6 results about "Functional expression" patented technology

This invention proposes an online correction method and system for sine and cosine signals of a rotary transformer, relating to the technical field of servo control. The method involves fitting the demodulated original sine and cosine signals using second-order polynomial functions to obtain second-order sine and cosine polynomial expressions, respectively. The term matrix and the parameter matrix to be optimized are then extracted to obtain the sine and cosine matrices. Based on these matrices, a sine and cosine correction error function is constructed. With the goal of minimizing the sine and cosine correction error function, the method uses the parameter matrix to perform online iterative solutions, thereby completing the online correction of the rotary transformer's sine and cosine signals. This method has low computational complexity and short processing time. Compared to directly decoding uncorrected sine and cosine signals, it improves the linearity of the subsequent decoding angle and reduces decoding speed fluctuations.

This application discloses a method, apparatus, device, and storage medium for determining the natural frequency of a linear motor, aiming to determine the natural frequency of a linear motor more quickly and accurately. The method includes: constructing an equivalent model of the linear motor based on whether it is mounted on a base; when the equivalent model is a double-layer plate structure, establishing a displacement function expression for the middle surface of the double-layer plate structure based on the first-order shear deformation theory; when the equivalent model is a triple-layer plate structure, establishing a displacement function expression for the middle surface of each single-layer plate in the triple-layer plate structure based on the first-order shear deformation theory and Zig-Zag theory; performing energy calculations on the equivalent model to obtain kinetic energy, strain energy, and spring potential energy; constructing a Lagrange energy function expression based on the function expression of the equivalent model, kinetic energy, strain energy, and spring potential energy, converting it into an eigenvalue equation, solving it, and obtaining the angular frequency of the linear motor to determine its natural frequency.

This invention relates to the field of open channel hydraulic calculation and hydraulic engineering design calculation technology, specifically to a method for solving the normal water depth of a flat-bottomed catenary linear open channel and related products. Addressing the problems of initial value sensitivity, candidate point overshooting, and instability in small-angle calculations in existing solutions, this invention introduces an angular variable to establish a water depth mapping, constructs a logarithmic domain univariate equation, and employs a combined solution using adaptive root envelope, Halley third-order update, and bisection backoff. Furthermore, it utilizes a stable hyperbolic function expression and Taylor expansion to suppress errors, outputting the normal water depth and corresponding hydraulic elements for channel design verification and water surface line calculation.

This invention discloses an automatic construction method for a parametric 3D geological-structural model for revetment engineering, belonging to the field of digital modeling technology. The method includes the following steps: acquiring and constructing a set of stratigraphic interface parameters for the revetment area; generating a 3D geological topology model based on the stratigraphic interface parameter set; identifying the bearing layer interface and weak layer distribution areas based on the 3D geological topology model, and extracting geological control parameters related to each structural foundation; acquiring an initial set of structural parameters and establishing a constraint mapping relationship between structural parameters and geological control parameters; embedding the constraint mapping relationship into the structural parameter expression, making the structural geometric parameters a functional expression of the geological control parameters; and triggering automatic recalculation of structural parameters when the 3D geological topology model undergoes parameter updates. This invention solves the problem of inconsistent mechanical semantics in traditional models by achieving automatic reconstruction of the structural model during geological updates.

This invention discloses a mathematical method for solving the inscribed circle of a Bezier-type flow channel, comprising the following steps: S1, obtaining curves 1 and 2 of the Bezier-type parameters on both sides of the flow channel; S2, establishing a mathematical model of the inscribed circle with "equal radius + tangency" geometric constraints based on the Bezier curve equation and its first derivative equation; S3, deriving a functional expression for the parameters by simultaneously applying two tangent and perpendicular constraints; S4, substituting the functional expression into the equal radius constraint to construct a single-variable nonlinear equation = 0; S5, solving the single-variable nonlinear equation = 0 using a numerical iteration method for the current input value; S6, calculating the coordinates of the inscribed circle center O(x,y), the coordinates of the tangency point T1 on curve 1, and the coordinates of the tangency point T2 on curve 2; S7, repeating steps S1 to S6 until traversing the interval [0,1], and outputting a set of geometric parameters for a series of inscribed circles.