Q_new = math.sqrt(abs(delta_p) * math.pi * D ** 5 / (8 * f * L * rho))

这个公式是用来计算在流体力学中，由于阀门、弯头、管道等摩擦阻力所造成的压力损失，从而计算出流量的公式。其中delta_p表示压力损失，D表示管道的直径，f表示摩擦系数，L表示管道长度，rho表示流体密度。

Q_new表示在这种情况下的流量。该公式的主要思路是通过对各种因素进行计算，来得出流量大小。

相关问题

将下面的python代码转成高效的C语言代码 for i in range(N): b, a = signal.butter(4, [6.0/(Cfg['Nt'][k]/2), 50.0/(Cfg['Nt'][k]/2)], 'bandpass') Hin[k][i, :] = signal.lfilter(b, a, Hin[k][i, :])

以下是将Python代码转换为C语言代码的示例：

#include <stdlib.h>
#include <stdio.h>
#include <math.h>

void butter(int N, double Wn[], char* type, double b[], double a[]) {
    double c1, c2, c3, c4, c5, c6, c7, c8, c9, c10;
    double d1, d2, d3, d4, d5, d6, d7, d8, d9, d10;
    double ar1, ar2, ai1, ai2;
    double f1, f2, f3, f4, f5, f6, f7, f8, f9, f10;
    double p1, p2, p3, p4, p5, p6, p7, p8, p9, p10;
    double q1, q2, q3, q4, q5, q6, q7, q8, q9, q10;
    double r1, r2, r3, r4, r5, r6, r7, r8, r9, r10;
    double s1, s2, s3, s4, s5, s6, s7, s8, s9, s10;
    double t1, t2, t3, t4, t5, t6, t7, t8, t9, t10;
    double u1, u2, u3, u4, u5, u6, u7, u8, u9, u10;
    double v1, v2, v3, v4, v5, v6, v7, v8, v9, v10;
    double w1, w2, w3, w4, w5, w6, w7, w8, w9, w10;
    double x1, x2, x3, x4, x5, x6, x7, x8, x9, x10;
    double y1, y2, y3, y4, y5, y6, y7, y8, y9, y10;
    double z1, z2, z3, z4, z5, z6, z7, z8, z9, z10;
    double qf1, qf2, qf3, qf4, qf5, qf6, qf7, qf8, qf9, qf10;
    double qb1, qb2, qb3, qb4, qb5, qb6, qb7, qb8, qb9, qb10;
    double af1, af2, af3, af4, af5, af6, af7, af8, af9, af10;
    double ab1, ab2, ab3, ab4, ab5, ab6, ab7, ab8, ab9, ab10;
    double a0, a1, a2, a3, a4, b0, b1, b2, b3, b4;
    double s, c, alpha, beta, gamma, delta;
    double pi = 3.14159265358979323846;
    
    if (strcmp(type, "lowpass") == 0) {
        s = sin(pi*Wn[0]);
        c = cos(pi*Wn[0]);
        alpha = s/(2*N);
        beta = sqrt(1 - alpha*alpha);
        gamma = (1 - c)/2;
        delta = (1 + c)/2;
        
        a0 = delta;
        a1 = gamma + beta*I;
        a2 = alpha*2 - delta;
        a3 = -(gamma + beta*I);
        a4 = delta;
        
        b0 = alpha;
        b1 = 0;
        b2 = -alpha;
        b3 = 0;
        b4 = alpha;
    }
    else if (strcmp(type, "highpass") == 0) {
        s = sin(pi*Wn[0]);
        c = cos(pi*Wn[0]);
        alpha = s/(2*N);
        beta = sqrt(1 - alpha*alpha);
        gamma = (1 + c)/2;
        delta = (1 - c)/2;
        
        a0 = delta;
        a1 = -(gamma + beta*I);
        a2 = alpha*2 - delta;
        a3 = gamma + beta*I;
        a4 = delta;
        
        b0 = alpha;
        b1 = 0;
        b2 = -alpha;
        b3 = 0;
        b4 = alpha;
    }
    else if (strcmp(type, "bandpass") == 0) {
        s = sin(pi*Wn[0]);
        c = cos(pi*Wn[0]);
        alpha = s*sinh(log(2)/2*N*Wn[1]/s);
        beta = sqrt(1 - alpha*alpha);
        gamma = c;
        delta = 1;
        
        a0 = delta;
        a1 = -2*gamma;
        a2 = 2*alpha*beta;
        a3 = 2*gamma;
        a4 = delta;
        
        b0 = alpha;
        b1 = 0;
        b2 = -alpha;
        b3 = 0;
        b4 = alpha;
    }
    else if (strcmp(type, "bandstop") == 0) {
        s = sin(pi*Wn[0]);
        c = cos(pi*Wn[0]);
        alpha = s/sinh(log(2)/2*N*Wn[1]/s);
        beta = sqrt(1 - alpha*alpha);
        gamma = c;
        delta = 1;
        
        a0 = delta;
        a1 = -2*gamma;
        a2 = 2*alpha*beta;
        a3 = 2*gamma;
        a4 = delta;
        
        b0 = beta;
        b1 = -2*beta*c;
        b2 = beta;
        b3 = beta;
        b4 = -2*beta*c;
    }
    else {
        printf("Invalid filter type.\n");
        exit(1);
    }
    
    ar1 = a[0];
    ar2 = a[1];
    ai1 = a[2];
    ai2 = a[3];
    f1 = b[0];
    f2 = b[1];
    f3 = b[2];
    f4 = b[3];
    f5 = b[4];
    p1 = 0;
    p2 = 0;
    p3 = 0;
    p4 = 0;
    p5 = 0;
    q1 = 0;
    q2 = 0;
    q3 = 0;
    q4 = 0;
    q5 = 0;
    r1 = 0;
    r2 = 0;
    r3 = 0;
    r4 = 0;
    r5 = 0;
    s1 = 0;
    s2 = 0;
    s3 = 0;
    s4 = 0;
    s5 = 0;
    t1 = 0;
    t2 = 0;
    t3 = 0;
    t4 = 0;
    t5 = 0;
    u1 = 0;
    u2 = 0;
    u3 = 0;
    u4 = 0;
    u5 = 0;
    v1 = 0;
    v2 = 0;
    v3 = 0;
    v4 = 0;
    v5 = 0;
    w1 = 0;
    w2 = 0;
    w3 = 0;
    w4 = 0;
    w5 = 0;
    x1 = 0;
    x2 = 0;
    x3 = 0;
    x4 = 0;
    x5 = 0;
    y1 = 0;
    y2 = 0;
    y3 = 0;
    y4 = 0;
    y5 = 0;
    z1 = 0;
    z2 = 0;
    z3 = 0;
    z4 = 0;
    z5 = 0;
    qf1 = 0;
    qf2 = 0;
    qf3 = 0;
    qf4 = 0;
    qf5 = 0;
    qb1 = 0;
    qb2 = 0;
    qb3 = 0;
    qb4 = 0;
    qb5 = 0;
    af1 = 0;
    af2 = 0;
    af3 = 0;
    af4 = 0;
    af5 = 0;
    ab1 = 0;
    ab2 = 0;
    ab3 = 0;
    ab4 = 0;
    ab5 = 0;
    
    for (int i = 0; i < N; i++) {
        qf5 = qf4;
        qf4 = qf3;
        qf3 = qf2;
        qf2 = qf1;
        qf1 = Hin[k][i];
        
        qb5 = qb4;
        qb4 = qb3;
        qb3 = qb2;
        qb2 = qb1;
        qb1 = qf5*a0 + qf4*a1 + qf3*a2 + qf2*a3 + qf1*a4 + qb5*b0 + qb4*b1 + qb3*b2 + qb2*b3 + qb1*b4;
        
        af5 = af4;
        af4 = af3;
        af3 = af2;
        af2 = af1;
        af1 = qb5*f1 + qb4*f2 + qb3*f3 + qb2*f4 + qb1*f5;
        
        ab5 = ab4;
        ab4 = ab3;
        ab3 = ab2;
        ab2 = ab1;
        ab1 = qb5*f1 + qb4*f4 + qb3*f3 + qb2*f2 + qb1*f5;
        
        Hin[k][i] = af1 - ab1;
    }
}

然后，您可以使用以下代码调用上面的函数：

int main() {
    double Wn[] = {6.0/(Cfg['Nt'][k]/2), 50.0/(Cfg['Nt'][k]/2)};
    double b[5], a[5];
    int N = ...; // 请用您的代码替换此处的 N
    
    butter(4, Wn, "bandpass", b, a);
    
    return 0;
}

用C语言通过无迹卡尔曼滤波算法编写一套电池SOC计算函数，其中电池的容量使用Peukert常数n=1.357来计算并加上UKF算法的实现部分，算法最终输出电池的内阻和当前的SOC值

好的，首先我们需要了解一下无迹卡尔曼滤波算法和Peukert常数的基本概念。

无迹卡尔曼滤波（Unscented Kalman Filter，UKF）是一种基于卡尔曼滤波的状态估计算法，它通过非线性变换将高斯分布传递到非线性函数，并通过最小化状态与观测之间的残差来估计系统状态。UKF算法相比于传统的卡尔曼滤波算法，在处理非线性系统时具有更好的表现。

Peukert常数是用来描述电池放电过程中能量转化效率的一个参数。它的取值范围通常在1.1到1.5之间，不同的电池类型具有不同的Peukert常数。在这里我们假设电池的Peukert常数为1.357。

接下来是电池SOC计算函数的代码实现。

#include <stdio.h>
#include <math.h>

#define PI 3.14159265358979323846

// 电池容量，单位：Ah
const double capacity = 100.0;
// Peukert常数
const double peukert = 1.357;
// 采样时间，单位：s
const double sample_time = 1.0;
// 初始SOC值
double soc = 100.0;
// 初始电池内阻值，单位：mOhm
double r0 = 10.0;

// UKF算法相关参数
const int n = 2;  // 状态向量维度
const int m = 1;  // 观测向量维度
const double alpha = 0.001;
const double beta = 2.0;
const double kappa = 0.0;

// 状态向量
typedef struct {
    double soc;
    double r;
} state_t;

// 观测向量
typedef double observation_t;

// 状态向量转移函数
void state_transition(state_t *state, double current, double voltage)
{
    // 计算电池当前的负载电流
    double current_load = voltage / state->r;
    // 计算电池的放电容量
    double discharge_capacity = pow(current_load, peukert) * sample_time;
    // 计算SOC值
    state->soc -= discharge_capacity / capacity * 100.0;
    // 计算内阻变化量
    double delta_r = current * sample_time / (voltage - current * r0) - state->r;
    // 计算新的内阻值
    state->r += delta_r;
}

// 观测向量转换函数
void observation_function(state_t *state, observation_t *observation)
{
    *observation = state->soc;
}

// 系统噪声协方差矩阵
void process_noise_covariance(double *Q)
{
    Q[0] = 1e-5;
    Q[1] = 1e-5;
}

// 观测噪声协方差矩阵
void observation_noise_covariance(double *R)
{
    R[0] = 1e-3;
}

// 初始化状态向量和协方差矩阵
void initialize(state_t *state, double *P)
{
    state->soc = soc;
    state->r = r0;
    P[0] = 1.0;
    P[1] = 0.0;
    P[2] = 0.0;
    P[3] = 1.0;
}

// 无迹卡尔曼滤波算法
void ukf_filter(state_t *state, double current, double voltage)
{
    // 状态向量和协方差矩阵
    double x[n];
    double P[n * n];
    // 观测向量和协方差矩阵
    double z[m];
    double R[m * m];
    // 系统噪声协方差矩阵
    double Q[n * n];
    process_noise_covariance(Q);
    // 观测噪声协方差矩阵
    observation_noise_covariance(R);
    // 初始化状态向量和协方差矩阵
    initialize(state, P);
    // 计算Sigma点
    double lambda = alpha * alpha * (n + kappa) - n;
    double c = sqrt(n + lambda);
    double Wm[2 * n + 1];
    double Wc[2 * n + 1];
    Wm[0] = lambda / (n + lambda);
    Wc[0] = lambda / (n + lambda) + (1 - alpha * alpha + beta);
    for (int i = 1; i <= 2 * n; i++) {
        Wm[i] = 1.0 / (2.0 * (n + lambda));
        Wc[i] = Wm[i];
    }
    double X[n][2 * n + 1];
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < 2 * n + 1; j++) {
            X[i][j] = state->soc;
        }
    }
    for (int i = 0; i < n; i++) {
        X[i][i + 1] += c;
        X[i][i + 1 + n] -= c;
    }
    // 预测状态向量和协方差矩阵
    for (int i = 0; i < 2 * n + 1; i++) {
        x[i] = X[0][i];
        state_transition(state, current, voltage);
        X[0][i] = state->soc;
        X[1][i] = state->r;
    }
    double x_mean = 0.0;
    double r_mean = 0.0;
    for (int i = 0; i < 2 * n + 1; i++) {
        x_mean += Wm[i] * X[0][i];
        r_mean += Wm[i] * X[1][i];
    }
    double P_xx = 0.0;
    double P_rr = 0.0;
    double P_xr = 0.0;
    for (int i = 0; i < 2 * n + 1; i++) {
        P_xx += Wc[i] * (X[0][i] - x_mean) * (X[0][i] - x_mean);
        P_rr += Wc[i] * (X[1][i] - r_mean) * (X[1][i] - r_mean);
        P_xr += Wc[i] * (X[0][i] - x_mean) * (X[1][i] - r_mean);
    }
    P[0] = P_xx;
    P[1] = P_xr;
    P[2] = P_xr;
    P[3] = P_rr + Q[1];
    // 测量更新状态向量和协方差矩阵
    observation_function(state, &z[0]);
    double z_mean = z[0];
    double P_zz = R[0];
    double P_xz = 0.0;
    for (int i = 0; i < 2 * n + 1; i++) {
        observation_function(&X[0][i], &z[i]);
        z_mean += Wm[i] * z[i];
    }
    for (int i = 0; i < 2 * n + 1; i++) {
        P_zz += Wc[i] * (z[i] - z_mean) * (z[i] - z_mean);
        P_xz += Wc[i] * (X[0][i] - x_mean) * (z[i] - z_mean);
    }
    double K[n];
    K[0] = P_xz / P_zz;
    K[1] = P_xz / P_zz;
    state->soc = x_mean + K[0] * (soc - z_mean);
    state->r = r_mean + K[1] * (r0 - z_mean);
    P[0] -= K[0] * P_zz * K[0];
    P[1] -= K[0] * P_zz * K[1];
    P[2] -= K[1] * P_zz * K[0];
    P[3] -= K[1] * P_zz * K[1];
}

int main()
{
    double current = 10.0;  // 电池负载电流，单位：A
    double voltage = 48.0;  // 电池电压，单位：V
    state_t state;
    ukf_filter(&state, current, voltage);
    printf("SOC = %.2lf%%\n", state.soc);
    printf("Internal Resistance = %.2lf mOhm\n", state.r);
    return 0;
}

在上面的代码中，我们定义了状态向量和观测向量的数据结构，以及状态向量转移函数、观测向量转换函数、系统噪声协方差矩阵、观测噪声协方差矩阵、初始化函数和无迹卡尔曼滤波算法函数。

在主函数中，我们给定了电池的负载电流和电压，然后调用ukf_filter函数进行SOC和内阻的计算，并输出结果。