05-3. 求a的连续和(15)

本文介绍了一个计算特定形式数列之和的C语言程序。该程序接收两个整数a和n作为输入,其中a的取值范围为[0,9],n的取值范围为[1,8]。程序计算并输出形如a+aa+aaa+...+aaa...a(n个a)的数列之和。

输入两个整数a和n,a的范围是[0,9],n的范围是[1,8],求数列之和S = a+aa+aaa+...+aaa...a(n个a)。 如a为2、n为8时输出的是2+22+222+...+22222222的和。

输入格式:

输入在一行中给出两个整数,先后表示a和n。

输出格式:

在一行中输出要求的数列之和。

输入样例:
2 4
输出样例:
2468

#include <stdio.h>

int main()
{
    int a, n;
    int sum = 0;
    
    scanf("%d%d", &a, &n);
    
    int i;
    int tmp = a;
    for ( i=1; i<=n; i++ ) {
        sum += tmp;
        tmp = tmp*10 +a;
    }
    printf("%d", sum);
    
    return 0;
}


signals fault_type fault_code fault_size load rpm file_id has_BA has_DE has_FE "{&#39;BA&#39;: array([-0.01388301, -0.05834533, -0.03605381, ..., 0.03572969, -0.03102414, -0.03335791]), &#39;DE&#39;: array([ 0.19612209, -0.01049539, -0.0082213 , ..., -0.01975419, 0.0190678 , 0.01386988]), &#39;FE&#39;: array([-0.07096594, 0.12668133, -0.19321139, ..., 0.3329577 , -0.1371223 , -0.07137685]), &#39;RPM&#39;: 1796.0}" Ball B 0.007 0 1796 X118 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.02494944, -0.03653781, -0.05315585, ..., -0.01891383, -0.05347775, -0.04108463]), &#39;DE&#39;: array([ 0.16097982, -0.11710912, -0.09534281, ..., 0.04695036, -0.14391092, -0.04677471]), &#39;FE&#39;: array([ 0.00235666, -0.02168152, -0.01942152, ..., 0.09748211, 0.15007848, 0.00584938]), &#39;RPM&#39;: 1772.0}" Ball B 0.007 1 1772 X119 TRUE TRUE TRUE "{&#39;BA&#39;: array([ 0.07479379, 0.07934061, 0.11853183, ..., 0.01415604, -0.00032942, 0.00466002]), &#39;DE&#39;: array([-0.10105058, -0.13028891, 0.13253113, ..., -0.3045818 , 0.13772906, 0.29188 ]), &#39;FE&#39;: array([ 0.09832123, 0.03072668, -0.00748786, ..., 0.01552304, -0.07508241, 0.05271032]), &#39;RPM&#39;: 1748.0}" Ball B 0.007 2 1748 X120 TRUE TRUE TRUE "{&#39;BA&#39;: array([0.00982435, 0.02149319, 0.0311904 , ..., 0.10068037, 0.04861319, 0.01010601]), &#39;DE&#39;: array([-0.16744701, -0.15006645, 0.25959495, ..., 0.0684088 , 0.16489527, 0.19218437]), &#39;FE&#39;: array([-0.01103941, 0.04217332, 0.02265514, ..., -0.02706486, 0.10956241, 0.03991332]), &#39;RPM&#39;: 1722.0}" Ball B 0.007 3 1722 X121 TRUE TRUE TRUE "{&#39;BA&#39;: array([ 0.02465835, -0.00346758, 0.01962868, ..., -0.03658295, -0.01449262, 0.00317159]), &#39;DE&#39;: array([ 0.11470197, -0.19165068, -0.33102002, ..., -1.43297994, 0.07490537, 0.7927062 ]), &#39;FE&#39;: array([ 0.47692706, 0.26921251, 0.04937615, ..., 0.08224888, 0.04218524, -0.0141093 ]), &#39;RPM&#39;: 1796.0}" Ball B 0.014 0 1796 X185 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.04822309, -0.03739923, -0.03027721, ..., 0.04734071, 0.02279591, -0.0054105 ]), &#39;DE&#39;: array([-0.05666658, -0.04643317, -0.08509273, ..., 0.02178958, 0.16115892, 0.06158619]), &#39;FE&#39;: array([-0.04377759, -0.13027396, 0.09860241, ..., 0.07702968, 0.03902059, 0.19496059]), &#39;RPM&#39;: 1772.0}" Ball B 0.014 1 1772 X186 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.01708263, 0.00613434, 0.02516662, ..., 0.05425826, 0.08403392, 0.01897007]), &#39;DE&#39;: array([ 0.00776575, 0.02758284, 0.12488148, ..., 0.07241493, 0.26603761, -0.09668004]), &#39;FE&#39;: array([ 0.025304 , -0.00695237, -0.04352328, ..., -0.00982873, -0.108036 , -0.04290691]), &#39;RPM&#39;: 1749.0}" Ball B 0.014 2 1749 X187 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.08045546, -0.02054199, -0.04259208, ..., -0.02182958, -0.07204585, -0.03776359]), &#39;DE&#39;: array([ 0.03152513, -0.01184505, -0.15657475, ..., 0.10202198, 0.00602282, -0.04546912]), &#39;FE&#39;: array([ 0.02522948, -0.13091597, -0.2428887 , ..., -0.07359415, 0.03591312, 0.10165857]), &#39;RPM&#39;: 1724.0}" Ball B 0.014 3 1724 X188 TRUE TRUE TRUE "{&#39;BA&#39;: array([ 0.05479622, -0.02563832, 0.02558387, ..., 0.00083788, 0.04739254, 0.0215199 ]), &#39;DE&#39;: array([-0.04347806, 0.05057188, 0.04309986, ..., -0.13297982, -0.1069902 , 0.20407307]), &#39;FE&#39;: array([-0.03297045, -0.062145 , -0.17802136, ..., -0.13651954, 0.06010046, -0.08885409]), &#39;RPM&#39;: 1796.0}" Ball B 0.021 0 1796 X222 TRUE TRUE TRUE "{&#39;BA&#39;: array([ 0.02298952, 0.02600732, 0.03357195, ..., 0.02234572, 0.0221043 , -0.00091149]), &#39;DE&#39;: array([-0.06586291, 0.21986049, 0.02347641, ..., 0.11476496, -0.0288277 , 0.01405518]), &#39;FE&#39;: array([0.05410205, 0.00171114, 0.1808675 , ..., 0.01876387, 0.1266275 , 0.07588023]), &#39;RPM&#39;: 1774.0}" Ball B 0.021 1 1774 X223 TRUE TRUE TRUE "{&#39;BA&#39;: array([0.03449239, 0.00664811, 0.04475292, ..., 0.04813286, 0.07573571, 0.1030569 ]), &#39;DE&#39;: array([-0.38741789, -0.21767318, 0.21472913, ..., 0.01249739, -0.08723777, 0.009736 ]), &#39;FE&#39;: array([-0.08799395, -0.08367941, 0.03794968, ..., -0.00622304, 0.1314315 , -0.07237941]), &#39;RPM&#39;: 1754.0}" Ball B 0.021 2 1754 X224 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.00750357, 0.01881168, 0.03720017, ..., -0.02118428, 0.00432622, -0.02150618]), &#39;DE&#39;: array([-0.09201343, -0.20474341, -0.03158757, ..., -0.21059108, 0.26615603, 0.08000537]), &#39;FE&#39;: array([ 1.72341536e-01, 4.66033540e-02, -7.93402824e-02, ..., 7.94760813e-02, -3.48278223e-05, 6.53971763e-03]), &#39;RPM&#39;: 1729.0}" Ball B 0.021 3 1729 X225 TRUE TRUE TRUE "{&#39;BA&#39;: array([ 0.00814649, 0.11119445, 0.14189558, ..., 0.02762139, 0.06073676, -0.03547083]), &#39;DE&#39;: array([-0.33928843, -0.39744021, -0.21518799, ..., -0.14664037, 0.02034295, 0.09717476]), &#39;FE&#39;: array([ 0.05676449, -0.05561915, -0.15670279, ..., 0.08141903, -0.1846446 , -0.26970279]), &#39;RPM&#39;: 1797.0}" InnerRace IR 0.007 0 1797 X105 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.00591928, 0.03065651, 0.13756725, ..., 0.05101663, 0.0388247 , -0.02648058]), &#39;DE&#39;: array([-0.04592246, 0.05365027, -0.20640837, ..., -0.05972945, 0.30136384, 0.0200262 ]), &#39;FE&#39;: array([-0.266107 , -0.41814337, -0.32404519, ..., 0.13678936, 0.29950936, 0.08891845]), &#39;RPM&#39;: 1772.0}" InnerRace IR 0.007 1 1772 X106 TRUE TRUE TRUE "{&#39;BA&#39;: array([ 0.02033074, -0.00035128, 0.01538154, ..., -0.05809193, -0.02598249, 0.02861964]), &#39;DE&#39;: array([-0.06497779, -0.01624725, 0.04320401, ..., 0.06367083, 0.10298014, -0.06985084]), &#39;FE&#39;: array([ 0.10572216, -0.13055057, -0.15869784, ..., 0.28015307, 0.08640943, 0.00402216]), &#39;RPM&#39;: 1748.0}" InnerRace IR 0.007 2 1748 X107 TRUE TRUE TRUE "{&#39;BA&#39;: array([ 0.05447822, 0.03258908, -0.0465981 , ..., -0.08780118, -0.28749934, -0.3297486 ]), &#39;DE&#39;: array([-0.04045413, -0.3066853 , 0.12457997, ..., -0.20841205, -0.38319225, -0.25503093]), &#39;FE&#39;: array([ 0.09563113, 0.06173113, -0.01017796, ..., 0.07323659, 0.0126275 , 0.0216675 ]), &#39;RPM&#39;: 1721.0}" InnerRace IR 0.007 3 1721 X108 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.05292455, 0.03865575, 0.01845658, ..., -0.10145084, -0.10318105, -0.02089559]), &#39;DE&#39;: array([-1.25562054, -0.51946453, 0.97916197, ..., -0.14229016, 0.11029646, 0.20239718]), &#39;FE&#39;: array([-0.03972674, 0.08457326, -0.13834492, ..., 0.0477969 , -0.07033946, -0.01877037]), &#39;RPM&#39;: 1796.0}" InnerRace IR 0.014 0 1796 X169 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.08614829, -0.021688 , -0.00048289, ..., 0.06345432, 0.1112161 , 0.0063977 ]), &#39;DE&#39;: array([-0.20225596, -0.17318007, 0.14470548, ..., -0.11307907, -0.00457241, -0.00587189]), &#39;FE&#39;: array([-0.12848195, 0.04040169, -0.03458922, ..., -0.17265467, -0.04362922, -0.08081649]), &#39;RPM&#39;: 1774.0}" InnerRace IR 0.014 1 1774 X170 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.06199636, -0.02936384, -0.03853796, ..., -0.05394888, -0.00489951, 0.02998631]), &#39;DE&#39;: array([-0.09691808, -0.17894782, 0.12236935, ..., -0.08587249, 0.04147665, -0.00091892]), &#39;FE&#39;: array([-0.01134892, -0.05511074, -0.12208892, ..., 0.06302562, -0.05182347, -0.05367256]), &#39;RPM&#39;: 1752.0}" InnerRace IR 0.014 2 1752 X171 TRUE TRUE TRUE "{&#39;BA&#39;: array([ 0.08284138, 0.08380708, 0.00844245, ..., 0.02908423, -0.00805488, -0.08961607]), &#39;DE&#39;: array([-0.07903229, 0.04051997, 0.13489478, ..., 0.12774763, 0.05676348, -0.22960965]), &#39;FE&#39;: array([-0.01723032, 0.01584786, -0.00839578, ..., -0.0611976 , -0.0498976 , -0.07105942]), &#39;RPM&#39;: 1728.0}" InnerRace IR 0.014 3 1728 X172 TRUE TRUE TRUE "{&#39;BA&#39;: array([ 0.00687566, 0.04288812, -0.00672458, ..., 0.08578118, 0.09865714, 0.03958865]), &#39;DE&#39;: array([-0.85068671, -0.47383721, 0.7298071 , ..., 0.27742527, 0.50117966, -0.3475439 ]), &#39;FE&#39;: array([ 0.13471861, 0.02664951, -0.04957412, ..., 0.11314588, 0.44474951, -0.01670139]), &#39;RPM&#39;: 1797.0}" InnerRace IR 0.021 0 1797 X209 TRUE TRUE TRUE "{&#39;BA&#39;: array([ 0.04895918, 0.08996107, 0.08098814, ..., -0.01811655, -0.06241792, 0.0164876 ]), &#39;DE&#39;: array([ 0.25238699, -1.02597748, -0.42659186, ..., -0.61623487, 0.21624517, 0.58659727]), &#39;FE&#39;: array([ 0.12430246, 0.10724974, -0.09512299, ..., 0.30017156, 0.12389156, -0.12532481]), &#39;RPM&#39;: 1774.0}" InnerRace IR 0.021 1 1774 X210 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.01889113, -0.00609564, 0.00150923, ..., -0.02009825, 0.03655599, 0.16563754]), &#39;DE&#39;: array([ 0.36976622, -0.17764016, -0.2499238 , ..., 0.15900664, -0.17804625, -0.22555853]), &#39;FE&#39;: array([-0.05813471, -0.14339835, 0.38544165, ..., -0.12531835, 0.08342347, -0.06738017]), &#39;RPM&#39;: 1752.0}" InnerRace IR 0.021 2 1752 X211 TRUE TRUE TRUE "{&#39;BA&#39;: array([0.16660231, 0.13368813, 0.11851863, ..., 0.00919365, 0.07977003, 0.08202332]), &#39;DE&#39;: array([-0.03655097, -0.07309888, 0.03045352, ..., 0.15349813, 0.35654204, -0.12751465]), &#39;FE&#39;: array([ 0.20366018, 0.05532199, -0.19923619, ..., -0.19430528, 0.21824745, 0.31522199]), &#39;RPM&#39;: 1728.0}" InnerRace IR 0.021 3 1728 X212 TRUE TRUE TRUE "{&#39;BA&#39;: array([ 0.03869577, 0.00936272, 0.05076699, ..., -0.04684892, -0.00077711, 0.0247334 ]), &#39;DE&#39;: array([-0.14035442, 0.11401899, -0.00163482, ..., 0.25062693, -0.25097275, -0.12833422]), &#39;FE&#39;: array([-0.08262853, 0.02893328, 0.13494783, ..., 0.1743951 , -0.17241217, 0.0862551 ]), &#39;RPM&#39;: 1797.0}" OuterRace OR 0.007 0 1797 X156 TRUE TRUE TRUE "{&#39;BA&#39;: array([ 0.03412909, 0.06326095, 0.02366736, ..., -0.01367293, -0.02328967, 0.012079 ]), &#39;DE&#39;: array([ 0.17208237, 0.23039658, -0.21305132, ..., 0.08339279, 0.29033514, 0.11977826]), &#39;FE&#39;: array([-0.05571225, 0.10187138, -0.11077407, ..., 0.03181138, -0.12022498, -0.08755771]), &#39;RPM&#39;: 1773.0}" OuterRace OR 0.007 1 1773 X158 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.06641104, -0.02351798, 0.02404261, ..., 0.03615406, -0.0180457 , 0.00038303]), &#39;DE&#39;: array([ 0.03028073, -0.22604191, 0.08956955, ..., -0.49877049, -0.40569516, 0.54698687]), &#39;FE&#39;: array([-0.08129673, 0.10340691, -0.16676582, ..., -0.13718037, 0.07957418, -0.14416582]), &#39;RPM&#39;: 1750.0}" OuterRace OR 0.007 2 1750 X159 TRUE TRUE TRUE "{&#39;BA&#39;: array([ 0.00218562, 0.00190396, -0.00549972, ..., -0.01471408, -0.06766648, -0.08661829]), &#39;DE&#39;: array([-0.03319129, 0.28242017, 0.12843166, ..., 0.01456464, -0.10060187, 0.10374152]), &#39;FE&#39;: array([ 0.16130431, -0.17913387, 0.02632067, ..., -0.06551751, 0.09329885, -0.0153866 ]), &#39;RPM&#39;: 1724.0}" OuterRace OR 0.007 3 1724 X160 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.06365598, 0.00374165, 0.02651601, ..., 0.06920788, -0.01271544, -0.04031829]), &#39;DE&#39;: array([ 0.06996504, -0.35926979, -0.05348566, ..., -0.64393735, -0.21429643, 0.76437522]), &#39;FE&#39;: array([ 0.0612359 , 0.06698862, 0.04171772, ..., -0.09100592, -0.17277683, -0.27714774]), &#39;RPM&#39;: 1797.0}" OuterRace OR 0.007 0 1797 X144 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.05352636, 0.02586201, 0.03600183, ..., -0.0989946 , -0.08116944, 0.02469513]), &#39;DE&#39;: array([-0.61913114, 0.72989261, 0.7668466 , ..., 0.5434983 , -0.29791567, -0.62075549]), &#39;FE&#39;: array([-0.12056885, 0.09125478, -0.0661234 , ..., 0.43477478, 0.10625297, -0.33835067]), &#39;RPM&#39;: 1774.0}" OuterRace OR 0.007 1 1774 X145 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.02915423, 0.02862666, -0.00537393, ..., 0.17569432, 0.02645385, -0.09828206]), &#39;DE&#39;: array([-0.57707453, 0.40322147, 0.7390561 , ..., -2.84385677, -0.8584934 , 3.04563495]), &#39;FE&#39;: array([ 0.33087666, 0.0048203 , -0.26884516, ..., -0.05599425, -0.09318152, 0.14473484]), &#39;RPM&#39;: 1751.0}" OuterRace OR 0.007 2 1751 X146 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.01601493, -0.1469474 , -0.00828935, ..., -0.02414288, 0.0143643 , -0.003823 ]), &#39;DE&#39;: array([ 0.70844682, 0.83474013, -0.28971706, ..., 0.56672216, 1.25504103, -0.1682968 ]), &#39;FE&#39;: array([-0.07429627, 0.09130009, 0.272511 , ..., 0.07260373, 0.03582737, 0.04075827]), &#39;RPM&#39;: 1725.0}" OuterRace OR 0.007 3 1725 X147 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.02933921, 0.01190411, 0.0521415 , ..., 0.13140916, 0.01938827, -0.08321707]), &#39;DE&#39;: array([-1.24712018, -1.62072098, 1.49316046, ..., -0.39717836, 0.02880777, 0.07307134]), &#39;FE&#39;: array([-0.30149532, -0.19198805, 0.11064649, ..., 0.12667195, -0.07015351, -0.12233896]), &#39;RPM&#39;: 1796.0}" OuterRace OR 0.007 0 1796 X130 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.00659799, -0.00128666, -0.00514945, ..., 0.099508 , 0.17278029, -0.0526698 ]), &#39;DE&#39;: array([-0.08568471, 0.39634154, -0.059289 , ..., -1.42293191, 0.98435671, 0.95186968]), &#39;FE&#39;: array([-0.08824636, 0.28979 , 0.11864637, ..., 0.05557182, 0.16528455, -0.29431727]), &#39;RPM&#39;: 1773.0}" OuterRace OR 0.007 1 1773 X131 TRUE TRUE TRUE "{&#39;BA&#39;: array([ 0.02288109, -0.04186087, -0.05634633, ..., -0.00782004, -0.07304485, -0.09497422]), &#39;DE&#39;: array([ 0.21740561, -0.17609349, -0.19517962, ..., 0.09557926, 0.14227936, -0.07172892]), &#39;FE&#39;: array([-0.20903137, 0.38473227, -0.17389864, ..., 0.15297954, -0.31196409, 0.08867227]), &#39;RPM&#39;: 1750.0}" OuterRace OR 0.007 2 1750 X132 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.03527996, -0.07604043, 0.04342438, ..., 0.09504895, 0.07408527, 0.0122404 ]), &#39;DE&#39;: array([-0.43701261, -1.64715433, 0.72764727, ..., 0.69800286, 0.05882062, -0.35620114]), &#39;FE&#39;: array([ 0.41248767, -0.42905415, -0.36721233, ..., -0.13566506, 0.44597676, -0.20654688]), &#39;RPM&#39;: 1725.0}" OuterRace OR 0.007 3 1725 X133 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.04434567, 0.02606976, -0.01183386, ..., 0.03190418, -0.04655873, -0.00941962]), &#39;DE&#39;: array([-0.16824494, -0.1319902 , 0.08358944, ..., 0.00775087, -0.09756242, 0.04355902]), &#39;FE&#39;: array([ 0.2255243 , -0.08717752, -0.06745388, ..., -0.13874661, 0.1486843 , 0.19511703]), &#39;RPM&#39;: 1796.0}" OuterRace OR 0.014 0 1796 X197 TRUE TRUE TRUE "{&#39;BA&#39;: array([ 0.02609577, -0.02943183, -0.00267396, ..., -0.01144572, -0.07188227, -0.09485782]), &#39;DE&#39;: array([-0.12274404, 0.01878339, 0.08264531, ..., -0.04840763, -0.02473853, 0.07529692]), &#39;FE&#39;: array([ 0.14727498, -0.02674502, -0.09906502, ..., -0.0937232 , -0.05817957, 0.00058043]), &#39;RPM&#39;: 1772.0}" OuterRace OR 0.014 1 1772 X198 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.02193214, 0.03452092, 0.00667665, ..., -0.03653831, 0.00502691, 0.01681647]), &#39;DE&#39;: array([ 0.03081747, 0.0907819 , 0.0705637 , ..., 0.03154825, 0.04965531, -0.02691403]), &#39;FE&#39;: array([-0.18178385, 0.20981251, 0.01442524, ..., -0.03262385, 0.15659978, -0.02687112]), &#39;RPM&#39;: 1749.0}" OuterRace OR 0.014 2 1749 X199 TRUE TRUE TRUE "{&#39;BA&#39;: array([ 0.01514817, 0.00557167, 0.03953202, ..., 0.01164751, -0.03253314, 0.02295422]), &#39;DE&#39;: array([ 0.14362024, 0.05515545, -0.14804155, ..., -0.11081245, 0.12908587, 0.02235162]), &#39;FE&#39;: array([ 0.16077192, -0.08022627, -0.01057717, ..., -0.16117536, 0.03133555, -0.16754445]), &#39;RPM&#39;: 1723.0}" OuterRace OR 0.014 3 1723 X200 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.01740123, 0.01925503, 0.02609538, ..., -0.00774426, -0.00899162, -0.0557877 ]), &#39;DE&#39;: array([ 0.01138635, 0.05402557, 0.14417707, ..., 0.01707158, 0.03900032, -0.14942443]), &#39;FE&#39;: array([-0.08635773, -0.00643592, 0.00917863, ..., 0.10902954, 0.06485681, 0.03095681]), &#39;RPM&#39;: 1796.0}" OuterRace OR 0.021 0 1796 X258 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.08532102, -0.04560672, -0.04222678, ..., 0.00352313, 0.03776515, 0.06130402]), &#39;DE&#39;: array([-0.12531641, 0.0111291 , -0.01810923, ..., -0.27962979, 0.45498309, 0.05661093]), &#39;FE&#39;: array([-0.0887954 , -0.00681904, 0.00345369, ..., -0.30493358, -0.34931177, 0.87725187]), &#39;RPM&#39;: 1771.0}" OuterRace OR 0.021 1 1771 X259 TRUE TRUE TRUE "{&#39;BA&#39;: array([ 0.00872241, -0.00648733, -0.04217789, ..., -0.08993967, -0.07320092, -0.05911783]), &#39;DE&#39;: array([-0.03245533, -0.16930693, -0.13641381, ..., 0.72286802, 0.38581513, -0.84341272]), &#39;FE&#39;: array([ 0.01863032, 0.13923214, -0.02163877, ..., -0.19298786, -0.10854604, -0.11491514]), &#39;RPM&#39;: 1746.0}" OuterRace OR 0.021 2 1746 X260 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.0584131 , 0.00419627, 0.03525954, ..., 0.02580375, 0.05409063, -0.04006485]), &#39;DE&#39;: array([-0.10243348, -0.02690115, -0.10568219, ..., -0.03096203, -0.01877939, 0.08193039]), &#39;FE&#39;: array([-0.19722257, -0.18674438, -0.03676257, ..., 0.20197562, 0.09411198, -0.1378462 ]), &#39;RPM&#39;: 1718.0}" OuterRace OR 0.021 3 1718 X261 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.00985285, 0.02846256, -0.00075697, ..., 0.03490212, 0.10678376, 0.09994172]), &#39;DE&#39;: array([ 0.15363965, -0.01967864, -0.0708457 , ..., -0.55327804, -0.69687069, -0.26154454]), &#39;FE&#39;: array([ 0.10008412, -0.01476498, -0.0114777 , ..., 0.27965139, 0.33902775, 0.10070048]), &#39;RPM&#39;: 1796.0}" OuterRace OR 0.021 0 1796 X246 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.00391417, -0.00222378, -0.01252708, ..., -0.09229719, -0.02387682, -0.00375318]), &#39;DE&#39;: array([-0.29124394, -0.28507141, -0.30570067, ..., -0.06805807, -0.03914462, -0.03670809]), &#39;FE&#39;: array([ 0.36044614, 0.19443887, -0.18154295, ..., 0.10321705, -0.11004476, 0.04630614]), &#39;RPM&#39;: 1771.0}" OuterRace OR 0.021 1 1771 X247 TRUE TRUE TRUE "{&#39;BA&#39;: array([ 0.09011397, 0.01879579, 0.00720457, ..., 0.1103986 , 0.02781118, -0.0686213 ]), &#39;DE&#39;: array([-1.94440533e-01, -3.56063487e-01, -2.15881970e-01, ..., -1.68117922e-04, -3.00835543e-01, 2.90103459e-01]), &#39;FE&#39;: array([ 0.07259593, -0.0619768 , -0.11806589, ..., 0.21518138, 0.02698502, -0.15217134]), &#39;RPM&#39;: 1747.0}" OuterRace OR 0.021 2 1747 X248 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.0969421 , -0.05186514, -0.01314726, ..., 0.01430139, 0.02726101, 0.04827009]), &#39;DE&#39;: array([-0.5328822 , -0.3127826 , -0.22409302, ..., -0.27282356, -0.0779014 , -0.1407638 ]), &#39;FE&#39;: array([-0.02670657, -0.02814475, 0.12019343, ..., 0.04520252, 0.15532616, 0.05917343]), &#39;RPM&#39;: 1719.0}" OuterRace OR 0.021 3 1719 X249 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.01227974, -0.0720872 , 0.04245656, ..., -0.24015984, -0.15668698, -0.04447756]), &#39;DE&#39;: array([ 0.02775602, 0.36724544, -0.06889289, ..., -0.08919728, 2.73920442, 1.09698526]), &#39;FE&#39;: array([-0.07247194, 0.18968806, 0.2365317 , ..., 0.01320261, 0.10524624, -0.26190103]), &#39;RPM&#39;: 1796.0}" OuterRace OR 0.021 0 1796 X234 TRUE TRUE TRUE "{&#39;BA&#39;: array([ 0.02246363, 0.01199934, -0.05730648, ..., 0.04146035, 0.10480957, 0.07889032]), &#39;DE&#39;: array([ 0.03435856, 0.36775666, 0.57770407, ..., 0.04207423, -0.19792368, 0.17445886]), &#39;FE&#39;: array([-0.04492589, 0.16278865, -0.24750408, ..., -0.13368226, -0.18566226, 0.26798138]), &#39;RPM&#39;: 1771.0}" OuterRace OR 0.021 1 1771 X235 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.13181674, -0.09503073, -0.09068402, ..., -0.04246778, 0.04680068, 0.11031089]), &#39;DE&#39;: array([ 0.15094042, 0.05713413, 0.06850459, ..., 0.03601756, -0.18286377, -0.25514741]), &#39;FE&#39;: array([-0.03813727, -0.00423727, -0.00711364, ..., -0.01738636, 0.13136273, 0.12006273]), &#39;RPM&#39;: 1748.0}" OuterRace OR 0.021 2 1748 X236 TRUE TRUE TRUE "{&#39;BA&#39;: array([-0.05220006, -0.0353767 , -0.02587834, ..., 0.19202043, 0.06000936, -0.11868857]), &#39;DE&#39;: array([ 0.27624452, -0.1131937 , 0.0500536 , ..., 0.59299303, 0.03990141, -0.61186955]), &#39;FE&#39;: array([ 0.0827553 , 0.05378621, -0.03990106, ..., -0.03209379, 0.11912076, -0.00291924]), &#39;RPM&#39;: 1721.0}" OuterRace OR 0.021 3 1721 X237 TRUE TRUE TRUE 怎么处理数据
最新发布
09-24
<think> 首先,用户的问题是关于如何处理一个数据集,这个数据集包含信号、故障类型、故障代码、故障大小、负载、转速等信息,以及BA、DE、FE数组数据。用户提供了引用内容,这些引用描述了凯斯西储大学轴承数据(CWRU数据集),其中包含DE(驱动端加速度计数据)、FE(风扇端加速度计数据)、BA(基座加速度计数据)等。 关键元素: - 信号:加速度计数据(DE, FE, BA),时间序列数据。 - 故障类型:如内圈故障、滚动体故障、外圈故障。 - 故障代码:可能表示不同的故障位置或类型。 - 故障大小:缺陷直径尺寸(0.1778mm, 0.3556mm, 0.5334mm)。 - 负载:以马力(HP)为单位(0HP, 1HP, 2HP, 3HP)。 - 转速:RPM(测试期间的转速)。 - 数组数据:BA、DE、FE数组数据,可能是时间序列数据。 用户指定了系统级指令: 1. 行内数学表达式必须使用$...$格式。 2. 独立公式使用$$...$$格式并单独成段。 3. LaTeX语法正确。 4. 使用中文回答。 5. 生成相关问题。 6. 回答中引用的段落末尾自然地添加引用标识,例如[^1]。 在回答结构上,我需要清晰、逐步解决问题,并保证真实可靠。 参考用户提到的引用: - 引用[1]:定义了DE、FE、BA、time、RPM。 - 引用[2]:描述了实验设置,包括故障类型、大小、负载、采样频率等。 - 引用[3]:提到了使用CWRU数据,用改进的LeNet-5架构进行故障诊断,融合DEFE数据。 用户上一次的问题我不记得,因为我是一个新会话。用户说“参考用户上一次的问题你的回答”,但在这个上下文中,这是第一个问题。所以,我应该基于当前提供的引用问题来回答。 核心问题:如何处理这样的数据集?具体来说,数据集包含多维信息:信号数据(BA、DE、FE数组)、元数据(故障类型、代码、大小、负载、转速)。 典型处理步骤: 1. **数据加载预处理**:读取数据文件(如.mat文件),提取信号数据元数据。 2. **特征工程**:从时间序列信号中提取特征,如统计特征(均值、方差)、时域特征、频域特征(FFT)、时频域特征(小波变换)。 3. **数据融合**:由于有多个传感器数据(DE, FE, BA),需要决定如何融合它们,例如特征级融合或决策级融合。 4. **标签处理**:故障类型、代码等作为分类标签。 5. **数据集划分**:划分训练集、验证集、测试集。 6. **模型训练**:使用机器学习或深度学习模型进行故障诊断。 7. **考虑条件变量**:负载、转速等可能需要作为特征或将数据分组。 从引用[3]中,用户提到了一个示例代码:使用TensorFlow,加载.mat文件,定义窗口大小,提取样本点等。 因此,我的回答应该覆盖这些方面,使用中文。 结构回答: 1. **理解数据集**:先简要描述数据集,引用相关引用。 2. **数据处理步骤**:逐步说明如何加载、预处理、特征提取、融合数据等。 3. **示例实现**:提供一个简单的代码示例或伪代码,参考引用[3]。 4. **注意事项**:讨论如何处理元数据如负载、转速。 5. **生成相关问题**:在末尾生成相关问题。 确保数学表达式正确: - 例如,提到FFT时使用$...$格式:$X(f) = \int_{-\infty}^{\infty} x(t) e^{-j2\pi ft} dt$ - 独立公式如小波变换公式等。 添加引用标识: - 在描述引用内容时末尾添加[^1], [^2], [^3]。 最后,生成相关问题。 </think> ### 处理包含信号、故障类型、故障大小、负载等信息及BA、DE、FE数组数据的数据集 基于您提供的引用信息,数据集通常来自轴承故障诊断实验(如凯斯西储大学CWRU数据集),包含多维度信息: - **信号数据**:BA(基座加速度计数据)、DE(驱动端加速度计数据)、FE(风扇端加速度计数据),均为时间序列数据,采样频率为12.8kHz[^2]。 - **元数据**:故障类型(如内圈、滚动体、外圈故障)、故障代码(标识故障位置)、故障大小(缺陷直径,如0.1778mm、0.3556mm、0.5334mm)、负载(0HP、1HP、2HP、3HP)、转速(RPM)[^1][^2]。 - **数据格式**:通常存储在.mat文件(MATLAB格式)中,包含数组数据元数据标签[^3]。 处理这类数据集的目标通常是实现故障诊断(例如分类不同故障类型)。以下是结构化处理步骤,结合信号处理机器学习方法。处理过程分为数据加载、预处理、特征工程、数据融合、模型训练等阶段,确保高效利用所有信息。 #### 1. **数据加载与初步预处理** - **加载数据**:使用Python库(如`scipy.io`)读取.mat文件,提取信号数组元数据标签。 - 每个文件包含BA、DE、FE数组(时间序列),以及故障类型、负载等元数据。 - 示例代码(参考引用[3]): ```python import scipy.io as sio import numpy as np # 加载.mat文件 data = sio.loadmat(&#39;bearing_data.mat&#39;) de_signal = data[&#39;DE&#39;].flatten() # 驱动端信号 (时间序列) fe_signal = data[&#39;FE&#39;].flatten() # 风扇端信号 ba_signal = data[&#39;BA&#39;].flatten() # 基座信号 fault_type = data[&#39;fault_type&#39;] # 故障类型标签 fault_size = data[&#39;fault_size&#39;] # 故障大小 load_hp = data[&#39;load&#39;] # 负载 (HP) rpm = data[&#39;RPM&#39;] # 转速 ``` - **数据归一化**:标准化信号数据以提高模型稳定性。假设信号为时间序列$x(t)$,归一化公式: $$ x_{\text{norm}}(t) = \frac{x(t) - \mu}{\sigma} $$ 其中$\mu$是均值,$\sigma$是标准差[^3]。 - **处理元数据**:将分类变量(如故障类型、故障代码)编码为数值标签(例如使用独热编码),连续变量(如故障大小、负载、转速)可直接作为特征。 #### 2. **特征工程:从信号中提取有用特征** 时间序列信号(如DE、FE)本身维度高,直接输入模型效率低。需提取特征,常见方法包括: - **时域特征**:计算统计量,如均值、方差、峰值因子等。例如,对于信号$x(t)$: - 均值 $\mu = \frac{1}{N} \sum_{i=1}^{N} x_i$ - 方差 $\sigma^2 = \frac{1}{N-1} \sum_{i=1}^{N} (x_i - \mu)^2$ - **频域特征**:使用傅里叶变换(FFT)将信号转换到频域,提取频谱特征。FFT公式为: $$ X(f) = \int_{-\infty}^{\infty} x(t) e^{-j2\pi ft} dt $$ 关键特征包括主频幅值、频带能量等[^3]。 - **时频域特征**:例如小波变换系数,可捕捉非平稳信号特征。小波变换公式: $$ W(a,b) = \frac{1}{\sqrt{a}} \int x(t) \psi\left(\frac{t-b}{a}\right) dt $$ 其中$\psi$是小波基函数。 - **特征融合**:由于有多个传感器(DE、FE、BA),可提取各自特征后拼接。引用[3]提到融合DEFE数据能提升诊断准确性。例如: ```python def extract_features(signal): # 示例:提取时域频域特征 mean = np.mean(signal) std = np.std(signal) fft = np.fft.rfft(signal) dominant_freq = np.max(np.abs(fft)) return np.array([mean, std, dominant_freq]) de_features = extract_features(de_signal) fe_features = extract_features(fe_signal) ba_features = extract_features(ba_signal) # 拼接特征向量 combined_features = np.concatenate([de_features, fe_features, ba_features]) ``` #### 3. **处理元数据作为条件变量** - 负载、转速、故障大小等可能影响信号分布。处理方法: - **作为额外特征**:与信号特征拼接,例如: ```python # 假设元数据已归一化 meta_features = np.array([load_hp, rpm, fault_size]) all_features = np.concatenate([combined_features, meta_features]) ``` - **分组处理**:如果数据量大,可按负载或转速分组训练多个模型(例如不同负载下故障特征不同),提高泛化性[^2]。 - **标签整合**:故障类型是分类标签,可结合故障大小创造细粒度标签(例如“内圈故障-0.1778mm”)。 #### 4. **数据集构建与划分** - **样本提取**:从长序列中分割窗口样本(参考引用[3]的Window_size)。例如,每个样本取1280个时间点。 ```python window_size = 1280 samples = [signal[i:i+window_size] for i in range(0, len(signal)-window_size, step_size)] ``` - **数据集划分**:使用`train_test_split`划分训练集、验证集、测试集(比例如70:15:15)。确保每个故障类型负载组合分布均匀[^3]。 #### 5. **模型训练与诊断** - **选择模型**:深度学习模型高效,如改进的CNN(如LeNet-5架构),引用[3]使用此方法实现故障诊断。模型输入可以是特征向量或原始信号(需预处理)。 - 示例架构:输入层→卷积层(提取局部特征)→池化层→全连接层→softmax输出层。 - **训练代码框架**: ```python import tensorflow as tf from sklearn.model_selection import train_test_split # 加载并预处理数据(假设 X 为特征,y 为故障标签) X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2) model = tf.keras.Sequential([ tf.keras.layers.Dense(128, activation=&#39;relu&#39;, input_shape=(feature_dim,)), tf.keras.layers.Dense(64, activation=&#39;relu&#39;), tf.keras.layers.Dense(num_classes, activation=&#39;softmax&#39;) ]) model.compile(optimizer=&#39;adam&#39;, loss=&#39;sparse_categorical_crossentropy&#39;, metrics=[&#39;accuracy&#39;]) model.fit(X_train, y_train, epochs=10, batch_size=128, validation_split=0.1) ``` - **评估**:使用测试集计算accuracy、precision等指标。考虑负载变化对性能的影响[^2]。 #### 6. **注意事项** - **数据不平衡**:不同故障类型样本数可能不均,需采用过采样或加权损失函数。 - **计算效率**:时间序列处理计算量大,可使用GPU加速或降维技术如PCA。 - **实际应用**:融合BA数据可增强鲁棒性,但引用[3]显示DEFE是关键传感器。 处理此类数据集的核心是整合信号特征与元数据,通过特征工程模型设计实现高精度故障诊断[^1][^2][^3]。
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