NL2030483A - Test System and Method for Separating Vibration Signals of Tubular Water Turbines - Google Patents

Test System and Method for Separating Vibration Signals of Tubular Water Turbines Download PDF

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NL2030483A
NL2030483A NL2030483A NL2030483A NL2030483A NL 2030483 A NL2030483 A NL 2030483A NL 2030483 A NL2030483 A NL 2030483A NL 2030483 A NL2030483 A NL 2030483A NL 2030483 A NL2030483 A NL 2030483A
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signal
vibration
test system
signals
separating
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NL2030483B1 (en
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Feng Jianjun
Wu Guangkuan
Li Kang
Luo Xingqi
Zhu Guojun
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Univ Xian Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H9/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves by using radiation-sensitive means, e.g. optical means
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/21—Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
    • G06F18/213—Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods
    • G06F18/2135—Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods based on approximation criteria, e.g. principal component analysis
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
    • F03B—MACHINES OR ENGINES FOR LIQUIDS
    • F03B17/00—Other machines or engines
    • F03B17/06—Other machines or engines using liquid flow with predominantly kinetic energy conversion, e.g. of swinging-flap type, "run-of-river", "ultra-low head"
    • F03B17/061—Other machines or engines using liquid flow with predominantly kinetic energy conversion, e.g. of swinging-flap type, "run-of-river", "ultra-low head" with rotation axis substantially in flow direction
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M15/00—Testing of engines
    • G01M15/14—Testing gas-turbine engines or jet-propulsion engines
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M7/00—Vibration-testing of structures; Shock-testing of structures
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05B—INDEXING SCHEME RELATING TO WIND, SPRING, WEIGHT, INERTIA OR LIKE MOTORS, TO MACHINES OR ENGINES FOR LIQUIDS COVERED BY SUBCLASSES F03B, F03D AND F03G
    • F05B2240/00—Components
    • F05B2240/10—Stators
    • F05B2240/12—Fluid guiding means, e.g. vanes
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05B—INDEXING SCHEME RELATING TO WIND, SPRING, WEIGHT, INERTIA OR LIKE MOTORS, TO MACHINES OR ENGINES FOR LIQUIDS COVERED BY SUBCLASSES F03B, F03D AND F03G
    • F05B2240/00—Components
    • F05B2240/10—Stators
    • F05B2240/14—Casings, housings, nacelles, gondels or the like, protecting or supporting assemblies there within
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05B—INDEXING SCHEME RELATING TO WIND, SPRING, WEIGHT, INERTIA OR LIKE MOTORS, TO MACHINES OR ENGINES FOR LIQUIDS COVERED BY SUBCLASSES F03B, F03D AND F03G
    • F05B2260/00—Function
    • F05B2260/83—Testing, e.g. methods, components or tools therefor
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
    • G06F2218/02—Preprocessing
    • G06F2218/04—Denoising
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
    • G06F2218/08—Feature extraction

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  • Bioinformatics & Computational Biology (AREA)
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  • Measurement Of Mechanical Vibrations Or Ultrasonic Waves (AREA)

Abstract

Disclosed is a hydraulic turbine vibration data acquisition test system for separating vibration signals of tubular turbines and a method for separating vibration signals of tubular turbines comprising the following steps: collecting vibration speed signals of runners by using a laser vibrometer to obtain a time series x(t) after sampling the vibration speed signals; then, the filtered vibration velocity signal X1(z‘) is obtained by filtering with a low-pass filter, and then the processed vibration velocity signal x1'(t) is obtained by averaging; and then whitening, variational modal decomposition and dimension reduction are carried out to obtain a new signal u’(z‘); finally u’(z‘) is subjected to independent component analysis, and the signal u is separated. The invention can quickly and accurately separate the vibration signal caused by cavitation from the general vibration signals.

Description

Test System and Method for Separating Vibration Signals of Tubular Water Turbines
TECHNICAL FIELD The invention belongs to the technical field of water turbine, and relates to a hydraulic turbine vibration data acquisition test system for separating vibration signals of tubular turbines and to a method for separating vibration signals of tubular water turbines.
BACKGROUND Cavitation generally occurs in hydraulic machinery, which is one of the important reasons for the decrease of efficiency and output of hydraulic machinery as well as unit vibration and unstable operation. Cavitation may also lead to cavitation erosion, and cavitation collapse will damage the surface of unit devices. Cavitation erosion, under the combined action of sediment wear, is more severe, which seriously affects the reliable operation and service life of the unit. Generally, cavitation can be divided into blade (air foil) cavitation, cavity cavitation, gap cavitation and other cavitation caused by local shedding according to the location where cavitation occurs. In the above cavitation erosion, gap cavitation may cause mechanical damage, which also has an influence on the efficiency of hydraulic machinery. However, the most common and harmful ones are air foil cavitation and cavity cavitation, which will not only damage hydraulic components, but also reduce the output and efficiency, and even cause strong vibration and thus lead to unstable operation of the unit. Tubular turbine is the key hydro- mechanical equipment for developing tidal ocean energy, and the safe and stable operation of the turbine is related to the efficient development and utilization of tidal energy. In the operation of tubular turbine, the local velocity increases and the pressure decreases when the water flows through the tip gap between runner and runner chamber, in which the gap cavitation often occurs. Therefore, the determination of cavitation is particularly important. However, when cavitation occurs, it is often accompanied by other excitation sources (hydraulic, mechanical and electrical, etc.). How to quickly and accurately separate the cavitation signal from the monitored signal source, especially the accurate determination of cavitation inception, is still a difficult point in cavitation testing.
SUMMARY The objective of the invention is to provide a method for separating vibration signals of tubular turbines, which can quickly and accurately separate vibration signals caused by cavitation from general vibration signals.
The invention relates to a method for separating vibration signals of a tubular turbine, which adopts a hydraulic turbine vibration data acquisition test system, comprising a water inlet pipe, a runner chamber and a draft tube which are sequentially communicated; a bulb body and a guide vane are sequentially arranged in the water inlet pipe according to the water flow direction, and the guide vane is connected with a runner; located in the runner chamber, a laser vibrometer is arranged outside the runner chamber, and the laser vibrometer is electrically connected with a data acquisition system through wires, and the data acquisition system is connected with a console.
The specifically steps are as follows.
Step 1, starting the water turbine vibration data acquisition test system, wherein water flows through a water inlet pipe, a bulb body, a guide vane, a runner and a draft tube in turn; Step 2, collecting the vibration speed signal of the runner by a laser vibrometer, and sending the measured data to the console through a data acquisition system to obtain the time series x(t) after sampling the vibration speed signal; Step 3, filtering the vibration speed signal x(t) collected in step 2 through a low-pass filter to obtain a filtered vibration speed signal x:{f); Step 4, de-averaging the filtered vibration speed signal x(t) to obtain the processed vibration speed signal x, (¢) ; Step 5, whitening the vibration velocity signal x, (4) after the mean value removal in step 4 to obtain the whitening signal z(¥); Step 6, performing variational modal decomposition on the whitened signal z(t) to obtain the decomposed signal u(t); Step 7, performing principal component analysis to reduce the dimension of the decomposed signal u(t) to obtain a new signal u(t); Step 8, performing independent component analysis on u/(t)to separate out the signal u.
The invention is also characterized in that the calculation method of x,(z) in step 4 is: x,(1) = xi(6) = E(x(1)) (4) in which E(x+(f)) represents the mean value of the vibration speed signal, and x:{{) represents the vibration speed signal filtered in step 3; E(xilt)) = Ls x(t) N= (2) in which N represents the length of the vibration speed signal.
The signal z(t) after whitening in step 5 is calculated as follows: z(f)=Ox(t) (3) in which Q is an albino matrix; Because the whitening signal satisfies the following formula (4), where / is the unit vector; Ede } = EQx (0x0) 0) = 1 (4) Eigenvalue decomposition is performed on the covariance matrix Rxx={ T} of the processed vibration velocity signal to obtain the following formula: Ru = EDE" (5)
in which E is an orthogonal matrix, which constitutes the eigenvectors from covariance matrix, and d is a diagonal matrix, which constitutes the eigenvalues from eigenvector correlation; According to (4) and (5), the whitening matrix is: O= DE! (6) Step 6 is as follows: Step 6.1, inputting the vibration signal z(t), determining the initial mode number K, and setting the penalty factor a and bandwidth T; Step 6.2, performing variational modal decomposition on the vibration signal according to the parameters set in step 6.1, and observing the central frequency ox of each modal component; Step 6.3, judging whether the centre frequency «x is close to the cavitation characteristic frequency f, the judging method is as follows: When |o,-f|£0.001, determine the modal number K=K-1, and execute step 6.4; When |a-f>0.001, determine the modal number K=K+1, and return to step 6.2; Step 6.4, output the decomposed signal u(t). The step 8 is as follows: Step 8.1, inputting signal u'(t); Step 8.2, initializing w(0) so that ||w(0)||=1 and k=1;
8.3, calculating the mathematical expectation E(u’) of the signal u'(f);
8.4, performing iteration according to the iteration formula wk) = Ea [wk Du T}—3w(k—1); Step 8.5, judging whether | w(k) w(k —1)|—1 close to 0, the judging method is as follows: when |w(k) w(k—1)|—-1<0.001, the separation matrix w(k) is output; when | w(k) w(k —1)|-1> 0.001, let k=k+1, and return to step 8.4; Step 8.6, transpose the separation matrix w(k) to obtain wk) and then multiply the transposed separation matrix by the signal u(t) to obtain the separated signal u = wk) w(t). The horizontal distance between the measuring point of the laser vibrometer and the position corresponding to the runner chamber is L,0.5m=L<30m. The invention has the following beneficial effects.
According to the method for separating the cavitation vibration signal of tubular turbine, the laser vibrometer is used to collect the vibration speed signal of tubular turbine runner, and the collected vibration speed signal is filtered, averaged and whitened, so that the noise components in the vibration speed signal can be effectively removed; and then the vibration signal caused by cavitation can be quickly and accurately separated from the general vibration signal by combining variational modal decomposition and independent component analysis, so that the pure cavitation vibration signal can be obtained, and the determination of cavitation initiation is further improved.
BRIEF DESCRIPTION OF THE FIGURES Fig. 1 is a schematic structural diagram of a turbine vibration data acquisition test system in a method for separating vibration signals of tubular turbines of the present invention; Fig. 2 is a positional relationship diagram of laser vibrometer and runner chamber in a method for separating vibration signals of tubular turbine according to the present invention; Fig. 3 is a flow chart of a method for separating vibration signal of tubular turbine according to the present invention; Fig. 4 is an original vibration signal collected in a method for separating cavitation vibration signals of tubular turbine according to the present invention; Fig. 5 is a vibration signal separated in a method for separating cavitation vibration signals of tubular turbine according to the present invention. In the figures: 1, water inlet pipe; 2, bulb body; 3, guide vane; 4. runner; 5, runner chamber; 6, draft tube; 7, laser vibrometer; 8, data acquisition system; 9, console.
DESCRIPTION OF THE INVENTION The present invention will be described in detail below with reference to the drawings and detailed description. The invention provides a method for separating vibration signals of tubular turbines, which adopts a hydraulic turbine vibration data acquisition test system, comprising a water inlet pipe 1, a runner chamber 5 and a draft pipe 6 which are sequentially communicated; a bulb body 2 and a guide vane 3 are sequentially arranged in the water inlet pipe 1 according to the water flow direction; guide vane 3 is connected with runner 4 which is located in runner chamber 5; a laser vibrometer 7 is arranged outside the wheel chamber 5, and the horizontal distance between the measuring point of the laser vibrometer 7 and the position corresponding to the wheel chamber 5isL, 0.5m < L < 30m; the laser vibrometer 7 is electrically connected with a data acquisition system 8 through wires, and the data acquisition system 8 is connected with a console 9; the specific operation steps are as follows: Step 1, a water turbine vibration data acquisition test system, wherein water flows through a water inlet pipe 1, a bulb body 2, guide vanes 3, a runner 4 and a draft tube 6 in turn; Step 2, collecting the vibration speed signal of the runner 4 with the laser vibrometer 7, and send the measured data to the console 9 through the data collection system 8 to obtain the time series x(t) after sampling the vibration speed signal, as shown in Fig. 4; Step 3, filtering the vibration speed signal x(t) collected in step 2 through a low-pass filter to obtain a filtered vibration speed signal x(t);
Step 4, de-averaging the filtered vibration speed signal x(t) to obtain the processed vibration speed signal x, (#), wherein, the calculation method of x, (£) is as follows: (1) = xi) = Eet) (1) in which E(x+(f)) represents the mean value of the vibration speed signal, and x:{{) represents 5 the vibration speed signal filtered in step 3; | & E(x) = 3) Ni (2) in which N represents the length of the vibration speed signal; Step 5, whitening the vibration velocity signal x, (4) after the mean removal in step 4 to obtain the whitened signal z(t), wherein the calculation method of z(t) is as follows:
z(t) = Ox (1) (3) in which Q is an albino matrix;
Because the whitening signal satisfies the following formula (4), where / is the unit vector; E{z(t)z(t)"} = E(Ox (x(t) 0") =1 (4) Eigenvalue decomposition is performed on the covariance matrix Ro={x({) x, (2) 7} of the processed vibration velocity signal to obtain the following formula:
R.. = EDE’ (5)
in which E is an orthogonal matrix, which constitutes the eigenvectors from covariance matrix, and d is a diagonal matrix, which constitutes the eigenvalues from eigenvector correlation;
According to (4) and (5), the whitening matrix is:
1 O=D'E (6)
Step 6, performing variational modal decomposition on the whitened signal z(t) to obtain the decomposed signal u(t), specifically as follows:
Step 6.1, inputting the vibration signal z(t), determine the initial mode number K, and set the penalty factor a and bandwidth T;
Step 6.2, performing variational modal decomposition on the vibration signal according to the parameters set in step 8.1, and observing the central frequency ox of each modal component;
Step 6.3, judging whether the centre frequency ox is close to the cavitation characteristic frequency f, the judging method is as follows:
when |o;-f50.001, determine the modal number K=K-1, and execute step 6.4;
when |a-f]>0.001, determine the modal number K=K+1, and return to step 6.2; Step 6.4, outputting the decomposed signals u(t), (Oz Su, =[us(t), uz(t), ust), ..., ux®]%; k=l
Step 7, performing principal component analysis to reduce the dimension of the decomposed signal u(t) to obtain a new signal u'(?); Step 8, performing independent component analysis on u(t) to separate out the signal u, specifically as follows: Step 8.1, inputting signal u(t); Step 8.2, initializing w(0) so that ||w(0)||=1 and k=1; Step 8.3, calculating the mathematical expectation E(u) of the signal u ($; Step 8.4, performing iteration according to the iteration formula; Step 8.5, judging whether| w(k)" w(k —1)|—1 is close to 0, the judging method is as follows: when |w(k) w(k —1)| —1< 0.001, the separation matrix w (k) is output; when|w(k) w(k —1)|—1> 0.001, let k=k+1, and return to step 8.4; Step 8.6, transposing the separation matrix w(k) to obtain wk)", and then multiplying the transposed separation matrix by the signal u'(t) to obtain the separated signal u = w(k) u(t) as shown in Fig. 5.
The invention relates to a method for separating cavitation vibration signals of tubular turbine, which collects vibration speed signals of tubular turbine runner by laser vibrometer, and filters, averages and whitens the collected vibration speed signals, in order to effectively remove noise components in the vibration speed signals; then, by combining variational modal decomposition with independent component analysis, the vibration signal caused by cavitation is quickly and accurately separated from the general vibration signal, so that the pure cavitation vibration signal can be obtained, and the determination of cavitation initiation is further improved.

Claims (6)

CONCLUSIESCONCLUSIONS 1. Een testsysteem door het verzamelen van vibratiegegevens voor het scheiden van vibratiesignalen uit buisvormige turbines, waarbij het testsysteem omvat een waterinlaatpijp 1, een doorloopkamer 5 en een uitstroompijp 6 die achtereenvolgens met elkaar in verbinding staan; een bolvormig lichaam 2 en een leischoep 3 die na elkaar in stroomrichting in de waterinlaatpijp 1 zijn geplaatst; waarbij leischoep 3 is verbonden met runner 4 die zich in doorloopkamer 5 bevindt; een laservibrometer 7 die buiten de doorloopkamer 5 is opgesteld; waarbij de laservibrometer 7 via bedrading elektrisch is verbonden met een gegevensverzamelsysteem 8, waarbij het gegevensverzamelsysteem 8 is verbonden met een console 9; waarbij het testsysteem als volgt werkt: stap 8.1:het laten lopen van water door het testsysteem, waarbij het water achtereenvolgens door een waterinlaatpijp 1, lang het bolvormige lichaam 2, leischoepen 3, runner 4 en een uitstroombuis 6 stroomt; stap 8.2:het verzamelen van het trillingssnelheidssignaal van runner 4 met de laservibrometer 7, en het verzenden van de gemeten gegevens naar de console 9 via het gegevensverzamelsysteem 8 om de tijdreeks x(t} te verkrijgen na bemonstering van het trillingssnelheidssignaal; stap 8.3:het filteren van het in stap 2 verzamelde ftrillingssnelheidssignaal x(f) door een laagdoorlaatfilter om een gefilterd trillingssnelheidssignaal x+(%) te verkrijgen; stap 8.4:het gemiddelde van het gefilterde trilsnelheidssignaal x(f) nemen om het bewerkte trilsnelheidssignaal x4'(f) te verkrijgen; stap 8.5:het wit maken van het trillingssnelheidssignaal x;'(f) na de gemiddelde verwijdering in stap 4 om het wit gemaakte signaal z(t) te verkrijgen; stap 8.6:het uitvoeren van variationele modale decompositie op het wit gemaakte signaal z(?) om het decompositiesignaal u(t) te verkrijgen; stap 8.7:het uitvoeren van principale componentenanalyse om de dimensie van het decompositiesignaal uf) te reduceren om een nieuw signaal u'(f) te verkrijgen; stap 8.8:het uitvoeren van principale componentenanalyse om de dimensie van het decompositiesignaal u{f) te reduceren om een nieuw signaal u'(t} te verkrijgen.A test system by collecting vibration data for separating vibration signals from tubular turbines, the test system comprising a water inlet pipe 1, a flow chamber 5, and an outflow pipe 6 successively communicating with each other; a spherical body 2 and a guide vane 3 placed one after the other in the flow direction in the water inlet pipe 1; wherein guide vane 3 is connected to runner 4 located in through-flow chamber 5; a laser vibrometer 7 arranged outside the flow-through chamber 5; the laser vibrometer 7 being electrically wired to a data collection system 8, the data collection system 8 being connected to a console 9; the test system operating as follows: step 8.1: running water through the test system, the water flowing successively through a water inlet pipe 1, along the spherical body 2, guide vanes 3, runner 4 and an outflow pipe 6; step 8.2: collect the vibration velocity signal from runner 4 with the laser vibrometer 7, and send the measured data to the console 9 through the data collection system 8 to obtain the time series x(t} after sampling the vibration velocity signal; filtering the vibration velocity signal x(f) collected in step 2 through a low-pass filter to obtain a filtered vibration velocity signal x+(%), step 8.4: averaging the filtered vibration velocity signal x(f) to obtain the processed vibration velocity signal x4'(f) step 8.5: whitening the vibration velocity signal x;'(f) after the mean removal in step 4 to obtain the whitened signal z(t) step 8.6: performing variational modal decomposition on the whitened signal z(?) to obtain the decomposition signal u(t); step 8.7: performing principal component analysis to reduce the dimension of the decomposition signal uf) to obtain a obtain new signal u'(f); step 8.8: perform principal component analysis to reduce the dimension of the decomposition signal u{f) to obtain a new signal u'(t}. 2. Het testsysteem door het verzamelen van vibratiegegevens voor het scheiden van vibratiesignalen uit buisvormige turbines volgens conclusie 1, waarbij in stap 4 de werkwijze voor het berekenen van x;'(¢) als volgt is: x, (6) = xi(1) = EC) (7 waarbij E(x+(f)) staat voor de gemiddelde waarde van het trillingssnelheidssignaal, en x(t) staat voor het in stap 3 gefilterde trillingssnelheidssignaal; 1 & Exit) = = xi(1) N= (2) waarbij N staat voor de lengte van het vibratiesnelheidssignaal.The test system by collecting vibration data for separating vibration signals from tubular turbines according to claim 1, wherein in step 4, the method of calculating x;'(¢) is as follows: x, (6) = xi(1 ) = EC) (7 where E(x+(f)) represents the average value of the vibration velocity signal, and x(t) represents the vibration velocity signal filtered in step 3; 1 & Exit) = = xi(1) N= ( 2) where N is the length of the vibration velocity signal. 3. Het testsysteem door het verzamelen van vibratiegegevens voor het scheiden van vibratiesignalen uit buisvormige turbines volgens conclusie 1, waarbij in stap 5 de werkwijze voor het berekenen van het wit gemaakte signaal z(t) als volgt is: z(t) = 0x’ (1) a waarbij Q staat voor een albinomatrix; omdat het wit makende signaal aan de volgende formule (4) voldoet, waarbij / gelijk is aan de eenheidsvector; Ede) } = EQ 0x) 0") = 1 @ wordt een eigenwaarde-decompositie uitgevoerd op de covariantiematrix Rxx={x+'(t) x:'(t)"} van het verwerkte vibratiesnelheidssignaal om de volgende formule te verkrijgen: Re = EDE (5) waarbij E staat voor een orthogonale matrix is, die de eigenvectoren van de covariantiematrix vormt, en D een diagonaalmatrix is, die de eigenwaarden van de eigenvectorcorrelatie vormt; waarbij volgens (4) en (5) de witmakingsmatrix luidt: Q= DE (6).The test system by collecting vibration data for separating vibration signals from tubular turbines according to claim 1, wherein in step 5, the method for calculating the whitened signal z(t) is as follows: z(t) = 0x' (1) a where Q represents an albino matrix; because the whitening signal satisfies the following formula (4), where / is equal to the unit vector; Ede) } = EQ 0x) 0") = 1 @ an eigenvalue decomposition is performed on the covariance matrix Rxx={x+'(t) x:'(t)"} of the processed vibration velocity signal to obtain the following formula: Re = EDE (5) where E is an orthogonal matrix, which forms the eigenvectors of the covariance matrix, and D is a diagonal matrix, which forms the eigenvalues of the eigenvector correlation; where according to (4) and (5) the whitening matrix is: Q=DE (6). 4. Het testsysteem door het verzamelen van vibratiegegevens voor het scheiden van vibratiesignalen uit buisvormige turbines volgens conclusie 1, waarbij stap 6 als volgt is: stap 6.1: het invoeren van het trillingssignaal z(t), het bepalen van het initiële modusgetal K, en het instellen van de straffactor a en de bandbreedte T; stap 6.2: het uitvoeren van een variationele modale decompositie op het trillingssignaal overeenkomstig de in stap 6.1 ingestelde parameters, en het observeren van de centrale frequentie wk van elke modale component; stap 6.3: het beoordelen of de centrale frequentie wk dicht bij de voor cavitatie karakteristieke frequentie f ligt; waarbij de beoordelingsmethode als volgt luidt: wanneer | wk -f| £ 0,001, het bepalen van het modale getal x = «-1, en uitvoeren van stap 6.4;The test system by collecting vibration data for separating vibration signals from tubular turbines according to claim 1, wherein step 6 is as follows: step 6.1: inputting the vibration signal z(t), determining the initial mode number K, and setting the penalty factor a and the bandwidth T; step 6.2: performing a variational modal decomposition on the vibration signal according to the parameters set in step 6.1, and observing the center frequency wk of each modal component; step 6.3: judging whether the central frequency wk is close to the cavitation characteristic frequency f; where the assessment method is as follows: when | wk -f| £0.001, determine the modal number x = «-1, and perform step 6.4; wanneer | wk -f| > 0,001, het bepalen van het modale getal x = «+1, en terugkeren naar stap 6.2; stap 6.4: het uitvoeren van de ontlede signalen ub), ut) = Su, = k=l lust), uxt), us, ..., Uk (OT.when | wk -f| > 0.001, determining the modal number x = «+1, and returning to step 6.2; step 6.4: outputting the decomposed signals ub), ut) = Su, = k=l lust), uxt), us, ..., Uk (OT. 5. Het testsysteem door het verzamelen van vibratiegegevens voor het scheiden van vibratiesignalen uit buisvormige turbines volgens conclusie 1, waarbij stap 6 als volgt is: stap 8.1: het invoeren van het signaal u'(}); stap 8.2: initialiseren van w(0) zodat |[w{0)|| = 1 en x= 1; stap 8.3: het berekenen van de wiskundige verwachting E(u’) van het signaal u'(t); stap 8.4: het uitvoeren van de iteratie volgens de iteratieformule; stap 8.5: het beoordelen of dicht bij 0 ligt, de beoordelingsmethode is als volgt: wanneer | w(k)" w{x-1) | - 1 £0,001 wordt de scheidingsmatrix w(x) uitgevoerd; wanneer | w(k)’ w{x-1) | -1 > 0,001, laat « = x +1, en keer terug naar stap 8.4; stap 8.6: het transponeren van de scheidingsmatrix w(x) om w(x)” te verkrijgen en vervolgens vermenigvuldigen van de getransponeerde scheidingsmatrix met het signaal u’'(t) om het gescheiden signaal u= w(x)” u'(t) te verkrijgen.The test system by collecting vibration data for separating vibration signals from tubular turbines according to claim 1, wherein step 6 is as follows: step 8.1: inputting the signal u'(}); step 8.2: initialize w(0) so that |[w{0)|| = 1 and x= 1; step 8.3: calculating the mathematical expectation E(u') of the signal u'(t); step 8.4: performing the iteration according to the iteration formula; step 8.5: judging whether is close to 0, the judging method is as follows: when | w(k)" w{x-1) | - 1 £0.001 the separation matrix w(x) is output; when | w(k)' w{x-1) | -1 > 0.001, let « = x +1 , and return to step 8.4, step 8.6: transposing the separation matrix w(x) to obtain w(x)” and then multiplying the transposed separation matrix by the signal u''(t) to obtain the separated signal u= w(x)” to obtain u'(t). 6. Het testsysteem door het verzamelen van vibratiegegevens voor het scheiden van vibratiesignalen uit buisvormige turbines volgens conclusie 1, waarbij de horizontale afstand tussen het meetpunt van de laservibrometer 7 en de positie die overeenkomt met de doorloopkamer 5 gelijk is aan L, waarbij 0,5m SL < 30 m.The test system by collecting vibration data for separating vibration signals from tubular turbines according to claim 1, wherein the horizontal distance between the measurement point of the laser vibrometer 7 and the position corresponding to the pass-through chamber 5 is L, where 0.5m SL < 30m.
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