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Research on a new linear piecewise interpolation method

1 introduction

in industrial production practice, the system error can be avoided and must be calibrated if there is a sensor under the non eccentric wheel. The typical treatment is to use the nonlinear correction of the model method, that is, to establish the system error model by theoretical analysis and mathematical treatment of the system error, and then use this model to determine the correction algorithm and mathematical expression. In the nonlinear correction of system error, the author not only adopts the traditional piecewise linear interpolation method, but also adopts the near linear interpolation method named "successive forcing" to maintain the ideal oil temperature. By comparing the results of the two methods, it is considered that the successive approximation linear interpolation method is effective and has certain practical value. The linearization processing software programming method is divided into three methods: calculation method, look-up table method and interpolation method; Among them, interpolation method is divided into piecewise linear interpolation method, quadratic interpolation method, piecewise curve fitting method, automatic fitting method of experimental curve, etc. Let's first introduce the piecewise linear interpolation method

figure 1

2 piecewise linear interpolation this method is commonly used. The basic method is to divide the y=f (x) curve into several straight lines to replace the curve. As shown in Figure 1. Let the nonlinear function y=f (x) be monotonic in the interval [x0, xm]. If (x0, f (x0)), (XM, f (XM)) makes a straight line u=f (x) =ax+b, then in the straight line segment, its fitting error:

f (x) if the maximum error point of the segment is not greater than the allowable error, the straight line u=f (x results show that the scaffold has supporting cell adsorption) can be used to fit the curve u=f (x), otherwise the segment can be subdivided into two sub segments, and the broken lines can be used to judge the error respectively. In this way, the intervals are divided continuously according to the above method until each sub interval m (x) is satisfied. Because the input-output function is nonlinear, and the maximum fitting error of each sub interval is required to meet △ Max ≤ δ, Therefore, the length of each sub interval is different. This involves the problem of interval division. The piecewise linear interpolation method uses the optimization method for interval division, that is, the coefficient is 0.618. As shown in Figure 1, a segment of xk=0.618 (xm-x0) is intercepted from XM to the low value as the second interval, (x0, XK) is the first interval. Connecting points (XK, f (XK)), (XM, f (XM)), the fitting line of the existing interval [xk, xm] is: f1=a1x+b1 a1= (f (XM) -f (XK))/(XM XK), b1=f (XM) -a1x1m, and so on. It can be seen that the fitting line of the ith sub interval is: fi=aix+bi ai= (f (x (i+1) m) -f (Xim))/(x (i+1) M-X can be operated and discussed in the field IM), bi=f (Xim) -aixim if f (x) is if it is a non monotonic curve, the poles can be obtained by df/dx=0 first, so as to turn it into a monotonic region, Then the above method is used to fit the monotone interval

Figure 2 dichotomy piecewise linear interpolation method

3 successive approximation linear interpolation method the author found that the coefficient of the formula in this method is 0.618, which is easy to cause programming illusion for uniform array. For example, when m-k=2, x=x[m]-0.618 (x[m]-x[k]), the conclusion of x[m]

135 can be seen from the above experimental data that the effect of successive approximation linear interpolation method is basically the same as that of the traditional piecewise linear interpolation method, with fewer piecewise intervals and good linearization. Its thinking method conforms to the programming habit, with clear programming and certain practical value. This method adds a new alternative for nonlinear correction

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