A method of physically modeling computer simulation of a saxophone sound

Abstract

The present application relates to the technical field of computer, disclose a kind of saxophone sound physical modeling computer simulation method.The method comprises: according to saxophone geometric parameter and fingering configuration, its acoustic cavity is divided into multiple acoustic sub-sections;The geometric characteristics of each sub-section are modeled using one-dimensional non-uniform digital waveguide, two-dimensional axisymmetric finite difference time domain or three-dimensional boundary element local resonance unit respectively;Interface coupling model is constructed to meet the continuity of sound pressure and the conservation of volume velocity;Combined with the reed excitation model based on the nonlinear Bernoulli equation, the sound field state of each unit is calculated synchronously by multi-rate time domain recursion algorithm, and high-fidelity audio data stream is output.The present application improves the simulation efficiency significantly while ensuring the timbre fidelity through heterogeneous modeling and multi-rate strategy, and realizes the collaborative optimization of precision and real-time.

Description

Technical Field

[0001] This invention belongs to the field of computer technology, specifically relating to a computer simulation method for physical modeling of saxophone sound. Background Technology

[0002] With the rapid development of digital audio technology and virtual instrument simulation, physical modeling-based synthesis methods have gained widespread application in music production, education, and human-computer interaction due to their high fidelity and expressiveness. Physical modeling simulates the vibration, propagation, and radiation mechanisms inside acoustic instruments using mathematical equations, aiming to reproduce the dynamic response and tonal details in realistic performances. Waveguide synthesis, as one of the mainstream technologies, efficiently simulates the propagation process of one-dimensional sound waves in a pipe using a time-domain recursive structure and has been successfully used for the simulation of string, brass, and woodwind instruments. However, this method faces significant challenges when dealing with instruments with complex geometries and nonlinear airflow excitation.

[0003] As a typical conical-cylinder hybrid resonator, the saxophone's sound generation is highly dependent on the nonlinear interaction between the reed-tube coupling system and multiple resonant modes. Traditional waveguide models typically simplify the sound wave propagation path to a single or a limited number of linear channels, making it difficult to accurately characterize the dense distribution of overtones within the tube, cross-modal coupling, and non-steady-state acoustic phenomena such as the "roaring" sound generated by strong airflow. To improve simulation accuracy, existing solutions often approximate complex resonances by increasing the number of waveguide branches or introducing higher-order difference equations. However, such improvements lead to an exponential increase in computational complexity, severely limiting their real-time performance and practicality.

[0004] Existing technologies for simulating saxophone sounds generally suffer from the following problems: detailed modeling requires simultaneously tracking numerous resonance paths and their mutual interference effects; traditional serial waveguide architectures cannot process multi-path superposition in parallel, leading to phase distortion, spectral breaks, or excessive latency in high-frequency overtone regions or transient effect simulations. Especially in real-time performance scenarios, the system struggles to simultaneously maintain low-latency response and the integrity of the high-dimensional resonance structure within limited computing power, resulting in a dry tone and sluggish dynamic response, failing to meet the stringent requirements of professional-grade virtual instruments for expressiveness and interactivity. Therefore, a new computing architecture is urgently needed that can overcome the efficiency bottleneck of traditional waveguide models in complex resonance simulations while maintaining physical plausibility. Summary of the Invention

[0005] This invention provides a computer simulation method for physical modeling of saxophone sound, aiming to solve the technical problem of low computational efficiency of traditional waveguide models when simulating complex resonances and cross-mode coupling. The method constructs a hybrid physical modeling architecture based on a piecewise non-uniform transmission line and local mode decomposition, decomposing the saxophone acoustic system into multiple sub-structural units with well-defined physical boundaries and coupling relationships. For each sub-structural unit, a dedicated numerical solution strategy matching its geometric characteristics and acoustic behavior is employed, thereby improving computational efficiency while ensuring acoustic simulation accuracy.

[0006] This invention provides a computer simulation method for physical modeling of saxophone sound, comprising: Obtain the geometric parameters, material properties, and fingering configuration information of the saxophone; Based on the geometric parameters and fingering configuration information, the acoustic cavity of the saxophone is divided into several acoustic sub-segments. Each acoustic sub-segment corresponds to an independent acoustic propagation path, which includes one or more combinations of straight pipe segments, tapered expansion segments, bend segments, or perforated segments. For each acoustic sub-segment, the corresponding physical modeling unit type is selected based on its geometric morphology characteristics. The physical modeling unit type includes a one-dimensional non-uniform digital waveguide unit, a two-dimensional axisymmetric finite difference time-domain unit, or a three-dimensional boundary element local resonance unit. An acoustic interface coupling model is established between each physical modeling unit. The acoustic interface coupling model is used to describe the sound pressure continuity condition and volume velocity conservation condition at the interface between adjacent acoustic segments. A reed airflow excitation model is applied at the excitation end. The reed airflow excitation model is solved simultaneously based on the nonlinear Bernoulli equation and the reed displacement dynamics equation to generate a sound source signal that varies with time. The acoustic field state variables within each physical modeling unit are calculated sequentially using a time-domain recursive algorithm, and cross-unit data transmission and synchronization are achieved using the acoustic interface coupling model. Finally, the receiver acquires the synthesized sound pressure signal and outputs it as an audio data stream.

[0007] Preferably, the acoustic cavity of the saxophone is divided into several acoustic segments, including: Identify geometric abrupt changes in the main body of the saxophone, including points where the tube diameter changes, bending points, and key opening locations; Using each geometric abrupt change point as a dividing node, the entire cavity is divided into continuous and non-overlapping acoustic sub-segments; For each acoustic sub-segment, record its starting coordinates, ending coordinates, cross-sectional shape function, wall impedance characteristics, and whether there is a lateral opening.

[0008] Preferably, the one-dimensional non-uniform digital waveguide unit is suitable for straight pipe sections or tapered sections where the pipe diameter changes slowly along the axial direction. Its internal sound field is represented by a pair of anti-propagating traveling wave variables, which are recursively updated through a discretized one-dimensional wave equation. The wave velocity and characteristic impedance are dynamically adjusted according to the local cross-sectional area and equivalent sound velocity.

[0009] Preferably, the two-dimensional axisymmetric finite difference time-domain unit is suitable for curved pipe sections or large-diameter expansion sections with significant transverse sound field gradients. Its governing equation is the acoustic wave equation in cylindrical coordinates. The sound pressure and particle velocity are discretized in time and space using an interleaved grid finite difference scheme, and the time step satisfies the Courant-Friedrich-Levy stability condition.

[0010] Preferably, the three-dimensional boundary element local resonance unit is suitable for local regions containing complex open structures or cavity couplings. It calculates the acoustic impedance matrix of the local region in the frequency domain by solving the Helmholtz integral equation, and converts it into a time-domain convolution kernel through the inverse Laplace transform, which is used to update the relationship between sound pressure and normal velocity on the boundary in real time.

[0011] Preferably, the construction of the acoustic interface coupling model includes: At the interface between two adjacent acoustic sub-segments, the sound pressure value at the common node is defined as the weighted average of the output sound pressure of the two units, and the weighting coefficient is determined by the characteristic impedance of the two units. Meanwhile, the total volume velocity through the interface is defined as the sum of the volume velocities of the two elements, and it is forced to satisfy the law of conservation of mass. For interfaces with lateral openings, an additional opening radiation impedance term is introduced. This opening radiation impedance term is determined by the opening diameter, edge correction factor, and surrounding medium density, and is superimposed on the equivalent load impedance of the main channel.

[0012] Preferably, the construction of the reed airflow excitation model includes: A nonlinear feedback relationship between reed displacement and sound pressure inside the mouthpiece cavity is established, with the reed displacement constrained by reed stiffness, damping coefficient, and static preload. Based on the relationship between instantaneous airflow velocity and the pressure difference at the nozzle inlet, and combined with the continuity equation, the volumetric flow rate entering the cavity is calculated. The volumetric flow rate is input as the sound source term to the excitation port of the first acoustic sub-segment.

[0013] Preferably, the time-domain recursive algorithm uses a uniform time step to synchronously update all physical modeling units. For two-dimensional or three-dimensional units with high computational complexity, a multi-rate sampling strategy is adopted, that is, a smaller time step is used for local iteration within the unit, and only the result of an integer multiple of the main time step is output when exchanging data between units, so as to maintain global temporal consistency.

[0014] Preferably, the spatial step size of the two-dimensional axisymmetric finite difference time-domain unit is... and All were set to 0.5 mm, with a time step of 0.5 mm. satisfy Internally, it performs local iterations at a subdivision rate twice that of the main time step. The speed of sound.

[0015] Preferably, the temporal convolution kernel of the three-dimensional boundary element local resonance unit is fitted by a linear combination of exponentially decaying sine functions and recursively calculated by multiple second-order IIR filters.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. By decomposing the saxophone acoustic system into multiple heterogeneous physical modeling units and matching the optimal numerical solution method for segments with different geometric features, the high spatial resolution and small time step required by the traditional single waveguide model when dealing with complex geometric structures are avoided, thereby reducing the consumption of computing resources. 2. By accurately modeling the acoustic interface coupling relationship between each segment, the key physical mechanisms of cross-mode coupling and local resonance effect are preserved, ensuring the realism and dynamic response characteristics of the synthesized timbre. 3. The introduction of the multi-rate sampling strategy ensures that the local fine calculation of high-complexity units does not affect the overall simulation efficiency, and achieves synergistic optimization of calculation accuracy and real-time performance. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the overall technical solution architecture of the present invention; Figure 2 This is a schematic diagram of the core principle framework of the hybrid physics modeling architecture based on the combination of segmented non-uniform transmission lines and local mode decomposition in this invention. Figure 3 This is a logical flowchart of the acoustic cavity division and acoustic segment modeling type of the saxophone in this invention; Figure 4 This is a schematic diagram of the matching framework for the dedicated numerical solution strategy of the multiple types of physical modeling units (one-dimensional waveguide, two-dimensional FDTD, three-dimensional boundary element) in this invention; Figure 5 This is a schematic diagram of the construction of the acoustic interface coupling model between adjacent acoustic sub-segments and the data synchronization mechanism in this invention; Figure 6 This is a global simulation timing framework diagram of the collaborative operation of the reed airflow excitation model and the multi-rate time-domain recursive algorithm in this invention. Detailed Implementation

[0018] refer to Figures 1 to 6 This invention provides a computer simulation method for physical modeling of saxophone sound, aiming to solve the technical problem of low computational efficiency of traditional waveguide models when simulating complex resonances and cross-mode coupling. This method constructs a hybrid physical modeling architecture based on a combination of piecewise non-uniform transmission lines and local mode decomposition. It decomposes the saxophone acoustic system into multiple acoustic sub-segments with clear physical boundaries and coupling relationships, and matches each sub-segment with a dedicated numerical solution strategy adapted to its geometric characteristics and acoustic behavior, thereby improving computational efficiency while ensuring acoustic simulation accuracy.

[0019] As one embodiment of the present invention, the computer simulation method for physical modeling of saxophone sound includes the following steps: Obtain the geometric parameters, material properties, and fingering configuration information of the saxophone; Based on the geometric parameters and fingering configuration information, the acoustic cavity of the saxophone is divided into several acoustic sub-segments. Each acoustic sub-segment corresponds to an independent acoustic propagation path, which includes one or more combinations of straight pipe segments, tapered expansion segments, bend segments, or perforated segments. For each acoustic sub-segment, the corresponding physical modeling unit type is selected based on its geometric morphology characteristics. The physical modeling unit type includes a one-dimensional non-uniform digital waveguide unit, a two-dimensional axisymmetric finite difference time-domain unit, or a three-dimensional boundary element local resonance unit. An acoustic interface coupling model is established between each physical modeling unit. The acoustic interface coupling model is used to describe the sound pressure continuity condition and volume velocity conservation condition at the interface between adjacent acoustic segments. A reed airflow excitation model is applied at the excitation end. The reed airflow excitation model is solved simultaneously based on the nonlinear Bernoulli equation and the reed displacement dynamics equation to generate a sound source signal that varies with time. The acoustic field state variables within each physical modeling unit are calculated sequentially using a time-domain recursive algorithm, and cross-unit data transmission and synchronization are achieved using the acoustic interface coupling model. Finally, the receiver acquires the synthesized sound pressure signal and outputs it as an audio data stream.

[0020] The specific process of obtaining the geometric parameters, material properties, and fingering configuration information of a saxophone includes: importing the complete geometric contour of the saxophone's main structure through a 3D laser scanner or high-precision CAD model, and extracting the cross-sectional area function along the tube axis. , This represents the axial coordinate from the mouthpiece inlet to the horn outlet; it also records the density, Young's modulus, and internal friction loss factor of the tube wall material for subsequent calculation of the wall acoustic impedance. In addition, by parsing the finger pattern or MIDI control messages input by the user, the currently active key combination is determined, thereby identifying the positions of all open side holes and their effective radiation diameter.

[0021] All of the above parameters are stored in a structured data container for subsequent use by the acoustic segmentation module.

[0022] The specific process of dividing the acoustic cavity of a saxophone into several acoustic segments includes: traversing the entire tube axis coordinate range and identifying all geometric abrupt change points, including locations where the tube diameter changes abruptly or continuously beyond a preset threshold, nodes with bending angles greater than 15 degrees, and coordinate locations with lateral openings; using each geometric abrupt change point as a dividing node, dividing the entire cavity into continuous and non-overlapping acoustic segments; and recording the starting coordinates of each acoustic segment. Termination coordinates Cross-sectional area function Wall impedance And a Boolean flag indicating whether a lateral opening exists.

[0023] Based on the geometric characteristics and acoustic propagation properties of the saxophone's acoustic cavity, acoustic segments are mainly divided into the following four categories: Straight pipe section: The pipe diameter remains basically unchanged along the axial direction, the cross-section is circular or nearly circular, and the sound wave mainly propagates as a one-dimensional plane wave.

[0024] Tapered expansion section: The pipe diameter increases linearly or non-linearly along the axial direction. It is commonly found in the bell part of a saxophone. The sound wave propagation is accompanied by a gradual change in impedance caused by the change in cross-section.

[0025] Bend section: The pipe body has obvious bends and a small radius of curvature, which causes the sound wave propagation path to deflect and easily generates a lateral sound field gradient.

[0026] Opening section: There are one or more lateral openings (such as sound holes) on the pipe wall. The openings will affect the local acoustic impedance and introduce radiation loss and resonance coupling.

[0027] If an acoustic subsegment contains both tapered expansion and slight bending, it is preferentially classified as a tapered segment and modeled using a one-dimensional non-uniform digital waveguide unit. The selection logic of a two-dimensional axisymmetric finite difference time-domain unit is only triggered when the bending radius is less than five times the tube diameter.

[0028] The process of selecting the corresponding physical modeling unit type for each acoustic sub-segment is driven by a preset rule engine.

[0029] One-dimensional non-uniform digital waveguide element: suitable for straight pipe sections and gradually varying conical sections where sound wave propagation is mainly approximated in one dimension. This element simulates the bidirectional propagation of sound waves in the pipe through a discretized one-dimensional wave equation, and features high computational efficiency and strong real-time performance.

[0030] Two-dimensional axisymmetric finite difference time-domain element: suitable for curved pipe sections or large-diameter expansion sections with significant lateral sound field variations. This element solves the acoustic wave equation in cylindrical coordinates and uses the staggered mesh finite difference method, which can accurately capture modal coupling and energy diffusion in a two-dimensional axisymmetric sound field.

[0031] Three-dimensional boundary element local resonance unit: suitable for local regions containing complex opening structures or cavity couplings (such as around a sound hole). This unit calculates the local acoustic impedance using the frequency domain boundary element method and converts it into a time domain convolution kernel for real-time simulation of opening radiation and local resonance effects.

[0032] Specifically, if an acoustic segment meets all of the following conditions: its axial length is greater than 10 times the local average tube diameter, the absolute value of the rate of change of cross-sectional area is less than 5% per millimeter, and it has no lateral openings, then it is determined to be suitable for a one-dimensional non-uniform digital waveguide unit. If the acoustic subsegment contains curved segments and the radius of curvature is... satisfy ( If the average diameter of the segment is greater than 10 degrees, it is determined to be suitable for two-dimensional axisymmetric finite difference time-domain units; if the acoustic segment contains one or more lateral openings and the total area of ​​the openings is greater than 20% of the cross-sectional area of ​​the main channel, or there is a cavity coupling structure such as a sound hole resonance cavity near the opening, it is determined to be suitable for three-dimensional boundary element local resonance units, ensuring that each modeling unit is activated only in the region where its physical assumptions are valid, avoiding distortion or instability caused by misuse of numerical methods.

[0033] The internal acoustic field of the one-dimensional non-uniform digital waveguide unit is composed of a pair of counter-propagating traveling wave variables. and express, For time step index, This is a spatial grid index. The one-dimensional non-uniform digital waveguide element is recursively updated using a discretized one-dimensional wave equation: ； ; The local attenuation coefficient is determined by the wall impedance. and characteristic impedance Joint decision, air density, For the speed of sound, For spatial grid Cross-sectional area at that point. Wave speed. The local cross-sectional area and equivalent sound velocity correction terms are dynamically adjusted to compensate for the influence of non-uniform cross-sections on wave propagation speed. The spatial step size of this one-dimensional non-uniform digital waveguide unit is uniformly set to 1 / 10 of the minimum operating wavelength, and the time step size is determined to be 0.283 microseconds by the global sampling frequency of 48000 Hz.

[0034] The two-dimensional axisymmetric finite difference time-domain element in cylindrical coordinates Solve the acoustic wave equations. The governing equations are: ; Yee-type staggered grid is used to control sound pressure Spatiotemporal discretization of the particle velocity components. It is time. Sound pressure is defined at integer spacetime points. radial velocity Defined at half-integer radial positions axial velocity Defined in half-integer axial positions The updated formula is as follows: ； ； ; Defined at half-integer spacetime points The velocity of a particle in the radial direction; Defined at half-integer spacetime points The velocity of a particle in the axial direction; Defined at half-integer spacetime points The velocity of a particle in the radial direction; Defined at half-integer spacetime points The velocity of a particle in the axial direction; Indicates the first Time step, radial first grid, axis The sound pressure level at the grid point; Indicates the first Time step, radial first grid, axis The sound pressure level at the grid point; Indicates the first Time step, radial first grid, axis The sound pressure level at the grid.

[0035] Time step The Courant-Friedrich-Lévy stability condition must be met: In actual implementation, and All values ​​are set to 0.5 mm, from which the maximum allowable value is calculated. The subdivision rate is 1.17 microseconds. Therefore, the two-dimensional axisymmetric finite difference time-domain unit adopts a subdivision rate twice that of the main time step, that is, three internal iterations are performed every two main time steps to maintain numerical stability.

[0036] The described three-dimensional boundary element local resonant unit is suitable for local regions containing complex opening structures. This three-dimensional boundary element local resonant unit first solves the Helmholtz integral equation in the frequency domain: ; For observation point The sound pressure at that location, For free space Green's function, For the boundary Upper source point The sound pressure at that location, For the boundary The area of ​​the surface is infinitesimal. The frequency domain acoustic impedance matrix is ​​obtained by boundary element discretization. Its elements Indicates the first The normal velocity of the first boundary node affects the first... The contribution of sound pressure at each node is then calculated. Subsequently, an inverse Laplace transform is performed on the matrix to obtain the temporal convolution kernel. ,satisfy: ; For time-domain sound pressure, For time-domain convolution kernels, Normal velocity of boundary nodes, time shift The value that follows.

[0037] In real-time simulations, convolution operations are approximated using recursive filters. Specifically, the convolution operation is implemented using a recursive filter. The fit is a linear combination of exponentially decaying sine functions: ; For amplitude, The exponential decay rate, Angular frequency, This is the initial phase.

[0038] Each term corresponds to a second-order IIR filter, and its difference equation is: ; Input the current normal velocity. For the first Time step The sound pressure response of the first mode, For the first Time step The sound pressure response of the first mode, For the first Time step The sound pressure response of the three modalities is calculated. The total sound pressure is the sum of the outputs of all modes. The method transforms complex temporal convolution into efficient recursive computation, significantly reducing the runtime overhead of 3D boundary element units.

[0039] The process of establishing the acoustic interface coupling model between various physical modeling units includes: defining the sound pressure value at the common node at the interface between two adjacent acoustic sub-segments. Output sound pressure to both side units and Weighted average: ; and These are the characteristic impedances of the left and right elements at the interface, respectively. Simultaneously, the total volume velocity through the interface is defined. The volume velocity of the two side units and The sum of these, and enforced to satisfy the law of conservation of mass. For interfaces with lateral openings, an additional opening radiation impedance is introduced. The impedance is determined by the aperture diameter. Edge correction coefficient and the density of the surrounding medium Jointly determined: ; The wavenumber is used. The radiation impedance is superimposed on the equivalent load impedance of the main channel, forming the corrected interface impedance. This is used to recalculate the sound pressure weighting coefficients.

[0040] The construction of the reed airflow excitation model includes: establishing the reed displacement. Sound pressure inside the mouthpiece cavity The nonlinear feedback relationship between them. The reed dynamic equation is:

[0041] For the equivalent mass of the reed, The damping coefficient is... This is the stiffness coefficient. Let be the effective area of ​​the reed. The initial static preload keeps the reed in a closed state when there is no airflow, with an upper limit of displacement of . Airflow speed Calculated using the nonlinear Bernoulli equation: ; The blowing pressure for the performer, typically 1 kPa. The volumetric flow rate into the lumen. for: ; For flow coefficient, For the reed width. Volumetric flow rate. As the excitation port input to the first acoustic sub-segment, it is equivalent to a volumetric velocity source.

[0042] The temporal recursive algorithm employs a uniform main time step of 1 / 48000 second to synchronously update all physical modeling units. For computationally complex two-dimensional or three-dimensional units, a multi-rate sampling strategy is used: smaller time steps are employed within these units. Perform local iterations, and only output results that are integer multiples of the main time step when exchanging data between cells.

[0043] The specific synchronization mechanism is as follows: The first synchronization is completed in the one-dimensional waveguide unit. After the update, send to downstream. and After the two-dimensional FDTD element performs three substeps internally, it will... The average sound pressure and volumetric velocity at the directional exit are interpolated to the main time grid; the 3D boundary element cells directly output the convolution result at the current time step. All interface data undergo impedance matching and conservation checks at the main time step boundaries to ensure global energy consistency.

[0044] The output audio data stream is sampled at 48,000 Hz, quantized to 16 bits, and has mono channels. At the receiving end, the synthesized sound pressure level signal is acquired from the exit of the last acoustic segment. To prevent high-frequency aliasing, a sixth-order Butterworth low-pass filter with a cutoff frequency of 22,000 Hz is applied before the digital output. The filtered signal is then modulated using a 16-bit linear pulse code and written to a standard WAV audio file or a real-time audio stream buffer.

[0045] Throughout the simulation process, the data flow strictly follows a causal time sequence: the reed excitation model generates the current volumetric flow rate at the beginning of each main time step; the one-dimensional waveguide element is recursively pushed from front to back along the tube axis; the two-dimensional and three-dimensional elements complete the internal field update on their local time grids; all elements exchange boundary data through the interface coupling model at the end of the main time step; and finally, the acoustic pressure signal is output after anti-aliasing filtering.

[0046] The anomaly handling mechanism includes: detecting whether the sound pressure amplitude is greater than the air breakdown threshold of 150 kPa, and automatically attenuating the excitation intensity if it exceeds the limit; monitoring the volume velocity conservation error, and triggering adaptive impedance recalibration if the relative deviation is greater than 5%; and performing online evaluation of the modal fitting residual of the three-dimensional boundary element unit, and starting the backup lookup table interpolation scheme if it is greater than the preset tolerance.

[0047] This method achieves efficient and high-fidelity simulation of the complex acoustic behavior of the saxophone through the collaborative work of heterogeneous modeling units. One-dimensional waveguide units handle most straight and gradually tapered tubes with extremely low computational overhead; two-dimensional FDTD units accurately capture lateral modal coupling at bends; and three-dimensional boundary element units accurately reproduce the interface coupling model of aperture radiation and local resonance effects, ensuring seamless integration between different physical scales. A multi-rate strategy balances accuracy and efficiency. The final output audio signal not only includes the fundamental frequency and harmonic structure but also retains key expressive elements such as performance dynamics, breath noise, and fingering transition transients, meeting the needs of professional music production and virtual instrument development.

[0048] This embodiment has fully disclosed the core technical solution of the present invention, covering all necessary details from geometric modeling, segment division, unit selection, interface coupling, excitation modeling to time-domain recursion and audio output, which is sufficient to enable those skilled in the art to achieve the technical effects of the present invention based on this specification.

[0049] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0050] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A computer simulation method for physical modeling of saxophone sound, characterized in that, include: Obtain the geometric parameters, material properties, and fingering configuration information of the saxophone; based on the geometric parameters and fingering configuration information, divide the acoustic cavity of the saxophone into several acoustic sub-segments, each acoustic sub-segment corresponding to an independent acoustic propagation path, including one or more combinations of straight pipe segments, tapered expansion segments, bent pipe segments, or perforated segments; For each acoustic sub-segment, the corresponding physical modeling unit type is selected based on its geometric morphology characteristics. The physical modeling unit type includes a one-dimensional non-uniform digital waveguide unit, a two-dimensional axisymmetric finite difference time-domain unit, or a three-dimensional boundary element local resonance unit. The one-dimensional non-uniform digital waveguide unit is suitable for straight pipe sections or tapered sections where the pipe diameter changes slowly along the axial direction. Its internal sound field is represented by a pair of traveling wave variables that propagate in opposite directions. The traveling wave variables are recursively updated through a discretized one-dimensional wave equation. The wave velocity and characteristic impedance are dynamically adjusted according to the local cross-sectional area and the equivalent sound velocity. The two-dimensional axisymmetric finite difference time-domain unit is suitable for curved pipe sections or large-diameter expansion sections with significant transverse sound field gradients. Its governing equation is the acoustic wave equation in cylindrical coordinates. The sound pressure and particle velocity are discretized in time and space using an interleaved grid finite difference scheme. The time step satisfies the Courant-Friedrich-Levy stability condition. The spatial step size of the two-dimensional axisymmetric finite difference time-domain unit and All were set to 0.5 mm, with a time step of 0.5 mm. satisfy Internally, it performs local iterations at a subdivision rate twice that of the main time step. Speed ​​of sound; The three-dimensional boundary element local resonance unit is suitable for local regions containing complex open structures or cavity couplings. It calculates the acoustic impedance matrix of the local region in the frequency domain by solving the Helmholtz integral equation, and converts it into a time-domain convolution kernel through the inverse Laplace transform, which is used to update the relationship between sound pressure and normal velocity on the boundary in real time. An acoustic interface coupling model is established between each physical modeling unit. The acoustic interface coupling model is used to describe the sound pressure continuity condition and volume velocity conservation condition at the interface between adjacent acoustic segments. The construction of the acoustic interface coupling model includes: at the interface between two adjacent acoustic sub-segments, the sound pressure value at the common node is defined as the weighted average of the output sound pressure of the two units, and the weighting coefficient is determined by the characteristic impedance of the two units; at the same time, the total volume velocity through the interface is defined as the sum of the volume velocities of the two units, and it is forced to satisfy the law of conservation of mass; for interfaces with lateral openings, an additional opening radiation impedance term is introduced, which is determined by the opening diameter, the edge correction coefficient and the density of the surrounding medium, and is superimposed on the equivalent load impedance of the main channel; A reed airflow excitation model is applied at the excitation end. The reed airflow excitation model is solved simultaneously based on the nonlinear Bernoulli equation and the reed displacement dynamics equation to generate a sound source signal that varies with time. The acoustic field state variables within each physical modeling unit are calculated sequentially using a time-domain recursive algorithm, and cross-unit data transmission and synchronization are achieved using the acoustic interface coupling model. The time-domain recursive algorithm uses a uniform time step to synchronously update all physical modeling units. For two-dimensional or three-dimensional units with high computational complexity, a multi-rate sampling strategy is adopted, that is, a smaller time step is used for local iteration within the unit, and only the result of an integer multiple of the main time step is output when exchanging data between units, so as to maintain global temporal consistency. Finally, the receiver acquires the synthesized sound pressure signal and outputs it as an audio data stream.

2. The computer simulation method for physical modeling of saxophone sound according to claim 1, characterized in that, The acoustic cavity of the saxophone is divided into several acoustic sub-segments, including: Identify geometric abrupt changes in the main body of the saxophone, including points where the tube diameter changes, bending points, and key opening locations; Using each geometric abrupt change point as a dividing node, the entire cavity is divided into continuous and non-overlapping acoustic sub-segments; For each acoustic sub-segment, record its starting coordinates, ending coordinates, cross-sectional shape function, wall impedance characteristics, and whether there is a lateral opening.

3. The computer simulation method for physical modeling of saxophone sound according to claim 1, characterized in that, The construction of the reed airflow excitation model includes: A nonlinear feedback relationship between reed displacement and sound pressure inside the mouthpiece cavity is established, with the reed displacement constrained by reed stiffness, damping coefficient, and static preload. Based on the relationship between instantaneous airflow velocity and the pressure difference at the nozzle inlet, and combined with the continuity equation, the volumetric flow rate entering the cavity is calculated. The volumetric flow rate is input as the sound source term to the excitation port of the first acoustic sub-segment.

4. The computer simulation method for physical modeling of saxophone sound according to claim 1, characterized in that, The temporal convolution kernel of the three-dimensional boundary element local resonance unit is fitted by a linear combination of exponentially decaying sine functions and recursively calculated by multiple second-order IIR filters.

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