract In order to solve the problem that the existing tower-type ultrasonic motors(USMs) cannot control the stator′s normal vibration or tangential vibration separately, a mode-control-decoupling linear ultrasonic motor(LUSM) with a tower-type stator is presented. The LUSM is designed to have two non-coplanar, orthogonal working modes: one is the symmetric vibration mode in thex-zplane that independently excites the driving tip′s normal vibration, while the other is the bending vibration mode in they-zplane that independently excites the driving tip′s tangential vibration. Further, the scheme of piezoelectric ceramics (PZTs) polarization and arrangement location is correspondingly designed as follows: The PZTs are divided into two phases, A and B, in which phase A is used to excite the symmetric vibration mode in thex-zplane, and phase B is used to excite the bending vibration mode in they-zplane. So the two working modes can be controlled in a decoupling way by controlling the phases separately. The experimental results show that under the mode-control-decoupling condition, when the driving voltage of phase A is equal to 400 Vp-pand the driving voltage of phase B is varied between 0 and 400 Vp-p, the motor offers a maximum velocity of 420 mm/s and a minimum velocity of 23 mm/s.

Keywords working mode; control-decoupling; ultrasonic motors(USMs); piezoelectric

Nonlinear Eddy Current Testing Method for Nondestructive Evaluation of Plastic Damage in Structural Materials

LiYunfei1,ChenZhenmao2

(1.Institute of Systems Engineering, China Academy of Engineering Physics Mianyang, 621900, China) (2.School of Aerospace, Xi′an Jiaotong University Xi′an, 710049, China )

Abstract An experimental system is built based on the nonlinear eddy current (NEC) detection method. Quantitative nondestructive evaluation of the plastic damage degree of structural materials, such as Q195 carbon steel and 304 stainless steel, is studied. It is found that structural materials′ plastic damage degree has a certain linear correlation with the fundamental frequency′s amplitude and the third harmonic component′s amplitude in the nonlinear eddy current detection signal spectrum. The linear correlation is different from each other. The detection signal of Q195 carbon steel decreases with increasing damage degree, while the detection signal of 304 stainless steel does the opposite. By developing this experimental system, importing plastic deformation, nonlinear eddy current testing experiment and analysis of detection signal, it is found that the amplitudes of the fundamental and third harmonic components of detection signals show good correlation with the degree of plastic damage. The feasibility and efficiency of the proposed method for quantitative nondestructive evaluation of structural materials′ plastic damage are also investigated.

Keywords nonlinear eddy current; structural materials; plastic deformation; non-destructive evaluation

Numerical Empirical Study on Structural Approximation Analysis of Neural Network for Blade of Wind Turbine

WangLei,LuJingui,ZhangJiande,HuaQi

(Computer Aided Design Center, Nanjing University of Technology Nanjing, 210009, China)

Abstract Structural approximation analysis is important for the design optimization of wind turbine blades. First, the method of structural approximation analysis of the neural network for the wind turbine blade is introduced, and the neural network for the blade is briefed. The empirical and relevant practical studies on the structural approximation analysis of the neural network is introduced, and the influence of the patterns of the wind turbine blade′s performance on the analysis is investigated. The numerical experiments of different learning rates to construct the model of the neural network for the structural approximation analysis are made. According to the experimental results, the number of patterns of the blade should be enough to describe the relationship between the performance and the blade′s parameters. It is concluded that the accuracy of the structural approximation analysis of the neural network is higher with a greater number of patterns of the blades. Based on the experiments, the large learning rate is helpful for obtaining a better model of the neural network. The empirical study is helpful for reducing the expensive cost of the design optimization of the wind turbine blade using the structural approximation analysis of the neural network.

Keywords blade of wind turbine; structural approximation analysis; neural network; approximation model

Method on Rotor Health Monitoring Signal Evolution Analysis and Damage Tracking

ZhuXucheng

(Department of Aircraft Engineering, Naval Aeronautical and Astronautical University Yantai, 264001, China)

Abstract To address helicopter rotor health monitoring issues and get a kind of the damage sensitivity but disturbance insensitive metrics, the evolving properties of damaged rotor behaviors are investigated in the reconstructed phase space, then a new damage tracking method is developed. First, an aeroelastic model of the rotor system is derived using the finite element method, and the simulated measurements are reconstructed in a higher state space according to the embedding theory. A globally nonlinear reference model to predict the rotor state is formulated using the Volterra series. The difference between the model-estimated state and measured results is used as the state prediction error, the average value of which is evaluated in some disjoint regions of the reconstructed phase space and combined into a damage tracking feature vector. Next, the time series of the damage tracking feature vectors are used directly to extract the dimension fact and trending information about the blade damage by solving an eigenvalue problem. In the case of fault to failure time prediction, the double exponential smoothing method is employed to establish damage trending prognosis models. The feasibility and effectiveness of the proposed method are verified using the data from the blade damage model and the rotor aeroelastic model simulations. The results show that this method can provide fault pattern auto-recognition capabilities and is suitable for tracking the hidden damage in situations in which no pre-knowledge about damage dimension or evolution models is available. The method can also reconstruct the dynamic nature of the underlying system in the phase space using the nonlinear property of the single monitoring signal, which provides a new way to study the system degeneration process in different dimensional spaces with a proper time scale.

Keywords helicopter; rotor; health monitoring; fault diagnosis; phase space

Pattern Recognition of Bearing Defect Severity Based on Multiwavelet Packet Sample Entropy Method

ZhangJianyu1,ZhangSuizheng1,GuanLei2,YangYang1

(1.Beijing Key Laboratory of Advanced Manufacturing Technology, Beijing University of Technology Beijing, 100124, China)(2.Jiangsu Myande Food Machinery Co., Ltd. Yangzhou, 225127, China)

Abstract In order to automatically recognize different scales of bearing faults, a method of pattern recognition based on the multiwavelet packet sample entropy method and BP neural network is put forth. First, the vibration signals of rolling bearings with five different scaled outer race defects are decomposed into three layers using the GHM multiwavelet packet. The signal sample entropy of 16 decomposed frequency bands are then used as the neural network′s input vector, so that the complete information of the multiwavelet packet decomposition can be thoroughly utilized. Based on the learning and training of a three-layer BP neural network, and in comparison with the dB10 wavelet packet, it can be concluded that the convergence speed and identification accuracy of the multiwavelet packet sample entropy method is much better than those of the traditional wavelet neural network classification. As a result, the multiwavelet packet sample entropy method is effective in automatically recognizing different scales of bearing faults.

Keywords fault severity; multiwavelet packet, sample entropy; back propagation; automatic identification

Research of Active Structural Acoustic Control in a Rectangle Enclosure with Two Flexible Plates

ChenDalin,ChenNan

(School of Mechanical Engineering, Southeast University Nanjing, 211189, China)

Abstract This paper studies the active structural acoustic control (ASAC) in a rectangular enclosure by applying different control forces to the elastic plate. The acoustic cavity model of a rectangular enclosure consisting of two simply supported flexible plates is developed to analyze the structural-acoustic coupled system of the enclosure. The formula is derived to calculate the sound pressure in the enclosure when some point forces are applied to the flexible plate. The optimal control model of ASAC is established and analyzed. Then the simulation of the sound pressure level (SPL) in the local cavity sound field when some of the second forces with different parameters are applied to the flexible plate is analyzed. Then, a simulated model to analyze the control effect on the partial acoustic field is developed. The results indicate that the parameters of the second forces to be given are more important to the control effect; but it is not better with an infinitely increasing number of parameters. Meanwhile, the number of second control forces isn′t better.

Keywords enclosure sound field; structural-acoustic coupling; structure acoustic radiation; active structural acoustic control (ASAC); sound pressure level (SPL)

Trend Prediction of Civil Aircraft Engine Vibration Signal Using Ensemble Process Neural Networks

LeiDa,ZhongShisheng

(School of Mechatronics Engineering, Harbin Institute of Technology Harbin, 150001, China)

Abstract An ensemble prediction model based on boosting process neural networks (PNN) is proposed to predict vibration signal trends of civil aircraft engines. First, the error functions of the AdaBoost.RT algorithm are improved, and an adaptive adjustment strategy is adopted to adjust the classification threshold during the training process. Then, the improved AdaBoost.RT is utilized as the ensemble framework so as to build the ensemble PNN prediction model. The performance of the proposed model is evaluated through the prediction of two actual civil aircraft engine vibration signal series. The results show that the ensemble model performs better than the single PNN model while with simpler structures. The proposed modification version of AdaBoost.RT is superior to the original AdaBoost.RT and a contrast modification version with only improved threshold adjustment strategy. Therefore, the proposed model is suitable for the prediction of civil aircraft engine vibration signal trends.

Keywords aircraft engine; vibration signal; trend prediction; ensemble learning; AdaBoost.RT; process neural networks

Virtual Axis Machine Tool Positioning Method

JiaYuqin,HuXiaoxiong

(School of Mechanical Engineering, Taiyuan University of Science and Technology Taiyuan, 030024, China)

Abstract To solve the dynamic virtual axis machine tool spindle positioning on the platform, a method is presented based on the improved consistency of multi-sensor data fusion virtual axis machine tool positioning, visual technology and electronic compass used in the measurement of the position and orientation of the virtual axis machine tool moving platform. This method is the virtual axis machine tools of each rod of the encoder information, visual information and the dynamic inertial measurement data fusion, obtained by dynamic calculation of the confidence distance relationship matrix, the position and attitude of the virtual axis machine tool moving platform (pose) the precise positioning of a good guarantee. After a simplified test of the direction of movement of a single axle measurement, the measurement of the virtual axis machine tool 6 degrees of freedom of the moving platform pose as the object of study, and its simulation test. The test results show that the proposed positioning method is feasible, effective, and practically significant.

Keywords virtual axis machine tool; multi-sensor; locating; data fusion

Correlated Jointly Frequency Rotor Fault Sources Number Estimation and Sub-band Blind Separation

LiJiyong1,LiShunming1,TianGuocheng2,ChenXiaohong3

(1.College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics Nanjing, 210016, China)(2.Shandong Zhongshi Yitong Group Co., Ltd. Jinan, 250000, China)(3.College of Science, Nanjing University of Aeronautics and Astronautics Nanjing, 210016, China)

Abstract Crosscover frequency response is produced by the rotor under abnormal vibration, so rotor jointly frequency fault sources cannot be satisfied statically independent request. The traditional source number estimation such as singular value decomposition method and standard independent standard analysis cannot extract fault sources. This paper estimates fault sources number with a non-negative method in the frequency domain, source and mixture system characteristics not in consider, and then to extract fault signals with wavelet packet, and separate recovered signals with small mutual information, to eliminate jointly frequency signal, to obtain independent non-correlated sources. The feasibility is verified by practical and theoretical methods.

Keywords correlated sources; non-negative matrix factorization; mutual information; sub-band decomposition; blind source separation

Dynamic Performance Analysis and Kinetic Parameters Optimization of High-Speed Elevator Based on VPT

LinYao1,2，LiuYanbin1，WuHui1，HuangYaozhi1

(1.College of Mechanical Engineering，F(xiàn)uzhou University Fuzhou, 350106, China)(2.Fujian Province Special Equipment Inspection & Research Institute Fuzhou, 350008, China)

Abstract The main factors that affect comfort in speed elevators are horizontal and vertical vibrations. To improve comfort and mitigate the effects of vibration and shock inside elevator equipment, the kinetic parameters of the elevator vibrations are optimized. The process of running the speed and acceleration of the high-speed elevator in the virtual prototype simulation by virtual prototype technology (VPT) technology is completed, a sensitivity analysis method is used, and the kinetic parameters of vibrations that affect the vertical and horizontal directions of the elevator system are optimized. The simulation results show that the vertical vibration acceleration of the optimized elevator system dropped from 1.12 m/s2to 1.04 m/s2, and the horizontal vibration acceleration of the lift car is less than 0.1 m/s2.This ensures that the maximum amplitude of the vertical and horizontal vibration acceleration is reduced, the ride comfort of the elevator is improved, and an effective way to optimize the research and design of the high-speed elevator system is provided.

Keywords virtual prototype technology(VPT); high-speed elevator; dynamic performance; kinetic parameters; simulation

Study on Modeling and Vibration Transmission Characteristics of Distributed Parameter Two-Stage Isolation Systems

YangMingyue，SunLingling，WangXiaole

(Key Laboratory of High-Efficiency and Clean Mechanical Manufacture, Shandong University Jinan, 250061, China)

Abstract Two analytical models of a typical two-stage vibration isolation system are established from the point of view of vibration power transmission and engineering practices. Considering the distributed parameter characteristics of the elastic raft, isolators and flexible foundation, dynamic equations of each subsystem are derived using the mobility matrix approach. The mechanism of the vibration transmission is revealed using the concept of power flow. Meanwhile, general rules which should be followed when designing the two-stage isolation systems are discussed. It is shown that the moment excitations play an important role in the vibration transmission process. Hence, the injection of power caused by the moment excitations should be reduced. In the permitting condition of the energy efficiency and installation spaces, a better isolation effect will be obtained when appropriately enlarging the intermediate mass. The distribution parameter characteristics of the elastic raft, isolators, and non-rigid foundation can lead to a deterioration of performance in the high-frequency domain. Using the scheme of the dispersion intermediate mass can effectively avoid the impact of the flexible raft, and can also significantly inhibit the interaction between the wave effects caused by the isolators and modals of the flexible raft, which may input more power to the installed foundation.

Keywords two-stage vibration isolation; intermediate mass; mobility matrix; distribution parameters; wave effects

A New Type of Large-Thrust Linear Piezoelectric Actuator

ZhuPengju,ShiYunlai,ZhaoChunsheng

(State Key Laboratory of Mechanics and Control of Mechanical Structures，Nanjing University of Aeronautics And Astronautics Nanjing, 210016, China)

Abstract A new type of large-thrust linear piezoelectric actuator is proposed. It achieves the goal of large-thrust and large-displacement output by accumulating the micro-amplitude of the piezoelectric stack through a kind of screw clamp mechanism. The driving mechanisms of the actuator and the key technology during the designing process are discussed in detail, including the design of the torque motor speed, the torsional stiffness of the flexible coupling, the design of the relationship between the nut and screw, and the best frequency phase of the stack after testing its performance. The length of the actuator is 140 mm, and the maximum diameter is 45 mm. The actuator weighs 0.7 kg with a stroke of 40 mm. The actuator exhibits a 130 N blocked force when the speed of the torque motor is 300 r/min and the frequency of the piezoelectric stack is 100 Hz.

Keywords piezoelectric actuator; feed-screw; inchworm; large-thrust

Contact and Friction Behavior of Piezoelectric Vibrator for Driving Track

HuangChong,WangLiang,ShuChengyou,ZhangHongxuan,JinJiamei

(State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics Nanjing, 210016, China)

Abstract In order to enhance the efficiency and velocity of the traditional piezoelectric vibrators for driving tracks, the operating mode of the piezoelectric vibrator is improved. The new operating mode uses the torsional vibration of the annular part of the piezoelectric vibrator instead of the bending vibration. Then, two torsional standing waves synthesize a torsional traveling wave. The new mode is more suitable for the piezoelectric vibrator to drive the track, and enhances the piezoelectric vibrator′s driving efficiency, which increases the contact area between the piezoelectric and track and reduces energy waste generated by the contact between the troughs of the traveling waves in the annular parts and track. The piezoelectric vibrator is designed using FEM analysis, and the prototype is manufactured. After that, experiments on contact and friction behavior are conducted. Based on the study of the velocity of the piezoelectric vibrator with different pre-pressures under track material surfaces with different levels of hardness and roughness, it can be found that the hardness of the material is greater, and the load capacity of the piezoelectric vibrator is stronger. There is an optimized collocation between hardness, roughness and pre-pressure, which will make the piezoelectric vibrator arrive at maximum velocity. The research results subsequently lay a foundation for the design of the track and the integral optimization of the driving system.

Keywords track; planetary exploration; piezoelectric vibrator; friction behavior; experimental research

Selection Method of Multiple Regression Elements for Load Calibration Test Data

DuanYaoqi,LiuKege,ZhaoLina,YanChuliang

(Beijing Aircraft Strength Institute Beijing, 100083, China)

*國(guó)家自然科學(xué)基金資助項(xiàng)目(50135010)

2014-09-03；

2014-12-09

10.16450/j.cnki.issn.1004-6801.2015.01.030

V217+.32； TH13

段垚奇，男，1986年4月生，工程師。主要研究方向?yàn)轱w機(jī)結(jié)構(gòu)可靠性。曾發(fā)表《基于最小航道法的實(shí)測(cè)數(shù)字信號(hào)奇異值剔除算法》(《農(nóng)業(yè)機(jī)械學(xué)報(bào)》2012年第43卷第5期)等論文。 E-mail：dyq319@126.com