CN102661866A - Engine fault identification method based on time-domain energy and support vector machine - Google Patents

Abstract

The invention relates to an engine fault identification method based on time-domain energy and a support vector machine. The method comprises the following steps of: (1), respectively installing an acceleration vibration sensor on each measuring point, wherein each acceleration vibration sensor is connected with a computer through a vibration signal acquisition instrument; (2) dividing time-domain vibration signals acquired from a top dead center into N sections, wherein each section comprises M vibration signal amplitudes; (3) evaluating the time-domain energy Ei of each of the N sections; (4) evaluating the sum ESUM of the time-domain energy of the N sections; (5) comparing the Ei with the ESUM, and constructing a feature vector after performing energy unitization to obtain N time-domain energy feature values; (6) performing classified counting by a support vector machine method to obtain classified parameters of running states of an engine; and (7) comparing to obtain an engine fault identification result. By the method, the fault identification speed of the engine is effectively improved; the fault identification time of the engine is shortened; the fault identification efficiency of the engine is improved; and the method is simple and is easy to operate, and facilitates the repair and the maintenance of the engine.

Description

Engine failure recognition methods based on time domain energy and SVMs

Technical field

The invention belongs to engine art, especially a kind of engine failure recognition methods based on time domain energy and SVMs.

Background technology

Along with people's growth in the living standard, automobile progress into common people family, along with automobile is more and more longer service time; The probability that the engine of automobile breaks down is also increasing, and present six cylinder engine is used more extensive on automobile, when in-engine cylinder body breaks down; Be difficult to accurately judge what fault has taken place engine interior; Must dismantle just engine and can carry out Fault Identification, but such method identification fault speed is slower, the time is longer; Efficient is lower, and maintenance maintenance is wasted time and energy.

Summary of the invention

The objective of the invention is to overcome the deficiency of prior art; A kind of engine failure recognition methods based on time domain energy and SVMs is provided, and this method has improved the engine failure recognition speed, has shortened the engine failure recognition time; Improved the engine failure recognition efficiency; Method is simple, and is easy to operate, made things convenient for the maintenance maintenance of engine.

The present invention solves its technical matters and realizes through following technical scheme:

A kind of engine failure recognition methods based on time domain energy and SVMs, the step that its method comprises is:

⑴, between first cylinder of six cylinder engine and second cylinder, be provided with to be provided with between first measuring point, second cylinder and the 3rd cylinder to be provided with between the 3rd measuring point, the 5th cylinder and the 6th cylinder between second measuring point, the 4th cylinder and the 5th cylinder the 4th measuring point is set; One acceleration vibration transducer is installed respectively on each measuring point, and this acceleration vibration transducer connects computing machine through the vibration signals collecting appearance;

⑵, be divided into the N section to the time domain vibration signal of the engine operating state that is begun to collect from top dead centre by the acceleration vibration transducer, every section comprises M vibration signal amplitude respectively;

⑶, obtain in the N section every section time domain energy E _i

⑷, obtain the time domain energy sum E of N section _SUM

, with every section time domain energy E _iWith time domain energy sum E _SUMCompare and construct proper vector after carry out energy unitization, obtain N time domain energy eigenwert;

⑹, N time domain energy eigenwert carried out classified calculating with support vector machine method obtain the engine operating state sorting parameter;

⑺, engine operating state sorting parameter and engine normal condition sorting parameter compared obtain the engine failure recognition result.

And the method that described engine normal condition sorting parameter obtains is:

⑴, between first cylinder of six cylinder engine and second cylinder, be provided with to be provided with between first measuring point, second cylinder and the 3rd cylinder to be provided with between the 3rd measuring point, the 5th cylinder and the 6th cylinder between second measuring point, the 4th cylinder and the 5th cylinder the 4th measuring point is set; One acceleration vibration transducer is installed respectively on each measuring point, and this acceleration vibration transducer connects computing machine through the vibration signals collecting appearance;

⑵, be divided into the N section to the time domain vibration signal of the engine normal condition that is begun to collect from top dead centre by the acceleration vibration transducer, every section comprises M vibration signal amplitude respectively;

⑶, obtain in the N section every section time domain energy E _i

⑷, obtain the time domain energy sum E of N section _SUM

, with every section time domain energy E _iWith time domain energy sum E _SUMCompare and construct proper vector after carry out energy unitization, obtain N time domain energy eigenwert;

⑹, N time domain energy eigenwert carried out classified calculating with support vector machine method obtain engine normal condition sorting parameter.

And, described obtain the engine failure recognition result after, comprise also and obtain engine failure state classification parameter that the method for obtaining engine failure state classification parameter is:

⑴, between first cylinder of six cylinder engine and second cylinder, be provided with to be provided with between first measuring point, second cylinder and the 3rd cylinder to be provided with between the 3rd measuring point, the 5th cylinder and the 6th cylinder between second measuring point, the 4th cylinder and the 5th cylinder the 4th measuring point is set; One acceleration vibration transducer is installed respectively on each measuring point, and this acceleration vibration transducer connects computing machine through the vibration signals collecting appearance;

⑵, be divided into the N section to the time domain vibration signal of the engine failure state that is begun to collect from top dead centre by the acceleration vibration transducer, every section comprises M vibration signal amplitude respectively;

⑶, obtain in the N section every section time domain energy E _i

⑷, obtain the time domain energy sum E of N section _SUM

, with every section time domain energy E _iWith time domain energy sum E _SUMCompare and construct proper vector after carry out energy unitization, obtain N time domain energy eigenwert;

⑹, N time domain energy eigenwert carried out classified calculating with support vector machine method obtain engine failure state classification parameter.

And described engine failure state classification parameter is engine intake valve malfunction sorting parameter, engine exhaust port malfunction sorting parameter and engine oil-break malfunction sorting parameter.

Advantage of the present invention and beneficial effect are:

1, this engine failure recognition methods based on time domain energy and SVMs can provide Fault Identification to engine abnormity work; Through processing to acceleration vibration transducer acquired signal; Quick and precisely the engine interior fault is discerned, convenient for maintaining is safeguarded.

2, this engine failure recognition methods based on time domain energy and SVMs can be provided with the acceleration vibration transducer according to actual condition, and this sensor is the vibration transducer of market sale, and cost is lower.

3, the present invention has effectively improved the engine failure recognition speed, has shortened the engine failure recognition time, has improved the engine failure recognition efficiency, and method is simple, and is easy to operate, has made things convenient for the maintenance maintenance of engine.

Description of drawings

Fig. 1 is 6 Cylinder engine inlet valve time domain waveform figure just often;

Time domain waveform figure when Fig. 2 is 6 Cylinder engine inlet valve faults;

Fig. 3 is 6 Cylinder engine exhaust valve time domain waveform figure just often;

Time domain waveform figure when Fig. 4 is 6 Cylinder engine exhaust valve malfunctions;

The time domain waveform figure of work one-period when Fig. 5 is 6 Cylinder engine inlet valve volatile faults;

Fig. 6 is engine normal signal figure;

Fig. 7 is engine failure 1 signal graph;

Fig. 8 is engine failure 2 signal graphs;

Fig. 9 is engine failure 3 signal graphs;

Figure 10 is engine failure 4 signal graphs;

Figure 11 is engine failure 5 signal graphs;

Figure 12 is inlet valve gap time domain waveform figure;

Figure 13 is emission valve clearance time domain waveform figure;

Figure 14 is the time domain waveform figure of oil-break fault;

Figure 15 is the geometry figure of optimum lineoid in the two-dimentional input space under the linear separability pattern;

Figure 16 is the classification chart of the dissimilar faults of engine single cylinder;

Figure 17 is the classification chart of engine air distribution system different faults amount.

Embodiment

Through specific embodiment the present invention is made further detailed description below, following examples are descriptive, are not determinate, can not limit protection scope of the present invention with this.

A kind of engine failure recognition methods based on time domain energy and SVMs, the step that its method comprises is:

⑴, between first cylinder of six cylinder engine and second cylinder, be provided with to be provided with between first measuring point, second cylinder and the 3rd cylinder to be provided with between the 3rd measuring point, the 5th cylinder and the 6th cylinder between second measuring point, the 4th cylinder and the 5th cylinder the 4th measuring point is set; One acceleration vibration transducer is installed respectively on each measuring point, and this acceleration vibration transducer connects computing machine through the vibration signals collecting appearance;

⑵, be divided into the N section to the time domain vibration signal of the engine operating state that is begun to collect from top dead centre by the acceleration vibration transducer, every section comprises M vibration signal amplitude respectively;

⑶, obtain in the N section every section time domain energy E _i

⑷, obtain the time domain energy sum E of N section _SUM

, with every section time domain energy E _iWith time domain energy sum E _SUMCompare and construct proper vector after carry out energy unitization, obtain N time domain energy eigenwert;

⑹, N time domain energy eigenwert carried out classified calculating with support vector machine method obtain the engine operating state sorting parameter;

⑺, engine operating state sorting parameter and engine normal condition sorting parameter compared obtain the engine failure recognition result.

The method that above-mentioned engine normal condition sorting parameter obtains is:

⑴, between first cylinder of six cylinder engine and second cylinder, be provided with to be provided with between first measuring point, second cylinder and the 3rd cylinder to be provided with between the 3rd measuring point, the 5th cylinder and the 6th cylinder between second measuring point, the 4th cylinder and the 5th cylinder the 4th measuring point is set; One acceleration vibration transducer is installed respectively on each measuring point, and this acceleration vibration transducer connects computing machine through the vibration signals collecting appearance;

⑵, be divided into the N section to the time domain vibration signal of the engine normal condition that is begun to collect from top dead centre by the acceleration vibration transducer, every section comprises M vibration signal amplitude respectively;

⑶, obtain in the N section every section time domain energy E _i

⑷, obtain the time domain energy sum E of N section _SUM

, with every section time domain energy E _iWith time domain energy sum E _SUMCompare and construct proper vector after carry out energy unitization, obtain N time domain energy eigenwert;

⑹, N time domain energy eigenwert carried out classified calculating with support vector machine method obtain engine normal condition sorting parameter.

After the present invention obtains the engine failure recognition result, comprise also and obtain engine failure state classification parameter that the method for obtaining engine failure state classification parameter is:

⑴, between first cylinder of six cylinder engine and second cylinder, be provided with to be provided with between first measuring point, second cylinder and the 3rd cylinder to be provided with between the 3rd measuring point, the 5th cylinder and the 6th cylinder between second measuring point, the 4th cylinder and the 5th cylinder the 4th measuring point is set; One acceleration vibration transducer is installed respectively on each measuring point, and this acceleration vibration transducer connects computing machine through the vibration signals collecting appearance;

⑵, be divided into the N section to the time domain vibration signal of the engine failure state that is begun to collect from top dead centre by the acceleration vibration transducer, every section comprises M vibration signal amplitude respectively;

⑶, obtain in the N section every section time domain energy E _i

⑷, obtain the time domain energy sum E of N section _SUM

, with every section time domain energy E _iWith time domain energy sum E _SUMCompare and construct proper vector after carry out energy unitization, obtain N time domain energy eigenwert;

⑹, N time domain energy eigenwert carried out classified calculating with support vector machine method obtain engine failure state classification parameter.Engine failure state classification parameter is engine intake valve malfunction sorting parameter, engine exhaust port malfunction sorting parameter and engine oil-break malfunction sorting parameter.

Carrying out time domain energy by the corresponding vibration signal of engine crankshaft corner below divides and calculates:

The present invention collects engine time domain vibration signal X (t) by the acceleration vibration transducer, and then time domain energy E is:

$E={\∫}_{-\∞}^{\∞}{X}^2\left(t\right)\mathrm{Dt}$ Formula (1)

The signal energy of being asked for formula (1) is one group of discrete point by the amplitude energy of trying to achieve behind the time discrete transform, be divided into the N segment signal according to crank angle after, the point that every segment signal comprises has M respectively, the set of discrete point is { x in every segment signal ₁, x ₂X _jJ=1,2, M}; The energy of then obtaining in every segment signal is:

$E_i=\underset{j=1}{\overset{M}{\mathrm{\Σ}}}{x}_j;$ $E_{\mathrm{Sum}}=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{E}_i,$ I=1,2 ..., N formula (2)

Time domain energy E with every section _iWith time domain energy sum E _SUMCompare and construct proper vector after carry out energy unitization, obtain N time domain energy eigenwert;

[E ₁/ E _Sum, E ₂/ E _Sum... E _n/ E _Sum] i=1,2 ..., N formula (3)

1.1.1 the method for distilling introduction of eigenwert

Principle of work according to engine; The moment that 6 cylinder intake valves are taken a seat and impacted; Approximately occur in about 150 ° before of 1 cylinder compression top centers; And the impact of other type takes place constantly not to be attended by in this impact, therefore can judge the inlet valve fault through impacting phase place, is the time domain waveform figure of 6 Cylinder engine inlet valves time domain waveform figure and Fig. 2 just often when being 6 Cylinder engine inlet valve faults like Fig. 1.

Principle of work according to engine; The 6 cylinder exhaust valves impact position of taking a seat occurs in behind the 1 cylinder exhaust top dead center about 20 °; Be example still with 6 cylinder emission valve clearances; Then exhaust valve is taken a seat to impact and just should be occurred in behind 1 cylinder compression top center about 20 °, since 1 cylinder compression top center, just in time corresponding 6 cylinder exhaust top dead centers.Fig. 3 is 6 Cylinder engine exhaust valve time domain waveform figure just often; Time domain waveform figure when Fig. 4 is 6 Cylinder engine exhaust valve malfunctions.

In the engine working process, its cylinder cap will receive burning impact, piston collisions, join the effect of multiple exciting force such as its mechanism of qi structure impact, thereby cause the structural vibration of cylinder cap.Because the difference cylinder of engine is worked in certain sequence, vibration signal is inevitable on time domain also to have certain sequence, so can confirm the moment of several main excitations basically from vibrational waveform.When Fig. 5 is 6 Cylinder engine inlet valve volatile faults, measuring point A1.56 place, the time domain waveform figure of engine operation one-period.

Can know through top analysis, judge the fault of the inlet valve or the exhaust valve of same cylinder, can judge through the position of crank angle.For at same CAP, impact of different nature can be judged from the amplitude energy.This just needs to propose a kind of new method and confirms the character that generation is impacted, actually the impact of what type is that the inlet and outlet door impacts, or the impact of other types, and then just can make correct fault diagnosis.

The selected engine operating condition of experiment is idling 900r/min, records the vibration signal under the various states of engine.Because the original signal of actual samples does not have clear and definite starting point; It or not the integral multiple of engine operating cycle; Cause the comparability between signal very poor like this; Therefore the fault diagnosis that is unfavorable for next step need be carried out the location of top dead centre to original signal, and a work period of intercepting engine is analyzed.Be in the engine operation one-period shown in Fig. 1, Fig. 2, Fig. 3, Fig. 4, can find that difference cylinder valve clearance fault all has different segments.By can clearly finding out among Fig. 5, the valve fault is impacted with burning has certain bent axle at interval.Therefore, can select for use the amount relevant to carry out feature extraction with crank angle and amplitude.

The corresponding crank angle of cycle period of engine is 720 °; The signal of intercepting is the standard cylinder with 1 cylinder compression top center; For faults such as the inlet valve of each cylinder of better distinguish engine, exhaust valve, oil-breaks, the engine cycle signal is divided into the N=12 section by crank angle by the gas distributing system fault.By formula (1) formula (2) formula (3) calculates different crank angle corresponding energy values.

1.1.2 the leaching process of eigenwert

Motor car engine will produce vibration when operation, and is comprising abundant information in the vibration signal.Vibration signal to the engine gathered extracts signal characteristic quantity, to engine intake valve, emission valve clearance, oil-break diagnosing malfunction on time domain.For the same fault between better each cylinder of differentiation and the different faults of every cylinder; Characteristics according to vibration signal are divided into 12 five equilibriums with one whole section periodic signal; Obtain the energy E under the various states of engine through formula (1), formula (2), these eigenwerts are come E=[E with Vector Groups ₁, E ₂..., E ₁₂] expression, utilize formula (3) to calculate after, with eigenwert Δ E=[E ₁/ E _Sum, E ₂/ E _Sum..., E ₁₂/ E _Sum] as the input vector of SVMs classification function, set up the training sample under the engine different faults state.

1.1.3 engine failure analysis

(1) engine air distribution system different faults quantitative analysis: Fig. 6 is engine normal signal figure; Fig. 7 engine failure 1 signal graph; Fig. 8 is engine failure 2 signal graphs; Fig. 9 is engine failure 3 signal graphs; Figure 10 engine failure 4 signal graphs; Figure 11 engine failure 5 signal graphs; Extract through the vibration signal under five kinds of different faults amounts of top engine air distribution system state being carried out fault signature, extract the characteristic energy under the engine air distribution system different faults amount state, and preliminary failure judgement type.The characteristic energy value of extracting is as shown in table 1.

The characteristic energy value of table 1 engine air distribution system different faults amount

Fault type	Normal condition	Fault	1	Fault 2	Fault 3	Fault 4	Fault 5
								E 1	1.0224	0.4240	-4.1109	2.9760	-0.2714	10.9968
E 2	1.1752	0.4874	-4.4181	2.2163	-0.4444	8.6884
							E 3	1.3661	0.9649	-4.8261	1.1721	-0.8581	8.2367
E 4	2.2266	1.9158	-2.2440	1.3830	-1.5316	6.6628
							E 5	2.3622	1.1439	-3.9014	2.1843	-1.5679	8.8609
E 6	2.5099	0.4188	-4.0075	2.4156	-0.7824	8.0068
							E 7	0.5708	-0.2144	-4.7719	1.2357	-1.7957	5.5502
E 8	1.9005	0.0528	-4.9747	1.2390	-1.1317	5.9950
							E 9	2.7005	-2.3848	-8.1876	2.2233	-2.9799	6.6480
E 10	3.5302	1.7849	-3.7924	20.5367	0.2041	30.9792
							E 11	1.4596	0.9134	-4.9749	18.5785	-1.4471	27.5814
E 12	2.3284	0.7924	-4.9477	18.9078	-0.7949	24.2304

Can find between the engine air distribution system different faults amount evident difference property is arranged through the comparison of table 1, the energy of fault occurrence positions provides condition much larger than the energy of other positions for carrying out Fault Identification with support vector machine method.

(2) the dissimilar faults analysis of engine single cylinder; Figure 12 is inlet valve gap time domain waveform figure; Figure 13 is emission valve clearance time domain waveform figure; Figure 14 is the time domain waveform figure of oil-break fault; When the dissimilar fault of engine, the vibration signal of top three kinds of faults is carried out fault signature extract, extract the characteristic energy value under the engine different faults.When engine intake valve fault, exhaust valve malfunction and oil-break fault, the eigenwert of extracting respectively under the dissimilar faults of engine is calculated, and concrete data are as shown in table 2.

The characteristic energy value of the dissimilar faults of table 2 engine single cylinder

Through relatively finding between the dissimilar faults of engine evident difference is arranged, just in time be that 6 cylinders get the oil-break fault the 8th section energy value correspondence, the fault energy is obviously greater than normal condition; The 1st section energy value correspondence just in time is 6 cylinder air inlet faults, and it is big that the fault energy obviously becomes; The 6th section energy value correspondence just in time is 6 cylinder exhaust failures, the significant change of fault energy; These all are that the Fault Identification of SVMs provides condition.

2 engine failure pattern-recognitions based on SVMs

2.1 SVMs (SVM) classification learning algorithm principle brief introduction

SVMs is a kind of feedforward neural network in essence, according to the structural risk minimization criterion, under the prerequisite that makes training sample error in classification minimization, improves the extensive popularization ability of sorter as far as possible.From the angle of implementing; The core concept of training SVMs is equivalent to the quadratic programming problem of finding the solution a linear restriction; Thereby construct a lineoid as the decision-making plane, make that the distance between two quasi-modes is maximum in the feature space, and its separating of can guaranteeing to obtain is globally optimal solution.

For the classification learning problem (SVC) of SVMs (SVM), dimensionality reduction is stressed in the traditional mode recognition methods, and SVC in contrast.For the nonlinear problem that two types of points in the feature space can not separate by lineoid, SVC adopts mapping method that it is mapped to the more space of higher-dimension, and tries to achieve the best lineoid equation of distinguishing two types of sample points, as the foundation of differentiating unknown sample.Though space dimensionality is higher like this, the VC dimension is very low, thereby has limited the problem of over-fitting.Such benefit is exactly under the less situation of known sample, and SVMs still can be made statistical fluctuation effectively.

The notion of VC dimension (Vapnik-Chervonenkis Dimension) is for research learning procedure function collection convergent speed and generalization, by an important indicator of the relevant collection of functions learning performance of Statistical Learning Theory definition.The VC dimension has reflected the learning ability of collection of functions, and it is more complicated that the VC dimension is more greatly then learnt machine.

2.1.1 SVMs classification (SVC) algorithm

(1) SVC linear classification method

The SVM algorithm is that the optimal classification face under the linear separability situation proposes.So-called optimal classification face requires classifying face not only can two types of sample points be separated error-free exactly, and will make two types classification space maximum.See that from the situation of linear separability pattern its main thought is set up a lineoid exactly as decision surface, this decision surface not only can correctly be classified all training samples, and makes in the training sample from the nearest point of classifying face to classifying face apart from maximum.Figure 15 has provided under the linear separability pattern geometry figure of optimum lineoid in the two-dimentional input space, and wherein: solid dot and hollow dots are represented two types of samples; H is a sorting track; H1, H2 be respectively all kinds of in from the nearest sample of sorting track and be parallel to the straight line of sorting track, the distance between them is called the class interval.

If sample set is: (y ₁, x ₁) ..., (y _l, x _l), x ∈ R ⁿ, y ∈ R, the general type of d dimension space neutral line discriminant function is g (x)=w ^TX+b, then classifying face equation H is w ^TX+b=0.

Before classifying; Generally need discriminant function be carried out normalization; Promptly replace original w and b respectively, two types of all samples all satisfied with w/||w|| and b/||w|| | g (x) |>=1, this moment is from the nearest sample of classifying face | g (x) |=1; And require classifying face that all samples can both correctly be classified, require it to satisfy exactly ^[39-40]:

y _i(w ^Tx _i+b)-1≥0,i=1,2,…,n (4-1)

Those samples that equal sign is set up are called support vector (Support Vectors).The gap size in the classification space (Margin) of two types of samples:

$M\arg \mathrm{in}=\frac{2}{\left|\right|w\left|\right|}---(4-2)$

Optimal classification face problem can be expressed as following constrained optimization problems, promptly under the constraint of formula (4-1), asks the minimum value of function (4-3).

For this reason, the Lagrange function that can be defined as follows:

$L(w,b,\mathrm{\α})=\frac{1}{2}{w}^{T}w-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_i[y_i(w^T{x}_i+b)-1]---(4-4)$

Wherein, α _iBe the Lagrange multiplier, problem is that w and b are asked Lagrange minimum of a function value.Wushu (4-4) is respectively to w, b, α _iAsk partial differential and make them equal 0:

$\left\{\begin{array}{c}\frac{\∂L}{\∂w}=0\⇒w=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_i{y}_i{x}_i\\ \frac{\∂L}{\∂b}=0\⇒\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_i{y}_i=0\\ \frac{\∂L}{{\∂\mathrm{\α}}_i}=0\⇒{\mathrm{\α}}_i[y_i(w^T{x}_i+b)-1]=0\end{array}\right.---(4-5)$

More than three formulas add that former constraint condition can be converted into former problem the dual problem of quadratic programming:

$\left\{\begin{array}{c}\max \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{a}_i-\frac{1}{2}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_i{\mathrm{\α}}_j{y}_i{y}_j\left(x_i^T{x}_j\right)\\ \begin{array}{cc}s.t& a_i\≥0,i=1,\·\·\·,n\end{array}\\ \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{a}_i{y}_i=0\end{array}\right.---(4-6)$

This is a quadratic function mechanism problem under the inequality constrain, has unique optimum solution.If

is optimum solution, then

$w^{*}=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{a}_i^{*}{y}_i{x}_i---(4-7)$

non-vanishing sample is support vector; Therefore, the weight coefficient vector of optimal classification face is the linear combination of support vector.

b ^*Can be by constraint condition α _i[y _i(w ^Tx _i+ b)-1]=0 find the solution the optimal classification function of trying to achieve thus

$f\left(x\right)=\mathrm{sgn}({\left(w^{*}\right)}^{T}x+b^{*})=\mathrm{sgn}(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{a}_i^{*}{y}_i{x}_i^{*}x+b^{*})---(4-8)$

Sgn () is a sign function.

(2) the non-linear sorting technique of SVC

Non-linear situation of dividing can adopt the method for kernel function, makes it to be converted into the problem of a structure linear classification lineoid in high-dimensional feature space through the kernel function mapping.

In the time can not separating two types of points fully, can introduce slack variable with a lineoid

Make lineoid w ^TX+b=0 satisfies:

y _i(w ^Tx _i+b)≥1-ξ _i (4-9)

When 0<ζ _i<1 o'clock sample point xi is still by correct classification, and works as ζ _i>=1 o'clock sample point xi is by mistake minute.For this reason, introduce following objective function:

$\mathrm{\&psi;}(w,\mathrm{\&xi;})=\frac{1}{2}{w}^{T}w+C\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&xi;}}_i---(4-10)$

Wherein C is a positive constant, is called penalty factor, and this moment, SVM can realize through the dual program in the quadratic programming:

$\left\{\begin{array}{c}\max \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{a}_i-\frac{1}{2}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{\mathrm{\&alpha;}}_j{y}_i{y}_j\left(x_i^T{x}_j\right)\\ \begin{array}{cc}s.\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HDA00001627661200011.png,HDA00001627661200012.png"\; state="\{\{state\}\}">t</figure-callout>}& 0\&le;a_i\&le;C,i=1,\&CenterDot;\&CenterDot;\&CenterDot;,n\end{array}\\ \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{a}_i{y}_i=0\end{array}\right.---(4-11)$

2.1.2 the kernel function of SVMs (SVM)

If simple lineoid in luv space can not obtain satisfied classifying quality, then must be with the hypersurface of complicacy as interphase.

At first the input space is transformed to a higher dimensional space, in this new space, ask for the optimum linearity classifying face then, and this nonlinear transformation is to realize through defining suitable kernel function (inner product function), order through nonlinear transformation:

K(x _i,x _j)=<Φ(x _i)·Φ(x _j)> (4-12)

With kernel function K (x _i, x _j) replace the dot product in the optimal classification plane Just be equivalent to transform to a certain new feature space to former feature space, this moment, majorized function became:

$Q\left(a\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{a}_i-\frac{1}{2}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{\mathrm{\&alpha;}}_j{y}_i{y}_{j}K(x_i,x_j)---(4-13)$

Corresponding discriminant function formula then is:

$f\left(x\right)=\mathrm{sgn}[{\left(w^{*}\right)}^T\mathrm{\&phi;}\left(x\right)+b^{*}]=\mathrm{sgn}(\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{a}_i^{*}{y}_{i}K(x_i,x)+b^{*})---(4-14)$

X in the formula (4-14) _iBe support vector; X is a unknown vector; (4-14) formula is exactly nonlinear SVC classification function, is similar to a neural network at classification function in form, and its output is the linear combination of some middle layer node; And therefore each middle layer node also is called the support vector network corresponding to the inner product of an input sample and a support vector ^[43-45]

Because the actual linear combination that only comprises the inner product of unknown vector and support vector in the final discriminant function, the computation complexity when therefore discerning depends on the number of support vector.

Kernel function form commonly used at present mainly contains following three types, and they all have corresponding relation with existed algorithms.

1. the kernel function of polynomial form, i.e. K (x, x _i)=[(x ^Tx _i)+1] ^q, corresponding SVM is a q rank polynomial expression sorter.

2. the kernel function of basic form radially, promptly

corresponding SVM is a kind of radial basis function classifiers.

3. the S forming core function of multi-layer perception form, i.e. K (x, x _i)=tanh (v (x ^Tx _i)+c), corresponding SVM is a two-layer perceptron neural network.

Depend on the data treatment requirement with any kernel function actually.Because radially basic RBF kernel function shows good classification performance in practical problems, so the radially basic RBF kernel function of general use.

2.2 SVMs (SVM) data pre-treatment

There is a good sorter no doubt important; But all do not look to sorter; The data pre-service also very important (normalization, dimensionality reduction, parameter optimization) in early stage, after the data pre-service, the words that feature extraction is suitable; The influence of sorter can not account for significantly, and promptly you use any sorter can obtain satisfied classification accuracy.

2.2.1 data normalization

It is in order to accelerate the convergence of training network, can not carry out normalization and handle that normalization is applied to SVMs.Normalized concrete effect is a statistical distribution property of concluding unified sample.Normalization is the probability distribution of statistics between 0-1, and normalization is that the coordinate of statistics distributes between-1 to+1.No matter be,, thereby must carry out normalization to data and handle because each data unit of gathering is inconsistent for modeling or in order to calculate.The sample data of SVMs after with normalization trained respectively and predicted.

Linear normalization function expression (4-15) is as follows:

y=(x-Min)/(Max-Min) （4-15）

Explain: x, y are respectively the forward and backward value of conversion, and Max, Min are respectively the maximal value and the minimum value of sample data.

2.2.2 data dimensionality reduction

Matrix for a k dimension; Each the dimension matrix and other dimensions that are equivalent to it all are quadratures; Be equivalent in multidimensional coordinate system, coordinate axis all is vertical, and we can change the coordinate system of these dimensions so; Thereby make this matrix big in some dimension upside deviation, and very little in some dimension upside deviation.So our way is exactly the projection matrix of trying to achieve a k dimensional feature, this projection matrix can drop to low dimension from higher-dimension with matrix.Projection matrix also can be called transformation matrix.New low dimensional feature must each be tieed up all quadratures, and proper vector all is a quadrature.Through asking the covariance matrix of sample matrix, obtain the proper vector of covariance matrix then, these proper vectors just can constitute this projection matrix.The size of the eigenwert of covariance matrix is depended in the selection of proper vector.The characteristic of higher-dimension multiply by this projection matrix, just can the dimension of high dimensional feature be dropped to the dimension of appointment.

2.2.3 parameter optimization

About the SVM parameter optimization, do not generally acknowledge unified the best way in the world, method commonly used at present now lets penalty factor (c) and kernel function (g) value in certain scope exactly.For getting fixed c and g; Training set is carried out classified calculating as raw data set; Obtain the classification accuracy of the training set data under this group c and g; Finally get and make the highest that of training set data classification accuracy group c and the parameter of g as the best, but a problem is arranged is exactly the c that possibly have many groups with g corresponding to the highest checking classification accuracy, the means that this situation adopts are to choose that can reach parameter c minimum in the highest checking classification accuracy to organize c and the g parameter as the best; If corresponding minimum c has many group g, just choose first group of c searching and g parameter as the best.The reason of doing like this is: too high c can cause learning state to take place; Be that the training set classification accuracy is very high and the test set classification accuracy is very low the generalization ability of the sorter (reduce); So among all paired c and g in can reaching the highest checking classification accuracy, less penalty parameter c is better alternative.

Can use genetic algorithm (GA), PSO parameter and mesh parameter (grid search) to carry out parameter optimization here; Promptly seek best parameter c and g with genetic algorithm parameter optimizing, PSO parameter optimization and mesh parameter optimizing; Though adopt grid search can find the highest classification accuracy under the cross validation meaning; It is globally optimal solution; If can be very time-consuming but sometimes think to seek best parameter c and g in the larger context, adopt genetic algorithm just can travel through all parameter points in the grid, also can find globally optimal solution.

2.3 fault diagnosis instance based on SVMs

2.3.1 the identification of diesel engine fault

Because the crank angle at the dissimilar impact of engine and the impact of difference cylinder place is different, and the energy that impacts is also different.Therefore the energy value that extracts the different crank angles of engine carries out fault diagnosis with the method for SVMs to it as characteristic quantity.

(1) identification of the dissimilar faults of engine single cylinder

Method with SVMs is predicted classification to the dissimilar faults of engine single cylinder.Through 1.1.2 breakdown in the motor feature extracting method; Extract that 16 groups of engines as shown in table 2 are normal, 12 segment signal energy under oil-break, inlet valve and four kinds of dissimilar faults of single cylinder of exhaust valve, pass through formula (3) again and obtain 16 groups of corresponding fault signature values under every kind of state.Wherein 10 groups of data are the fault training sample, and 6 groups of data are forecast sample.

Through after the data pre-treatment of SVMs, in the nonlinear SVC classification function of fault training set substitution formula (4-14), through the classification accuracy of forecast sample collection check fault.The result is shown in figure 16 to be the classification chart of the dissimilar faults of engine single cylinder.

Through can finding to the classification of the dissimilar faults of engine single cylinder, normal, oil-break, inlet valve and exhaust valve malfunction, every kind of state 10 groups of training datas and 6 groups of predicted data have down all obtained accurate classification, do not have the fault of judging by accident.Verified the feasibility of SVMs to the dissimilar failure predictions of engine single cylinder.

(2) identification of engine air distribution system different faults amount

Same quadrat method is used SVMs engine air distribution system different faults amount is predicted classification.Through 1.1.2 breakdown in the motor feature extracting method; Extract that 16 groups of engines as shown in table 1 are normal, 12 segment signal energy under fault 1, fault 2, fault 3, fault 4 and fault 5 these six kinds of engine air distribution system different faults degree, pass through formula (3) again and obtain 16 groups of corresponding fault signature values under every kind of state.Choose wherein that 10 groups of data are the fault training sample, 6 groups of data are forecast sample.Through after the data pre-treatment of SVMs, the fault training set is updated in the nonlinear SVC classification function of formula (4-14), and the classification accuracy of test specimen collection check fault.The result is shown in figure 17 to be the classification chart of engine air distribution system different faults amount.Through can find to the classification of engine air distribution system different faults degree; Engine is normal, every kind of state 10 groups of training datas and 6 groups of predicted data down of fault 1, fault 2, fault 3, fault 4 and fault 5 have all obtained accurate classification, does not have the fault of judging by accident.Verified the feasibility of SVMs to the prediction of engine air distribution system different faults amount.

Claims (4)

1. engine failure recognition methods based on time domain energy and SVMs, it is characterized in that: the step that this method comprises is:

⑴, between first cylinder of six cylinder engine and second cylinder, be provided with to be provided with between first measuring point, second cylinder and the 3rd cylinder to be provided with between the 3rd measuring point, the 5th cylinder and the 6th cylinder between second measuring point, the 4th cylinder and the 5th cylinder the 4th measuring point is set; One acceleration vibration transducer is installed respectively on each measuring point, and this acceleration vibration transducer connects computing machine through the vibration signals collecting appearance;

⑵, be divided into the N section to the time domain vibration signal of the engine operating state that is begun to collect from top dead centre by the acceleration vibration transducer, every section comprises M vibration signal amplitude respectively;

⑶, obtain in the N section every section time domain energy E _i

⑷, obtain the time domain energy sum E of N section _SUM

, with every section time domain energy E _iWith time domain energy sum E _SUMCompare and construct proper vector after carry out energy unitization, obtain N time domain energy eigenwert;

⑹, N time domain energy eigenwert carried out classified calculating with support vector machine method obtain the engine operating state sorting parameter;

⑺, engine operating state sorting parameter and engine normal condition sorting parameter compared obtain the engine failure recognition result.

2. the engine failure recognition methods based on time domain energy and SVMs according to claim 1 is characterized in that: the method that described engine normal condition sorting parameter obtains is:

⑴, between first cylinder of six cylinder engine and second cylinder, be provided with to be provided with between first measuring point, second cylinder and the 3rd cylinder to be provided with between the 3rd measuring point, the 5th cylinder and the 6th cylinder between second measuring point, the 4th cylinder and the 5th cylinder the 4th measuring point is set; One acceleration vibration transducer is installed respectively on each measuring point, and this acceleration vibration transducer connects computing machine through the vibration signals collecting appearance;

⑵, be divided into the N section to the time domain vibration signal of the engine normal condition that is begun to collect from top dead centre by the acceleration vibration transducer, every section comprises M vibration signal amplitude respectively;

⑶, obtain in the N section every section time domain energy E _i

⑷, obtain the time domain energy sum E of N section _SUM

, with every section time domain energy E _iWith time domain energy sum E _SUMCompare and construct proper vector after carry out energy unitization, obtain N time domain energy eigenwert;

⑹, N time domain energy eigenwert carried out classified calculating with support vector machine method obtain engine normal condition sorting parameter.

3. the engine failure recognition methods based on time domain energy and SVMs according to claim 1; It is characterized in that: described obtain the engine failure recognition result after; Also comprise and obtain engine failure state classification parameter, the method for obtaining engine failure state classification parameter is:

⑴, between first cylinder of six cylinder engine and second cylinder, be provided with to be provided with between first measuring point, second cylinder and the 3rd cylinder to be provided with between the 3rd measuring point, the 5th cylinder and the 6th cylinder between second measuring point, the 4th cylinder and the 5th cylinder the 4th measuring point is set; One acceleration vibration transducer is installed respectively on each measuring point, and this acceleration vibration transducer connects computing machine through the vibration signals collecting appearance;

⑵, be divided into the N section to the time domain vibration signal of the engine failure state that is begun to collect from top dead centre by the acceleration vibration transducer, every section comprises M vibration signal amplitude respectively;

⑶, obtain in the N section every section time domain energy E _i

⑷, obtain the time domain energy sum E of N section _SUM

, with every section time domain energy E _iWith time domain energy sum E _SUMCompare and construct proper vector after carry out energy unitization, obtain N time domain energy eigenwert;

⑹, N time domain energy eigenwert carried out classified calculating with support vector machine method obtain engine failure state classification parameter.

4. the engine failure recognition methods based on time domain energy and SVMs according to claim 1 is characterized in that: described engine failure state classification parameter is engine intake valve malfunction sorting parameter, engine exhaust port malfunction sorting parameter and engine oil-break malfunction sorting parameter.

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