CN104796116A - Shock waveform peak value measurement method based on parameter fitting - Google Patents

Abstract

The invention relates to a shock waveform peak value measurement method based on parameter fitting, and belongs to the fields of vibration shock and mechanical engineering and the technical field of metrology testing. The method comprises the following specific steps: generating shock excitation by using a shock excitation source, and performing waveform measurement by using a sensor and a matched waveform data acquisition system to obtain a complete shock measurement waveform uniformly-spaced sampling sequence; acquiring the maximum value and the minimum value of a shock waveform by using a comparison method; intercepting an approximate half-sine part waveform close to a peak value between the maximum value and the minimum value from the shock measurement waveform uniformly-spaced sampling sequence for use in peak value calculation; performing a four-parameter fitting process of a shock waveform peak value by using a sine wave fitting method; iteratively calculating a shock measurement waveform peak value by using a fitting sine wave amplitude value and a direct-current component; and giving a fitting residue effective value serving as an assistant criterion for judging the performance of peak value fitting. The shock waveform peak value measurement method has the calculation effects of omission of a peak value filter, higher accuracy and higher resolution.

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, relate to a kind of peak measurement methods of surge waveform, the peak measurement methods of the surge waveform particularly formed due to mechanical collision, electrical impact, gas impact, hydraulic shock, acoustic shock, light impact, blast etc.

Background technology

Surge waveform belongs to impulse wave, the calculating of peak value of pulse with determine it is the basic problem in impulsive measurement.Shock measurement under many circumstances all with fail safe and weaponry etc. to injure performance relevant.Such as, people can measure peak acceleration when it lands when spacecraft landing is reclaimed so that assessment and determine whether beyond human body and equipment the ability to bear 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 maximum impact acceleration will embody its fragmentation effect, and people need the parameter such as peak value by measuring impact acceleration, how to understand the lethality of the weaponry of various different model; The helmet, safety cap etc. bear great impact acceleration can not be cracked, embodies its protective capability to people, and people can obtain this information by measuring impact acceleration peak value; And in high-voltage electric system, people need to understand circuit structure and system and can not occur arcing under how high impact high voltage, the fault effect such as puncture, to carry out electrical safety and protection Design.In a word, people are in the measurement of many kinds of impact signals, and all main have much at its peak value impacted of care on earth.

In shock measurement, namely final result is a physical pulse waveform.The peak value of its pulse and pulsewidth are two basic parameters, and after they are determined, main impact information summarises substantially, and based on this, can determine other impact parameter and shock characteristic further.As being elevated edge, frequency spectrum, power spectrum etc.In most cases, people wish the peak shape smoother, mild and have single-peak response of single-impact, like this, will be easy to judge the position of peak value and obtain the value of its peak value.When distortion, noise, burr, the tinkling of pieces of jade etc. that shakes occur near peak value, the measurement of the determination of peak and peak value self value obtains just to become to compare and difficult for.Especially in this case, people also want to obtain higher peak value measurement accuracy, and this problem will be made to become more difficult.In order to address this problem, in different industries, what people taked is different modes.

In radio industry, radio wave pulses peak power measurement is also one of main measure the item.In order to avoid noise, respond overshoot, impact that the tinkling of pieces of jade that shakes etc. calculates peak value, International Electrotechnical Commission (InternationalElectro technical Commission, be called for short IEC) define the basic terms such as " top ", " end " of pulse in standard, be used for describing the peak value of pulse and valley, and determine with mode method on " top " and " end " of pulse.For the impulse waveform that " tops " such as square waves and " end " are more smooth, this definition and method have excellent adaptability, are able to extensive use.But for there is the non-square wave class surge waveform that compares pinnacle and being not exclusively applicable to, mainly also face and need compared with multi-point sampling and the not high problem of accuracy of measurement.

In vibratory impulse field; the mechanical engineering problem often faced; particularly HI high impact situation and super high impact situation; due to the semisinusoidal type that the is similar to pulse that the impact characteristics such as materials and structures produce; its peak value is often uneven, irregular and sampled measurements point is also insufficient; at this moment, use the mode method in radio industry usually can run into the poor problem of adaptability, the most directly performance is exactly that measurement reproducibility is poor.

Thus, in vibratory impulse field, Comite Internationale de Normalisation (International Organization forStandardization, be called for short ISO) way of recommending carries out filtering to the surge waveform measured, the peak value of surge waveform is filtered more smooth after direct maximizing determination peak value of pulse again.But choosing of filtering bandwidth, and the judgement of affecting greatly whether to after filtering the peak value of surge waveform, be the basic problem that metering is impacted in puzzlement, and make the accuracy of shock measurement be difficult to improve, accuracy is about about 5% always always.

The present invention is directed to the problems referred to above, impact peak value measurement is regarded as the unimodal optimum decision problem of a residual cycle sinusoidal curve of local, do not use the means such as filtering, thus avoid Parameters variation that filter may bring to the impact of accuracy of measurement, carry out optimum with model parameter to judge, also can carry out certain suppression to impacts such as noise, burr, spike, quantization errors, thus be expected to obtain higher impact peak value accuracy of measurement.

Summary of the invention

The object of the invention is the needs filtering in advance in order to overcome ISO recommend method thus affect the defect of accuracy of measurement, and IEC recommend method is not exclusively applicable to the problem of semisinusoidal and gaussian shape surge waveform, for the purpose of the accuracy improving semisinusoidal shape class and the calculating of gaussian shape class surge waveform peak value measurement, a kind of surge waveform peak measurement methods based on parameter fitting is proposed.With the peak value of semisinusoidal approximating method determination surge waveform, and when not using filter, directly carrying out least square curve fitting with acquired original Wave data, obtaining the peak value of semisinusoidal surge waveform, to improve accuracy of measurement and repeatability.

For achieving the above object, the technical solution adopted in the present invention is as follows:

Based on a surge waveform peak measurement methods for parameter fitting, comprise the following steps:

Step one, use source excited by impact to produce waveform, this waveform can be similar to the excitation of semisinusoidal excited by impact or Gaussian shocks.Carry out waveform measurement by transducer and supporting Wave data acquisition system, obtain complete shock measurement waveform equal interval sampling sequence.

Step 2, obtain the maximum of surge waveform and minimum value by comparison method, intercept the waveform of approximate semisinusoidal part between the maximum of surge waveform and minimum value, calculate for peak value.

Under normal circumstances, be centered by peak, from the amplitude range that waveform maximum and minimum value limit, in 3/4 ~ 1/10 scope, descending order intercepts more than 3 intervals, and determines interval number.

Step 3, the approximate semisinusoidal portion waveshape being used for peak value calculating section step 2 intercepted, adopt surge waveform four parameter fitness method to carry out least square waveform fitting.Specific as follows:

First, if the equal interval sampling sequence (belong to step one obtain the part of complete shock measurement waveform equal interval sampling sequence) for surge waveform the Fitting Calculation is x ₁, x ₂..., x _n.The function expression of its portion waveshape least square fitting curve is:

Wherein, A is matching sinusoidal waveform amplitude; ω is matching sinusoidal waveform angular frequency; for matching sinusoidal waveform initial phase; D is matching sinusoidal waveform DC component; I is sampled point sequence number; N is sampled point number; x _ibe i-th sampled point; Y (i) is the match value of i-th sampled point.

Then, to equal interval sampling sequence x ₁, x ₂..., 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 carried out four parameter fittings according to sinusoidal wave rule, its sine wave freuqency desired value to be estimated is f ₀, the cycle is T ₀=1/f ₀, then angular frequency desired value is ω ₀=2 π f ₀/ v, contained by sinusoidal wave sample sequence to be estimated, signal waveform holding time length is τ; Then there is τ≤T ₀, f ₀≤ 1/ τ.Find parameter q, make τ/T ₀>=q; Thus f ₀∈ [q/ τ, 2/ τ].

(1) setting matching iteration stopping condition is h _e.H can be chosen _e=1 × 10 ^-20.

(2) from known moment t ₁, t ₂..., t _nsurge waveform collecting sample x ₁, x ₂..., x _n.Using point count to obtain signal waveform holding time length is τ=(n-1)/v; Estimate factor q, determine target frequency f ₀existence interval [q/ τ, 2/ τ];

(3) determine iteration left margin frequency: 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: ω according to optimum seeking method principle _m=ω _l+ 0.618 × (ω _r-ω _l); ω _t=ω _r-0.618 × (ω _r-ω _l)

(4) at ω _lupper execution three parameter sine wave curve-fit, obtains A _l, d _l, ρ _l; At ω _rupper execution three parameter sine wave curve-fit, obtains A _r, d _r, ρ _r; At ω _mupper execution three parameter sine wave curve-fit, obtains A _m, d _m, ρ _m; At ω _tupper execution three parameter sine wave curve-fit, obtains A _t, d _t, ρ _t.

(5) if ρ _m< ρ _t, then ρ=ρ _m, have ω ₀∈ [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, have ω ₀∈ [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 so, then stop iteration, and as ρ=ρ _ttime, obtaining four parameter fitting sinusoids parameter is A=A _t, ω=ω _t, d=D _tand regression criterion effective value ρ, fit procedure terminates.As ρ=ρ _mtime, obtaining four parameter fitting sinusoids parameter is A=A _m, ω=ω _m, d=D _m, and regression criterion effective value ρ, fit procedure terminates; Otherwise, repeat (4) ~ (6) process.

Described regression criterion effective value ρ is:

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

When only containing noise factor error in sample sequence, ρ is the experimental standard deviation being superimposed upon noise on sinusoidal waveform.

Finally, obtaining surge waveform peak estimation value is A+D.

Step 4, judge to intercept number between peak region and whether complete, if do not complete, then convert the peak value range of waveforms intercepted, re-start fitting operation, obtain new matching peak estimation value and new regression criterion effective value; If number completes between intercepting peak region, then regression criterion effective value ρ respective under adopting more all intercepting conditions judges to compare matching quality, and the less then fitting effect of ρ is better, and provides impact peak value fitting result so that ρ is minimum for condition, terminates measurement.

Beneficial effect

The present invention, by compared with the mode method of suitable square wave peak estimation, is more applicable to top curve summit peak value of pulse survey calculation smooth not, and has unlimited amplitude resolutio, and the amplitude resolutio of mode method limits by width between mode Statistical Area.

In addition, to carry out after first filtering with current shock wave shape peak value, with compared with the method for extreme value determination peak value, there is no filter to the impact of peak value measurement, more accurate and objective peak value of pulse can be obtained,

Further, the quality of regression criterion auxiliary judgement peak estimation can be used.Uneven at peak value, irregular and sampled measurements point is insufficient especially there is advantage.

Accompanying drawing explanation

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

The impact acceleration waveform that Fig. 2 produces for using source excited by impact described in the specific embodiment of the invention;

Fig. 3 is for intercepting portion waveshape and fitting result curve chart near peak value described in the specific embodiment of the invention.

Embodiment

Elaborate below in conjunction with the execution mode of accompanying drawing to the inventive method.

Based on a surge waveform peak measurement methods for parameter fitting, its concrete steps comprise:

Step one, as shown in Figure 1, uses source excited by impact to produce waveform, and this waveform can be similar to the excited by impact or Gaussian shocks excitation of semisinusoidal.Carry out waveform measurement by transducer and supporting Wave data acquisition system, obtain complete shock measurement waveform equal interval sampling sequence.

Step 2, obtain the maximum 3.8V of surge waveform and minimum value 0.2V by comparison method, intercept the waveform of approximate semisinusoidal part between the maximum of surge waveform and minimum value, calculate for peak value.Here centered by peak, the amplitude range limited from waveform maximum and minimum value from descending order in 3/4 ~ 1/2 scope intercept more than 3 interval, and determine that interval number is 3.

Step 3, the approximate semisinusoidal portion waveshape being used for peak value calculating section step 2 intercepted, adopt surge waveform four parameter fitness method to carry out least square waveform fitting.Specific as follows:

First, if the equal interval sampling sequence for surge waveform the Fitting Calculation is x ₁, x ₂..., x _n, the function expression of its portion waveshape least square fitting curve is:

Wherein, A is matching sinusoidal waveform amplitude; ω is matching sinusoidal waveform angular frequency; for matching sinusoidal waveform initial phase; D is matching sinusoidal waveform DC component; I is sampled point sequence number; N is sampled point number; x _ibe i-th sampled point; Y (i) is the match value of i-th sampled point.

Then, to equal interval sampling sequence x ₁, x ₂..., 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 carried out four parameter fittings according to sinusoidal wave rule, its sine wave freuqency desired value to be estimated is f ₀, the cycle is T ₀=1/f ₀, then angular frequency desired value is ω ₀=2 π f ₀/ v, contained by sinusoidal wave sample sequence to be estimated, signal waveform holding time length is τ; Then there is τ≤T ₀, f ₀≤ 1/ τ.Find parameter q, make τ/T ₀>=q; Thus f ₀∈ [q/ τ, 2/ τ].

(1) setting matching iteration stopping condition is h _e.H can be chosen _e=1 × 10 ^-20.

(2) from known moment t ₁, t ₂..., t _nsurge waveform collecting sample x ₁, x ₂..., x _n.Using point count to obtain signal waveform holding time length is τ=(n-1)/v; Estimate factor q, determine target frequency f ₀existence interval [q/ τ, 2/ τ];

(3) determine iteration left margin frequency: 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: ω according to optimum seeking method principle _m=ω _l+ 0.618 × (ω _r-ω _l); ω _t=ω _r-0.618 × (ω _r-ω _l)

(4) at ω _lupper execution three parameter sine wave curve-fit, obtains A _l, d _l, ρ _l; At ω _rupper execution three parameter sine wave curve-fit, obtains A _r, d _r, ρ _r; At ω _mupper execution three parameter sine wave curve-fit, obtains A _m, d _m, ρ _m; At ω _tupper execution three parameter sine wave curve-fit, obtains A _t, d _t, ρ _t.

(5) if ρ _m< ρ _t, then ρ=ρ _m, have ω ₀∈ [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, have ω ₀∈ [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 so, then stop iteration, and as ρ=ρ _ttime, obtaining four parameter fitting sinusoids parameter is A=A _t, ω=ω _t, d=D _tand regression criterion effective value ρ, fit procedure terminates.As ρ=ρ _mtime, obtaining four parameter fitting sinusoids parameter is A=A _m, ω=ω _m, d=D _m, and regression criterion effective value ρ, fit procedure terminates; Otherwise, repeat (4) ~ (6) process.

Described regression criterion effective value ρ is:

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

When only containing noise factor error in sample sequence, ρ is the experimental standard deviation being superimposed upon noise on sinusoidal waveform.

Four parameter fitting process of surge waveform peak value are carried out, final acquisition fitting parameter A=0.959759V, D=2.422325V by sine wave fitting method; Regression criterion effective value ρ=91.86892mV.

Finally, if not peak fitting first, then by this regression criterion ρ compared with last time, the peak value corresponding to the little person of regression criterion is as best fit result;

Obtaining surge waveform peak estimation value is A+D=3.382084V.

Step 4, acquisition regression criterion effective value ρ=91.86892mV.Judge to intercept number between peak region whether to complete, if do not complete, then turn to and again intercept peak fractions waveform, reselect the interval approximate semisinusoidal portion waveshape for 2/3 amplitude ((3.8-0.2) × 2/3) near peak value of peak value intercepting and be used for peak value calculating completing steps, enter matching next time; If complete, then stop the iterative process that waveform interval is chosen, regression criterion effective value ρ respective under adopting more all intercepting conditions judges to compare matching quality, and ρ reckling fitting effect is best, and provide impact peak value fitting result so that ρ is minimum for condition, terminate to measure.The result of 3 matchings is as shown in table 1:

Table 1

Judge by comparing 3 different regression criterion values intercepting interval, when intercepting waveform length is 1/2 amplitude, regression criterion ρ is minimum, and its impact peak value 3.407392V is best fit measurement result.

Drawings describe embodiments of the present invention although combine, to those skilled in the art, under the premise without departing from the principles of the invention, can also make some improvement, these also should be considered as belonging to protection scope of the present invention.

Claims (3)

1., based on a surge waveform peak measurement methods for parameter fitting, it is characterized in that comprising the following steps:

Step one, use source excited by impact to produce the waveform being similar to the excitation of semisinusoidal excited by impact or Gaussian shocks, carry out waveform measurement by transducer and supporting Wave data acquisition system, obtain complete shock measurement waveform equal interval sampling sequence;

Step 2, obtain the maximum of surge waveform and minimum value by comparison method, intercept the waveform of approximate semisinusoidal part between the maximum of surge waveform and minimum value, calculate for peak value;

Step 3, the approximate semisinusoidal portion waveshape being used for peak value calculating section step 2 intercepted, adopt surge waveform four parameter fitness method to carry out least square waveform fitting, obtains surge waveform peak estimation value;

Step 4, judge to intercept number between peak region and whether complete, if do not complete, then convert the peak value range of waveforms intercepted, re-start fitting operation, obtain new matching peak estimation value and new regression criterion effective value; If number completes between intercepting peak region, regression criterion effective value respective under then adopting more all intercepting conditions judges to compare matching quality, the less then fitting effect of effective value is better, and provides impact peak value fitting result so that effective value is minimum for condition, terminates to measure.

2. a kind of surge waveform peak measurement methods based on parameter fitting as claimed in claim 1, it is characterized in that, described peak value calculates centered by peak, from the amplitude range that waveform maximum and minimum value limit, in 3/4 ~ 1/10 scope, 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 characterized in that, the method that described employing surge waveform four parameter fitness method carries out least square waveform fitting is as follows:

First, if the equal interval sampling sequence for surge waveform the Fitting Calculation is x ₁, x ₂..., x _n, the function expression of its portion waveshape least square fitting curve is:

Wherein, A is matching sinusoidal waveform amplitude; ω is matching sinusoidal waveform angular frequency; for matching sinusoidal waveform initial phase; D is matching sinusoidal waveform DC component; I is sampled point sequence number; N is sampled point number; x _ibe i-th sampled point; Y (i) is the match value of i-th sampled point;

Then, to equal interval sampling sequence x ₁, x ₂..., 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 carried out four parameter fittings according to sinusoidal wave rule, its sine wave freuqency desired value to be estimated is f ₀, the cycle is T ₀=1/f ₀, then angular frequency desired value is ω ₀=2 π f ₀/ v, contained by sinusoidal wave sample sequence to be estimated, signal waveform holding time length is τ; Then there is τ≤T ₀, f ₀≤ 1/ τ; Find parameter q, make τ/T ₀>=q; Thus f ₀∈ [q/ τ, 2/ τ];

(1) setting matching iteration stopping condition is h _e;

(2) from known moment t ₁, t ₂..., t _nsurge waveform collecting sample x ₁, x ₂..., x _n, using point count to obtain signal waveform holding time length is τ=(n-1)/v; Estimate factor q, determine target frequency f ₀existence interval [q/ τ, 2/ τ];

(3) determine iteration left margin frequency: 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: ω according to optimum seeking method principle _m=ω _l+ 0.618 × (ω _r-ω _l); ω _t=ω _r-0.618 × (ω _r-ω _l);

(4) at ω _lupper execution three parameter sine wave curve-fit, obtains A _l, d _l, ρ _l; At ω _rupper execution three parameter sine wave curve-fit, obtains A _r, d _r, ρ _r; At ω _mupper execution three parameter sine wave curve-fit, obtains A _m, d _m, ρ _m; At ω _tupper execution three parameter sine wave curve-fit, obtains A _t, d _t, ρ _t;

(5) if ρ _m< ρ _t, then ρ=ρ _m, have ω ₀∈ [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, have ω ₀∈ [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 so, then stop iteration, and as ρ=ρ _ttime, obtaining four parameter fitting sinusoids parameter is A=A _t, ω=ω _t, d=D _tand regression criterion effective value ρ, fit procedure terminates; As ρ=ρ _mtime, obtaining four parameter fitting sinusoids parameter is A=A _m, ω=ω _m, d=D _m, and regression criterion effective value ρ, fit procedure terminates; Otherwise, repeat (4) ~ (6) process;

Described regression criterion effective value ρ is:

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

When only containing noise factor error in sample sequence, ρ is the experimental standard deviation being superimposed upon noise on sinusoidal waveform.