Overview of curve fitting models and methods in labview – national instruments electricity projects for 4th graders


The purpose of curve fitting is to find a function f( x) in a function class Φ for the data ( x i, y i) where i=0, 1, 2,…, n–1. The function f( x) minimizes the residual under the weight W. The residual is the distance between the data samples and f( x). A smaller residual means a better fit. In geometry, curve fitting is a curve y= f( x) that fits the data ( x i, y i) where i=0, 1, 2,…, n–1.

Before fitting the data set, you must decide which fitting model to use. An improper choice, for example, using a linear model to fit logarithmic data, leads to an incorrect fitting result or a result that inaccurately determines the characteristics of the electricity transmission loss data set. Therefore, you first must choose an appropriate fitting model based on the data distribution shape, and then judge if the model is suitable according to the result.

Every fitting model VI in LabVIEW has a Weight input. The Weight input default is 1, which means all data samples have the same influence on the fitting result. In some cases, outliers exist in the data set due to external factors such as noise. If you calculate the outliers at the same nyc electricity consumption weight as the data samples, you risk a negative effect on the fitting result. Therefore, you can adjust the weight of the outliers, even set the weight to 0, to eliminate the negative influence.

Different fitting methods can evaluate the input data to find the curve fitting model parameters. Each method has its own criteria for evaluating the fitting residual in finding the fitted curve. By understanding the criteria for each method, you can choose the most appropriate method to apply to the data set and fit the curve. In LabVIEW, you can apply the Least Square (LS), Least Absolute Residual (LAR), or Bisquare fitting method to the Linear Fit, Exponential Fit, Power Fit, Gaussian Peak Fit, or Logarithm Fit VI to find the function f( x).

Because the LS, LAR, and Bisquare methods calculate f( x) differently, you want to choose electricity transmission costs the curve fitting method depending on the data set. For example, the LAR and Bisquare fitting methods are robust fitting methods. Use these methods if outliers exist in the data set. The following sections describe the LS, LAR, and Bisquare calculation methods in detail. LS Method

The LS method calculates x by minimizing the square error and processing data that has Gaussian-distributed noise. If the noise is not Gaussian-distributed, for example, if the data contains outliers, the LS method is not suitable. You can use another method, such as the LAR or Bisquare method, to process data containing non-Gaussian-distributed noise electricity history facts. LAR Method

In each of the previous equations, y is a linear combination of the coefficients a 0 and a 1. For the General Linear Fit VI, y also can be a linear combination of several coefficients. Each coefficient has a multiplier of some function of x. Therefore, you can use the General Linear Fit VI to calculate and represent the coefficients of the functional models as linear combinations of the coefficients.

If the Balance Parameter input p is 0, the cubic spline model is equivalent to a linear model. If the Balance Parameter z gas cd juarez input p is 1, the fitting method is equivalent to cubic spline interpolation. p must fall in the range [0, 1] to make the fitted curve both close to the observations and smooth. The closer p is to 0, the smoother the fitted curve. The closer p is to 1, the closer the fitted curve is to the observations. The following figure shows the fitting results when p takes different values.

The nonlinear Levenberg-Marquardt method is the most general curve fitting method and does not require y to have a linear relationship with a 0, a 1, a 2, …, a k. You can use the nonlinear Levenberg-Marquardt method to fit linear or nonlinear curves. However, the most common application of the method is to fit a nonlinear curve, because the general linear fit method is better for linear curve fitting.

The Goodness of Fit VI evaluates gas 6 weeks pregnant the fitting result and calculates the sum of squares error (SSE), R-square error (R 2), and root mean squared error (RMSE) based on the fitting result. These three statistical parameters describe how well the fitted model matches the original data set. The following equations describe the SSE and RMSE, respectively.

In the real-world testing and measurement process, as data samples from each experiment in a series of experiments differ due to measurement error, the fitting results also differ. For example, if the measurement error does not correlate and distributes normally among all experiments, you can use the confidence interval to estimate the uncertainty of the fitting parameters. You also can use the prediction interval to estimate the uncertainty of the dependent values of the data set.

The prediction interval estimates the uncertainty of the data samples in the subsequent gasco abu dhabi location measurement experiment at a certain confidence level . For example, a 95% prediction interval means that the data sample has a 95% probability of falling within the prediction interval in the next measurement experiment. Because the prediction interval reflects not only the uncertainty of the true value, but also the uncertainty of the next measurement, the prediction interval is wider than the confidence interval. The prediction interval of the i th sample is:

LabVIEW provides VIs to calculate the confidence gas exchange in the lungs takes place in the interval and prediction interval of the common curve fitting models, such as the linear fit, exponential fit, Gaussian peak fit, logarithm fit, and power fit models. These VIs calculate the upper and lower bounds of the confidence interval or prediction interval according to the confidence level you set.

From the Confidence Interval graph, you can see that the confidence interval is narrow. A small confidence interval indicates a fitted curve that is close to the real curve. From the Prediction Interval graph electricity units calculator in pakistan, you can conclude that each data sample in the next measurement experiment will have a 95% chance of falling within the prediction interval. Back to top

For example, examine an experiment in which a thermometer measures the temperature between –50ºC and 90ºC. Suppose T 1 is the measured temperature, T 2 is the ambient temperature, and T e is the measurement error where T e is T 1 minus T 2. By measuring different temperatures within the measureable range of –50ºC and 90ºC, you obtain the following data table:

In digital image processing, you often need to determine the shape of an object and then detect and extract the edge of the shape. This process is called edge extraction. Inferior conditions, such as poor lighting and overexposure, can result in an edge that is incomplete or blurry. If the edge of an object is a regular curve, then the curve fitting method is useful for processing the initial edge.

To extract the edge of an object, you first can use the watershed algorithm. This algorithm separates the object image from the background image. Then you can use the morphologic algorithm to fill in missing pixels and filter the gas constant mmhg noise pixels. After obtaining the shape of the object, use the Laplacian, or the Laplace operator, to obtain the initial edge. The following figure shows the edge extraction process on an image of an elliptical object with a physical obstruction on part of the object.

As you can see from the previous figure, the extracted edge is not smooth or complete due to lighting conditions and an obstruction by another object. Because the edge shape is elliptical, you can improve the quality of edge by using the coordinates of the initial edge to fit an ellipse function. Using an iterative process, you can update the weight of the edge pixel in order to minimize the influence of inaccurate pixels in the initial edge. The following figure shows gas upper back pain the front panel of a VI that extracts the initial edge of the shape of an object and uses the Nonlinear Curve Fit VI to fit the initial edge to the actual shape of the object.

The standard of measurement for detecting ground objects in remote sensing images is usually pixel units. Due to spatial resolution limitations f gas regulations, one pixel often covers hundreds of square meters. The pixel is a mixed pixel if it contains ground objects of varying compositions. Mixed pixels are complex and difficult to process. One method of processing mixed pixels is to obtain the exact percentages of the objects of interest, such as water or plants.

In the previous images, black-colored areas indicate 0% of a certain object of interest, and white-colored areas indicate 100% of a certain object of interest. For example, in the image representing plant objects, white-colored areas indicate the presence of plant objects. In the image representing water objects, the white-colored, wave-shaped region indicates the presence of a river. You can compare the water representation in the previous figure with Figure 15.