What's least square method?

In "The Analects of Confucius, Book 11," Confucius said, "A noble person is not born different, but is good at learning from things." This means that noble people do not have essential differences from ordinary people. Noble people refer to individuals who possess morality and virtue, and this passage indicates that there is no fundamental distinction between noble people and ordinary people. There is no fundamental difference in people's birth; everyone has similar talents and potential, without any special advantages or disadvantages. The reason why noble people can surpass ordinary people in morality and behavior is that they are good at utilizing the things and resources around them, constantly learning, imitating, and drawing from experience, in order to gain wisdom and knowledge and to grow and progress better.
least square method
So, how can we use the ARCiNTU visual measuring instrument series to determine the shape tolerances of workpieces? This is also a necessary practice to become a noble person in our industry. Let's take a look!

We recommend using the least squares method, which is a commonly used mathematical optimization method for fitting data and estimating model parameters. The basic idea is to find a set of parameters that minimize the sum of squared residuals between the model's predicted values calculated using these parameters and the actual observed data.
In certain cases, the least squares method can be used to estimate the shape tolerances of elements from measurement data. Here is an implementation method for reference:
Collect measurement data: First, collect a set of measurement data related to the element to be measured using appropriate measurement equipment such as visual measuring instruments or coordinate measuring machines. These data can be point sets, contour lines, or other geometric features.
Determine the shape model: Based on the geometric shape of the element to be measured and the defined shape tolerance, select an appropriate shape model. The shape model can be a straight line, a curve, a plane, or other geometric shapes.
Build the objective function: Represent the parameters of the model as a vector (in three-dimensional geometric space, usually represented by three real numbers or components, representing the projection of the vector on the X-axis, Y-axis, and Z-axis, respectively. For example, a three-dimensional vector can be represented as (x, y, z)). Based on the measurement data and shape model, construct an objective function that measures the error between the measurement data and the shape model. The most common objective function is the sum of squared residuals, which is the sum of the squares of the distances between the measurement data points and the shape model. A smaller value of the objective function indicates a better fit between the model's predicted values and the actual observed values.
Minimize the objective function: Use the principle of least squares to adjust the parameters of the shape model to minimize the objective function. This usually involves optimization algorithms such as gradient descent or the Levenberg-Marquardt algorithm, which will not be further elaborated here due to their length.
Estimate the shape tolerances: During the process of minimizing the objective function, the parameters of the shape model will converge to the optimal solution. By analyzing the optimal solution's corresponding shape model parameters, it is possible to infer the shape tolerances of the element. For example, if the shape model is a straight line, the optimal solution may correspond to the slope and intercept of the line, which can be used to estimate the position and tilt of the line.
The least squares method is widely used in various fields such as data fitting, regression analysis, signal processing, and optimization problems. It provides a basic mathematical tool for extracting model parameters from observational data and predicting and inferring unknown data.
It should be noted that using the least squares method to estimate shape tolerances from measurement data is an approximate method, and the accuracy of the results depends on the quality of the measurement data, the selection of the shape model, and the performance of the optimization algorithm. Therefore, it is recommended to cooperate with professional engineers or quality control experts in practical applications to ensure the reliability and accuracy of the results. In this regard, our ARCiNTU Intelligent has a team of experienced experts waiting for your inquiries.

Send Inquiry