add enhanced Steinmetz equation

Author: tillpiepenbrock

docs/wordlist

@@ -70,4 +70,5 @@ popt
 rtype
 steinmetz
 sqrt
-linspace
+linspace
+qT

materialdatabase/processing/complex_permeability.py

@@ -104,21 +104,22 @@ def fit_permeability_amplitude(self):
                                              mu_abs, maxfev=100000)
         return popt_mu_abs
 
-    def fit_losses(self):
+    def fit_losses(self, log_pv_fit_function):
         """
         Fit the magnetic power loss density p_v as a function of frequency, temperature, and magnetic flux density.
 
         The losses are calculated from the imaginary part of the permeability using the helper function `pv_mag()`,
         and then fitted using e.g. the Steinmetz-based `..._steinmetz_...(f, T, b, ...)`.
 
+        :param log_pv_fit_function: e.g. mdb.log_steinmetz_qT, mdb.log_enhanced_steinmetz_qT
         :return: Fitted parameters (popt_pv) of the Steinmetz-based power loss model.
         :rtype: np.ndarray
         """
         mu_abs = np.sqrt(self.measurement_data["mu_real"] ** 2 + self.measurement_data["mu_imag"] ** 2)
         pv = pv_mag(self.measurement_data["f"],
                     -self.measurement_data["mu_imag"] * mu_0,
                     self.measurement_data["b"] / mu_abs / mu_0)
-        popt_pv, pcov_pv = curve_fit(log_steinmetz_qT,
+        popt_pv, pcov_pv = curve_fit(log_pv_fit_function,
                                      (self.measurement_data["f"],
                                       self.measurement_data["T"],
                                       self.measurement_data["b"]),

materialdatabase/processing/utils/empirical.py

@@ -49,7 +49,7 @@ def steinmetz_qT(fTb: tuple[float | np.ndarray, float | np.ndarray, float | np.n
 
 
 def log_steinmetz_qT(fTb: tuple[float | np.ndarray, float | np.ndarray, float | np.ndarray],
-                 alpha: float, beta: float, c_0: float, c_1: float, c_2: float) -> float | np.ndarray:
+                     alpha: float, beta: float, c_0: float, c_1: float, c_2: float) -> float | np.ndarray:
     """
     Temperature-dependent Steinmetz model using quadratic temperature function.
 
@@ -64,6 +64,69 @@ def log_steinmetz_qT(fTb: tuple[float | np.ndarray, float | np.ndarray, float |
     return np.log(steinmetz_qT(fTb, alpha, beta, c_0, c_1, c_2))
 
 
+def enhanced_steinmetz(fb: tuple[float | np.ndarray, float | np.ndarray],
+                       alpha: float, beta: float, k: float,
+                       k_b: float, k_f: float, k_alpha2: float) -> float | np.ndarray:
+    """
+    Enhanced Steinmetz loss model incorporating additional scaling terms dependent on frequency and flux density.
+
+    :param fb: Tuple (f, B) of frequency and magnetic flux density
+    :param alpha: Frequency exponent
+    :param beta: Flux density exponent
+    :param k: Base scaling factor
+    :param k_b: Coefficient for flux density-dependent scaling
+    :param k_f: Coefficient for frequency-dependent scaling
+    :param k_alpha2: Exponent for frequency in additional scaling term
+    :return: Power loss density
+    """
+    f, b = fb
+    return (k + k_b * b + k_f * f ** k_alpha2) * f ** alpha * b ** beta
+
+
+def enhanced_steinmetz_qT(fTb: tuple[float | np.ndarray, float | np.ndarray, float | np.ndarray],
+                          alpha: float, beta: float,
+                          k_b: float, k_f: float, k_alpha2: float,
+                          c_0: float, c_1: float, c_2: float) -> float | np.ndarray:
+    """
+    Temperature-dependent enhanced Steinmetz model using quadratic temperature function and additional scaling terms.
+
+    :param fTb: Tuple (f, T, B) of frequency, temperature, and flux density
+    :param alpha: Frequency exponent
+    :param beta: Flux density exponent
+    :param k_b: Coefficient for flux density-dependent scaling
+    :param k_f: Coefficient for frequency-dependent scaling
+    :param k_alpha2: Exponent for frequency in additional scaling term
+    :param c_0: Constant coefficient for temperature scaling
+    :param c_1: Linear temperature coefficient
+    :param c_2: Quadratic temperature coefficient
+    :return: Power loss density
+    """
+    f, T, b = fTb
+    k = quadratic_temperature(T, c_0, c_1, c_2)
+    return (k + k_b * b + k_f * f ** k_alpha2) * f ** alpha * b ** beta
+
+
+def log_enhanced_steinmetz_qT(fTb: tuple[float | np.ndarray, float | np.ndarray, float | np.ndarray],
+                              alpha: float, beta: float,
+                              k_b: float, k_f: float, k_alpha2: float,
+                              c_0: float, c_1: float, c_2: float) -> float | np.ndarray:
+    """
+    Logarithm of the temperature-dependent enhanced Steinmetz model with frequency and flux-density dependent scaling.
+
+    :param fTb: Tuple (f, T, B) of frequency, temperature, and flux density
+    :param alpha: Frequency exponent
+    :param beta: Flux density exponent
+    :param k_b: Coefficient for flux density-dependent scaling
+    :param k_f: Coefficient for frequency-dependent scaling
+    :param k_alpha2: Exponent for frequency in additional scaling term
+    :param c_0: Constant coefficient for temperature scaling
+    :param c_1: Linear temperature coefficient
+    :param c_2: Quadratic temperature coefficient
+    :return: Logarithm of power loss density
+    """
+    return np.log(enhanced_steinmetz_qT(fTb, alpha, beta, k_b, k_f, k_alpha2, c_0, c_1, c_2))
+
+
 def fit_mu_abs(fb: tuple[float | np.ndarray, float | np.ndarray],
                A: float, beta: float, b0: float, C: float, f0: float, n: float) -> float | np.ndarray:
     """