CN104796116B - A kind of surge waveform peak measurement methods based on parameter fitting - Google Patents

Abstract

The present invention relates to a kind of surge waveform peak measurement methods based on parameter fitting, belong to vibratory impulse, mechanical engineering field and metrological testing technology field.Specific method is excited by impact using source excited by impact generation, and waveform measurement is carried out with sensor and supporting Wave data acquisition system, obtains complete shock measurement waveform equal interval sampling sequence；The maximum and minimum value of surge waveform are obtained with comparison method；The approximate semisinusoidal portion waveshape between maximum and minimum value near peak value is intercepted from shock measurement waveform equal interval sampling sequence is used for peak computational；Four parameter fitting process of surge waveform peak value are carried out with sine wave fitting method；To be fitted sinusoidal amplitude value and DC component Iterative calculation method shock measurement waveform peak；Regression criterion virtual value is provided as the good and bad assistant criteria of peak fitting.With not needing peak filter, the degree of accuracy and the higher calculating effect of resolving power.

Description

A kind of surge waveform peak measurement methods based on parameter fitting

Technical field

The invention belongs to vibratory impulse, mechanical engineering field and metrological testing technology field, it is related to a kind of surge waveform Peak measurement methods, more particularly to due to mechanical collision, electrical impact, gas impact, hydraulic shock, acoustic shock, light impact, The peak measurement methods of the surge waveforms of formation such as blast.

Background technology

Surge waveform belongs to impulse wave, and calculating and the determination of peak value of pulse are the basic problems in impulsive measurement.Impact is surveyed Amount under many circumstances all with security and weaponry etc. to injure performance relevant.For example, people can land in spacecraft Peak acceleration during its landing is measured during recovery, to assess and determine whether the ability to bear pole beyond human body and equipment Limit, and and then take protective technical measures；When the kinetic energy weapons such as bullet, shell, rocket projectile direct hit on the target, its most favourable opposition Its fragmentation effect will be embodied by hitting acceleration, and people need the parameters such as the peak value by measuring impact acceleration, with understand it is various not How is the lethality of the weaponry of same model；The helmet, safety cap etc. bear great impact acceleration being capable of not fragmentation, embodiment Its protective capability to people, people by measuring impact acceleration peak value can obtain the information；And in high-voltage electric system In, people are it should be understood that circuit structure and system such as can occur without arcing, puncture at the failure under how high impact high voltage imitates Should, to carry out electrical safety and protection Design.In a word, people are main to be concerned about in the measurement of many kinds of impact signals Its peak value impacted has much on earth.

In shock measurement, final result is a physical pulse waveform.The peak value and pulsewidth of its pulse be its two Individual basic parameter, after they are determined, main impact information is substantially summarised, it is possible to based on this, further really Fixed other impact parameters and shock characteristic.Such as lift edge, frequency spectrum, power spectrum.In most cases, people are intended to single punching It is the peak shape smoother hit, gentle and with single-peak response, so, it will be easy to judge the position of peak value and obtain it The value of peak value.When distortion, noise, burr, the tinkling of pieces of jade that shakes etc. occur near peak value, the determination of peak and peak value are from height The measurement of value, which is obtained, just becomes relatively difficult.Especially in this case, people still want to obtain higher peak value measurement The degree of accuracy, will make the problem become more difficult.In order to solve this problem, in different industries, what people took is different Mode.

In radio industry, radio wave pulses peak power measurement is also one of main measure the item.In order to avoid making an uproar The influence to peak computational such as sound, response overshoot, the tinkling of pieces of jade that shakes, International Electrotechnical Commission (International Electro Technical Commission, abbreviation IEC) basic terms such as " tops ", " bottom " of pulse are defined in standard, for describing arteries and veins The peak value and valley of punching, and determine with mode method " top " and " bottom " of pulse.It is flatter for square wave etc. " top " and " bottom " Impulse waveform, this definition and method have excellent adaptability, are able to extensive use.But for the non-square wave for comparing pinnacle Class surge waveform is not fully adapted to, and mainly also faces the problem of needs are compared with multi-point sampling and not high accuracy of measurement.

In vibratory impulse field, often mechanical engineering problem, particularly HI high impact situation and the super high impact feelings faced Condition, semisinusoidal type pulse is similar to due to what the impact characteristics such as material and structure were produced, its peak value is often uneven, irregular, And sampled measurements point is also insufficient, at this moment, the problem of adaptability is poor can be usually run into using the mode method in radio industry, Most directly performance is exactly that measurement reproducibility is poor.

Thus, in vibratory impulse field, Comite Internationale de Normalisation (International Organization for Standardization, abbreviation ISO) recommend way be that the surge waveform of measurement is filtered, by the peak value of surge waveform Filter it is relatively flat after again direct maximizing determine peak value of pulse.However, the selection of filtering bandwidth, and after filtering whether The judgement that peak value to surge waveform is affected greatly, is always the basic problem of puzzlement impact metering, and impact is surveyed The degree of accuracy of amount is difficult to improve always, and the degree of accuracy is about 5% or so.

The present invention in view of the above-mentioned problems, by impact peak value measurement regard as residual cycle sinusoidal curve of local it is unimodal most Excellent decision problem, without using means such as filtering, so as to avoid Parameters variation that wave filter may bring to accuracy of measurement Influence, optimal judgement is carried out with model parameter, and noise, burr, spike, quantization error etc. can also be influenceed to carry out certain suppression System, so as to be expected to obtain higher impact peak value accuracy of measurement.

The content of the invention

It is pre-filtered the need for the invention aims to overcome ISO recommendation methods, so as to influence accuracy of measurement Defect, and IEC recommend the problem of method is not exclusively adapted to semisinusoidal and gaussian shape surge waveform, to improve semisinusoidal shape For the purpose of the degree of accuracy that class and gaussian shape class surge waveform peak value measurement are calculated, a kind of shock wave based on parameter fitting is proposed Shape peak measurement methods.The peak value of surge waveform is determined with semisinusoidal approximating method, and in the case of without using wave filter, directly Connect and least square curve fitting is carried out with acquired original Wave data, the peak value of semisinusoidal surge waveform is obtained, to improve measurement The degree of accuracy and repeatability.

To achieve the above object, the technical solution adopted in the present invention is as follows：

A kind of surge waveform peak measurement methods based on parameter fitting, comprise the following steps：

Step 1: produce waveform using source excited by impact, this waveform can be similar to that semisinusoidal is excited by impact or Gaussian shocks Excitation.Waveform measurement is carried out with sensor and supporting Wave data acquisition system, complete shock measurement waveform is obtained at equal intervals Sample sequence.

Step 2: obtaining the maximum and minimum value of surge waveform with comparison method, the maximum and most of surge waveform is intercepted The waveform of approximate semisinusoidal part between small value, for peak computational.

Under normal circumstances, it is the amplitude range limited from waveform maximum and minimum value, from 3/ centered on peak Descending order intercepts more than 3 intervals in the range of 4~1/10, and determines interval number.

Step 3: the approximate semisinusoidal portion waveshape for peak computational part that step 2 is intercepted, using shock wave The parameter fitness method of shape four carries out least square waveform fitting.It is specific as follows：

First, if the equal interval sampling sequence for surge waveform the Fitting Calculation (belongs to step one and obtains complete impact survey Measure a part for waveform equal interval sampling sequence) it is x₁,x₂,...,x_n.The function table of its portion waveshape least square fitting curve It is up to formula：

Wherein, A is fitting sinusoidal waveform amplitude；ω is fitting sinusoidal waveform angular frequency；It is initial for fitting sinusoidal waveform Phase；D is fitting sinusoidal waveform DC component；I is sampled point sequence number；N is sampled point number；x_iFor ith sample point；y(i) For the match value of ith sample point.

Then, to equal interval sampling sequence x₁,x₂,...,x_n, carry out least square sine curve fitting.Process is as follows：

If surge waveform sampling rate is v, waveform near surge waveform peak value is subjected to four parameters according to sine wave rule Fitting, its sine wave freuqency desired value to be estimated is f₀, the cycle is T₀=1/f₀, then angular frequency desired value is ω₀=2 π f₀/ v, Signal waveform holding time length contained by sine wave sample sequence to be estimated is τ；Then there is τ≤T₀, f₀≤1/τ.Parameter q is found, So that τ/T₀≥q；Thus f₀∈[q/τ,2/τ]。

(1) fitting iteration stopping condition is set as h_e.H can be chosen_e=1 × 10^-20。

(2) from known moment t₁,t₂,...,t_nSurge waveform collecting sample x₁,x₂,...,x_n.Believed using point count Number waveform holding time length is τ=(n-1)/v；Estimate factor q, determine target frequency f₀Presence it is interval [q/ τ, 2/ τ]；

(3) iteration left margin frequency is determined：f_L=q/ τ；ω_L=2 π f_L/v；Iteration right margin frequency：f_R=2/ τ；ω_R=2 π f_R/v；Median frequency is chosen according to optimum seeking method principle：ω_M=ω_L+0.618×(ω_R-ω_L)；ω_T=ω_R-0.618×(ω_R- ω_L)

(4) in ω_LThree parameter sine wave curve-fits of upper execution, obtain A_L、D_L、ρ_L；In ω_RThree parametric sinusoidals of upper execution Curve matching, obtains A_R、D_R、ρ_R；In ω_MThree parameter sine wave curve-fits of upper execution, obtain A_M、D_M、ρ_M；In ω_TOn Three parameter sine wave curve-fits are performed, A is obtained_T、D_T、ρ_T。

If (5) ρ_M<ρ_T, then ρ=ρ_M, there is ω₀∈[ω_T,ω_R], ω_L=ω_T, ω_T=ω_M；ω_M=ω_L+0.618× (ω_R-ω_L)；If ρ_M>ρ_T, then ρ=ρ_T, there is ω₀∈[ω_L,ω_M], ω_R=ω_M, ω_M=ω_T；ω_T=ω_R-0.618×(ω_R- ω_L)。

(6) determine whether | (ρ_M(k)-ρ_T(k))/ρ_T(k) | ＜ h_e, if it is, stop iteration, and as ρ=ρ_TWhen, obtain It is A=A to obtain four parameter fitting sinusoids parameters_T, ω=ω_T、D=D_TAnd regression criterion virtual value ρ, it was fitted Journey terminates.As ρ=ρ_MWhen, four parameter fitting sinusoids parameters of acquisition are A=A_M, ω=ω_M、D=D_MAnd intend Residual error virtual value ρ is closed, fit procedure terminates；Otherwise, (4)~(6) process is repeated.

The regression criterion virtual value ρ is：

When only containing noise factor error in sample sequence, ρ is the experiment mark for being superimposed upon noise on sinusoidal waveform Quasi- deviation.

Finally, it is A+D to obtain surge waveform peak estimation value.

Step 4: judging whether the interval number of interception peak value completes, if not completing, intercepted peak value waveform model is converted Enclose, re-start fitting operation, obtain new fitting peak estimation value and new regression criterion virtual value；If it is interval to intercept peak value Number has been completed, then judges to compare fitting quality, ρ using respective regression criterion virtual value ρ under the conditions of more all interceptions Smaller then fitting effect is better, and provides impact peak value fitting result with the minimum conditions of ρ, terminates measurement.

Beneficial effect

The present invention is by compared with the mode method of suitable square wave peak estimation, being more suitable for top not enough flat curve peak Smpa pulse peak value measurement is calculated, and has unlimited amplitude resolutio, and the amplitude resolutio of mode method is by wide between mode Statistical Area Degree limitation.

In addition, compared with determining the method for peak value after current shock wave shape peak value first filter with extreme value, not filtering Influence of the ripple device to peak value measurement, can obtain more accurate and objective peak value of pulse,

And it is possible to use the quality of regression criterion auxiliary judgement peak estimation.It is uneven, irregular and adopt in peak value Especially there is advantage in the case that sample measurement point is insufficient.

Brief description of the drawings

Fig. 1 is the schematic flow sheet of the inventive method；

Fig. 2 is the impact acceleration waveform produced described in the specific embodiment of the invention using source excited by impact；

Fig. 3 is nearby portion waveshape and the fitting result curve map of interception peak value described in the specific embodiment of the invention.

Embodiment

The embodiment to the inventive method elaborates below in conjunction with the accompanying drawings.

A kind of surge waveform peak measurement methods based on parameter fitting, its specific steps include：

Step 1: as shown in figure 1, producing waveform using source excited by impact, it is excited by impact that this waveform can be similar to semisinusoidal Or Gaussian shocks excitation.Waveform measurement is carried out with sensor and supporting Wave data acquisition system, complete shock measurement is obtained Waveform equal interval sampling sequence.

Step 2: obtaining the maximum 3.8V and minimum value 0.2V of surge waveform with comparison method, interception surge waveform is most The waveform of approximate semisinusoidal part between big value and minimum value, for peak computational.Here centered on peak, from waveform The descending order in the range of 3/4~1/2 for the amplitude range that maximum and minimum value are limited intercepts more than 3 intervals, and It is 3 to determine interval number.

Step 3: the approximate semisinusoidal portion waveshape for peak computational part that step 2 is intercepted, using shock wave The parameter fitness method of shape four carries out least square waveform fitting.It is specific as follows：

First, if the equal interval sampling sequence for surge waveform the Fitting Calculation is x₁,x₂,...,x_n, its portion waveshape is most The function expression that a young waiter in a wineshop or an inn multiplies matched curve is：

Wherein, A is fitting sinusoidal waveform amplitude；ω is fitting sinusoidal waveform angular frequency；It is initial for fitting sinusoidal waveform Phase；D is fitting sinusoidal waveform DC component；I is sampled point sequence number；N is sampled point number；x_iFor ith sample point；y(i) For the match value of ith sample point.

Then, to equal interval sampling sequence x₁,x₂,...,x_n, carry out least square sine curve fitting.Process is as follows：

If surge waveform sampling rate is v, waveform near surge waveform peak value is subjected to four parameters according to sine wave rule Fitting, its sine wave freuqency desired value to be estimated is f₀, the cycle is T₀=1/f₀, then angular frequency desired value is ω₀=2 π f₀/ v, Signal waveform holding time length contained by sine wave sample sequence to be estimated is τ；Then there is τ≤T₀, f₀≤1/τ.Parameter q is found, So that τ/T₀≥q；Thus f₀∈[q/τ,2/τ]。

(1) fitting iteration stopping condition is set as h_e.H can be chosen_e=1 × 10^-20。

(2) from known moment t₁,t₂,...,t_nSurge waveform collecting sample x₁,x₂,...,x_n.Believed using point count Number waveform holding time length is τ=(n-1)/v；Estimate factor q, determine target frequency f₀Presence it is interval [q/ τ, 2/ τ]；

(3) iteration left margin frequency is determined：f_L=q/ τ；ω_L=2 π f_L/v；Iteration right margin frequency：f_R=2/ τ；ω_R=2 π f_R/v；Median frequency is chosen according to optimum seeking method principle：ω_M=ω_L+0.618×(ω_R-ω_L)；ω_T=ω_R-0.618×(ω_R- ω_L)

(4) in ω_LThree parameter sine wave curve-fits of upper execution, obtain A_L、D_L、ρ_L；In ω_RThree parametric sinusoidals of upper execution Curve matching, obtains A_R、D_R、ρ_R；In ω_MThree parameter sine wave curve-fits of upper execution, obtain A_M、D_M、ρ_M；In ω_TOn Three parameter sine wave curve-fits are performed, A is obtained_T、D_T、ρ_T。

If (5) ρ_M<ρ_T, then ρ=ρ_M, there is ω₀∈[ω_T,ω_R], ω_L=ω_T, ω_T=ω_M；ω_M=ω_L+0.618× (ω_R-ω_L)；If ρ_M>ρ_T, then ρ=ρ_T, there is ω₀∈[ω_L,ω_M], ω_R=ω_M, ω_M=ω_T；ω_T=ω_R-0.618×(ω_R- ω_L)。

(6) determine whether | (ρ_M(k)-ρ_T(k))/ρ_T(k) | ＜ h_e, if it is, stop iteration, and as ρ=ρ_TWhen, obtain It is A=A to obtain four parameter fitting sinusoids parameters_T, ω=ω_T、D=D_TAnd regression criterion virtual value ρ, it was fitted Journey terminates.As ρ=ρ_MWhen, four parameter fitting sinusoids parameters of acquisition are A=A_M, ω=ω_M、D=D_MAnd intend Residual error virtual value ρ is closed, fit procedure terminates；Otherwise, (4)~(6) process is repeated.

The regression criterion virtual value ρ is：

When only containing noise factor error in sample sequence, ρ is the experiment mark for being superimposed upon noise on sinusoidal waveform Quasi- deviation.

Four parameter fitting process of surge waveform peak value are carried out with sine wave fitting method, it is final to obtain fitting parameter A= 0.959759V, D=2.422325V；Regression criterion virtual value ρ=91.86892mV.

Finally, if not peak fitting first, then compared this regression criterion ρ with last time, the small person institute of regression criterion is right The peak value answered is used as best fit result；

It is A+D=3.382084V to obtain surge waveform peak estimation value.

Step 4: obtaining regression criterion virtual value ρ=91.86892mV.Judge whether the interval number of interception peak value completes, If not completing, interception peak fractions waveform again is turned to, interval 2/3 width near peak value of peak value interception is reselected Spend the approximate semisinusoidal portion waveshape of ((3.8-0.2) × 2/3) and be used for peak computational and complete step, into being fitted next time；If It has been completed that, then the iterative process that Stop Waveform interval is chosen is had using respective regression criterion under the conditions of more all interceptions Valid value ρ, which judges to compare, is fitted quality, and ρ recklings fitting effect is optimal, and provides impact peak value fitting knot with the minimum conditions of ρ Really, measurement is terminated.The result of 3 fittings is as shown in table 1：

Table 1

Judged by comparing 3 interval regression criterion values of different interceptions, when interception waveform length is 1/2 amplitude, fitting Residual error ρ is minimum, and its impact peak value 3.407392V is best fit measurement result.

Although combining accompanying drawing describes embodiments of the present invention, it will be apparent to those skilled in the art that not On the premise of departing from the principle of the invention, some improvement can also be made, these also should be regarded as belonging to protection scope of the present invention.

Claims (3)

1. a kind of surge waveform peak measurement methods based on parameter fitting, it is characterised in that comprise the following steps：

It is similar to the waveform that semisinusoidal is excited by impact or Gaussian shocks are encouraged Step 1: being produced using source excited by impact, with sensing Device and supporting Wave data acquisition system carry out waveform measurement, obtain complete shock measurement waveform equal interval sampling sequence；

Step 2: obtaining the maximum and minimum value of surge waveform with comparison method, the maximum and minimum value of surge waveform are intercepted Between approximate semisinusoidal part waveform, for peak computational；

Step 3: the approximate semisinusoidal portion waveshape for peak computational part that step 2 is intercepted, using surge waveform four Parameter fitness method carries out least square waveform fitting, obtains surge waveform peak estimation value；

Step 4: judging whether the interval number of interception peak value completes, if not completing, intercepted peak value waveform scope is converted, Fitting operation is re-started, new fitting peak estimation value and new regression criterion virtual value is obtained；If intercepting interval of peak value Number has been completed, then judges to compare fitting quality using respective regression criterion virtual value under the conditions of more all interceptions, effectively The smaller then fitting effect of value is better, and provides impact peak value fitting result with the minimum condition of virtual value, terminates measurement.

2. a kind of surge waveform peak measurement methods based on parameter fitting as claimed in claim 1, it is characterised in that described Peak computational is centered on peak, the amplitude range limited from waveform maximum and minimum value, in the range of 3/4~1/10 Descending order intercepts more than 3 intervals, and determines interval number.

3. a kind of surge waveform peak measurement methods based on parameter fitting as claimed in claim 1, it is characterised in that described The method for carrying out least square waveform fitting using the parameter fitness method of surge waveform four is as follows：

First, if the equal interval sampling sequence for surge waveform the Fitting Calculation is x₁,x₂,...,x_n, its portion waveshape most young waiter in a wineshop or an inn The function expression for multiplying matched curve is：

Wherein, A is fitting sinusoidal waveform amplitude；ω is fitting sinusoidal waveform angular frequency；For fitting sinusoidal waveform initial phase；D For fitting sinusoidal waveform DC component；I is sampled point sequence number；N is sampled point number；x_iFor ith sample point；Y (i) is i-th The match value of individual sampled point；

Then, to equal interval sampling sequence x₁,x₂,...,x_n, least square sine curve fitting is carried out, process is as follows：

If surge waveform sampling rate is v, waveform near surge waveform peak value is subjected to four parameter fittings according to sine wave rule, Its sine wave freuqency desired value to be estimated is f₀, the cycle is T₀=1/f₀, then angular frequency desired value is ω₀=2 π f₀/ v, waits to estimate Signal waveform holding time length contained by the sine wave sample sequence of meter is τ；Then there is τ≤T₀, f₀≤1/τ；Find parameter q so that τ/T₀≥q；Thus f₀∈[q/τ,2/τ]；

(1) fitting iteration stopping condition is set as h_e；

(2) from known moment t₁,t₂,...,t_nSurge waveform collecting sample x₁,x₂,...,x_n, signal wave is obtained using point count Shape holding time length is τ=(n-1)/v；Estimate factor q, determine target frequency f₀Presence it is interval [q/ τ, 2/ τ]；

(3) iteration left margin frequency is determined：f_L=q/ τ；ω_L=2 π f_L/v；Iteration right margin frequency：f_R=2/ τ；ω_R=2 π f_R/ v；Median frequency is chosen according to optimum seeking method principle：ω_M=ω_L+0.618×(ω_R-ω_L)；ω_T=ω_R-0.618×(ω_R- ω_L)；

(4) in ω_LThree parameter sine wave curve-fits of upper execution, obtain A_L、D_L、ρ_L；In ω_RThree parametric sinusoidal curves of upper execution Fitting, obtains A_R、D_R、ρ_R；In ω_MThree parameter sine wave curve-fits of upper execution, obtain A_M、D_M、ρ_M；In ω_TIt is upper to perform Three parameter sine wave curve-fits, obtain A_T、D_T、ρ_T；

If (5) ρ_M<ρ_T, then ρ=ρ_M, there is ω₀∈[ω_T,ω_R], ω_L=ω_T, ω_T=ω_M；ω_M=ω_L+0.618×(ω_R- ω_L)；If ρ_M>ρ_T, then ρ=ρ_T, there is ω₀∈[ω_L,ω_M], ω_R=ω_M, ω_M=ω_T；ω_T=ω_R-0.618×(ω_R-ω_L)；

(6) determine whether | (ρ_M(k)-ρ_T(k))/ρ_T(k) | ＜ h_e, if it is, stop iteration, and as ρ=ρ_TWhen, obtain four Parameter fitting sinusoids parameter is A=A_T, ω=ω_T、D=D_TAnd regression criterion virtual value ρ, fit procedure knot Beam；As ρ=ρ_MWhen, four parameter fitting sinusoids parameters of acquisition are A=A_M, ω=ω_M、D=D_MAnd be fitted residual Poor virtual value ρ, fit procedure terminates；Otherwise, (4)~(6) process is repeated；

The regression criterion virtual value ρ is：

$\mathrm{\&rho;}=\sqrt{\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(y\left(i\right)-x_i)}^2}$

When in sample sequence only contain noise factor error when, ρ be superimposed upon noise on sinusoidal waveform experimental standard it is inclined Difference.