WO2023103826A1 - 一种基于正弦激励的频响测量用两点采样优化方法及系统 - Google Patents

一种基于正弦激励的频响测量用两点采样优化方法及系统 Download PDF

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WO2023103826A1
WO2023103826A1 PCT/CN2022/134754 CN2022134754W WO2023103826A1 WO 2023103826 A1 WO2023103826 A1 WO 2023103826A1 CN 2022134754 W CN2022134754 W CN 2022134754W WO 2023103826 A1 WO2023103826 A1 WO 2023103826A1
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刘自鹏
刘进军
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西安交通大学
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
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    • G06F30/20—Design optimisation, verification or simulation
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    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations

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  • the invention belongs to the technical field of frequency response measurement, in particular to a two-point sampling optimization method and system for frequency response measurement based on sinusoidal excitation.
  • excitation signals for different frequency response measurement methods: composite excitation signals and sinusoidal excitation signals.
  • the composite excitation signal is mainly suitable for linear systems, otherwise it will cause spectrum aliasing and reduce the measurement accuracy; while the sinusoidal excitation signal has good universality for both linear and nonlinear systems, so it still plays an important role in frequency response measurement. irreplaceable role.
  • the most traditional frequency sweep method can easily cause problems in measurement speed or measurement accuracy. For example, if the measurement step size is too large, the measurement accuracy cannot be guaranteed; if the step size is too small, the measurement time will be greatly extended. At the same time, the data inheritance of the frequency sweep method is not good, which means that it cannot reuse the existing sampling information well. This also reduces measurement efficiency.
  • the technical problem to be solved by the present invention is to provide a two-point sampling optimization method and system for frequency response measurement based on sinusoidal excitation, which can be directly embedded in existing frequency response analyzers without relying on specific hardware, to achieve a rapid decrease in the overall interpolation error.
  • the present invention adopts following technical scheme:
  • a two-point sampling optimization method for frequency response measurement based on sinusoidal excitation estimating the interpolation error of each sub-frequency band divided by existing sampling points according to existing sampling information; selecting the sub-frequency band with the largest interpolation error among the estimated sub-frequency bands; Add two sampling points in the sub-frequency band with the largest interpolation error; repeat the above steps until the number of sampling points reaches the total number of sampling points, and the current round of sampling ends; add new sampling points, and restart the estimation until the end of sampling.
  • the existing sampling information includes initial sampling points and new sampling points obtained through subsequent iterative calculations.
  • N s points are first collected as initial information, and then iterations are started, and each subsequent sampling point is the global optimal point calculated based on the sampled information.
  • the total number of sampling points is greater than or equal to 4.
  • estimating the interpolation error of each sub-frequency band is specifically: taking all sampled points one by one as the starting point to construct a triangle, and calculating the corresponding triangle area, and estimating the interpolation error of all sub-frequency bands.
  • selecting the sub-frequency band with the largest interpolation error among the estimated sub-frequency bands is specifically: comparing all 2N-4 interpolation errors of gain and phase together, selecting the largest value, and determining the corresponding sub-frequency band [f i ,f i+1 ,f i+2 ].
  • the two newly added sampling points are located in [f i , f i+1 ] of the sub-band [f i , f i +1 , f i + 2 ], or in [f i+1 , f i +2 ] Among them.
  • the two newly added sampling points select the midpoint or any equal division point within the range of [f i , f i+1 ] and [f i+1 , f i+2 ].
  • the number of sampling points added by the user is an even number.
  • Another technical solution of the present invention is a two-point sampling optimization system for frequency response measurement based on sinusoidal excitation, characterized in that it includes:
  • An estimation module estimating the interpolation error of each sub-band divided by the existing sampling points according to the existing sampling information
  • the sampling module repeats the estimation module to the optimization module until the number of sampling points reaches the total number of sampling points, and the current round of sampling ends;
  • the loop module adds new sampling points, and transfers to the estimation module until the sampling ends.
  • the present invention has at least the following beneficial effects:
  • the present invention is a two-point sampling optimization method for frequency response measurement based on sinusoidal excitation, which can optimize the position of each sampling point in the frequency response measurement and make the distribution of sampling point positions more reasonable.
  • the frequency response measurement based on sinusoidal excitation is regarded as the frequency domain sampling of the system under test, and the interpolation between the piecewise linear interpolation model of the existing sampled values and the theoretical model of the system under test is estimated In each iteration, two new sampling points are placed in the sub-band with the largest interpolation error, so as to achieve the fastest decline in the overall interpolation error.
  • N s points are first collected as initial information, and then iterations are started, and each subsequent sampling point is the global optimal point calculated based on the sampled information. Its advantage is that the method always efficiently uses each sampling point, making each point a globally optimal result. Different from the commercial frequency sweep method, this method does not calculate all the positions to be sampled at the beginning (uniform sampling), but first samples a small number of initial points, and then iteratively adds new sampling points according to the information of the initial points. Each iteration uses all the sampled information to calculate the best position for the new sample point.
  • the total number of sampling points requires at least four sampling points, so that subsequent iterative calculations can be performed normally.
  • the interpolation error will be compared according to the trapezoidal rule, and this comparison process requires at least two sub-frequency bands to participate, and each sub-frequency band contains three sampling points. Assume that the two sub-frequency bands are adjacent and partially overlapped, that is, the first sub-frequency band is [f i ,f i+1 ,f i+2 ], and the second sub-frequency band is [f i+1 ,f i+2 ,f i+3 ], the total number of sampling points is at least four.
  • estimating the interpolation error e i of each sub-frequency band specifically includes: constructing a triangle with all sampled points one by one as the starting point, and calculating the corresponding triangle area, and estimating the interpolation error of all sub-frequency bands. Its purpose is to directly use the trapezoidal rule to estimate the interpolation error between the sampling value and the system theoretical model under the premise that the system theoretical model is unknown.
  • This estimation can be realized because the present invention regards the frequency response measurement based on sinusoidal excitation as a mathematical interpolation problem, therefore, the method of interpolation error estimation in the interpolation theory, such as the trapezoidal rule, can be directly applied to the frequency response measurement . This will help the frequency response analyzer to adaptively place the newly added sampling point at the position where the interpolation error (that is, the actual sampling error) is the largest, so that the sampling accuracy is continuously improved.
  • all 2N-4 interpolation errors of gain and phase are compared together, the largest value is selected, and the corresponding sub-frequency band [f i , f i+1 , f i+2 ] is determined. This is to select the position where the interpolation error (that is, the actual sampling error) in the gain and phase is the largest.
  • comparing the gain and the phase together is also to achieve a global comparison, that is, the comparison is not only for the gain or the phase, but simultaneously compares the sampling information of the gain and the phase. Obviously, the global comparison can more effectively select the position with the largest interpolation error.
  • the two newly added sampling points are located in [f i ,f i+1 ] of the determined sub-frequency band [f i ,f i +1 ,f i +2 ], or located in [f i+1 , f i+2 ].
  • the sub-band [f i ,f i+1 ,f i+2 ] itself contains two smaller sub-bands [f i ,f i+1 ] and [f i+1 ,f i+2 ] , therefore, it is a natural choice to directly add two sampling points in a single iteration to sample [f i ,f i+1 ] and [f i+1 ,f i+2 ] respectively.
  • this method can also disperse the two newly added sampling points as much as possible to sample more information.
  • a counter-example is to place two sampling points too close together, for example, both points are placed in [f i ,f i+1 ]. Although this is allowed by the algorithm, it is not the most efficient way.
  • the two newly added sampling points select the midpoint or other equally divided points of [f i ,f i+1 ] and [f i+1 ,f i+2 ], because these positions are fixed, It is easy to determine and is a common point selection location. However, in these point selection strategies, only the midpoint is uniquely determined, so it has the best data inheritance; other options are also available, but the overall efficiency is reduced. In practical applications, the midpoint should be the preferred choice.
  • the new sampling point N′ m is an even number, because this method will add two new sampling points for each iteration, therefore, if the user still needs to add new sampling points after the sampling task is over, then the new The number of upsampling points N′ m must also be an even number, otherwise the algorithm will make mistakes.
  • the present invention has the characteristics of low calculation load, strong usability, high precision, strong stability, and good data inheritance.
  • Fig. 1 is a flowchart of the present invention
  • Fig. 2 is the bode diagram of the transfer function of the system under test in the numerical test
  • Fig. 3 is the schematic diagram that constructs triangle according to existing sampling information in the present invention.
  • Fig. 4 is the sampling process example diagram of two-point sampling optimization method in the present invention.
  • Figure 5 is a comparison chart of the sampling error of three frequency response measurement methods based on sinusoidal excitation in the numerical test.
  • the invention provides a two-point sampling optimization method for frequency response measurement based on sinusoidal excitation.
  • the frequency response measurement based on sinusoidal excitation is regarded as the frequency domain sampling of the system under test.
  • two new sampling points are placed in the sub-frequency band with the largest interpolation error in each iteration, so as to realize the overall interpolation error fastest descent.
  • a kind of frequency response measurement based on sinusoidal excitation of the present invention uses two-point sampling optimization method, comprises the following steps:
  • the sampling start frequency f start , the end frequency f end and the total number of sampling points N m are the three preset parameters that the sampling task must have. Among them, the start frequency f start and the end frequency f end specify the sampling frequency range, and the total The number of sampling points N m specifies the number of sampling times required to sample the target system. The setting of these three parameters depends entirely on the measurement requirements without any empirical rules, so it is very user-friendly. At the same time, the total number of sampling points N m must be an even number and satisfy N m ⁇ 4.
  • each sampling point is the global optimal point calculated based on the sampled information.
  • the present invention first collects some points as initial information, that is, N s points, and then starts to iterate; at the same time, it requires that the N s points of initial sampling must be equally spaced samples, wherein, equal spaced sampling is for more uniform sampling system, and N s usually takes a value of 4.
  • these initial sampling points do not need to strictly satisfy equidistant sampling (equally spaced sampling is only the optimal situation); and the number of initial sampling points N s also only needs to satisfy N s ⁇ 4.
  • the present invention sets it to 4, that is, sets the theoretically allowed minimum value. This is why the total number of sampling points N m must satisfy N m ⁇ 4.
  • the phase tends to be between [-180°, 180°], while the gain (magnitude) may have a rather small order of magnitude. Therefore, the calculation of the absolute value and relative value of the area of the triangle is a step that must not be ignored in the present invention, which is also a necessary condition for realizing the global comparison of interpolation errors.
  • the two newly added sampling points are located in [f i , f i+1 ], or in [f i+1 , f i+2 ].
  • the best position of two sampling points is the midpoint of [f i ,f i+1 ] and [f i+1 ,f i+2 ], that is, the midpoint of a point sampling [f i ,f i+1 ] , another point samples the midpoint of [f i+1 ,f i+2 ].
  • the two sampling points are not necessarily strictly set as the midpoint, but can also be other fixed positions, such as the third point, quarter point or other equal points; choosing the midpoint here is the safest choice . This is because the system itself is unknown and contains a lot of unsampled information, therefore, the midpoint will be a conservative but stable strategy.
  • step S6 Ask the user whether new sampling points are needed. If so, after the user designates a new number of sampling points N′ m , go to step S2; otherwise, the sampling ends.
  • the number of newly added sampling points N′ m must be an even number.
  • the invention allows the user to input a new number of sampling points N' m again after a round of sampling is finished, and continue sampling on the basis of all existing sampling values.
  • This is also data inheritance, that is, for the same system, it can always perform new sampling tasks based on existing sampling values, and first sample N m points, and then sample N′ m points, and at the beginning.
  • the results of directly sampling N m +N' m points are completely consistent. In practical applications, after the user completes a sampling task, he may not be satisfied with the sampling accuracy.
  • sampling can be continued on the basis of existing sampling data, and the sampling accuracy can be continuously improved; and the newly added sampling points are still With data inheritance, in other words, the process of increasing sampling points can continue until the sampling accuracy meets the user's needs.
  • the traditional commercial frequency sweep method can only start sampling again, which will greatly prolong the sampling time and reduce the sampling efficiency.
  • Fig. 2 is a Bode plot for supplementary description of the transfer function of the system under test, that is, the frequency domain characteristic curve of the system under test.
  • the characteristic changes of the curves in the Bode diagram selected here are relatively complicated, including straight parts and steep curved parts.
  • a two-point sampling optimization system for frequency response measurement based on sinusoidal excitation is provided.
  • This system can be used to implement the above-mentioned two-point sampling optimization method for frequency response measurement based on sinusoidal excitation.
  • the The two-point sampling optimization system for frequency response measurement based on sinusoidal excitation includes an estimation module, a selection module, an optimization module, a sampling module and a circulation module.
  • the optimization module adds two sampling points in the sub-frequency band [f i , f i+1 , f i+2 ] with the largest interpolation error;
  • the sampling module repeats the estimation module to the optimization module until the number of sampling points N reaches the total number of sampling points, and the current round of sampling ends;
  • the loop module adds a new sampling point N' m , and transfers to the estimation module until the sampling ends.
  • the interpolation errors of all sub-bands will be estimated according to the trapezoidal rule, that is, for all sampled points, a triangle is constructed with each point as the starting point, and the area of the corresponding triangle is calculated, as shown in Figure 3. Afterwards, from all estimated errors, select the one with the largest relative value, and find the corresponding sub-frequency band, and then add two sampling points in the sub-frequency band. This sampling process is shown in Figure 4.
  • the frequency sweep method is selected, and the adaptive frequency injection method is tested together with the present invention. It can be seen from Fig. 5 that as the number of sampling points increases, the overall errors of the three frequency response measurement methods decrease, and the present invention always has the lowest error. This proves the effectiveness of this method.
  • a two-point sampling optimization method and system for frequency response measurement based on sinusoidal excitation in the present invention has the following advantages:
  • This method can always perform new sampling tasks based on all sampled information, thereby improving sampling efficiency and reflecting good data inheritance.

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Abstract

一种基于正弦激励的频响测量用两点采样优化方法及系统，设置采样起始频率，终止频率和总采样点数；在起始频率和终止频率范围内等间距采样若干个点作为初始信息；根据已有采样信息，估算各子频段的插值误差；挑选出插值误差最大的子频段；在插值误差最大的子频段内合适的位置新增两个采样点；不断循环直至采样点数达到用户设定的总数；询问用户是否需要新增采样点，如果是，则在用户指定新的采样点数后，重新估算各子频段的插值误差并继续采样，否则采样结束。

Description

一种基于正弦激励的频响测量用两点采样优化方法及系统 技术领域
本发明属于频响测量技术领域，具体涉及一种基于正弦激励的频响测量用两点采样优化方法及系统。
背景技术
目前，在各类复杂系统的分析和调试中，不同的频响测量方法的激励信号仅有两类：复合激励信号和正弦激励信号。复合激励信号主要适用于线性系统，否则会引发频谱混叠现象，降低测量精度；而正弦激励信号对线性和非线性系统都有着良好的普适性，因此，它在频响测量中仍然发挥着不可替代的作用。
在使用正弦激励的频响测量方法中，最传统的扫频法很容易引发测量速度或测量精度的问题。例如，如果测量的步长选得太大，便无法保证测量精度；而步长选得太小，又会大大延长测量时间。同时，扫频法的数据继承性也不好，这意味着它无法很好地重复使用已有的采样信息。这也会降低测量效率。
发明内容
本发明所要解决的技术问题在于针对上述现有技术中的不足，提供一种基于正弦激励的频响测量用两点采样优化方法及系统，可直接嵌入现有频响分析仪中，不依赖特定硬件，实现总体插值误差的快速下降。
本发明采用以下技术方案：
一种基于正弦激励的频响测量用两点采样优化方法，根据已有采样信息估算由已有采样点划分的各子频段的插值误差；挑选估算的各子频段中插值误差最大的子频段；在插值误差最大的子频段内新增两个采样点；重复以上步骤，直至采样点数达到总采样点数时，本轮采样结束；增加新的采样点，重新开始 估算直至采样结束。
具体的，已有采样信息包括初始采样点及后续迭代计算所得的新增采样点。
进一步的，首先采集N s个点作为初始信息，然后开始迭代，且后续每个采样点都是基于已采样信息所计算出的全局最优点。
进一步的，总采样点数大于等于4。
具体的，估算各子频段的插值误差具体为：将所有已采样点逐一作为起始点构建三角形，并计算对应的三角形面积，估算得到所有子频段的插值误差。
具体的，挑选估算的各子频段中插值误差最大的子频段具体为：将增益和相位的全部2N-4个插值误差一同进行比较，选出最大的值，并确定对应的子频段[f i,f i+1,f i+2]。
进一步的，新增的两个采样点位于子频段[f i,f i+1,f i+2]的[f i,f i+1]之中，或者位于[f i+1,f i+2]之中。
进一步的，新增的两个采样点选取[f i,f i+1]和[f i+1,f i+2]范围内的中点或任一等分点。
具体的，用户新增的采样点数为偶数。
本发明的另一个技术方案是，一种基于正弦激励的频响测量用两点采样优化系统，其特征在于，包括：
估算模块，根据已有采样信息估算由已有采样点划分的各子频段的插值误差；
选择模块，挑选估算的各子频段中插值误差最大的子频段；
优化模块，在插值误差最大的子频段内新增两个采样点；
采样模块，重复估算模块至优化模块，直至采样点数达到总采样点数时，本轮采样结束；
循环模块，增加新的采样点，转入估算模块，直至采样结束。
与现有技术相比，本发明至少具有以下有益效果：
本发明一种基于正弦激励的频响测量用两点采样优化方法，可优化频响测 量中每个采样点的位置，使采样点位置的分布更为合理。从频响测量的数学实质出发，将基于正弦激励的频响测量视为对被测系统的频域采样，通过估算已有采样值的分段线性插值模型和被测系统理论模型之间的插值误差，在每个迭代内把两个新增采样点放置于插值误差最大的子频段内，从而实现总体插值误差的最速下降。
进一步的，首先采集N s个点作为初始信息，然后开始迭代，且后续每个采样点都是基于已采样信息所计算出的全局最优点。其优势在于该方法总是高效地使用每个采样点，使得每个点都是全局最优的结果。不同于商用的扫频法，该方法不是在一开始就已经算出了所有待采样的位置(均匀采样)，而是首先采样少量初始点，再根据初始点的信息逐步迭代增加新的采样点。每个迭代都会利用所有已采样信息进行计算，以得到新增采样点的最佳位置。
进一步的，总采样点数最少需要四个采样点，使得后续的迭代计算可以正常进行。后续迭代中，会根据梯形法则进行插值误差的比较，而这个比较的过程至少需要两个子频段参与，每个子频段包含三个采样点。假设这两个子频段是相邻且部分重合的，即第一个子频段为[f i,f i+1,f i+2]，第二个子频段为[f i+1,f i+2,f i+3]，则总采样点数最少为四。
进一步的，估算各子频段的插值误差e i具体为：将所有已采样点逐一作为起始点构建三角形，并计算对应的三角形面积，估算得到所有子频段的插值误差。其目的是在系统理论模型未知的前提下，直接利用梯形法则估算采样值和系统理论模型之间的插值误差。这一估算之所以可以实现，是因为本发明将基于正弦激励的频响测量视为一个数学插值问题，因此，插值理论中插值误差估算的方法，如梯形法则，就可以直接应用于频响测量。这将有助于频响分析仪自适应地将新增采样点置于插值误差(也即实际采样误差)最大的位置，使得采样精度不断提升。
进一步的，将增益和相位的全部2N-4个插值误差一同进行比较，选出最大的值，并确定对应的子频段[f i,f i+1,f i+2]。这是为了选出增益和相位中插值误 差(也即实际采样误差)最大的位置。此外，将增益和相位一同进行比较，也是为了实现全局比较，即该比较并非仅针对增益或者相位，而是把增益与相位的采样信息同时比较。显然，全局比较能够更为有效地选出插值误差最大的位置。
进一步的，新增的两个采样点位于确定的子频段[f i,f i+1,f i+2]的[f i,f i+1]之中，或者位于[f i+1,f i+2]之中。这是由于子频段[f i,f i+1,f i+2]本身就包含[f i,f i+1]和[f i+1,f i+2]两个更小的子频段，因此，单次迭代中直接新增两个采样点以分别采样[f i,f i+1]和[f i+1,f i+2]就是一个自然而然的选择。同时，这种方法也可以尽可能使两个新增采样点分散开，以采样更多的信息。反例则是将两个采样点放置得过于靠近，如两个点都置于[f i,f i+1]之中。尽管这也是算法允许的，但这不是效率最高的方式。
进一步的，新增的两个采样点选取[f i,f i+1]和[f i+1,f i+2]的中点或其他等分点，这是因为这些位置是固定的，易确定的，且为常见的选点位置。但是，在这些选点策略中，仅有中点是唯一确定的，因此具备最好的数据继承性；其他选择亦可，但总体效率有所降低。实际应用中，应以中点为优先选择。
进一步的，新的采样点N′ m为偶数，这是因为该方法每个迭代都会新增两个采样点，因此，假如用户在采样任务结束后，仍要增加新的采样点，那么，新增采样点数N′ m也必须是偶数，否则算法将出错。
综上所述，本发明具有计算负荷低、用性强、精度高、稳定性强，且数据继承性好的特点。
下面通过附图和实施例，对本发明的技术方案做进一步的详细描述。
附图说明
图1为本发明流程图；
图2为数值测试中待测系统传递函数的波特图；
图3为本发明中根据已有采样信息构建三角形的示意图；
图4为本发明中两点采样优化方法的采样过程示例图；
图5为数值测试中三种基于正弦激励的频响测量方法的采样误差对比图。
具体实施方式
本发明提供了一种基于正弦激励的频响测量用两点采样优化方法，从频响测量的数学实质出发，将基于正弦激励的频响测量视为对被测系统的频域采样，通过估算已有采样值的分段线性插值模型和被测系统理论模型之间的插值误差，在每个迭代内把两个新增采样点放置于插值误差最大的子频段内，从而实现总体插值误差的最速下降。
请参阅图1，本发明一种基于正弦激励的频响测量用两点采样优化方法，包括以下步骤：
S1、设置采样起始频率，终止频率和总采样点数，在起始频率和终止频率范围内等间距采样N s个点，，此时采样的N s个点将作为迭代启动的初始信息；
采样起始频率f start，终止频率f end和总采样点数N m是采样任务必须具备的三个预设参数，其中，起始频率f start和终止频率f end指定了采样的频段范围，而总采样点数N m指定了采样目标系统所需要的采样次数。这三个参数的设置完全取决于测量要求，无需任何经验性法则，因此对用户是非常友好的。同时，总采样点数N m必须是一个偶数，且满足N m≥4。
值得注意的是，本发明将采用迭代采样方法，即每个采样点都是基于已采样信息所计算出的全局最优点。本发明将首先采集一些点作为初始信息，也即N s个点，然后再开始迭代；其同时要求初始采样的N s个点必须为等间距采样，其中，等间距采样是为了更均匀地采样系统，而N s常取值为4。实际上，这些初始采样点无需严格满足等间距采样(等间距采样只是最优的情况)；而初始采样点数N s也只需满足N s≥4。本发明设置为4，即是设置了理论上允许的最小值。这也是总采样点数N m必须满足N m≥4的缘故。
S2、根据已有采样信息，估算各子频段的插值误差e i，i＝1,2,…2N-4， 其中N表示已经采样的点的数量；
使用梯形法则估算插值误差，即针对任意连续三个采样点构成的子频段[f i,f i+1,f i+2]，将其采样值相连构成三角形后，三角形面积约等于该子频段插值误差的三倍。该法则是数学原理中相当经典的插值误差估计方法，因此其对应的数学证明在此处略去。
在应用梯形法则时，只需将所有已采样点逐一作为起始点构建三角形，并计算对应的三角形面积，就可以估算对应子频段的插值误差。注意，插值误差本质就是真实的采样误差的良好估计。由于一共有N个采样点，因此对增益(幅值)和相位分别可以构建N-2个三角形(最后两个采样点无法再继续构建新的三角形)，所以对应的插值误差一共有2N-4个。由于这些三角形面积的计算值可能为正，也可能为负，因此所有计算值都应该取绝对值，以体现采样值和系统理论模型之间的真实差异；同时，由于增益(幅值)和相位的三角形会放在一起比较，因此，也必须对这些三角形的面积取相对值，即相对于增益(幅值)和相位中的三角形面积均值分别取相对值，以实现数量级上的公平比较。而如果这些三角形面积既不取绝对值计算，也不转换为相对值，那么，在绝大多数应用中，相位的插值误差将占据绝对主导，从而无法实现增益(幅值)和相位的公平比较。这是因为相位往往在[-180°,180°]之间，而增益(幅值)却可能有着相当小的数量级。因此，对三角形面积的绝对值计算和相对值计算是本发明中绝不可以忽略的步骤，这也是实现插值误差的全局比较的必要条件。
值得说明的是，尽管本方法在估算插值误差时使用了梯形法则，但其他相似的插值误差估计方法也应涵盖在保护范围内。
S3、挑选出插值误差最大的子频段[f i,f i+1,f i+2]，其对应误差为max(e i)；
增益(幅值)和相位的全部2N-4个插值误差将一同进行比较，以选出其中最大的值，并找到对应的子频段[f i,f i+1,f i+2]。显然，该子频段的误差就是max(e i)。需要再次强调的是，子频段的插值误差实际就是采样误差的良好估计，因此，搜寻最大插值误差对应的子频段，即是搜寻采样误差最大的子频段。
此外，目前已有许多筛选最大值的算法，本方法在筛选最大误差时并不局限为某一特定算法。常见算法如逐个比对法，或是分治算法，都可以实现寻找最大值的目的。由于这些算法往往有相当成熟的商业工具包或是开源代码，此处不再详述。
S4、在该子频段内合适的位置新增两个采样点；
新增的两个采样点位于[f i,f i+1]之中，或者位于[f i+1,f i+2]之中。
两个采样点的最佳位置是[f i,f i+1]和[f i+1,f i+2]的中点，即一个点采样[f i,f i+1]的中点，另一个点采样[f i+1,f i+2]的中点。
当然，两个采样点也并不一定严格设置为中点，也可以是其他固定的位置，如三分点，四分点或其他等分点；此处选取为中点，是最稳妥的选择。这是因为系统本身是未知的，含大量未采样信息，因此，中点将是一个保守但稳定的策略。
S5、不断循环步骤S2至步骤S4，直至采样点数N达到用户设定的总数，也即当N＝＝N m时，本轮采样结束；
N是对已采样点数的计数，每经过一次迭代，都会使N＝N+2，并判断是否已经满足N＝＝N m。如果还未满足该条件，则转入步骤S2，继续采样新点；而如果已经满足该条件，则本轮采样结束。需要指出的是，由于每个迭代新增两个采样点，因此，本发明只需进行(N m-4)/2次迭代，即可完成一轮采样任务，这将显著降低计算负荷。
S6、询问用户是否需要新增采样点，如果是，则在用户指定新的采样点数N′ m后，转入步骤S2，否则采样结束。
新增采样点数N′ m必须是一个偶数。本发明允许用户在一轮采样结束后，再次输入一个新的采样点数N′ m，并在全部已有采样值的基础上继续进行采样。这也就是数据继承性，即针对同一个系统，它总是可以基于已有采样值进行新的采样任务，并且，先采样N m个点，再接着采样N′ m个点，和一开始就直接采样N m+N′ m个点的结果是完全一致的。在实际应用中，用户在完成一次采样任务 后，可能对采样精度不满足，应用本发明则可以在已有采样数据的基础上继续进行采样，不断提升采样精度；并且，新增采样点也仍然具备数据继承性，换言之，这个增加采样点的过程可以持续进行下去，直到采样精度达到了用户的需求。而传统商用扫频法则只能重新开始采样，这将大大延长采样时间，降低采样效率。
请参阅图2，为待测系统传递函数进行补充说明的波特图，也即待测系统的频域特性曲线。为了更好地体现本发明的优势与适用性，此处所选波特图中的曲线特性变化较为复杂，既有平直的部分，也有弯曲陡峭的部分。
本发明再一个实施例中，提供一种基于正弦激励的频响测量用两点采样优化系统，该系统能够用于实现上述基于正弦激励的频响测量用两点采样优化方法，具体的，该基于正弦激励的频响测量用两点采样优化系统包括估算模块、选择模块、优化模块、采样模块以及循环模块。
其中，估算模块，根据已有采样信息估算由已有采样点划分的各子频段的插值误差e i，i＝1,2,…2N-4，N为采样点数；
选择模块，挑选估算的各子频段中插值误差最大的子频段[f i,f i+1,f i+2]；
优化模块，在插值误差最大的子频段[f i,f i+1,f i+2]内新增两个采样点；
采样模块，重复估算模块至优化模块，直至采样点数N达到总采样点数时，本轮采样结束；
循环模块，增加新的采样点N′ m，转入估算模块，直至采样结束。
在使用本方法时，将依据梯形法则估算所有子频段的插值误差，即对所有已采样点，以每一个点为起点构建三角形，并计算对应三角形的面积，如图3所示。之后，从所有估算的误差中，挑选出相对值最大的一个，并找到相应的子频段，然后在该子频段中新增两个采样点。这一采样过程如图4所示。针对图一所示系统进行数值测试时，选用了扫频法，自适应频率注入法和本发明共同进行测试。从图5可见，随着采样点数的不断增多，三种频响测量方法的总体误差随之下降，并且，本发明总是有着最低的误差。这就证明了本方法的有 效性。
综上所述，本发明一种基于正弦激励的频响测量用两点采样优化方法及系统，具有以下优点：
1、计算负荷低，本方法每次迭代将采样两个点，因此对于N m个采样点，仅需估算(N m-4)/2次插值误差；
2、易用性强，本方法仅需用户指定采样起始频率，终止频率和总采样点数，无需指定任何其他经验参数；
3、精度高，本方法基于梯形法则估算各子频段插值误差，并总是在插值误差最大的子频段内新增采样点，因此，随着采样点增多，总体插值误差会以几乎最快的速度下降；
4、稳定性强，本方法的采样机制确保了更多的采样点总是有更高的采样精度，因此不会存在稳定性问题；
5、数据继承性好，本方法总是可以基于所有已采样信息进行新的采样任务，从而提高采样效率，体现了良好的数据继承性。
以上内容仅为说明本发明的技术思想，不能以此限定本发明的保护范围，凡是按照本发明提出的技术思想，在技术方案基础上所做的任何改动，均落入本发明权利要求书的保护范围之内。

Claims (10)

  1. 一种基于正弦激励的频响测量用两点采样优化方法，其特征在于，根据已有采样信息估算由已有采样点划分的各子频段的插值误差；挑选估算的各子频段中插值误差最大的子频段；在插值误差最大的子频段内新增两个采样点；重复以上步骤，直至采样点数达到总采样点数时，本轮采样结束；增加新的采样点，重新开始估算直至采样结束。
  2. 根据权利要求1所述的基于正弦激励的频响测量用两点采样优化方法，其特征在于，已有采样信息包括初始采样点及后续迭代计算所得的新增采样点。
  3. 根据权利要求2所述的基于正弦激励的频响测量用两点采样优化方法，其特征在于，首先采集N s个点作为初始信息，然后开始迭代，且后续每个采样点都是基于已采样信息所计算出的全局最优点。
  4. 根据权利要求2所述的基于正弦激励的频响测量用两点采样优化方法，其特征在于，总采样点数大于等于4。
  5. 根据权利要求1所述的基于正弦激励的频响测量用两点采样优化方法，其特征在于，估算各子频段的插值误差具体为：将所有已采样点逐一作为起始点构建三角形，并计算对应的三角形面积，估算得到所有子频段的插值误差。
  6. 根据权利要求1所述的基于正弦激励的频响测量用两点采样优化方法，其特征在于，挑选估算的各子频段中插值误差最大的子频段具体为：将增益和相位的全部2N-4个插值误差一同进行比较，选出最大的值，并确定对应的子频段[f i,f i+1,f i+2]。
  7. 根据权利要求6所述的基于正弦激励的频响测量用两点采样优化方法，其特征在于，新增的两个采样点位于子频段[f i,f i+1,f i+2]的[f i,f i+1]之中，或者位于[f i+1,f i+2]之中。
  8. 根据权利要求6所述的基于正弦激励的频响测量用两点采样优化方法，其特征在于，新增的两个采样点选取[f i,f i+1]和[f i+1,f i+2]范围内的中点或任一等分点。
  9. 根据权利要求1所述的基于正弦激励的频响测量用两点采样优化方法， 其特征在于，新增的采样点数为偶数。
  10. 一种基于正弦激励的频响测量用两点采样优化系统，其特征在于，包括：
    估算模块，根据已有采样信息估算由已有采样点划分的各子频段的插值误差；
    选择模块，挑选估算的各子频段中插值误差最大的子频段；
    优化模块，在插值误差最大的子频段内新增两个采样点；
    采样模块，重复估算模块至优化模块，直至采样点数达到总采样点数时，本轮采样结束；
    循环模块，增加新的采样点，转入估算模块，直至采样结束。
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